Cu₂O Substrates and Epitaxial Cu₂O/ZnO T

Cu₂O Substrates and Epitaxial Cu₂O/ZnO Thin Film Heterostructures for Solar Energy Conversion - CaltechTHESIS
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Cu₂O Substrates and Epitaxial Cu₂O/ZnO Thin Film Heterostructures for Solar Energy Conversion
Citation
Darvish, Davis Solomon
(2013)
Cu₂O Substrates and Epitaxial Cu₂O/ZnO Thin Film Heterostructures for Solar Energy Conversion.
Dissertation (Ph.D.), California Institute of Technology.
doi:10.7907/0KEM-KG56.
Abstract
Future fossil fuel scarcity and environmental degradation have demonstrated the need for renewable, low-carbon sources of energy to power an increasingly industrialized world. Solar energy with its infinite supply makes it an extraordinary resource that should not go unused. However with current materials, adoption is limited by cost and so a paradigm shift must occur to get everyone on the same page embracing solar technology. Cuprous Oxide (Cu₂O) is a promising earth abundant material that can be a great alternative to traditional thin-film photovoltaic materials like CIGS, CdTe, etc. We have prepared Cu₂O bulk substrates by the thermal oxidation of copper foils as well Cu₂O thin films deposited via plasma-assisted Molecular Beam Epitaxy. From preliminary Hall measurements it was determined that Cu₂O would need to be doped extrinsically. This was further confirmed by simulations of ZnO/Cu₂O heterojunctions. A cyclic interdependence between, defect concentration, minority carrier lifetime, film thickness, and carrier concentration manifests itself a primary reason for why efficiencies greater than 4% has yet to be realized. Our growth methodology for our thin-film heterostructures allow precise control of the number of defects that incorporate into our film during both equilibrium and nonequilibrium growth. We also report process flow/device design/fabrication techniques in order to create a device. A typical device without any optimizations exhibited open-circuit voltages Voc, values in excess 500mV; nearly 18% greater than previous solid state devices.
Item Type:
Thesis (Dissertation (Ph.D.))
Subject Keywords:
solar, photovoltaics, pv, cu2o, copper oxide, cuprous oxide, oxide semiconductors, semiconductors, p-n junctions, thin-films, epitaxy, heterojunctions, molecular beam epitaxy
Degree Grantor:
California Institute of Technology
Division:
Engineering and Applied Science
Major Option:
Materials Science
Thesis Availability:
Public (worldwide access)
Research Advisor(s):
Atwater, Harry Albert
Thesis Committee:
Atwater, Harry Albert (chair)
Greer, Julia R.
Gray, Harry B.
Johnson, William Lewis
Defense Date:
17 December 2012
Non-Caltech Author Email:
ddarvish (AT) gmail.com
Funders:
Funding Agency
Grant Number
Dow Chemical Company
DOWSOLAR.GRA-1.1 HAA-DOW.THINFILM
Record Number:
CaltechTHESIS:06042013-144822210
Persistent URL:
DOI:
10.7907/0KEM-KG56
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No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:
7834
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CaltechTHESIS
Deposited By:
Davis Darvish
Deposited On:
08 Jul 2013 17:54
Last Modified:
08 Nov 2023 00:12
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Cu2O Substrates and Epitaxial Cu2O/ZnO Thin
Film Heterostructures for Solar Energy Conversion
Thesis by
Davis Solomon Darvish

In Partial Fulfillment of the Requirements
for the Degree of
Doctor of Philosophy

California Institute of Technology
Pasadena, California
2013
(Defended Dec 17, 2012)

Davis Solomon Darvish

In dedication to the Sun
for without this huge spheical plasma in the center of our solar system, life would
cease to exist on earth.
Fiat Lux!

‫יְהִי אוֹר‬
Let there be light!

iii

Acknowledgements
It feels like only a couple months ago I was a senior at Cal applying to grad schools
when my Dad asked if I applied to Caltech. I am thankful he brought up the topic
that day because I would have surely missed the application deadline which was the
end of the next day had he not said anything.
My time at Caltech has been interesting to say the least. These past years have
brought many delightful surprises as well as several unexpected challenges. If it was
not for each and every one of the many people who lent me a hand when I needed
one I would not be here today. First and foremost I would like to thank my advisor,
Professor Harry Atwater, for his guidance and support. When time came to chose
a grad school to go to I wanted to pick a place and research group that I could be
excited about waking up for it every day. Harry has provided a place for his grad
student to excel, providing them with the tools they need to do cutting edge research
and make great scientific contributions to society.
I would like to thank the US DOE for start the funding for this project my first
couple years! I am forever grateful that the project was later picked up by the Dow
Chemical Company which provided an extra supportive layer whether it be access to
analysis and equipment that did not have or were not trained on to the informative
and bi-weekly meetings.
I would like to thank the following people who had a direct impact on the
technical aspect of my graduate career. Harry Atwater, Marty DeGroot, Jim Stevens,
Rebekah Feist, Gregory Kimball, Mathew Dicken, Carrie Hofmann, The Dow Chemical
Company, The Earth Abundant Subgroup, Atwater Research Group.
I would also like to thank all the people in my life who were there when I needed
strength, courage, advice, honesty, friendship, and love. Sarah Hanna Bigle my fiancee
then girlfriend, my mother and father Moez and Shahanaz Darvish, my brother
Ryan Darvish, my friends since childhood Arya Tabibnia, David Yadegaran, Ramin
Kohansedgh, and new friends JK, Danny Rubin, Ramin Haverim, and everyone else
who made life what it was outside of Caltech.

As for what is next? I will be traveling a path I did not necessarily expect traveling
only a year ago. The Portland metro area is where I will soon call home, working at
Logic Technology Development at Intel, a childhood dream of mine now come true. I
am extremely excited about the next chapter and can not wait to see what is in store
for me.

Davis S. Darvish
Dec. 2012
Pasadena, CA

Abstract
Future fossil fuel scarcity and environmental degradation have demonstrated the need
for renewable, low-carbon sources of energy to power an increasingly industrialized
world. Solar energy with its infinite supply makes it an extraordinary resource that
should not go unused. However with current materials, adoption is limited by cost
and so a paradigm shift must occur to get everyone on the same page embracing solar
technology. Cuprous Oxide (Cu2 O) is a promising earth abundant material that can
be a great alternative to traditional thin-film photovoltaic materials like CIGS, CdTe,
etc. We have prepared Cu2 O bulk substrates by the thermal oxidation of copper foils
as well Cu2 O thin films deposited via plasma-assisted Molecular Beam Epitaxy. From
preliminary Hall measurements it was determined that Cu2 O would need to be doped
extrinsically. This was further confirmed by simulations of ZnO/Cu2 O hetero-junctions.
A cyclic interdependence between, defect concentration / minority carrier lifetime,
film thickness, and carrier concentration has been the primary reason why efficiencies
well above 6-7% have not been realized. Our thin-film hetero structures may be able
to kinetically control growth thus preventing the number of defects that arise as a
result of the material being allowed to reach equilibrium. While the efficiencies of
the cells were not high at all (most of the power lost is due to series and contact
resistance which hopefully would be rectified, open circuit voltages above 500mV are
very promising and show signs of progress in the right direction.

Contents

List of Figures

List of Tables

xiii

1 Introduction

1.1

Cu2 O: A Brief Background of Many Firsts . . . . . . . . . . . . . . .

1.2

Elemental Abundance, Scalability, Toxicity and their Cost Impact on

Photovoltaics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.3

Cu2 O as a Photovoltaic Material . . . . . . . . . . . . . . . . . . . .

1.4

Cu2 O: A Review of Properties . . . . . . . . . . . . . . . . . . . . . .

1.4.1

Crystal Structure . . . . . . . . . . . . . . . . . . . . . . . . .

1.4.2

Optoelectronic Properties and Electronic Band Structure . . .

1.4.3

Copper-Oxygen Equilibrium Phase Diagram . . . . . . . . . .

1.4.4

Review of Growth Methods and Cu2 O Heterojunctions. . . . .

2 Detailed Balance Efficiency and Band Transport Model for ZnO/Cu2 O
Solar Cells

2.1

Detailed Balance Model for a Cu2 O Solar Absorber . . . . . . . . . .

2.1.1

Model Background . . . . . . . . . . . . . . . . . . . . . . . .

2.1.1.1

Bulk . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.1.1.2

Generation . . . . . . . . . . . . . . . . . . . . . . .

2.1.1.3

Recombination . . . . . . . . . . . . . . . . . . . . .

2.1.1.4

Heterojuntion Interface . . . . . . . . . . . . . . . .

vii

2.1.1.5

Contacts and Boundary Conditions . . . . . . . . . .

2.2

Cu2 O\ZnO Materials Models and Simulation Parameters . . . . . . .

2.3

Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3 Growth of High Quality Cu2 O Thin Films via Plasma-Assisted Molecular
Beam Epitaxy

3.1

Vacuum Science Basics[1, 2, 3] . . . . . . . . . . . . . . . . . . . . . .

3.2

Molecular Beam Epitaxy[4, 5, 6, 7, 8] . . . . . . . . . . . . . . . . . .

3.3

Reflective High Energy Electron Diffraction . . . . . . . . . . . . . .

3.4

Cu2 O Deposition via Plasma Enhanced MBE and Characterization. .

3.5

Conclusion of PA-MBE Growth of Cu2 O . . . . . . . . . . . . . . . .

3.6

Cu2 O/ZnO heterojunction Design, Metallization, and Results . . . .

3.7

Cu2 O/ZnO Hetero-structure Devices . . . . . . . . . . . . . . . . . .

4 Synthesis of Cu2 O Templates and Bulk Substrates via Thermal Oxidation 67
4.1

Cu2 O Synthesis from Oxidation of Copper Foils . . . . . . . . . . . .

4.1.1

Characterization of Cu2 O substrates . . . . . . . . . . . . . .

4.2

Extrinsic Doping of Cu2 O Substrate . . . . . . . . . . . . . . . . . . .

4.3

Cu2 O Templates Fabricated by Thermal Oxidation . . . . . . . . . .

5 Final Thoughts

A Matlab Code for Detailed Balance Model

B Photolithography Flow Process

C AFORS-Het

viii

List of Figures
1.1

Map showing area of land covered by 10% efficient modules to supply
all US energy consumption . . . . . . . . . . . . . . . . . . . . . . . .

1.2

Abundance (atom fraction) of the chemical elements in Earths upper
continental crust as a function of atomic number normalized to silicon.

1.3

Cu2 O unit cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.5

Calculated semirelativistic electronic band structure for Cu2 O which
underestimates the band gap by downward shift of 1.5eV[9]. . . . . .

1.4

Band structure of Cu2 O near the Γ point labeld with the transitions
that give rise to the 4 exciton series. . . . . . . . . . . . . . . . . . .

1.6

Cu2 O Phase Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.7

cu2obinary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.8

Binary phase diagram overlayed with map of predominate point defects
that form at equilibrium[10]. . . . . . . . . . . . . . . . . . . . . . . .

1.9

A 48 atom super-cell with native defects to calculate defect formation
energies as a function of Fermi level for both a)copper-rich and b)
oxygen-rich conditions. . . . . . . . . . . . . . . . . . . . . . . . . . .

1.10 A schematic of a typical setup used for electrochemical deposition. . .

1.11 Cross sectional view of inside a sputtering chamber. . . . . . . . . . .

1.12 This figure illustrates the typical setup of a commercially available
vacuum furnace setup. It is quite possibly the easiest, fastest, and
cheapest method of fabricating Cu2 . . . . . . . . . . . . . . . . . . . .

2.1

NREL’s AM1.5D golbal tilt solar spectrum used in the calculation of
the detailed balance efficiency . . . . . . . . . . . . . . . . . . . . . .

2.2

The top figure illustrates spectrum splitting in order to increase efficiency
of solar cells; the principal behind multijunction cells, the image below
shows why spectrum splitting is needed as solar cells are not great
broadband absorbers and therefore are either unable to absorb light
or lose energy from photons whose bandgap is much greater than the
solar absorber through thermalization. . . . . . . . . . . . . . . . . .

2.3

IV characteristics and external quantum efficiency plots for simulated
Mittiga heterostructure vs their published experimental results. The
shape of the curves are nearly identical and are slightly different due to
the omission of some optical layers in our simulation. . . . . . . . . .

2.4

The efficiency of a ZnO/Cu2 O heterostructure vs interface recombination
velocity which can be converted to trap density at the heterostucture
interface. This plot shows results for four different minority carrier
diffusions lengths. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.5

The efficiency of a ZnO/Cu2 O heterostructure vs the electron affinity of
the Cu2 O layer. This plot demonstrates how Cu2 O low electron affinity
is unfavorable for this heterostructures band bending. This plot also
shows results for four different minority carrier diffusions lengths. . .

2.6

Efficiency of the Cu2 O/ZnO cell as a function of intrinsic carrier
concentration as well as diffusion length. This is because intrinsic
dopants act as deep level traps which destroy minority carrier diffusion
lengths in the bulk.

2.7

. . . . . . . . . . . . . . . . . . . . . . . . . . .

The efficiency of a ZnO/Cu2O cell vs thickness of the cell. This plot
shows results for four different minority carrier diffusions lengths. . .

3.1

Pressure ranges of physical and chemical analytic methods. . . . . . .

3.2

Schematic cross-section of a typical MBE Chamber. . . . . . . . . . .

3.3

Illustration of intensity vs. time in layer by layer growth also known
as the specular beam phenomena that produces RHEED oscillations.
Below is a depiction of what a RHEED image when the electron beam
fulfills the diffraction condition known as Braggs Law.

3.4

. . . . . . . .

On the right hand column are in situ RHEED images from a continuous
Cu2 O(001) on MgO(001) where the film thickness is equal to 0nm (a),
30nm (b), and 65nm (c). On the left hand column are in situ RHEED
images of a clean SiO2 surface (d), followed by 15nm deposition of
IBAD MgO(001) (e), followed by 60nm of Cu2 O (f). . . . . . . . . . .

3.5

(a) RHEED oscillations demonstrating layer by layer epitaxial growth
of Cu2 O on MgO. (b) Fourier transform of RHEED oscillations to
determine growth rate.

. . . . . . . . . . . . . . . . . . . . . . . . .

3.6

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.7

Spectroscopic ellipsometry data for real and imaginary index of refraction
for Cu2 O thin film. Inset shows alpha square vs. energy which allows
extrapolation of band gap of Cu2 O to 2eV. . . . . . . . . . . . . . . .

3.8

In situ RHEED images of (a) Cu2 O(001) on MgO(001) followed by the
30nm deposition of epitaxial m-plane ZnO (b). . . . . . . . . . . . . .

Photomask designs used for metallization. . . . . . . . . . . . . . . .

3.10 Optical micrograph images of heterostructures being paterned. . . . .

3.11 FF=26% ,Voc = 515mV, Jsc ≈=.8 . . . . . . . . . . . . . . . . . . . .

3.12 FF=35.6% ,Voc = 520mV, Jsc ≈3.78 . . . . . . . . . . . . . . . . . . .

4.1

Cu foils pre and post oxidation in a vacuum furnace at 1010o C. . . .

4.2

A detailed schmatics illustrating the process and conditions for oxidation

3.9

of copper foils to Cu2 O . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3

X-ray diffraction measurement of a bulk substrate showing phase pure
Cu2 O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.4

TOF-SIMS data showing dopant atom detection prior to but not after
oxidation of alloyed films. . . . . . . . . . . . . . . . . . . . . . . . .

4.5

In-situ ion beam sputtering used to clean an as grown thermally oxidized
substrate followed by subsequent deposition . . . . . . . . . . . . . .

4.6

An example of orientation suppression and cube on cube epitaxy using
Surface oxidation Epitaxy both on Ni and Cu to produce NiO and Cu2 O 81

xii

List of Tables
1.1

ICSD powder diffraction table for Cu2 O based off the data collected by
M.L. Foo et al. [11] . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.1

AFORS-HET model Parameters & Cu2 O Properties . . . . . . . . . .

4.1

Impurities concentrations in ppm found in Cu foil. . . . . . . . . . . .

4.2

Hall Measurements of Alloyed Substrates . . . . . . . . . . . . . . . .

xiii

Chapter 1

Introduction
This thesis details the fabrication, characterization, and device performance of solar
cells based on cuprous oxide (Cu2 O), a non-traditional semi-conductor. Chapter 1
provides an introduction to Cu2 Os discovery and details the importance of Cu2 O’s
use as an earth abundant, low cost, and scalable material. The chapter continues
with providing a brief review of Cu2 O’s properties pertinent to its use in photovoltaic
applications such as crystal structure, opto-electronic properties and band stucture.
Chapter 2 calculates and discusses both a detailed balance and device physics model
for efficiency of a Cu2 O heterostructure solar cell. Chapter 3 investigates the epitaxial
growth of high quality Cu2 O and epi-ZnO\epi-Cu2 O thin films on MgO templated and
bulk substrates by plasma-enhanced molecular beam epitaxy. The chapter finishes
with device design and device results. Chapter 4 reviews methods of creating bulk
Cu2 O substrates, and investigates the growth of doped and undoped Cu2 O bulk
substrates via thermal oxidation of copper thin films and copper foils. Finally, Chapter
5 attempts to summerize the highlights and the important findings that will help
Cu2 O technology to get near or pass the 10% efficiency mark.

1.1

Cu2O: A Brief Background of Many Firsts

Cuprous oxide (Cu2 O) is the oldest semiconductor known to man, yet until recently
very little was understood about its electronic properties. Both rectifying diodes
and solar cells based on Cu2 O were fabricated in the 1920’s [12] and much of the
data collected on these devices were used as the basis in developing the theory of
semiconductors. By the 1950’s Cu2 O devices slowly faded into the background as

their short minority carrier lifetime[13] and device performance could not compete
with the recent advancements made in purification and doping of both silicon and
germanium which allowed fabrication of devices from those two materials to be far
superior than those made by Cu2 O. Cu2 O has a rich history in semiconductor physics
whose research has discovered many phenomena studied today such as Bose-Einstein
condensates, excitons, and phonoritons yet there are still many basic properties of
this material that are not well understood or measured.

1.2

Elemental Abundance, Scalability, Toxicity and
their Cost Impact on Photovoltaics

Today’s natural disasters and their socioeconomic policies have made it clear that
the world’s dependence on oil and fossil fuels must come to end. Not only is climate
change slowly killing our planet by increasing the average temperature, it is thought to
also have a significant impact in the frequency and severity of many natural disasters
that have occurred in our recent past. In addition, cost of fossil fuels have dramatically
increased as resources have become limited due to several natural and artificial causes.
Because of these reasons it is now important more than ever that the world transitions
to a new source of energy; the direct source of all energy in our solar system. Not only
is solar energy the most abundant source of energy on our planet, it is also the primary
source of energy for our planet as the energy stored in fossil fuels at some point and
time came from the sun. The sun provides 1.2x105 TW of energy at the earths surface,
a number that is over 10,000 times the current worlds energy use. Photovoltaics
allow the direct conversion of sunlight (photons) to a form of energy that we can use
(electricity). Unfortunately, the energy from the sun is diffuse, thus requiring systems
with a very low cost per square meter. If solar technology is to take over or at least
make a big impact in our energy needs, it must be deployed at a massive scale. An
estimate of the total area of photovoltaics required to completely supplant fossil fuel
use in the United States is roughly 2⁄3’s the total area of developed urban land in the

Figure 1.1. The area enclosed within the black square shows the
amount of land needed for a solar energy farm to match the 3 TW
of power currently used in the United States if the solar farm had an
operating efficiency of only 10%.
United States. Figure 1.1 shows a map of the United States with a box outlining the
area of land that needs to be covered in solar cells with 10% conversion efficiency
to supply all of the United States current energy needs.For reasons of scalability it
is then important that the materials chosen are both abundant in the earth’s crust
and also easily extractable. ”Easily extractable” simply means that there are known
methods or industries that extract the element needed in a cost effective manner and
for its availability not to be completely dependent on the use/extraction of some other
mineral or element. It is also important that the materials do not consist of any toxic
elements. Solar panels have a finite lifetime before they must be thrown out and
replaced. Therefore, it is advantageous to use a material that can be easily disposed of
or recycled, as opposed to an environmentally unfriendly material which would have
an expensive and complicated disposal protocol. Finally figure 1.2 is a plot made by
the United States Geological Survey which shows the relative abundance of elements
in the earths crust normalized to the abundance of Si. A line is drawn at y=1. This
choice is a good approximation used to determine if terawatt scaling of photovoltaics

12/7/2012

normalized to silicon.

in Earths
upper
continental
crust
as a function
of atomic
number
Copper
Oxide
Solar Cells
‐ Spectrolab
Interview
Presentation

Figure 1.2. Abundance (atom fraction) of the chemical elements

US Geological Survey

• Earth abundant, non‐toxic, easy to mine and extract.

Motivations of Copper Oxide (Cu2O) for PVs

would be possible if that element was chosen as one of the materials needed to make
solar cells. Everything above the line is fine while we would like to avoid everything
below it. The circled elements in the plot are in materials discussed throughout this
thesis and were highlighted so that they are brought to your attention.

1.3

Cu2O as a Photovoltaic Material

There are several important characteristics of Cu2 O that make it a great candidate
for use as a solar cell. Cuprous oxides band-gap of 2.0eV [14], though not optimal
(1.5eV), can convert an acceptable fraction of solar spectrum to energy when operated
in a single junction configuration yielding a theoretical efficiency that is around 20%.
When used as a top cell in a dual junction solar cell, its band gap is nearly ideal. Its
direct band gap and optical absorption coefficients make it a suitable material for use
in thin-film cells. Deposition of thin layers of any material is an important fabrication
technique, especially in the photovoltaic industry where it is meant to dramatically
lower costs. Its bandgap is also nearly ideal for use as photo-electrochemical cell
which would be used to create hydrogen based fuels by splitting water, an important
topic that needs further investigation. If it is our intention to use solar energy as our
primary and only source of energy, then the excess energy produced sunlight must be
stored in the form of chemical potential energy such as fuel for use in applications
where a fuel is absolutely necessary.
Other less favorable characteristics of Cu2 O have prevented the realization of a
Cu2 O solar cells. Several factors contribute to Cu2 O’s poor showing of efficiency,
which currently is only at a world record 3.89% [15]. Point defects in cuprous oxide
play a dominate role in preventing the fabrication of high efficiency cells. Copper
vacancies are the main mechanism by which Cu2 Os p-type conductivity is observed. In
addition Cu2 O is a self-compensating semiconductor. Self-compensation is a process
that occurs when the free energy of formation for point defects varies linearly with
the Fermi level. As a result of this phenomena, an increase in the concentration of
donor impurities lowers the free energy of formation of acceptors, thus it is always

more favorable to have more acceptors than donors. The inability to dope Cu2 O
n-type means that there likely will not be a way to fabricate homojunctions with
rectifying behavior and thus attention must be turned to Cu2 O Schottky junctions or
semiconductor heterojunction. Specifically considering Cu2 O solar cells, the general
consens is that a heterojunction will not out perform its homojunction counterpart.
This is due to many reason including differences in the energy band alignment between
Cu2 O and its heterojunction partner, which manifests itself as loss in the open-circuit
potential. An idealized view of band offsets, known as the Anderson rule, states that
the conduction band offset depends only on the electron affinity difference between the
two semiconductors. Anderson’s idealized model also ignores the quantum size effect,
defect states and other perturbations, which in many cases do affect the bandstructure
model quite a bit. In addition, the junction is now a non-continuous interface, which
causes carrier recombination and loss of current. These point defects also present
another problem which has to do with minority carrier lifetime of the material. It is
typically desirable to increase the doping of a semiconductor which increases the the
open circuit voltage via the relation:

Voc =

kT
((NA + ∆n)∆n)
).
ln(
n2i

(1.1)

In the case of Cu2 O, that is not the case as its conductivity is dominated by copper
vacancies, whose acceptor levels are much greater than traditional shallow acceptor
energy levels within the bandgap, essentially destroying the minority carrier lifetime
as doping increases.

1.4

Cu2O: A Review of Properties

The remaining sections of this chapter will focus on properties and growth/synthesis of
Cu2 O. We will first review physical properties of Cu2 O as a bulk material, synthesized
at equilibrium or near equilibrium conditions as it pertains to its use as a photovoltaic
material. Immediately proceeding will be a review of growth methods.

1.4.1

Crystal Structure

Figure 1.3. Representation of the simple cubic crystal structure of
Cu2 O with the red spheres correspond to oxygen atoms and the pink
spheres correspond to copper atoms.
Cu2 Os crystal structure has 2 molecules (i.e. 6 atoms) in its simple cubic unit
cell which crystallizes in a structure known as cuprite shown in Figure 1.3. It has
the symmetry of the 224th space group (O 4h , Pn3m). If an oxygen atom is chosen
to be at the origin, the structure can then be thought of as a bcc oxygen sub-lattice
interpenetrating a fcc copper sub-lattice that has been translated by a( 14 , 14 , 14 ), where
a is the unit cell lattice constant. The only other compounds with the same structure
are Pb2 O, Ag2 O, Cd(CN)2 , and Zn(CN)2 with the cyanides being anti-structures [16].
Based upon x-ray diffraction studies using a Cu Kα radiation source, the lattice
constant was determined to be a = 4.27Å and bond lengths based on d-spacings as
dCu-O =2.85Å, dO-O =3.68Å, and dCu-Cu =3.02Å[11, 17]. By simple calculation, the
density of the material is ρ=6.10 g/cm3 , which agrees with our experimentally
calculated values[18] as well as others [17]. Using Bragg’s law, one can then determine

the h,k,l values that satisfy the equation’s conditions such that Bragg peaks exist.
A table of the Miller indices as well as d-spacing, and 2θ, are calculated and are
consistent with the observed peaks seen experimentally listed in Table [11].
Table 1.1. ICSD powder diffraction table for Cu2 O based off the data
collected by M.L. Foo et al. [11]

2θ

Mult Intensity

0 29.60 3.0176

41.4

1 36.47 2.4639

1000.0

0 42.36 2.1338

382.0

1 52.52 1.7422

10.9

0 61.45 1.5088

358.9

1 65.63 1.4225

0.0

0 69.67 1.3495

3.5

1 73.61 1.2867

329.2

2 77.48 1.2320

77.6

1 85.05 1.1406

3.4

Note: The lattice constant and crystal structure data tabulated by us and other
sources used Cu Kα radiation and collected a powder diffraction spectra in the θ/2θ
mode.
Finally we will note that like many other materials, when Cu2 O is subject to
extreme pressures the crystal structure undergoes a phase change to a hexagonal
crystal structure [17].

1.4.2

Optoelectronic Properties and Electronic Band Structure

While Cu2 Os band gap may not be ideal for a single junction solar cell it certainly has
potential as top subcell in multijunciton solar cell or as a photocathode in splitting
water. The electrical potential of a cell as well as many other properties are related

to its band gap and band structure. An extremely oversimplified understanding of
semiconductor band structures could be understood from the vibrational modes of
atoms in a lattice known as phonons. Phonons play an important role as they provide
the means for energy to transfer via a change in momentum. A a very basic quantum
mechanical treatment of the band structure is necessary in order to fully understand
what is going on. The Bloch theorem uses the fact that the Bravais lattice of a material
is a periodic potential of many electron wave functions, which then can be written in
the form of a plane wave, multiplied by a function with the periodicity of the lattice
for all lattice vectors R:

ψn,k (r) = eik•r un,k (r) with un,k (r + R) = un,k (r)

(1.2)

The wave vector k is then used to solve the Eigenvalue problem:

Hk uk (r) = En (k)uk (r)

(1.3)

This E vs. k relationship, also known as the dispersion relation or band structure
and for each quantum number n, there exists a set of electronic levels specified by
En (k) which is called the band structure. Using information about the degeneracy
of the valance and conduction band spatial wave functions, along with measured
photoluminescence (PL) spectra of exciton emission, [9, 19, 20] one can construct the
electronic band structure of Cu2 O at the Brillouin zone (gamma point) as seen in
Figure 1.4. The measured band gap Eg =2.17eV at 4.2 K is obtained as the limit of
the yellow exciton series[21]. Using first principles band structure methods, theorists
develop computational models to calculate the electronic band structure. One of the
more popular models known as the local density approximation (LDA) [22, 23], does a
fair job of calculating the semirelativistic electronic band structure for Cu2 O except for
the calculated band gap which is smaller than the experimental value. However, the
error in the calculation of the band gap is a known flaw of this model. The correct band

Figure 1.5. Calculated semirelativistic electronic band structure
for Cu2 O which underestimates the band gap by downward shift of
1.5eV[9].

structure can be obtained simply by shifting all the conduction bands upward (in this
case by 1.5eV) to correct the error[9]. Figure 1.5 shows the calculated band structure
using LDA. In order to obtain the corrected band structure, the conductions bands
simply need to be shifted upward by 1.5eV, such that the fundamental direct band
gap at the center of the Brillouin zone is equal to the experimentally measured value
of the band gap. The band structure brings crucial insight about the optoelectronic

Violet

Blue

Green

Yellow

Energy

properties.

Figure 1.4. Band structure of Cu2 O near the Γ point labeld with the
transitions that give rise to the 4 exciton series.
As a result of the band structure calculation, we already know that Cu2 O is a direct
gap semiconductor and thus an electrons probobility of transition from the valence
band to conduction band does not require a substantial change in the electron’s
momentum k, unlike indirect band gap semiconductors, which would require the
absorption or emission of a phonon, making the absorption process of a indirect
semiconductor much less likely to occur. The main advantage of a direct band gap
semiconductor is that the incident light can be absorbed in the few microns of thickness,
whereas several hundred microns of material is required for the absorption of all the

light in the indirect band gap semiconductor.
Two other important material properties can be extracted from the electronic band
structure. The first property is known as the effective mass of the charged carrier, and
the second is known as the mobility of the charged carrier, which is a function of the
effective mass by the equation:
µ=

qτ
m∗

(1.4)

The two can easily be solved for by using equation 1.3, the solution to the Eigen value
problem, as well as Newton’s second law of motion
dv
dt

(1.5)

dp
~k
dt
dt

(1.6)

F = ma =
F =

and solving for m∗ yields

m∗ =

( ddkE2 )

(1.7)

where the quantity ( ddkE2 ) is the curvature of the band. Thus highly parabolic curves
indicate smaller effective mass for the charge carriers, hence high mobility. High
mobility may as well be a requirement in the case of indirect gap semiconductors
where the charged carriers must travel a long distance through the thickness of the
material to be collected before they recombine. The likelihood for carriers to recombine
is expressed in terms of either minority carrier diffusion length LD or minority carrier
lifetime τr (LD = Dτr ) where diffusivity of the charge carriers D is related to mobility
through the Nernst-Einstein relation:
D=

kb T µ
e−

(1.8)

Minority carrier properties reported for Cu2 O are quite good and allow for high
quantum efficiency yields, an important figure of merit needed for practical solar
conversion. Diffusion lengths have been measured to be greater than 5µm, which
is greater than the optical absorption depth. The valence and conduction bands in
Figure 1.4 are labeled with their respective effective mass, where LH is light hole, HH
is heavy hole, and SPH is Split-off hole. The effective masses of the free carriers are
measured by cyclotronic resonance to be m e =.99, m h =.58 expressed in units of the
free electron mass m o [24].There is no experimental data for electron mobility in Cu2 O
simply because the lack of n-type Cu2 O prohibits the experiment to be done. However,
there is plenty of experimental data measuring the mobility of holes. Typical values

range between 10-100 Vcm
[25, 26, 27]which spans an order of magnitude, and often
·sec
times gives a clue as to what process or processes are contributing to hole scattering,
resulting in lower quality material[28]. Masumi et al.[29] conducted temperature
dependent Hall measurements. As the temperature is lowered in a crystal, thermalized
vibrations (phonons) start to freeze out and if the temperature is low enough, the
mobility eventually becomes constant and no longer varies with temperature, and
the only scattering process is due to neutral impurities. An interesting relation can
be derived by knowing the the mobility of charge carriers when the only scattering
mechanism is by neutral defects by using equation 1.4, and substituting in for τ , which
is a function of carrier concentration. After a few simple substitutions it can be shown
that
Ndef ect =

20adef ~µ

(1.9)

A surprising result of this derivation is that it not only gives an estimate for defect
concentration knowing the mobility, but the expression is independent of temperature.
This result, along with the substitutions used to obtain it, will later be used in
the following chapter, 2, where crystal defects, scattering cross sections, and defect
densities are inputs into our device physics model.

1.4.3

Copper-Oxygen Equilibrium Phase Diagram

The copper-oxygen system naturally exists in only two chemical compounds known as
Cu2 O (cuprite, κ) and CuO (Tenorite, τ ) [30].

1 atm
Oxygen pressure (Torr)

Cu2O (liq)
+ O2

CuO + O2
10

-2

-4

Cu2O + O2
Cu (liq) + O2

Cu + O2
10

-6

600

800

1000

1200

1400

Temperature (°C)
Figure 1.6. P(O2 )-T phase diagram for the Cu-O compound phases.
The copper-oxygen binary phase diagram is shown in Figure 1.6 as a function
of temperature and the partial pressure of oxygen P(O2 ). The other important
regions of the phase diagram are the areas to the right and left of Cu2 O. There are
obvious difference between copper metal, Cu2 O, CuO and although phase space can
be controlled to select Cu2 O, the conditions necessary to make Cu2 O an attractive
material to synthesize border near these other phases. In particular, it is preferable
to synthesize Cu2 O at 1 atm. Because of this, similar conditions can result in a
mixture of the three different phases, which is not only undesirable, but often times
difficult or impossible to remove in subsequent processing steps. Note that the phase
diagram suggests that at one atmosphere, Cu2 O is thermodynamically stable only in
14

(K)

Figure 2.12. Phase diagram pO2 -T of Cu2 O. After [104, 247, 655, 820].

1650
(21.5%,1621K)
-4

1600

-2

log

( p(O ) [atm] )

L2+O

L1+L2

1550

1551K
1502K
1496K

Cu O + L2

L1+Cu O

1400

CuO + L2

31.0%

CuO+O

9.57%

1450

(K)

1500

1358.02K

1350

1354K
1338K
39%

1.7%

Cu O

Cu+Cu O
Cu

1250

20
100 x(O)

Cu O+CuO

CuO

1300

Atomic Percent Oxygen

Figure 2.13. T -x diagram for Cu2 O. After [104, 247].

Figure 1.7. T-at% O Binary phase diagram after [31]
a small temperature range near 1025 ◦ C. However, because of slow reaction kinetics,
the phase transformation of Cu2 O to CuO at room temperature is virtually non
existent, and Cu2 O is considered meta-stable as a bulk material. Observation of the
p-T phase diagram tells us that there exists a large window of temperatures and
pressures at which one could produce Cu2 O. This unfortunately does not translate in
the practicality during crystal growth of the material. The temperature and pressure
at which processing occurs has profound impacts on both its structural and electronic
properties. Most of the properties of Cu2 O are determined by the conditions at which
the material is processed. The area bounded within the Cu2 O+O2 region of Figure
1.6 is of course all pure phase Cu2 O, but small deviations from stoichiometry exist,
depending on where the material in that region was fabricated. Knowing information
about the materials stoichiometry and conductivity as a function of the oxygen partial
pressure and temperature, are important to identify the dominate defects in the
material.
Very basic knowledge of inorganic chemistry explains that cations have multiple

oxidation states and because the existence of a material with higher oxidation number
exists Cu(II), the oxide has the tendency to be more cation deficient and thus brings
about a deviation from equilibrium. These deviations from equilibrium impose the
condition for other atoms to rearrange from their previous positions in order for the
system to minimize its chemical potential / Gibbs free energy (∆G). Atoms that have
moved from their ideal position introduce two defects, one at their new location and
one at where they were supposed to be and these are refered to as point defects. Point
defects are defects that occur only at or around a single lattice point and are not
extended in space in any dimension. Special notation is used to describe the different
type of point defects and some have been named after those who discovered them.
There three basic types of point defect and a few different defect complexes are as
follows:
• Vacancies are lattice sites in the crystal where one would expect an atom in a
defect-free perfect crystal but the atom is not there.
• Interstitial defects are atoms that occupy space in the crystal lattice where
usually there is no atom. They are high energy configurations and often times
tend to be atoms with small Bohr radii so they may fit in the space in between
atoms in their normal crystal lattice sites without introducing an unreasonable
amount of strain to the lattice.
• Defect complexes and pairs, which are some combination of the three point
defects described above. These include anti-site defects, Frenkel defect (a nearby
pair of a vacancy and an interstitial), etc.
We introduce the following notation used throughout the thesis to represent a particular
type of point defect. Using Axy as a generic example, A is the symbol that identifies
the nature of the defect, the subscript y describes the location of the point defect,
and the superscript x describes the electrical charge of the defect with respect to the
ideal crystal. The most common point defect observed in Cu2 O is VCu
, which is a Cu

vacancy. There are seven possible point defects or complexes that exist for pure Cu2 O
16

at thermodynamic equilibrium. VCu , VO , Cui , Oi , (2VCu − VO ), (VCu − Cui ), (VO − Oi )
with the latter three being non stoichiometrical defects. Using the stoichiometry
equation for our compound Cu2-y O in equation: 1.10 , in addition to the law of mass
action and neutrality conditions at equilibrium the concentration of the seven point
34 mentioned above can be calculated and mapped out on top
2. Cu
a review
defects
of2aO:phase
diagram,

giving insight to the types of defects that can be expected for a sample processed in a
particular way. Experimentalist have devised several different methods for determining

p(O ) in air, 159Torr

CuO

-2

-4

-5

-6

-7

2V ~O

h >e

-3

2-y

p(O )

(Torr)

-1

- h

-8

900

1000

1100

1200

1300

1400

1500

1600

(K)

FigureFigure
2.19. 1.8.
PhaseBinary
diagramphase
of cuprous
oxideoverlayed
showing the
different
intrinsic
point defects
diagram
with
map of
predominate
predominating in the various stability regions according to the model of Xue et al. [14,137,819]
point
defects
formtoathequilibrium[10].
for neutral
defects
and that
according
model of Porat and Riess [598] for charged defects.

the deviation from stoichiometry and while their data can all be expressed using the
same best-fit equation, the constant used in their fit vary quite a bit, thus leading
to the speculation that the variation from stoichiometry is greatly influenced by the
grain
size2.6.
of the
samples enthalpies
they wereand
making
[32,
33].
Table
Experimental
entropies
of formation
of neutral defects according
to the model of Xue et al. [14, 137, 819] and of charged defects according to the model of
Porat and Riess [598]. The entropy for the neutral copper vacancy is taken from [597].
Defect

[Cu]
[O]
∆H (kJ/mol) ∆H (eV/defect)
y =2−

−∞≤y ≤2

∆Sf (J/(K mol))

(1.10)

∆Sf (eV/defect)

It was
observed that the
variation in 0.77
y was much greater
in smaller grained
samples
V0
74
−10
−0.10
Cu

compared
to larger grain
there as a limit at witch grain size no longer
VO0
294 samples and
3.06
VCu

174

1.81

Oi2−

300

3.12

(VO0 − 2VCu

440

4.58

0.9

0.009

1.4

0.014

play a role. This confirms suspicions that there are a higher density of defects at grain
boundaries. Of course method of growth, kinetics, and equilibrium play a big role in
determining the final microstructure of the material. A review of oxidation kinetics
was conducted by Yongfu Zhu et. al. [34] and the following conclusions where made:
• The rate determining step in the oxidation of copper is the outward diffusion of
Cu.
• Lattice diffusion contributes to high temperature diffusion while at low temperatures
grain boundaries do. In the intermediate temperature range it is somewhat of
an equal contribution.
• Impurities play an important role of impeding growth because at high temperatures
they slow down the diffusion of Cu, while at lower temperatures they impede
the diffusion of atoms through the grain boundaries; this is where they tend to
segregate, thus only enhancing a small intermediate temperature range between
the two.
It is extremely important that one understands defects and their capabilities in
Cu2 O as they can be both detrimental and beneficial. As previously mentioned,
attempts at doping Cu2 O n-type has been futile. Though there are a handful of
reports claiming successfully doping Cu2 O n-type, the source of n-type doping and
voltage observed in their measurements remain controversial[35]. The fact that n-type
doping has yet to be achieved successfully is no surprise. The free energy of formation
∆G can be calculated for each defect using the either experimental or theoretical
values of both enthalpies and entropies. Soon et al.[36] used density functional theory
(DFT) to theoretically calculate these values.
Figure 1.4.3 shows their calculation for the free energy of formations under both
copper-rich and oxygen-rich conditions. The figure shows that the copper vacancy
has the lowest formation energy under both copper-rich and oxygen-rich conditions.
The copper vacancy acts as a moderately shallow electron acceptor and accounts for
Cu2 Os intrinsic p-type semiconductivity. Another important observation is that the
18

clearly shows that, in principle, a rather large supercell is
required to achieve absolute convergence. However, by plotting the calculated formation energies for all considered defects as a function of the Fermi energy 共in Fig. 5兲 and comparing that to the recent work of Raebiger et al. 共see Fig. 3 in
Ref. 14兲, we find that the qualitative trend regarding the relative stability of the various defects is already captured when
using the 48-atom supercell. Also from Table I, it is noted
that reported values in this work appear to be lower 共by 0.22
eV兲 than that found by Raebiger et al.14 which uses the DFTGGA approach including additional corrections such as taking the image charge effect due to the supercell approach and
(a )

(b )

E g (D F T )

C u - r ic h

C u O

F o r m a t io n e n e r g y [ e V ]

O - r ic h

C u O

C u

C u i( t e t )

i( o c t )

i( t e t )

C u i( o c t )

V O

0 .5

1 .0

i( o c t )

1 .5

2 .0

0 .0

F e rm i e n e rg y [e V ]

C u

i( t e t )

V C u (s)

V C u

V C u
0 .0

C u i( o c t )

V C u (s)

V O

0 .5

1 .0

1 .5

2 .0

F e rm i e n e rg y [e V ]

Figure
A 48 atom
super-cell
native defects
to calculate
defect
FIG. 5.1.9.共Color
online兲
Defectwith
formation
energies
for native
deformation
energies
function ofasFermi
level forofboth
a)copper-rich
fects
in a 48-atom
Cuas2Oa supercell
a function
the Fermi
energy
under
copper-richconditions.
and 共b兲 oxygen-rich conditions. Following
and 共a兲
b) oxygen-rich
Ref. 14, the VBM is adjusted by pushing down the DFT-derived
VBM by 0.32 eV while extending the CBM to match the experimental band gap of 2.17 eV. ⌬EF = 0 now corresponds to the VBM
after this adjustment. The dashed vertical gray lines define the otherwise smaller DFT-calculated band gap.

⌬EOR-CR, is ex

where ⌬NCu a
and O atoms b
ideal reference
Cu2O which
tot
where ECu
2O
Cu2O, bulk Cu
is calc
⌬HCu
2O
the copper an
yielding ⌬EOR
vacancy and c
respectively, a
interstitials is
oxygen antisi
electronic tran
defects in Cu2
Under both
共see Fig. 5兲, t
mation energy
tion energy fo
while the nex
vacancy comp
corresponding
lated ⌬⑀共0 / −1
respectively. T
et al.14 is slig
theoretical val
the experimen
transient spect
tified another
tively assigne
it is evident th
increasing sup

035205-7

PtCo
rE

Co
rOx
De
no
nF

Figure 1.10. A schematic of a typical setup used for electrochemical
deposition.
formation energy of charged defects varies linearly with the Fermi level and as the
Fermi-level nears 1eV (around the where the oxygen vacancy defect energy lies in the
bandgap) the free energy of formation for creating copper vacancies is now zero or
negative which means the crystal prefers, because of both entropy and enthalpy, to
compensate the increasing fermi-level. This is what is meant by ”self-compensation”
and is the basis for intrinsic doping in Cu2 O. A more detail discussion of Cu2 O doping
will continue in Chapter 4.

1.4.4

Review of Growth Methods and Cu2 O Heterojunctions.

The growth of synthetic Cu2 O has been done using several methods, though mainly
by oxidation of copper in a furnace [37, 38, 39], by electrodeposition [40, 41], and
sputtering[42, 43]. More specialized techniques for both growth and purification such
as hydrothermal growth[44], floating zone[24] are also used but often times are too

ArGa
Figure 1.11. Cross sectional view of inside a sputtering chamber.
complex and do not yield results significantly different than the methods mentioned
above. Of the three most popular growth methods, we will review electrodeposition
and RF-Sputtering in this section. The review and discussion of Cu2 O grown by
thermal oxidation will be deferred to Chapter 4. Electrodeposition is a deposition
technique used for well over a couple hundred years with a variety of different materials.
It has the advantages of low cost of operation and source material. It also has the
advantage of being a low temperature non vacuum technique. It is versatile in the
sense that it can be done via both anodic oxidation of a copper sheet or cathodic
reduction of a copper salt solution[40, 41]. Unfortunately, Cu2 O solar cells fabricated
by Electrodeposition have not shown much promise in terms of their efficiencies
because the technique generally does not offer control of orientation and epitaxial
growth. In addition, the surface roughness becomes a big problem for films that are
thicker than several hundred nanometers, thus creating interface issues at both the
heterojunction and surface of the solar cell. For those reasons, efficiencies greater than
.5% have not been realized [45].
Reactive Sputtering or RF sputtering are two similar techniques used to make
thin films of Cu2 O on a substrate. Reactive sputtering uses a Cu metal target as the
source material, and that material reacts with oxygen that is leaked into the chamber

Figure 1.12. This figure illustrates the typical setup of a commercially
available vacuum furnace setup. It is quite possibly the easiest, fastest,
and cheapest method of fabricating Cu2 .
to create Cu2 O thin films. RF sputtering uses a Cu2 O target instead of a Cu target.
The use of a radio frequency (RF) generator is essential to maintain the discharge
and to avoid charge buildup when sputtering semiconducting or insulating materials
such as Cu2 O. The sputtering process consists of initiating a glow discharge in the
vacuum chamber under pressure controlled gas.
The glow discharge consists of partially ionized gas ions, electrons and neutral
species.The ions are then accelerated at very high voltages to the target material
where they bombard the target and eject atoms from the source, which then go across
the chamber and nucleates on the substrate. Since process is conducted in vacuum,
22

control of the crystal orientation, growth rate, and whether the films growth was
kinetically controlled or thermodynamically controlled. One of the biggest advantages
sputtering has over the previous technique, is the species of gas and their partial
pressure are all completely controlled by the user. Unfortunately, there are a few
serious problems with sputtering, and one must make sure to design their experiments
such that they minimize their effect. Because atoms are being accelerated at high
speeds, there is the potential that they will damage the surface of the sample. More
importantly, any atoms that are in the discharge area have the potential of being
incorporated into your film via ion implantation. While both of these methods would
be wonderful if they could be implemented in commercial manufacturing, their current
state of progress makes it not vary likely. Using new age scientific tools and fabrication
techniques we hope to progress the field in understand the fundamental issues that
prevent higher efficiency cells. Two of the chapters in the remainder of this thesis will
focus on growth of Cu2 O using two additional techniques which have already shown
the prospect of great progress in this field.

Chapter 2

Detailed Balance Efficiency and Band
Transport Model for ZnO/Cu2O Solar
Cells
This chapter explores two different modeling techniques for determining the efficiency
of a copper oxide heterojunction solar cell in order to determine if there is sufficient
opportunity for efficiency improvements over existing devices, or if there is any way
to enhance the efficiency of an existing device by coupling it with a Cu2 O solar
cell. This first half of this chapter introduces detailed balance efficiency modeling,
which is also known as the thermodynamic efficiency limit of solar cell, for both a
single-junction and doubled junction cell. The second half of this chapter will focus on
a band transport model for a ZnO/Cu2 O heterojunction solar cell. While both models
calculate the efficiency for a Cu2 O solar cell, the detailed balance model gives the
theoretical maximum or asymptotic limit of efficiency for an ideal cell, while the device
physics model calculates an efficiency for realistic cell and is great for determining the
suitability of various real materials . Details of each model will be outlined in their
respective sections.

2.1

Detailed Balance Model for a Cu2O Solar Absorber

The detailed balance limit, also known as the Shockley-Queisser limit[46], is a technique
used to calculate the efficiency of a photovoltaic cell. This method was proposed by
Shockley and Queisser in 1961. The model is an excellent tool for gauging the promise

of different solar materials and is valuable in assessing if further optimization of a given
cell is beneficial given the cost and time as one approaches the asymptotic efficiency
limited. Efficiency limits of a solar cell can be calculated either by thermodynamic or by
detailed balance approaches. These approaches are equivalent, but the detailed balance
model allows the calculation to be made without explicit calculation of entropies by
making the following fundamental assumptions:
• All recombination of carriers occurs radiatively. There are no recombination
centers such that the minority carrier lifetime is infinite.
• The radiation is non-thermal with a chemical potential that is equal to the
separation of the quasi-Fermi energy levels, also known as the voltage of the cell.
• The number of photons absorbed by the cell must be equivalent to the number
of photons that are re-emitted through the radiative recombination process, plus
the number of electron-hole pairs extracted from the cell.
The original model only accounted for a single-junction cell and one sun. A
modified version of the detailed balance method presented by C. Henry in 1980[47],
extends the model to include efficiency calculations for multijunction/tandem cells and
concentrator cells (i.e. more than one sun). The efficiency of a solar cell is calculated
by dividing the power extracted from the cell by the integrated power of the solar
spectrum incident up on the cell.
η=

J(V ) · V

(2.1)

Where, V is the operating voltage of the cell and J(V ) is the current density generated
by the solar cell as a function of operating voltage. For the work presented in this
section, the measured solar spectra for AM 1.5, as measured by the National Renewable
Energy Laboratory will be used (figure reffig:am1.5) as opposed to the sun’s black a
body spectrum originally used by Shockley and Queisser. This spectrum takes into
account absorption of photons in the atmosphere before they are incident upon the
solar cell surface. Using the spectra, the number of photons arriving in the cell can be
25

A M 1 .5 D

G lo b a l T ilt S p e c tr u m

fro m

N R E L

1 .8

P h o to n F lu x [W * m - 2 * n m - 1 ]

1 .6
1 .4
1 .2
1 .0
0 .8
0 .6
0 .4
0 .2
0 .0
5 0 0

1 0 0 0

1 5 0 0

2 0 0 0

W a v e le n g th [n m ]

2 5 0 0

3 0 0 0

P h o to n F lu x

Figure 2.1. NREL’s AM1.5D golbal tilt solar spectrum used in the
calculation of the detailed balance efficiency

determined as a function of energy, thus a generation profile and number of carriers
generated by solar illumination is given by

AM 1.5

N (Eg , ∞, C) = C

ρ(E)∆(E)

(2.2)

E=Eg

where,
Eg = the band gap of the cell.
C= The concentration of the incident solar spectrum.
ρ(E)∆(E) = the number of photons per delta unit energy for the AM1.5
spectrum.
The number of carriers lost due to radiative recombination is given by the generalization
of Kirchoff’s law for selective photon emission in the equation below
rad

N (Eg , ∞, T, V, ) = 3 3 2
4π ~ c

Z ∞

{(~ω)2 [exp

~ω − qV
− 1]−1 }d~ω
kT

(2.3)

where,
T = the operating temperature of the cell.
V = the operating voltage of the cell.
= πn2 sin2 (θc ) a factor which characterizes how ”spread out” light is in area
and angle known as the ètendue.
θc =the critical angle for emission to a medium of a different refractive index.
thus for a single-junction cell the operating current is
J AM 1.5
N (Eg , ∞, C) − rad N (EG , ∞, T, V, )

(2.4)

and thus the efficiency can be calculated using equation 2.1. The ètendue is an
important factor that describes how light leaves the cell once radiative recombination
takes place. When calculating the detailed balance efficiency, it is important to
calculate the ètendue correctly by carefully considering the geometry that is going to
be simulated. For example, a thin single-junction cell on a low-index support substrate
would require that the emission from the back surface into the cell be altered by the
critical angle for emission into the support material. Using an approximate value of 2
for the refractive index of a typical low index substrate material (MgO, glass, sapphire)
the ètendue for the back surface is calculated to be 4π; a significant reduction when
compared to a thin single junction on a thick substrate which can have a ètendue of
12π. This information is used to not only optimize efficiency, but also to lower the
cost of the cell itself. The cost of the main absorber materials can be nearly cut in
half by having to use less material as an optimized back surface would likely be a light
reflector (a mirror), essentially causing any light to be refelect back into the cell and
thus effectively doubling the material thickness. This engineering design is one many
designs that tries to confine light within the cell in a technique known as light trapping.
Of course the ètendue is just as important in multijunction solar cell calculations, as
its value (a function of index matching the different layers) will determine how many
photons with energy less than the band gap of the top cell in the tandem will be able
to be absorbed in the lower layer. Because of Cu2 Os high band gap it will always be
considered the top cell in a two or three-junction solar cell. It is important to note
that the distribution of power in the solar spectrum is broad, and cannot be efficiently
harnessed using a single band gap cell. the work being presented is not intended to
displace any present and mature technology such as Si, but to possibly supplement
and enhance it. Using the work of prior group member Brendan Kayes as reference,
Matlab code for a detailed balance model of a single and dual-junction Cu2 O solar
cell was written. The generic code for the model is located in A. Using the simulation
program in Matlab, we calculate the detailed balance efficiency for a Cu2 O/ZnO on
MgO substrate single junction cell to be 22%. For comparison the calculated detailed
balance efficiency for a silicon single junction cell is 29.17% which is in agreement
28

Figure 2.2. The top figure illustrates spectrum splitting in order to
increase efficiency of solar cells; the principal behind multijunction
cells, the image below shows why spectrum splitting is needed as
solar cells are not great broadband absorbers and therefore are either
unable to absorb light or lose energy from photons whose bandgap is
much greater than the solar absorber through thermalization.
29

with previous detailed balance model calculations[47]. The reason why the detailed
balance efficiency of Cu2 O is not as high other solar materials like silicon, is because
of its band gap. The sun is a broadband light source while our solar cell Cu2 O (but
true of any other material) is only a really good narrow band collector. Looking at
the AM1.5D spectrum in figure 2.1, Cu2 O is unable to absorb any photon less than its
bandgap energy which is 2eV or less greater 619nm in wavelength which is equivalent
to the integrated area under the curve to the right of 619nm in figure 2.1. While
photons greater than the bad gap get absorbed by the material, there is a point at
which it is wasteful to absorb those higher energy photons as they must release energry
in the form of heat to thermalize down from their incident energy to the operating
voltage of the cell; so for example a 3eV photon would waste 1eV of energy in the
form of heat if incident upon a copper oxide cell. One method, to more efficiently
capture the photons from the sun is to split its broadband light spectrum and use a
solar cell that is optimized to each respective section of the spectrum. This design is
known as multijunction or tandem photovoltaic cells. Simulation were conducted for
a dual-junction cell. The plot shown in figure ?? shows two curves. The solid curve
calculates the efficiency of a tandem Cu2 O/PV
This section has been broken down into several subsections. First is a section generally
describes the band transport model implemented and its assumptions. The next
section outlines our model in specific, and describes the inputs, materials parameters,
and changes to the standard model the programs expects in order to properly simulate
our cell structure, whose results and discussion are saved for the last section.

2.1.1

Model Background

The modeling conducted in this chapter was done using the software AFORS-HET
v 2.2[48] (automat for simulation of heterostructures), designed and distributed by
the Helmholtz-Zentrum Berlin fur Materialien und Energie. AFORS-HET is a one
dimensional numerical simulation program designed to model multilayer homo/heterojunction
solar cells as well as providing tools to “characterize” the cells virtually. The
30

simulation is composed of two part: optical and electrical sub-simulations. The
optical sub-simulation calculates the generation rate of carriers (electron-hole pairs)
per second per unit volume at a certain depth (x) of the model structure. In addition
the standard optical model of Lambert-Beer absorption can be modified to include
affects such as reflections, scattering, and etc. The electrical sub-simulation calculates
the charged carriers densities, and the electric potential at any given depth (x) of the
structure while operating under specific conditions such as open-circuit voltage. In
order to conduct an electrical simulation, an optical simulation must be carried out
first the create the generation profile of the charged carriers and a recombination rate
has to be stated in terms of the unknown independent variables n, p, electric potential
and can be designed by the user of the software to include effects such as radiative
recombination, Auger recombination, Shockley-Read-Hall recombination, and dangling
bond recombination. The program numerically solves the one dimensional differential
equations equations with boundary conditions under steady state at discretized points
xi along the depth of the structure. All other unknown quantaties in the equations
can be written in terms of the free electron and free hole density, ni , pi and the cell
potential φi at each gridpoint xi .The equations are solved using Newton-Raphson
method. This methods solves for the internal cell characteristics such as the generation
and recombination profiles, carrier densities and band diagrams. In order to calculate
certain properties, the time-dependent differential equations would be typically needed,
but using instead can be accomplished using small sinusoidal perturbations to the
boundary conditions. Only first order terms are considered and allow the quantities
to be described the equations below:
2.1.1.1 Bulk
n(x, t) = n(X) + ñ(x)eιωt

(2.5)

p(x, t) = p(x) + p̃(x)eιωt

(2.6)

ϕ(x, t) = ϕ(x) + ϕ̃(x)eιωt

(2.7)

The solution to the three differential equations that describe the characteristics of the
bulk of the material use Poisson’s equation and the transport equations for holes and
electrons.
ε0 εr ∂ 2 ϕ (x, t)
(x,
t)
(x,
t)
ρt (x, t)
∂x2
def ect

(2.8)

−1 ∂jn (x, t)
= Gn (x, t) − Rn (x, t) − n (x, t)
∂x
∂t

(2.9)

1 ∂jp (x, t)
= Gp (x, t) − Rp (x, t) − p (x, t)
∂x
∂t

(2.10)

The variables n, p, and ϕ are the independent variables solved in the system.
The remaining variables such as the layer’s absolute and relative dielectric constant,
concentration of donors and acceptors ND , NA and defect concentration are variables
assigned a value by the user prior to the simulation being conducted. The electron/hole
currents are determined from the gradient set by the quasi-Fermi energy which is
equivalent to the summation of the drift and diffusion currents with their corresponding
mobilities.

jn (x, t) = qµn n(x, t)

∂EF n (x, t)
µn kT ∂n(x, t)
∂ϕ(x, t)
=−
+ µn n(x, t)
∂x
q∂x
∂x

(2.11)

jp (x, t) = qµp p(x, t)

∂EF p (x, t)
µp kT ∂p(x, t)
∂ϕ(x, t)
=−
− µp p(x, t)
∂x
q∂x
∂x

(2.12)

2.1.1.2 Generation
There are several methods by which a generation profile can be generated. In order to
not digress too far off topic we describe the most common method. A simple model is
used where the incoming photon flux is a function of wavelength, a parameter that is
set by the user by selecting a particular spectra. Photons with energy E ≥ hc
then
are exponentially absorbed by the Lambert-Beer Law.
2.1.1.3 Recombination
In the model to be presented at the end of this chapter, only Radiative and Schokley-Read-Hall
recombination are considered. The former is built-in to the recombination profile
automatically and thus the user must only concern themselves with SRH recombination.
As discussed earlier in section 1.4.3 there are plenty of point defects in copper oxide
and they are responsible not only for the materials conductivity but ultimately also
responsible for SRH recombination. The program places and arbitrary number of
defects, distributed arbitrarily withing the bandgap. The SRH recombination then is
required to specify the distribution of the defects in energy space. The emission rate
is calculated using the defects electron/hole capture coefficients which then is used
in conjunction with the distribution of occupied defect states to calculate the SRH
recombination rate due to defect. The result of the derivation for both n and p type
carriers is shown in equation 2.13.

SRH
R̃p/n
(x) =

dE{cp/n Nt (E)ft (E, x)(p̃/ñ)(x)+cp/n Nt (E)f˜t (E, x)+ep/n (E, x)Nt (E)f˜t (E, x)}
(2.13)

2.1.1.4 Heterojuntion Interface
AFORS-HET uses one of two models for transport of carriers across the interface. The
first is a model that uses an interface layer of a certain thickness specified by the user
when creating the mesh, in which the material properties change linearly across the
junction from the values of the properties of semiconductor A to semiconductor B with
33

defect that are homogeneously distributed through out this thin layer. The carrier
transport then is simply thought of as bulk-like (drift/diffusion driven). The band
alignment is treated as simple as possible by using differences in electron affinities in
order to establish the quasi-Fermi level, thus establishing the maximum operating
voltage of the cell. The current then is simply calculated as the gradient of the
quasi-Fermi levels. The second model for transport across the heterojuntion interface
is currents driven by thermionic emission which is an appropriate model when the
band alignment of your heterojunction includes energetic barriers such as spikes or
cliffs where a probability factor for thermionic tunneling is included in the solution.
In addition the interface is not considered continuous in this calculation but rather a
boundary condition. The built-in module for simulating interface defects was giving
unphysical results. We were able to work around this issue by including our own ∆ X
layer at the interface that had the same characteristics as what is described in the
documentation and were able to to continue our calculations, obtaining results that
were expected.
2.1.1.5 Contacts and Boundary Conditions
The electric potential is fixed at 0V on one contact. A boundary condition must then
be specified at the second contact so that there can be a relation between the external
current/voltage and internal quantities. These are the final sets of conditions needed
in order to solve the differential equations to calculate n(x), p(x), and ϕ(x)
ϕ(0) = φf ront − φback + Vext

(2.14)

ϕ(L) = 0

(2.15)

jn (0) = qSnf ront (n(0) − neq (0))

(2.16)

jn (L) = −qSnback (n(L) − neq (L))

(2.17)

jp (0) = −qSpf ront (p(0) − peq (0))

(2.18)

jp (L) = qSpback (p(L) − peq (L))

(2.19)

Where the following variables are inputs into the model; ϕ : metal work function, S:
surface recombination velocity). The density of majority carriers are either (neq or
peq ) which is determined by the energy barrier height of the contact/semiconductor
interface. Then the minority carrier density can be derived from the law of mass
action;
neq = Nc exp

qφ − qχ
kT

or peq = NV exp

Eg − qφ + qχ
kT

neq peq = Nc NV exp

2.2

Eg
2kT

(2.20)

Cu2O\ZnO Materials Models and Simulation
Parameters

Using Afors-Het, a device physics model of a Cu2 O /ZnO heterojunction cell was
developed and allowed us to gain a better understating of how the defects and band
structure of the heterojunction affect the efficiency of the cell. Most often, if Cu2 O is
being used as a solar absorber in a heterojunction it is usually paired to ZnO. This is
because the Cu2 O/ZnO heterojunction is the material system to be studied in most
detail and still offers the most promise in making higher efficiency heterojunctions.
To simplify the simulation ZnO was not included in the numerical calculation as an
electrical layer since it gives a negligible contribution to the photocurrent. Instead,
the effect of Air/ZnO stack on the optical absorption of the Cu2 O layer was included
in the simulations. The main effect of the ZnO is the generation of a built-in voltage
(band bending) in the Cu2 O layer and so we employed the Schottky heterojunction
interface approximation where the following conditions are set.
1. ZnO is modeled as a metal (that means it is degenerately doped) whose work
function is equal to the electron affinity of ZnO.
2. Optical absorption of ZnO is still taken into account via an optical layer on top
of our solar cell.
35

3. Interface defects can be controlled by both inserting a thin Cu2 O defect layer or
by varying the surface recombination velocity at the heterojunction interface.
Table 2.1. AFORS-HET model Parameters & Cu2 O Properties
Optical Data Input = Spectroscopic Ellipsometry Data
N c/N v = 2.44x1019 /1.1x1019
V ac
DiV ac
ECu
/ECu
/EOV ac = .45eV /.25eV /.91eV

Eg = 1.95eV
χ = 3.3eV
me /mh = .59me /.98me
The parameters below were varied in the simulation if and where appropriate.
χ, µn , µp , Na , Nd , Ntrap , thickness = x

The materials models used in the simulation were developed from both optical and
electronic measurements of thin film samples primarily fabricated in our labs using
plasma-assisted molecular beam epitaxy of Cu2 O, and ZnO. When characterized these
thin film samples had a range of different properties dependent on their deposition
conditions. In addition the proper deposition conditions were determined for fabricating
thin film samples such that their electrical and optical properties properties were
reaching the bulk like limit. Certain measurements were not conducted on our samples,
either because they had well established values which were obtained from literature, or
because their value was a variable or directly dependent on a variable that was being
varied in the simulations. The values that were obtained from literature were electron
affinity and the effective mass of holes and electrons. Table 2.1 shows the information
that was inputted into the simulation software. The adjusted model as well as our
materials models was evaluated in order to determine if the solution produced were
both valid and accurate. This evaluation was conducted by importing the simulated
structures of several different published Cu2 O/ZnO heterojunction solar cells and
and simulating several different characteristics for result. Specifically the model was

used to simulate their IV characteristics under AM1.5D illumination as well as their
spectral response.

The results of our validity simulations conducted was in close

S im u la te d
E x p e r im e n ta l

C u r r e n t [m A /c m

0 .0

0 .1

0 .2

0 .3

0 .4

0 .5

0 .6

0 .7

V o lta g e [V ]

1 .0 0
E x p e r im e n ta l
S im u la te d

E Q E

0 .7 5

0 .5 0

0 .2 5

0 .0 0
4 0 0

4 5 0

5 0 0

5 5 0

6 0 0

6 5 0

W a v e le n g th [n m ]

Figure 2.3. IV characteristics and external quantum efficiency plots
for simulated Mittiga heterostructure vs their published experimental
results. The shape of the curves are nearly identical and are slightly
different due to the omission of some optical layers in our simulation.
agreement (well within a small margin of error) to efficiency calculations and produced
nearly identical IV and Q.E. curves when compared to the results and curves in the
published work we simulated. One such set of validity data is included in figure 2.3,
which show our simulated data in comparison to the experimental work and data
published by Mittiga[37]. These results seemed to validate our model which made us
37

comfortable enough to proceed using the model for a series of simulation with a high
degree of confidence that those results outputted by the simulation would be would
be correct and accurate. Another example of a Cu2 O/ZnO heterostructure is listed in
appendix C which includes all input parameters of our model as well as a simulated
output in text mode. Content with the accuracy of the validation simulations, our
materials models were implemented into a new generic structure often referred to as
the “typical” Cu2 O/ZnO heterojunction, because of the number of groups and people
who have experimentally fabricated and reported values for a very similar if not exact
structure. The crucial choice of our base simulation, which will be the start point or
reference point for all the simulations conducted, was thought through very carefully
because it is one of only a few points that allows easy comparison between important
properties without too much convolution and because of that allows one to essentially
rank in order which parameters have the most or least affect on the performance
of the cell. These results would point out the critical parameters or properties of a
Cu2 O/ZnO heterojunction solar cell and serve as cost benefit guidelines for further
optimization and research of these cells. The five properties which have are believed
to have the greatest impact on solar cell performance were varied in our Cu2 O/ZnO
heterojunction model and simulated I-V and quantum efficiency plots were generated
to determine effect on solar cell efficiency. The five parameters varied were thickness,
p-type carrier concentration, diffusion length, band offset, and heterojunction interface
recombination velocity (a figure of merit for heterojunction interface quality) of the
Cu2 O. For most of the results presented, the simulations were conducted four times
for differing minority carrier diffusion lengths, significant of poor quality material
when the diffusion length is at 100nm diffusion and very high quality material at
diffusion lengths reaching near 10µm . It has been long speculated that the Cu2 O/ZnO
heterojunction interface, or lack thereof, has been the most detrimental effect to the
devices performance. The interface has two primary effects on the cell, both of which
have been modeled. The more obvious problems are the interface are defects and
traps which facilitate recombination of charged carriers in the cell. Because of our
earlier choice to simplify the simulation so that we did not need to include ZnO in any
38

numerical calculation due to its negligible contribution to photocurrent, we are not
able to simply obtain efficiency as function of varying Ntrap . Instead we simulate the
efficiency of the cell vs. surface recombination velocity at the heterojunction interface
as seen in figure 2.4 and use relation refeq:ntrap to back calculate the number of traps
present at the interface.
Ntrap =

Sinterf ace
Vth σtrap

(2.21)

1 0 0 n m
5 0 0 n m
1 u m
1 0 u m

E ffic ie n c y

1 0

1 0 0

1 0 0 0

1 0 0 0 0

1 0 0 0 0 0

1 0 0 0 0 0 0

1 E 7

In te r fa c e R e c o m b in a tio n V e lo c ity [c m /s ]

Figure 2.4. The efficiency of a ZnO/Cu2 O heterostructure vs interface
recombination velocity which can be converted to trap density at the
heterostucture interface. This plot shows results for four different
minority carrier diffusions lengths.
At 100nm minority carrier diffusion length the material is essentially bulk recombination
limited while at 10µm it is interface recombination limited. Most experimental cells
are closer to the bulk recombination limit where minority carrier diffusion lengths are
in the 100-500nm range[49]. The other important feature the heterojunction interface
creates is band bending. To simulate band bending, the electron affinity of Cu2 O was
39

artificially changed and brought closer to the value of the ZnO electron affinity. Figure
2.5 shows that the efficiency increases significantly as the heterojunction bands go
from being almost a type II to type I heterojunction. Because of Cu2 O low electron
affinity (3.3 eV) compared to ZnO (wide range) the maximum voltage a Cu2 O solar
cell cannot be realized in this heterojunction [14]. Unfortunately, there is very little
that can be done for a particular heterojunction in terms of changing the band bending
at the interface for a particular heterojunction pair. The exception is when one has
complete control over the texture of the thin films. Certain crystal orientations of
ZnO have different values of electron affinity due to the polar nature of its crystal
lattice [50]. Before conducting these simulations, we believed that these two properties
would have the greatest effect on the efficiency of the solar cell. However another

1 0 0 n m
5 0 0 n m
1 u m
1 0 u m

E ffic ie n c y

3 .3

3 .4

3 .5

3 .6

3 .7

3 .8

E le c tr o n A ffin ity [e V ]
Figure 2.5. The efficiency of a ZnO/Cu2 O heterostructure vs the
electron affinity of the Cu2 O layer. This plot demonstrates how
Cu2 O low electron affinity is unfavorable for this heterostructures
band bending. This plot also shows results for four different minority
carrier diffusions lengths.

property of the solar cell clearly dominated its performance. The doping, and more
importantly type of dopant, plays an integral role. The simulated model only took into
account Cu2 Os intrinsic doping mechanism where equilibrium point defects determine
the carrier concentration. These point defects are outlined in Table 2.1 and have
energies deep in the forbidden band gap of Cu2 O. Copper vacancies are responsible
for Cu2 Os conductivity and were used in the materials defect and doping model as
well as including the self-compensating mechanism that produces oxygen vacancies.
Both of these defects play a critical role in the conductivity and lifetime of a Cu2 O
cell. Copper and oxygen vacancies were varied along with the carrier concentration
Na . Figure 2.6 shows when Cu2 Os carrier concentration is low, it behaved like an
intrinsic semiconductor and as the doping increased so did the cells conductivity
and open-circuit voltage thus increasing the efficiency.

An unexpected feature

was discovered in the simulation. When the doping reached 1x1014 carriers/cm3 any
increase seen in the cells current was at the expense of the cell’s open circuit voltage.
This phenomenon can be explained by an indirect connection between bulk minority
carrier diffusion length and the p-type intrinsic carrier concentration. As previously
mentioned, it has been established that Cu vacancies are the main mechanism which
leads to Cu2 O’s p-type conductivity. This equilibrium point defect mediates Cu2 O’s
self-compensation mechanism where the more acceptor impurities are inserted (Cuvac ),
the more the energy of formation of donors are lowered and more donor defects are
formed thus increasing the number of traps in the midgap of Cu2 O and decreasing
the cell’s mobility, and minority carrier lifetime. The cell’s efficiency as a function of
diffusion length which is related to the cell minority carrier lifetime is shown in figure
2.6 as well on the top axis. From this plot it can be deduced that the two parameters
are intimately connected to one another in the particular case where no extrinsic
dopant was used. Using the diffusion length corresponding to a particular intrinsic
doping concentration, one can go back to any of the previous plots to get an idea of
the efficiency of the cell with those given parameters. The plot demonstrates how
the efficiency is most greatly affected by diffusion length and how the cell efficiency
increases dramatically if one could dope the cell without creating additional defects.
41

M i n o r i t y C a r r i e r D i f f u s i o n L e n g t h [ µm ]

1 0

-1

4 .5

4 .0

3 .5

3 .0

2 .5

2 .0

1 .5

1 .0

0 .5

0 .0

E ffic ie n c y

1 0
4 .5

1 0

1 2

1 0

1 3

1 0

1 4

1 0

1 5

p - C a r r ie r C o n c e n tr a tio n [c m

1 0
-3

1 6

1 0

1 7

Figure 2.6. Efficiency of the Cu2 O/ZnO cell as a function of intrinsic
carrier concentration as well as diffusion length. This is because
intrinsic dopants act as deep level traps which destroy minority
carrier diffusion lengths in the bulk.

1 0 0 n m
5 0 0 n m
1 u m
1 0 u m

E ffic ie n c y

1 0

-2

1 0

-1

1 0

T h ic k n e s s [u m ]
Figure 2.7. The efficiency of a ZnO/Cu2O cell vs thickness of the cell.
This plot shows results for four different minority carrier diffusions
lengths.

Unfortunately as it stands now no dopant has been found which introduces a shallow
acceptor level and does not introduce a new recombination channel for the minority
carries. For that reason, having a large Na is undesirable which makes the Cu2 O layer
very resistive. For that reason, the thickness of the cell played a more important
role than expected. When the Cu2 O layer was too thin the cell simply could not
absorb enough light and created negligible current. As the cell thickness increased so
did the efficiency, but at some point the cell became too thick as demonstrated by
the inflection point at roughly 1x105 cm in figure 4d. This feature is attributed to a
decrease in the cells fill factor as the minority carrier collected by the junction must
traverse the thickness of a fairly resistive semiconductor to be extracted from the cell.
Therefore the final three parameters discussed above have an indirection relation with
one another that greatly affect the efficiency of the cell.

2.3

Conclusion

By conducting these simulations of a Cu2 O/ZnO heterojunction, we have identified
the critical properties and parameters of the heterojunction that have been keeping
efficiencies far from their theoretical values. More importantly the results of these
simulations have allowed us to rank the importance of tweaking these parameters/properties
in order to obtain higher efficiencies. The simulations revealed the most important
property to focus on is the urgency of finding an extrinsic dopant, as current intrinsic
doping limits both diffusion length of our material due to them acting as deep level
traps as well as lowering our open circuit voltage as it pins the firm level away from the
valence band edge. We also discovered the importance of having a defect free interface
as the number of traps at the heterojunction interface also greatly affects the efficiency
of the cell. This issue may be overcome by using growth methods such as MBE or
clever oxidation techniques that allow epitaxial growth of our heterojunction layers
thus dramatically lowering the concentration of interfacial defects at the heterojunction
interface. Attempting to solve these problems, Cu2 O/ZnO heterojunction solar cells
will be able to achieve efficiencies well above 10%.
44

Chapter 3

Growth of High Quality Cu2O Thin Films
via Plasma-Assisted Molecular Beam
Epitaxy
Molecular Beam Epitaxy (MBE) is one of the more difficult fabrication techniques
to use and master. However, it allows precise control over almost any parameter
one can think of. In addition, MBE systems often include a vast variety of in-situ
characterization tools, which provide real time information on the evolution of growth
and state of the sample. It is not necessary for one to wait for a deposition process to
be complete before being able to probe the material in order to determine the phase
material grown; whether or not it is strained, possibly because of impurities, or if
the material is crystalline or amorphous. This chapter begins with an introductory
section on vacuum science, and thin film deposition; specifically the fabrication of
thin films using molecular beam epitaxy. The chapter continues with a description of
the experimental setup used to fabricate Cu2 O/ZnO heterojunctions and investigates
the epitaxial growth of high quality Cu2 O and ZnO thin films on both bulk MgO
substrates as well as biaxially textured ion-beam assisted MgO templated substrates
using plasma enhanced molecular beam epitaxy. The structural, optical and electrical
characterization conducted on these thin films will be discussed. Finally, we present a
process for creating a Cu2 O/ZnO heterojunction device with 0% shadowing loss using
an interdigitated metallization contacts scheme, and present device results.

3.1

Vacuum Science Basics[1, 2, 3]

In its most basic definition, a vacuum is space that is empty of matter and that is
extremely important in the discussion of thin films. Because it is impossible to achieve
a perfect vacuum , there will always be some “matter” in space; and typically it is
matter that we do not want there when we are talking about thin film deposition
systems. The quality of a vacuum is often divided into several categories and while
the there is no official standard for the ranges of quality, they are most often the same,
even across scientific disciplines. The four main ranges are rough vacuum (RV) from 1
atm to approx 1torr, medium vacuum (MV) from 1 torr to 1mtorr, high vacuum (HV)
from 1mtorr to .1µtorr, and finally ultra high vacuum (UHV) from µtorr to essentially
perfect vacuum. While these pressures are general guidelines, most people prefer to
delineate the pressure regime they are in by the nature of gas flow. There are two main
flow regimes that are encountered in vacuum technology: viscous or continuous flow,
and molecular flow. Some may consider Knudsen flow, which is the transition between
the two flow regimes; its own type of flow, but that label is unnecessary. Viscous flow
is the type of flow that is determined by the interaction of molecules. That is because
the mean free path λ of atoms or molecules is much less than the chamber or pipe
diameter d (λ¡¡d). Molecular flow begins to prevail when the mean free path of atoms
is on the order of or greater than the size of the chamber or pipe. The mean free
path λ describes the distance an atom or molecule can move freely in space without
interference of any other molecule or atom. In molecular flow that distance is often on
the order of meters, and this regime is typically what allows high quality defect free
films to be fabricated. In order to achieve a vacuum in space, a pump must be used to
evacuate the air present in the chamber. There are a plethora of pump to pick from,
and each type of pump is specifically designed and fitted for a particular application.
A combination of pumps must be used in order to typically reach and maintain HV
and UHV systems. The final stage pump on these type of systems are always oil free
and are typically backed by other pumps in case of a catastrophic failure of the main
pump. There are so many different pumps that taking the time to discuss all of them

Ultrahigh vacuum: < 10 mbar
• Nuclear fusion, storage rings for
accelerators, space research, and
surface physics.

(mostly water or organic) arise.
Distinctions between the two categories
are described briefly:

In the removal of water vapor from liquids
or in their distillation, particularly in
degassing columns, vacuum filling, and

Ultrahigh vacuum

High vacuum

Medium vacuum

Rough vacuum

Mass spectrometers
Molecular beam apparatus
Ion sources
Particle accelerators
Electron microscopes
Electron diffraction apparatus
Vacuum spectographs
Low-temperature research
Production of thin films
Surface physics
Plasma research
Nuclear fusion apparatus
Space simulation
Material research
Preparations for
electron microscopy
10–13

10–10

10–7

10–3

100

103

Pressure [mbar]

Fig. 2.71 Pressure ranges (p < 1000 mbar) of physical and chemical analytical methods

Figure 3.1.
D00.56

Pressure ranges of physical and chemical analytic
LEYBOLD VACUUM PRODUCTS AND REFERENCE BOOK 2001/2002

methods.

would require a written thesis of its own. But this will highlight the types of pumps
connected to our MBE system, which is a fairly typical setup for growth of oxides
using MBE. Like most other vacuum systems, our MBE is roughed from atmosphere to
high vacuum using a series of mechanical pumps Rotary pumps, and turbo molecular
pumps. The final stage of pumping is conducted by cryogenic pump which uses ultra
pure helium and compresses the gas on a cold head bringing the temperature down
to nearly 10o Kelvin. Not only does a cryopump operate fundamentally differently
then most other pumps, but it also is one of few pumps that does not exhaust the
gas that captures. Furthermore, but it rather freezes it on the array of carbon discs
till a regeneration cycle is able to be conducted. Cryo pumps are effectively able to
remove all gases from the system, and if it operates properly, the ultimate pressure of
nitrogen in the chamber at 20o Kelvin should be below 5x10−11 torr. In figure 3.1 you
can see the typical pressures that different systems operate at.

3.2

Molecular Beam Epitaxy[4, 5, 6, 7, 8]

You may ask why is a vacuum so important? Semiconductor processing at all steps
requires a super clean environment. that includes anything from hair, to tiny dust
particles. As consumers demand for more efficient and smaller devices increase,
new techniques which miniaturize electronic components need to be deployed. The
miniaturization of technology is done either via lithography or through growth of
patterned thin film structures. It is then implied that any defects or unwanted
molecules that are on the size scale of the wanted pattern will result in high yield
loss. MBE is a technique that is both very similar to standard evaporation, and yet it
couldn’t be more different or complex. That is because MBE is used as a controlled
growth method, capable of deposition at atomic resolution, as well as the continuous
growth of a single crystal, also known as epitaxy. The films are formed on single-crystal
substrates by slowly evaporating the elemental or molecular constituents of the film
from evaporation source known as a effusion or Knudsen cell, onto substrates that
are at a particular condition, such that the proper reaction and phase is present at
the surface of the substrate. The spot size of these cells are on the order of a couple
inches, though commercial deployments have been successful at making larger one, in
the very recent past. The growths are typically conducted at a rate of 3000Åper hour,
thus the importance of ultra high vacuum can not be emphasized enough. Figure 3.2
shows a standard schematic diagram of an MBE chamber. It also shows the most
commonly used in-situ characterization system including:
• A beam flux monitor which detects the rate at which atoms emerging from an
effusion cell impinge onto the substrate.
• A mass spectrometer/residual gas analyzer which can detect with high sensitivity
the partial pressure of any give molecule or atom. An electron gun, also known
as a RHEED gun, accelerates an electron beam towards the sample where it
diffracts off the top couple nm of material revealing dynamic information about
the crystal structure and film thickness.

Figure 3.2. Schematic cross-section of a typical MBE Chamber.

3.3

Reflective High Energy Electron Diffraction

Of the three characterization techniques mentioned above, RHEED is the most
important technique used during thin-film growth in a MBE system. In RHEED,
a high-energy beam of electrons hit the sample at grazing incidence, which reflects
off the top couple nanometers of your sample. The reflected beam is scattered, as
a result of interacting with atoms on the surface of the sample, and impinges on a
phosphorescent screen placed on the other side of the chamber opposite the gun, which
displays a diffraction pattern which can be observed. Of course, for diffraction to
occur, the electrons that interact with the top layers of material must obey Bragg’s
law.
λ = 2dsin(θ)

(3.1)

This law relates the wavelength of the electron beam λ, periodicity, d, of the lattice,
and the diffraction angle, θ of the beam with respect to the sample surface, in order
to construct a diffraction sphere known as a Ewald sphere. The location where the
reciprocal lattice rods (probing 2-D planes in k-space produces rods) and the Ewald
sphere intersect are where the Bragg conditions are satisfied, and thusly create a
diffraction pattern. RHEED intensity oscillations can be recorded during growth in
order to resolve atomic resolution of layered growth. During monolayer-by-monolayer
growth in an MBE chamber, the surface of the sample changes from smooth to rough
(at partial coverage), and back to smooth again in the completion of one monolayer
growth cycle. During the periods of the cycle when the sample surface is rough,
most of the specular beam incident on the sample is scattered and produces a low
intensity spot. When the sample returns to a period where its surface is smooth, the
diffracted intensity is at a maximum. The result is that for monolayer-by-monolayer
growth, the diffracted RHEED intensity varies sinusoidally with time, with the period
of oscillation corresponding to the period of monolayer growth. Counting RHEED
oscillations during growth allows one to accurately determine flux rates as well as
thicknesses of their layers.

In‐situ RHEED

Specular Beam Phenomenon

Figure 3.3. Illustration of intensity vs. time in layer by layer growth
also known as the specular beam phenomena that produces RHEED
oscillations. Below is a depiction of what a RHEED image when the
electron beam fulfills the diffraction condition known as Braggs Law.

3.4

Cu2O Deposition via Plasma Enhanced MBE
and Characterization.

Plasma assisted molecular beam epitaxy (MBE) is a promising method for the
fabrication of Cu2 O thin films, as it provides the greatest control over critical growth
conditions such as temperature, flux, base pressure, and interface sharpness. We
used two types of substrates for film growth: 1) cubic magnesium oxide (MgO
(001), a=.422nm) and biaxially-texture thin films of MgO/SiO2 /Si grown by ion
beam-assisted deposition (IBAD) [51]. A relatively small lattice mismatch of 1.1%
between Cu2 O (a=4.27Å) and MgO facilitates epitaxial growth. A copper effusion
cell (beam equivalent pressure of 5x10−7 torr) in the presence of a RF oxygen plasma
(P=300W) at 10−6 torr was used. The MgO substrate was heated to a temperature of
T=650o C. All samples were annealed for one hour at T=650o C with varying partial
pressures of oxygen from PO2 =10−4 -10−6 torr. The pressure PO2 =10−6 torr provided
the sharpest RHEED. IBAD is a process in which a bi-axially textured thin film of
MgO is grown on any atomically smooth surface. We use silicon substrates that have
been thermally oxidized to give us a 1µm amorphous SiO2 layer. Using electron-beam
evaporation, thin films of MgO were deposited at room temperature on our SiO2
substrates at a rate of 0.2nm/sec with simultaneous ion bombardment of a 750 eV
Ar+ ion from an ion gun till the film thickness approximately reaches 10nm. A second
e-beam evaporation step is conducted at an elevated substrate temperature without
the ion beam to produce a higher quality surface. The surfaces and the evolution of
the bi-axially textured film is carefully monitored using RHEED. The second step
adds approximately another 10 nm of MgO, making in total 20nm of MgO used in
this process to prepare our template substrate. ZnO thin films were grown (growth
rate of .2nm/sec) on MgO (001) substrate and on Cu2 O (001)/ MgO (001) by MBE
using a zinc effusion cell and an RF oxygen plasma. Prior to the ZnO growth the
substrates were thermally cleaned at T=450o C in the presence of the oxygen plasma
for 15 minutes. ZnO was then grown at a substrate temperature T=of 350o C in the
presence of a RF oxygen plasma (P=200W) at 10−4 torr with a beam equivalent
52

D.S. Darvish, H.A. Atwater / Journal of Crystal Growth 319 (2011) 39–43

substrate (e.g., Si bottom cell). For bulk MgO substrates there is a
lattice mismatch of only 1.1% between Cu2O (a ¼0.427 nm) and
MgO (a ¼0.422 nm), which facilitated epitaxial growth. In MBE
growth, a copper effusion cell was operated with a beam equiva-

lent pressure of 5 10 7 Torr in the presence of a RF oxygen
plasma (P¼300 W) at 10 6 Torr , which resulted in a deposition
rate of .025 nm/s. MgO substrates were annealed for 1 hour at
T¼650 1C with varying partial pressures of oxygen in the range

Fig. 1. In situ RHEED images from a clean MgO(0 0 1) substrate (a) followed by the deposition of a 70 nm Cu2O ﬁlm (b) and 70 nm m-plane ZnO on top of the Cu2O layer are
shown on the right hand column. In situ RHEED images of a clean SiO2 surface (d) followed by 10 nm deposition of IBAD MgO(0 0 1) (e) and 70 nm of Cu2O (f) are shown on
the left hand column.

Figure 3.4. On the right hand column are in situ RHEED images
from a continuous Cu2 O(001) on MgO(001) where the film thickness
is equal to 0nm (a), 30nm (b), and 65nm (c). On the left hand column

are in situ RHEED images of a clean SiO2 surface (d), followed by
15nm deposition of IBAD MgO(001) (e), followed by 60nm of Cu2 O
(f).

53
Fig. 2. (a) RHEED oscillations demonstrating layer-by-layer epitaxial growth of Cu2O on MgO. (b) Fourier transform of RHEED oscillations to determine growth rate.

pressure of 1x10−6 torr. Slow growths at the beginning stages were critical to obtain
m-plane (101̄0) orientation of ZnO as opposed to the typical c-plane (0001) growth of
ZnO. In-situ characterizations of our films were done with RHEED. Further analysis
was done via x-ray diffraction.
Both the MgO substrate and Cu2 O have a cubic crystal structure and closely
matched lattice parameters. Cube on cube epitaxy of Cu2 O (001) was observed to
grow on MgO (001). In-situ RHEED was used to confirm the epitaxial growth, which
can be seen in figure 3.4. RHEED oscillations (figure 3.5) were observed, indicating
that the thin film was growing in a layer-by-layer growth regime, typically seen if
growth of the film can be well controlled and grown slowly (approximately 2 Å/sec).
The streaky nature of the RHEED images indicated that the Cu2 O films grown were
very smooth. X-ray diffraction was conducted on the thin films and confirmed the
results seen in the RHEED images. XRD rocking curve analysis also showed epitaxial
growth of Cu2 O on MgO with the two peaks at ω=21.58o and at ω=21.61o respectively.
IBAD growth of bi-axially textured MgO (001) on SiO2 (amorphous) was conducted
and confirmed via RHEED (figure 3.4). IBAD is a three phase process where a 750
eV Ar+ ion beam is directed at an amorphous substrate at a 45o angle during the
deposition of MgO using e-beam evaporation. During the first phase an amorphous
MgO film is deposited (0-4nm). During the second phase of growth, MgO crystals
nucleate via solid phase crystallization with out-of-plane texturing. In the third stage
of growth, in-plane texturing is evolved due to the amorphization of grains with
misaligned in-plane texturing from the Ar+ ions. The Ar+ ions channel in the (011)
direction and amorphize the grains not in the (001) direction. When enough material
has been deposited, an energetically low surface of (001) is formed and is not damaged
due to the channeling of the ions. This Ar+ ion beam is then turned off and epi MgO
is deposited at an elevated substrate temperature to create a near perfect and defect
free substrate template. It is then possible to deposit Cu2 O exactly the same way as
one would on bulk MgO substrates described above with results and properties of
Cu2 O being the same. The advantages of this method are, that it allows a fraction of
the substrate material to be used, allows the process of creating very cheap substrates
54

in comparison to bulk MgO substrates, and allows the growth of any Cu2 O device on
top of an already existing device for use in tandem solar cells. In addition, because
the template is thin, the resulting film that is grown on top will be less strained and
consequently will be of higher quality.
Epitaxial growth of Cu2 O is quite difficult to maintain at very high deposition
rates ( greater than 120nm/hr of Cu2 O)or thicknesses greater than 1.5 µm. RHEED
images in figure 3.6 shows the break down of epitaxy over a 1.5 hour period of time.
In addition to the structural properties of our film being characterized, we took a
look at the electronic and optical properties. Energy dispersive x-ray spectroscopy
further confirmed the composition of the film and did not indicate impurities in the
film. Hall mobility measurements showed mobilities in the range of 50-100 cm2 /V ·sec
and carrier concentrations typically in the range of 1016 cm−3 , which is dependent on
substrate temperature and oxygen plasma partial pressure. A very smooth film and the
ability of in-situ passivation of our interface will hopefully provide the quality interface
needed to achieve much higher cell efficiencies. Optical ellipsometry was conducted
on the films to determine index of refraction and absorption (figure 3.7). The data
measured was subsequently used on other samples to verify film thicknesses and quality
post growth. We were also able to extrapolate the band gap of the Cu2 O film grown
(figure 3.7) which agrees with previously reported studies. As mentioned previously,
heterostructures of Cu2 O are the most promising ways to create photovoltaic devices
due to the difficulty in creating homojunctions of Cu2 O that display photovoltaic
properties. MgO substrates were also used for the growth of ZnO. Because of the
different crystal structures and lattice constants we hoped to develop a technique
that would allow textured growth of our films. Oxygen plasma assisted MBE allowed
us to gain the control on the growth of the ZnO thin film and allowed us to obtain
higher quality material. Upon nucleation of the film, the RHEED pattern transitioned
from a streaky to a spotty pattern, indicating a predominate single orientation of
growth. The crystalline orientations as determined both by analysis of the RHEED
pattern (figure 3.8) and XRD showed a preferential orientation of ZnO in the (101̄0)
with a very weak peak corresponding to the commonly observed (0002) ZnO peak.
55

56
oscillations to determine growth rate.

epitaxial growth of Cu2 O on MgO. (b) Fourier transform of RHEED

Figure 3.5. (a) RHEED oscillations demonstrating layer by layer

Fig. 2. (a) RHEED oscillations demonstrating layer-by-layer epitaxial growth of Cu2O on MgO. (b) Fourier transform of RHEED oscillations to determine growth rate.

St
twi
hc
nMg
OSu

Co
rOx
eDe
no
nMg
O001

Af
r1h
ro
na
tr
e1.
5t
me
su

yb
gd
wn
tb
yr
gp

Figure 3.6.

4 .0

3 .5

3 .0

2 .5

2 .0

A lp h a - S q u a r e d ( n m - 2 )

5 0 0
1 .0 x 1 0

-4

8 .0 x 1 0

-5

6 .0 x 1 0

-5

4 .0 x 1 0

-5

2 .0 x 1 0

-5

W a v e le n g th ( n m )
A lp h a - S q u a r e d

0 .0

E n e rg y (e V )

Figure 3.7. Spectroscopic ellipsometry data for real and imaginary
index of refraction for Cu2 O thin film. Inset shows alpha square vs.
energy which allows extrapolation of band gap of Cu2 O to 2eV.

D.S. Darvish, H.A. Atwater / Journal of Crystal Growth 319 (2011) 39–43

amorphized the grains that were not in the (0 0 1) direction.
When a sufﬁciently thick MgO ﬁlm was deposited, a (0 0 1) MgO
ﬁlm texture was formed as a result of a competitive amorphization process in which Ar + ion channeling along [1 1 0] directions
minimizes damage for the (0 0 1) ﬁlm orientation but amorphizes
grains with other orientations. This Ar + ion beam was then turned
off after 10 nm of growth and epitaxial MgO was deposited at an
elevated substrate temperature to create a reduced defect density
MgO (0 0 1) substrate template. It was then possible to grow Cu2O
with microstructure and properties similar to ﬁlms grown on bulk
MgO substrates.
We used thermally oxidized silicon wafers with a 1 mm
amorphous SiO2 layer as starting substrates for IBAD growth.
Using e-beam evaporation, thin ﬁlms of MgO were deposited at
room temperature on our SiO2 substrates at a rate of 0.2 nm/s
with simultaneous ion bombardment by 750 eV Ar + ions from a

Kaufman source ion gun until the MgO ﬁlm thickness reached
approximately 10 nm. A second electron-beam evaporation step
was conducted at an elevated substrate temperature without the
ion beam to produce a higher quality MgO ﬁlm. The surface
morphology and its evolution during growth of the biaxially
textured MgO ﬁlms were monitored using RHEED analysis. The
second MgO deposition step added approximately 5 nm of MgO
for a total MgO thickness of 15 nm in the biaxially textured
template substrate.
ZnO thin ﬁlms were grown (growth rate of 0.2 nm/s) on MgO
(0 0 1) substrates and on Cu2O (0 0 1)/MgO (0 0 1) substrates by
MBE using a zinc effusion cell and a RF
2 oxygen plasma. Prior to
the ZnO growth, the substrates were thermally cleaned at
T¼450 1C in the presence of the oxygen plasma for 15 min. ZnO
was then grown at a substrate temperature T ¼350 1C in the
presence of a RF oxygen plasma (P¼ 200 W) at 5 10 5 Torr with

The dominate peak (101̄0) is known as the m-plane of ZnO. We believe there is some
degree of polycrystallinity near the growth interface that quickly changes and develops
into m-plane texturing throughout the entire film. Below are RHEED images of this
growth. Similar results were obtained when growing ZnO on Cu O thin films that
were deposited on MgO.

Fig. 4. (a) o–2y X-ray scan of (1 0 1̄ 0) ZnO (70 nm)/(0 0 2) Cu2O (70 nm)/(0 0 2) MgO with o rocking curve of (0 0 2) Cu2O on (0 0 2) MgO peak. (b) o–2y X-ray scan of
(0 0 2) Cu2O (70 nm) on (0 0 2) IBAD MgO (10 nm) grown on an oxidized silicon substrate with o rocking curve of (0 0 2) Cu2O on (0 0 2) MgO peak.

Figure 3.8. In situ RHEED images of (a) Cu2 O(001) on MgO(001)
followed by the 30nm deposition of epitaxial m-plane ZnO (b).

3.5

Conclusion of PA-MBE Growth of Cu2O

We have achieved epitaxial growth of Cu2 O and ZnO on both single crystal MgO and
IBAD MgO substrates. MBE growth of the Cu2 O /ZnO heterojunction should allow
us to obtain higher Voc and efficiencies due to the high degree of control we have over
the crystal orientations of the thin films and the quality of the interface. We have
successfully demonstrated MBE growth of epitaxial Cu2 O on (001) bulk MgO and
IBAD bi-axially textured MgO. Structural, optical and electrical qualities of the film
were characterized using RHEED, x-ray diffraction, EDS, spectroscopic ellipsometry
and Hall mobility measurements. These measurements confirmed the high electrical
quality of our films and that our Cu2 O had a band gap in accord with the literature.
We have successfully demonstrated MBE growth of epitaxial ZnO on (101̄0) bulk MgO
(001) and on top of our Cu2 O films.

3.6

Cu2O/ZnO heterojunction Design, Metallization,
and Results

In this section, we will discuss the design challenges of make a Cu2 O/ZnO heterojunction
device, followed by introducing several different device designs, and finally the
performance of these devices. Earlier, the idea of using templated substrates was
introduced. We demonstrated that MgO films as thin as 5nm could be deposited on
any smooth substrate (amorphous, glass, etc) using IBAD to create bi-axially texture
thin-film template which can be used in a subsequent Cu2 O deposition step. Yet a
barrier to making a device still remains. Traditionally, devices made on bulk substrates
or thin films use conductive substrates which facilitates adding front or back contacts.
The small lattice mismatch between Cu2 O and ZnO is one of the primary reasons
for its use. While an exhaustive literature search revealed several materials with
lattice parameters very close to that of Cu2 Os , their lack of structural, mechanical
and thermal stability away from standard pressure and temperature automatically
60

disqualified their use as a choice. Two compounds were discovered that were very
soluble in water and that were relatively lattice matched to Cu2 O: cesium chloride
(CsCl)[52], with a lattice constant of 4.11Å(4% mismatch), and cesium bromide
(CsBr)[53], with a lattice constant of 4.28Å(practically zero mismatch). However, both
compounds have melting temperatures in the 600-700 o C range, which is too low for
Cu2 O growths using the MBE. Several different ideas were considered in order to place
a back contact on Cu2 O. These included using lateral contacts, etching through the
MgO substrate and even patterning a contact grid on the substrate prior to deposition
of the hetero-structure. In theory any of these would work if properly if engineered
properly. Cu2 O is pretty resistive therefore lateral contacts would introduce a large
amount of series resistance. Pre-patterning back contacts would likely destroy the
epitaxial relation between the thin film and substrate as well as diffuse throughout
the structure during the deposition process. Etching through the MgO substrate to
make contacts is only viable if dry etching is considered as wet chemistry etching
would not have enough selectivity to etch away a thick MgO substrate before either
damaging or etching away the hetero structure. After giving the issue thoughtful
consideration, we decide that photolithography offered the best solution. While
MgOs lack of electrical conductivity is the reason why making electrical contacts is
difficult to being with, it least offers some advantages in a photolithography process.
Because MgO is transparent, the entire cell can be flipped over thus operating the
cell in an upside down configuration where the light would pass through the MgO
and be absorbed first by Cu2 O. This design automatically provides a protective top
layer to the cell (MgO) in addition to not losing current due to shadowing loss of
a metal contact grid. Therefore, the focus of creating metallized contacts shifted
to using photolithography-assisted etching to create an all-front contact pattern. A
photolithography mask pattern was designed to for etching through the ZnO layer
(≈ 150 nm thick), exposing Cu2 O to then be contacted. The pattern (figure 3.9) was
designed with fingers to minimize the amount of ZnO etched away on the device, while
still exposing enough Cu2 O to reduce the distance traveled by carriers and therefore
to minimize the sheet resistance. In addition, a complementary pattern was designed
61

Figure 3.9. Photomask designs used for metallization.
(figure 3.9) for contacting ZnO if an additional metallization step was needed, such
that the fingers would interlace with the fingers from the Cu2 O pattern. Markers
were located at the top of both patterns, to allow for easy alignment. In order to
minimize the number of photolithography steps, the deposition of ITO or another
TCO on top of ZnO before any photolithography steps would be sufficient as contacts
for ZnO. In order to determine the optimal design, an array of nine patterns was
designed with varying finger widths (5, 10, and 15 µm) and finger spacings (150, 200
and 500 µm). The fingers were 700 µm in length, and each pattern was roughly 1 mm
in width, which allowed for all 9 devices to be patterned on one 1 cm x 1 cm stack of
MgO/Cu2 O/ZnO. Additionally, the patterns each have a 200 µm x 200 µm square
tab at the top, which allows for easy probing when performing measurements.
Similarly, nine ZnO patterns were aligned on the mask, each corresponding to
one Cu2 O pattern.Two different types of photoresist were used in order to create an
overhang and avoid shorting the device. First, 3A liftoff resist (LOR) was applied on
top of the ZnO, with spin settings of 1500 rpm for 40 seconds, followed by a five minute
bake at 160 o C. Next, 1813 positive resist was applied, with spin settings of 300 rpm
for 60 seconds, and a 120 second bake at 115 o C. The samples were then patterned
(exposure for 70 seconds) and developed in MF-319 for 80 seconds. Because LOR
62

3A has a higher dissolution rate than 1813 resist, the result is an overhang therefore,
when the ZnO is etched, the feature size will match that of the overdeveloped LOR,
whereas when metal contacts are deposited, they will match the smaller feature size
of the 1813. This allows for extra space between the contact and the walls of the ZnO
layer, avoiding any possibility of shorting the device.
For the etching process, different chemical etchants were explored. It was determined
that, as was the case with etchants of MgO, most known etchants of ZnO tend to react
with all metal oxides (including Cu2 O). However, because the ZnO layer is on the
order of 150 nm and the Cu2 O layer is significantly thicker at roughly 2-3 µm, a timed
etch that does not completely eat through the Cu2 O would be possible. Different
concentrations of HNO3 (nitric acid) were used for varying amounts of time, in order to
determine the optimal conditions for etching through the ZnO layer. After the etching
process was completed, samples were contacted using either metal evaporation or
sputtering of gold and Remover PG was used to liftoff the metal from the unpatterned
parts of the sample. You may reference appendix B to see a flow diagram of the
process described above.

paterned.

Figure 3.10. Optical micrograph images of heterostructures being

ZnO

Cu2O

3.7

Cu2O/ZnO Hetero-structure Devices

The devices fabricated above were tested contact side up with gold probe tips contacting
both the ITO layer (ZnO) and contacting the gold contact pads patterned during
photolithography. Many of our samples exhibited no photovoltaic properties. This
was likely attributed to some steps during the lithography process as devices made
from Cu2 O substrates went from exhibiting photoresponse to no photoresponse right
after lithography. The last series of devices fabricated had IV curves that indicated
photovoltaic activity was present. Still these devices had very low current densities
and fill factors, indicative of series resistance. Figure 3.11 shows the photovoltaic
performance of the cell under simulated AM 1.5 illumination. The cell if figure 3.11
has a fill factor of 26% Voc = 515mV and Jsc ≈.8, and the cell in figure 3.12 has a
fill factor of 35.6% Voc = 520mV and Jsc ≈3.78. We would expect slightly greater
performance from these cells via increase in open-circuit voltage had the contacts been
annealed. Unfortunately the conditions at which the anneal took place damaged the

devices.

C u r r e n t D e n s ity [m A /c m

V o lta g e [V ]

-1 .0

-0 .5

0 .0

0 .5

-1

-2

Figure 3.11. FF=26% ,Voc = 515mV, Jsc ≈=.8

1 .0

-1

C u r r e n t D e n s ity [m A /c m

V o lta g e [V ]

-2

-4

Figure 3.12. FF=35.6% ,Voc = 520mV, Jsc ≈3.78

Chapter 4

Synthesis of Cu2O Templates and Bulk
Substrates via Thermal Oxidation
In this chapter we present growth techniques and conditions used to synthesis bulk
cuprous oxide samples. Post growth processing of these samples in one of two ways will
determine their use. The first way will directly incorporate them into a photovoltaic
device therefore we quickly look at methods to dope and increase conductivity of these
samples so that they exhibit better performance as the active layer in a photovoltaic
device. They may also be used as templates for subsequent homoepitaxy of higher
quality Cu2 O material.

4.1

Cu2O Synthesis from Oxidation of Copper Foils

The most common method and easiest method create Cu2 O is by thermal oxidation
of Copper foils in a furnace. Referring back to figure 1.6 and the discussion in section
1.4.3 on the Cu-O phase diagram, we know that it is possible to make Cu2 O in various
conditions. Using a vacuum furnace allows us to be practically anywhere in the phase
stable region of Cu2 O in the phase diagram and is the most versatile method for
oxidation of copper foils. Generally, the procedure involves the oxidation of high purity
copper at an elevated temperature for times ranging from few minutes to a few hours
depending on the thickness of the starting material. The oxidation process can be
carried out either in pure oxygen or air. Commercially available copper foil at a purity
of 99.999% was purchased at a variety of different thicknesses ranging from 10 to 500
microns from ESPI metals. As previously discussed, Cu2 O only needs several microns
67

of material for full absorption but handling foils that thin is impractical. Cu2 O is a
brittle material and the sole purpose of using thicker foils was for mechanical stability
and handling reasons. The impurity analysis for the foils is provided in table 4.1.
Table 4.1. Impurities concentrations in ppm found in Cu foil.
Element Purity
Ag

0.3

0.1

0.2

0.1

0.2

The copper foils were precut to .5”x.5”squares and had a hole placed along the
top of the square. The whole was used to hang the foil to a quartz boat specially
designed for this process. Copper wire of the same purity also purchased from ESPI
metals was used to hang them. This was done in order to reduce the likelihood of
contaminating the substrates as well as to prevent the reaction of copper oxide with
quartz which cause the two materials to fuse together. The copper foils were cleaned
and packed in a class 10 clean room, therefore no cleaning steps were performed prior
to oxidation of the foils. Large grained polycrystalline substrates were synthesized by
thermal oxidation of 100µm thick copper foils. Oxidation was initiated by evacuating
the tube furnace to a pressure less than 5x10-5 torr followed by heating the furnace to
a temperature of 1010o C. Once the system reached a stable 1010o C., the temperature

Figure 4.1. Cu foils pre and post oxidation in a vacuum furnace at
1010o C.
at which our oxidation takes place, a leak valve introducing ultra high purity oxygen in
the tube was opened where the oxidation of the copper foils commenced at a pressure
of 5 torr for 2 hours. following oxidation, the vacuum furnace was quarreled through
a stepwise process down to room temperature under successively decreasing oxygen
pressures in order to stay within the phase stable region of Cu2 O in the Cu-O phase
diagram. A schematic for our process is shown in figure 4.2.
Using a vacuum furnace is far more advantageous than a traditional tube furnace
because one is able to control both pressure and temperature of the sample whereas
in a standard tube furnace one really only has control over temperature. This
allows samples of varying electronic properties and grain sizes to easily be made.
Remember that electronic properties of the substrates depend on the region in the
phase diagram they were processed at and by processing samples at lower temperatures
fewer defects are introduced and therefore the samples have higher mobilities and are
more conductive. In addition the ability to control the oxygen pressure prevents the
deleterious side reaction of cuprous oxide going to cupric oxide. In the case where
cupric oxide is formed on the surface a quick dip high molarity nitric acid removes
69

it immediately. Other etch methods such as bromine methanol or hydrochloric acid
has been used by others in literature, but we found that they are not necessary and
often times leave behind other impurities or form new surfaces that are even harder
to remove than CuO such as CuCl. A photograph showing Cu foils before oxidation
and the resulting cuprous oxide substrates after oxidation is show in figure 4.1. The
following are observational notes and hints for making bulk substrates using thermal
oxidation.
• Grain sizes on the order of cm’s may be obtained by annealing samples at high
temperature for a long period of time.
• Impurities largerly influence grain size and microstructure below 1000o C[? ].
• The oxidation process is one where VCu diffuse into the substrate and for sufficient
thickness forms a plane of voids called the inner porous layer.
• It is interesting to note that even at 450C the copper vacancies can diffuse up
to 70µm, the minimum distance to to reach the surface of our 150 µm thick
samples in about two minutes.
• Without a doubt thin layers of Cu2 O are the way to go but it is important to
handle the samples with lots of care otherwise they disintegrate into powder.
Using a handle substrate after the initial oxidation saves a lot of time .

4.1.1

Characterization of Cu2 O substrates

X-ray diffraction data was collected by a Philips XRD with Cu Kα radiation was
collected and plotted (figure 4.3). All the peak present were indexed and they
indicated that our substrates were composed of phase pure Cu2 O. Subsequently
a substrate was cut down to size and had gold contacts evaporated at room
temperature to its four corners using a shadow mask in order to conduct room
temperature Van der Pauw and Hall effect measurements. As expected, the
polycrystalline Cu2 O substrates were found to be p-type with a hole concentration
70

1010oC for 2 hours
Figure 4.2.

A detailed schmatics illustrating the process and

conditions for oxidation of copper foils to Cu2 O

1 0 0 0

In te n s ity [a .u .]
2 5

3 5

4 0

4 5

5 0

2 1 1

2 T h e ta [d e g re e s ]

2 0 0

5 5

S u b s tra te

6 0

2 2 0

6 5

phase pure Cu2 O

Figure 4.3. X-ray diffraction measurement of a bulk substrate showing

3 0

1 1 0

1 1 1

X R D fo r B u lk C u 2 O

7 0

of 7x1013 atoms
and a Hall mobility of roughly 60 cm2 ·V −1 ·sec−1 which compared
cm3
to literature values[37, 54] as well as measured values for our own thin films.
Spectroscopic ellipsometry was performed in a procedure identical to the one
done for our thin film samples (this procedure will be detailed in its own section)
and the resulting absorption data was consistent with the reported bandgap of
2.0eV.

4.2

Extrinsic Doping of Cu2O Substrate

The substrate that were produced and described above turn out to be quite
similar to our “base-structure” used in our simulations in chapter 2. Because of
this, it should be quite obvious that the next step in processing the samples in
order to make a device involves finding methods to extrinsically dope our material.
Many attempts have been made to further dope copper oxide without destroying
minority carrier diffusion lengths[55, 56, 57]. Among the impurities investigated
up to now, only three of them have given a a slight increase in conductivity:
silicon, nitrogen and chlorine though their mode of action is still not understood.
As for other elements, there are several that increase p-type carrier concentration
even by several orders of magnitude but do it at the expensive of decreasing
carrier mobility near zero thus conductivity remains unchanged or is even worse.
Our first attempts at doping Cu2 O involved either evaporating a thin film of
our dopant material or measuring a small amount of the dopant material and
placing it in a sealed tube along with a prepared Cu2 O substrate and annealing
the sample in a furnace. This method is also known as the “drive-in” method
that is most commonly used with silicon semiconductor devices. As previously
mentioned Cu2 O is metastable at room temperature and the reason why it
does not spontaneously transform to CuO is because of extremely slow reaction
kinetics. But at slightly elevated temperatures (above 200 degrees C) kinetics
no longer are a barrier to the diffusion of Cu around the lattice and instead
of incorporating our dopant atom into our Cu2 O lattice, Cu drives out of the
73

lattice and either reacts with the alloy material thus being reduced from Cu+
to Cu or dependent on the dopant source the exact opposite can happen where
Cu+ transforms to Cu2+ , and based on how the results are very similar to
the deleterious reactions that occur at occur at the heterojunction interface,
we have concluded that this method, at least done this way, is not a viable
method for doping Cu2 O with any element. Our simulations also taught us that
doping is extremely important due to the fact that cuprous oxide homojunctions
are impossible to make, but at the same time introducing ”dopants” into the
material will likely create a more compensated Cu2 O substrate that has poor
electrical properties. In order to avoid allowing the system to equilibrate post
introduction of the dopant atoms, two methods for doping Cu2 O were tried. The
first method involved starting with foils of Cu alloyed with whatever we wanted
our dopant to be as opposed to pure copper foils. Then the rest of the oxidation
steps were identical to that of oxidizing a pure copper foil. Using this method,
we hoped the system would avoid creating extra point defects to compensate
the dopant atoms. We specifically focused used Ni and Zn as our dopant atoms
as they sit directly to the right and left of copper in the periodic table.
Table 4.2. Hall Measurements of Alloyed Substrates
Dopant Carrier Conc. [cm-3 ] Mobility [ cm2 · V −1 · sec−1 ] Carrier Type
Ni

2.45x1013

24.8

p-type

7x1010

5.1

p-type

The results summarized in the table 4.2 were quite disappointing.In addition
the morphology of the substrates looked different when compared to the same
process done to pure Cu foil. We decided to use time of flight secondary ion
mass spectroscopy, or TOF-SIMS[58] to probe the chemical composition of the
surface as well as obtain a chemical composition vs thickness of sample plot to
see if our dopant atoms were doing anything unexpected such as segregating at

surfaces or grain boundaries or if they were starting to precipitate out of solution.
The TOF-SIMS measurement were conducted by Lynelle Takahashi at the Dow
Chemical Company. Because of the amount of work, time and cost involved in
these measurements we started with our Zn doped samples as they seemed most
interesting.The following are general notes about the SIMS method.
– ToF-SIMS can detect the positive or negative ions from a surface from the
top few nm.
– A 25 keV Bi+ probe is used to for imaging and can focus down to to sizes
below 100 nm.
– There is a tradeoff between spatial resolution and mass resolution, thus
knowing either the species your are looking for or the area you are searching
you will obtain much better data.
– Similar to ion beam milling, Cs atoms are used to sputter away layers for
depth profiles.
The measurements taken using the TOF-SIMS threw another twist into this
already difficult problem. SIMS analysis was unable to detect amy dopant atoms
in our Cu2 O substrates after the alloyed foils were oxidized. Because of the the
large concentration of impurity atoms we started with it was surprising that we
saw none at all. We prepared SIMS standards which needed to be used in order
to determine the detection limit of each element in our lattice. The detection
limit is a function of the lattice being looked at so standards must be created for
each and every sample that one wants to look at and get conclusive quantitative
results. The SIMS standards were created by sending our copper oxide substrates
to a commercial ion-implantation foundry to have a specific dose and energy
of our dopant atoms implanted into our samples. Then using the free software
SRIM and TRIM[59] we were able to conduct ion implantation monte-carlo
simulations with the same conditions that our real samples were being subjected
75

to. Finally the ion implanted samples once again were submitted for analysis to
determine at what point did the system no longer detect the implanted ion (i.e.
when the detection level reaches the background noise level) and it turned out
to be much higher than we thought. This number corresponds to 1.98x1010 cm3
while we are interested in detecting doping levels 5 to six orders of magnitude
below that value concluding that this method is not viable for further use for
our purposes. The last interesting thought to note is that most of these methods
required some sort heating step or treatment step that made knowing the carrier
concentration and profile almost impossible, especially with copper’s ability to
diffuse around the lattice quite quickly (several microns a minute at 500 degrees
celcius). Ion implantation of dopants has not been studied or reported on at
all for Cu2 O, and using light elements like Lithium who also have an electronic
configuration like that of Cu in Cu2 O needs further investigation. Typically
ions as light and small as Li+ get implanted in interstitial lattice sites. The
implantation conditions can be conducted such that there is no heating of the
substrate during implantation and thus no chance for Li+ to move around and no
chance for the Cu2 Os crystal to thermodynamically equilibrate thus preventing
self compensation mechanism from happening. It is clear to me that Cu2 O solar
cells will not see progress above the 6-8% efficiency range if an extrinsic dopant
is not part of the heterojunction cell design.

68Zn+

Zn‐doped Cu (surface)

Zn‐doped Cu2O (surface)

Zn‐doped Cu2O
(depth profile)

Ni+

Ni‐doped Cu (surface)

Ni‐doped Cu2O
(surface)
Ni‐doped Cu2O
(depth profile)

Figure 4.4. TOF-SIMS data showing dopant atom detection prior to
but not after oxidation of alloyed films.

4.3

Cu2O Templates Fabricated by Thermal Oxidation

In this section, the motivation and background work laid out by others, for
other materials systems, will be presented. Then preliminary work and proof of
concept work done for Cu2 Os will be shown.
A templated substrates would be a thin film process engineers dream. That is
because they provide a lattice matched substrate for the subsequent deposition
material to grown on, they can infinitely simplify the method needed to create
contact to said layer, and can dramatically decrease the cost of a cell by replacing
the bulk substrate used with one that is composed of much cheaper materials or
creating only a thin layer of the template on top of a cheap substrate like glass
such that only a small fraction of expensive material is being used in comparison
to before. The essential goal is to create a template substrate that is cheaper
than the substrate material it is going to replace, that can be used for subsequent
epitaxial thin film growth.
The first approach involved direct utilization of the Cu2 O substrates as the
templates. In order for this to work the samples needed to be etched with a
quick dip nitric acid or if they were not specular or planar enough then they
would need to be lapped using diamond abrasive films, and polished in a colloidal
silica slurry (South Bay Technology), to produce substrates that had a specular
finish. Another method for use of bulk substrates as templates was the use of
in-situ ion beam sputtering which under the right conditions would allow one to
both to both clean and somewhat planarize the surface of our substrate prior
to thin film deposition of the active layer[60, 61, 62]. Figure 4.3 has a series
of RHEED images that shows the transformation of morphology from a dirty
pretty much amorphous surface to a cleaned deposition ready surface as evident
by the appearance of diffraction spots and ring that were not there moments
before.
The last approach I would like to discuss is a method known as surface oxidation
epitaxy[63]. It is method that is most commonly used with Ni metal in the
78

750V Beam Voltage
500V Accelerating Voltage

After roughly 140 nm of
ZnO deposition

thermally oxidized substrate followed by subsequent deposition

Figure 4.5. In-situ ion beam sputtering used to clean an as grown

Copper oxide substrate place in
chamber as grown

After 30sec of Ar+ ion bombardment

superconductor field of research but the methods can be extended to be used
with Cu as well. Using either nickel foils or nickel thin films deposited via
evaporation as the starting material, very great care and attention is paid to
avoid pre-oxidation of the surface at lower temperatures. Then sample then goes
through a surface treatment and annealing all pre-oxidation before conditions in
the furnace are set at such that nucleation control surface oxidation epitaxy is
favored over competitive grain growth. Shi et. al. mentioned that they believed
the critical steps for ensuring the method worked and that it was reproducible
was to place the samples at very high temperature and anneal then for several
hours in forming gas. Consequently, cube textured epitaxial NiO layers of around
1µm were grown on pure Ni. In figure 4.6 the top two plots show results from
Shi et. al. and below are results from applying the very same principals to
form cube on cube copper and to suppress as many different crystallographic
orientations as possible.

1hr forming gas anneal at 1000o, followed by 3hr oxidation in Air. Cooled during high flow nitrogen purge.

110

1010oC

1020oC

110

211

220

110
110

Figure 4.6. An example of orientation suppression and cube on
cube epitaxy using Surface oxidation Epitaxy both on Ni and Cu to
produce NiO and Cu2 O

Chapter 5

Final Thoughts
This work tried to better understand the fundamental reasons why Cu2 O solar
cells have been unable to reach much higher efficiencies. Clearly, intrinsic
defects are holding progress back because they are necessary in order to have a
conductive sample and at the same time unwanted because they decrease the
minority carrier lifetime and cause lots of recombination. It is the battle between
high open circuit voltage or a larger current and it looks like that problem is
close to being maximized. In order to get over this hump, I believe a majority of
the efforts should go toward doping experiments or methods of engineering ultra
thin layers. We can conclude from the simulation in chapter two that there is no
substitute for finding an extrinsic dopant if we want to process samples easily by
using foils in a furnace. Molecular beam epitaxy has allowed single crystal like
material to be grown while both kinetically controlling defect concentrations and
allowing films to stay ultra thin. We have achieved epitaxial growth of Cu2 O
and ZnO on both single crystal MgO and IBAD MgO substrates. In addition
more recently we have been successful in textured growth of MBE grown Cu2 O
on Cu2 O bulk substrates. While MgO is a good substrate, nothing can replace a
Cu2 O substrate for subsequent Cu2 O thin film deposition. While MgOs lack of
conductivity has made it a less than popular choice of substrate when making
contacts, our interdigitated contact design seems to get around all barriers and
as a bonus provides the benefit of protecting our heterostructure. It is clear that
the demand for clean and cheap energy is here and is not leaving. Whether or
not Cu2 O turns out to a major part of that solution remains to be seen but it is
82

certain that no matter what, the fundamental of science that we learn from our
research of Cu2 O will play a big role in how we study other materials. It is clear
that both the need and demand for clean and cheap energy is present and is
not leaving. Whether or not Cu2 O turns out to play a major role in solving the
worlds energy needs remains to be seen, but it is certain that no matter what
the fundamental science learned from the research of Cu2 O will play a big role
in how we study other materials.

Appendix A

Matlab Code for Detailed Balance
Model

function [Ei,Es,J,V,P,Jn,Vn,Pn] = detailedbalance multi(T,C,Eg,ni top,ni bot,

% Detailed Balance Calculations for a 'N' multi−junction Solar Cell

% Determine number of junctions

Nj=length(Eg);

% Constants

hbar=1.05457148e−34; %m2kg/s

c=299792458; %m/s

k=1.3806503e−23; % m2kg/s2K

q=1.60217646e−19; %C

kT=k*T/q;

13
14

% First define the refractive index of the substrate the cell is on

% If on a solid reflective back metal contact, nibottom=0, otherwise, use n o

% substrate material.

% radiative emission from the cell.

% mechanism in detailed balance calculations.

The etendue defines the total escape area for
Radiative emission is the only loss

19
20

% The total current in the cell is equal to the difference between the genera

% electron hole pairs from photons and radiative recombination of electron

% hole pairs.

% equal in energy to the band gap of the material, one electron hole pair is

For every photon that enters the material greater than or

% created.

25
26

etendue=ni top *pi+pi*ni bot.ˆ2;

27
28

load E flux

% E in eV and flux in 1/cm2eV

Ltot = 1240./E;

% wavelength in nm

Pdens = E.ˆ3.*flux*10000*1.6E−19/1240;

% Power density in W/(cm2 nm)

31
32
33

% Number of electron−hole pairs photogenerated, Ngen [=] 1/cm2−s and

% photocurrent Jgen [=] C/cm2−s [=] A/cm2

num=1000;

n=length(flux);

37
38

% for Eg(1) must calculate separately...

m(1)=length(E(E≤Eg(1)));

Ngen(1,1)=C*trapz(E(m(1):end),flux(m(1):end));

if Nj>1
for i=2:Nj

42
43

m(1,i)=length(E(E≤Eg(i)));

if Eg(i)≥Eg(i−1)

Ngen(1,i)=0;
else

Ngen(1,i)=C*trapz(E(m(i):m(i−1)),flux(m(i):m(i−1)));

end

49
50

end

Jgen=q*Ngen;

52
53
54

v=zeros(num,Nj);

x=zeros(num,Nj);

for i=1:Nj

v(:,i)=linspace(0,Eg(i)−0.001,num)';

x(:,i)=logspace(log10(Eg(i)),log10(Eg(i)+10),num)';

end

60
61
62

N=zeros(num,Nj);

Nc=zeros(n−1,num,Nj);

Jrad=N; Jtot=N; Pn=N;

for j=1:Nj

% N is in units of eVˆ3

for i=1:num

N(i,j)=trapz(x(:,j),x(:,j).ˆ2./(exp(x(:,j)/kT)−1)−x(:,j).ˆ2./(exp((x(

67
68

end

Jrad(:,j)=(qˆ3*N(:,j)).*etendue(j).*q./(4*piˆ3*hbarˆ3*cˆ2*100ˆ2);

Jtot(:,j)=Jgen(j)+Jrad(:,j);

Pn(:,j)=Jtot(:,j).*v(:,j);

end

73
74
75
76

% Meshing the current vectors and splining the V to add them

dJn=diff(Jtot);

Jn=NaN(n,Nj);

Vn=NaN(n,Nj);

for i=1:Nj

Ji=Jtot(:,i);

Vi=v(:,i);

o=length(Ji(dJn(:,i)6=0));

Jn(1:o+1,i)=[Ji(dJn(:,i)6=0); Ji(end)];

Vn(1:o+1,i)=[Vi(dJn(:,i)6=0); Vi(end)];

end

87
88

J=[];

for i=1:Nj
J=[J; Jn(:,i)];

90
91

end

J=sort(J); J=−J;

dJ=diff(J);

J=[J(dJ6=0); J(end)];

96
97

for i=1:Nj

Jv=Jn(:,i); Jv(isnan(Jn(:,i)))=[];

Vv=Vn(:,i); Vv(isnan(Jn(:,i)))=[];

100

Vinterp(:,i)=interp1(Jv,Vv,J,'nearest');

101

end

102

V=sum(Vinterp,2);

103
104

% Power = J*V

105

P=J.*V;

106

xmax=find(P==max(P));

107

Pmax=P(xmax);

108

Vmax=V(xmax);

109

Jmax=J(xmax);

110
111
112

%Efficiency

113

Psun=q*C*trapz(E,flux.*E);

114

En=max(Vn.*Jn)/Psun;

115

Ei=sum(En);

116

Es=Pmax/Psun;

117
118
119
120

if figson==1

121

figure

122

plot(Ltot,Pdens,'k−','LineWidth',1.2); hold on

123

fill([Ltot(m(1));Ltot(m(1):end);Ltot(end)],[0;En(1).*Pdens(m(1):end);0],s

124

if Nj<2

125

else
for i=2:Nj;

126

fill([Ltot(m(i));Ltot(m(i):m(i−1));Ltot(m(i−1))],...

127
128

[0;En(i).*Pdens(m(i):m(i−1));0],...

129

spectrumRGB(mean(Ltot(m(i):end))))
end

130
131

end

132

Leg(1)={'Solar spectrum'};

133

for i=1:Nj; Leg(i+1)=strcat({num2str(Eg(i))},{'eV'}); end

134

legend(Leg)

135

ylabel('W mˆ{−2} sˆ{−1} nmˆ{−1}')

136

xlim([200,2000])

137

else

138

end

139
140
141

% Meshing the current vectors and splining the V to add them

142

% % % J1=Jtot(:,1);

143

% % % J2=Jtot(:,2);

144

% % % dJ1=diff(J1);

145

% % % dJ2=diff(J2);

146

% % % J1=[J1(dJ16=0); J1(end,1)];

147

% % % J2=[J2(dJ26=0); J2(end,1)];

148

% % %

149

% % % v1=V(:,1);

150

% % % v2=V(:,2);

151

% % % v1=[v1(dJ16=0);v1(end)];

152

% % % v2=[v2(dJ26=0);v2(end)];

153

% % %

154

% % % J=[J1;J2];

155

% % % J=sort(J); J=−J;

156

% % % J=sort(J); J=−J;

157

% % % dJ=diff(J);

158

% % % J=[J(dJ6=0); J(end)];

159

% % %

160

% % % V1=interp1(J1,v1,J,'nearest');

161

% % % V2=interp1(J2,v2,J,'nearest');

162

% % %

163

% % % V=V1+V2;

164

% % % P=J.*V;

165

% % % maxP=max(P);

166

% % %

167

% % % Psun=q*C*trapz(E,flux.*E);

168

% % % IndEff=(max(v1.*J1)/Psun)+(max(v2.*J2)/Psun)

169

% % % SeriesEff=maxP/Psun

170
171
172

% x oc=find(Jtot≤0,1,'first')

173

% maxP=P(x max)

174

% maxV=V(x max)

175

% maxJ=Jtot(x max)

176

177

% Voc=V(x oc)

178

179

% figure

180

% plot(V,Jtot,'k−','LineWidth',1.5); hold on

181

% plot(maxV,maxJ,'ro','MarkerSize',6,'MarkerFaceColor','r')

182

% plot([0,maxV],[maxJ,maxJ],'r−−');

183

% plot([maxV,maxV],[0,maxJ],'r−−');

184

% plot(Voc,0,'ko','MarkerFaceColor','k')

185

% ylim([0,1.2*max(Jtot)])

186

% xlim([0,1.1*max(Voc)])

187

188

% %Efficiency

189

% Psun=q*C*trapz(E,flux.*E)

190

% Eff=maxP/Psun

90
ZnO
Cu2O
MgO

Cu2O

MgO

Slight Overdevelopment of
LOR

MgO

Cu2O

ZnO

LOR

Patterned Exposure
and Development

MgO

Cu2O

ZnO

LOR

MgO

Cu2O

Timed HNO3 etch

MgO

Cu2O

ZnO

LOR

1813 Photoresist

ZnO on Cu2O Device Fabrication Process

Appendix B

Photolithography Flow Process

2nd Metal Deposition

Cu2O
MgO

Cu2O

MgO

Cu2O

Remove both resists

Patterned Exposure
and Development

MgO

Cu2O

Gold Deposition

MgO

Cu2O

Remove Resist

MgO

Cu2O

ONLY OF NECESSARY
Apply 1813 PR again

ZnO on Cu2O Device Fabrication Process

Appendix C

AFORS-Het

simulation hetero
printed at 12/13/2012

results:
Voc=691.4 mV Jsc=11.24 mA/cm^2 FF=58.75 % Eff=4.566 %

working conditions:

calculation mode:
dc
T:
300 K temperature
/illumination
illumination side:
front
spectral illumination: on
spectral file:
AM15.in
lambda[nm],flux[1/(cm^2*s*nm)]
i_spectral:
spectral intensity factor
monochromatic illumination:
off
/end of illumination
fix potential at: front
v_ext: 0 V
boundary external voltage
j_ext: 0 A/cm^2
external current
/end of working conditions

cell parameter:

/general parameters
Rs:
17 Ohm*cm^2 serial resistance
MISf: 17 Ohm*cm^2 fraqtion
initialvaluesfromfile:
false
initialgridfromfile:
false
/end of general parameters

/layer
name: vacuum/air
width: 1E-6 cm
layer thickness
incoherent:
false
incoherent calculation
n:
optical coefficient n
k:
optical coefficient k
/end of layer

/layer
name: ZnO
width: 1E-5 cm
layer thickness
incoherent:
false
incoherent calculation
nk-file: ZnO_thinfilm.nklambda[nm],n[-],k[-]
/end of layer

/frontcontact
name: Frontcontact
BandBending: Band-bending
phi:
4.23 eV metal work function
ref:
constant reflection
abs:
constant absorption
int_ref: 0
constant internal reflection
/end of frontcontact

/interface
interfacename: Schottky interface Sn1e7 Sp1
numeric-model: 0
MS-Schottky-Contact
/modelparameters
model-name: MS-Schottky-Contact
sn:
100000 cm/s electron surface recombination velocity
sp:
100000 cm/s hole surface recombination velocity
/end of modelparameters
Qif:
0 cm^-3
Interface Charge

no defects
/end of interface

/layer
name: Cu2O
numeric-model: 0
standard
functional_dependance:Constant
xd_dk: 1E99
xd_chi: 1E99
xd_Eg: 1E99
xd_Egopt:
1E99
xd_Nc: 1E99
xd_Nv: 1E99

xd_me: 1E99
xd_mh: 1E99
xd_Na: 1E99
xd_Nd: 1E99
xd_ve: 1E99
xd_vh: 1E99
xd_rho: 1E99
xd_rae: 1E99
xd_rah: 1E99
xd_rbb: 1E99
decr_type:
rightside
xD:
0.05
width: 0.005 cm
layer thickness
dk:
7.2
dielectric constant
chi:
3.3 eV electron affinity
Eg:
2.05 eV bandgap
Egopt: 2.05 eV optical bandgap
Nc:
2.44E19 cm^-3 effective conduction band density
Nv:
1.104E19 cm^-3
effective valence band density
me:
110 cm^2/Vs effective electron mobility
mh:
65 cm^2/Vs
effective hole mobility
Na:
10000000000000 cm^-3
doping concentration acceptors
Nd:
50000000000 cm^-3 doping concentration donators
ve:
67920 cm/s
electron thermal velocity
vh:
88520 cm/s
hole thermal velocity
rho:
6.09 g*cm^-3 layer density
rae:
2.2E-31 cm^6/s
auger electron recombination coefficient
rah:
9.9E-32 cm^6/s
auger hole recombination coefficient
rbb:
1E-10 cm^3/s band to band recombination coefficient
nk-file: GregNewCu2O.nk
lambda[nm],n[-],k[-]
incoherent:
false
incoherent calculation

/defect
name: Defect_1
text:
Cu Vacancy
type: single
charge: acceptor
hurkx: off
cn:
1E-9 cm^2
electron thermal cross section
cp:
1E-9 cm^2
hole thermal cross section
meff: 0.25 cm^2
efective tunneling mass
cnplus: 1E-12 cm^2
electron thermal cross section
cpminus:
1E-12 cm^2
hole thermal cross section
cnzero: 1E-15 cm^2
electron thermal cross section
cpzero: 1E-15 cm^2
hole thermal cross section
cno:
0 cm^2 electron optical cross section
cpo:
0 cm^2 hole optical cross section
Ntr:
10000000000000 cm^-3
trap density
E:
0.45 eV characteristic energy
Ntr specific:
10000000000000 cm^-3/eV
specific trap density
Taun: 1.47232037691402E-9 s
mean electron lifetime
Taup: 1.47232037691402E-9 s
mean hole lifetime
Ln:
6.4706037271029E-5 cm
mean electron diffusion length
Lp:
4.97399265137983E-5 cm
mean hole diffusion length
/end of defect

/defect
name: Defect_2
text:
Cu Di Vacancy
type: single
charge: acceptor
hurkx: off
cn:
1E-15 cm^2
electron thermal cross section
cp:
1E-15 cm^2
hole thermal cross section
meff: 0.25 cm^2
efective tunneling mass
cnplus: 1E-12 cm^2
electron thermal cross section
cpminus:
1E-12 cm^2
hole thermal cross section
cnzero: 1E-15 cm^2
electron thermal cross section
cpzero: 1E-15 cm^2
hole thermal cross section
cno:
0 cm^2 electron optical cross section
cpo:
0 cm^2 hole optical cross section
Ntr:
4E16 cm^-3
trap density
E:
0.25 eV characteristic energy
Ntr specific:
4E16 cm^-3/eV specific trap density
Taun: 3.68080094228504E-7 s
mean electron lifetime
Taup: 3.68080094228504E-7 s
mean hole lifetime
Ln:
0.00102309228070099 cm
mean electron diffusion length
Lp:
0.000786457292165006 cm
mean hole diffusion length
/end of defect

/defect

name: Defect_3
text:
Oxygen Vac
type: single
charge: donor
hurkx: off
cn:
1E-15 cm^2
electron thermal cross section
cp:
1E-15 cm^2
hole thermal cross section
meff: 0.25 cm^2
efective tunneling mass
cnplus: 1E-12 cm^2
electron thermal cross section
cpminus:
1E-12 cm^2
hole thermal cross section
cnzero: 1E-15 cm^2
electron thermal cross section
cpzero: 1E-15 cm^2
hole thermal cross section
cno:
0 cm^2 electron optical cross section
cpo:
0 cm^2 hole optical cross section
Ntr:
100000000000000 cm^-3
trap density
E:
0.91 eV characteristic energy
Ntr specific:
100000000000000 cm^-3/eV specific trap density
Taun: 0.000147232037691402 s
mean electron lifetime
Taup: 0.000147232037691402 s
mean hole lifetime
Ln:
0.0204618456140197 cm
mean electron diffusion length
Lp:
0.0157291458433001 cm
mean hole diffusion length
/end of defect
/end of layer

/interfacebackside
interfacename: Interface back
numeric-model: 0
MS-Schottky-Contact
/modelparameters
model-name: MS-Schottky-Contact
sn:
10000000 cm/s electron surface recombination velocity
sp:
10000000 cm/s hole surface recombination velocity
/end of modelparameters
Qif:
0 cm^-3
Interface Charge

no defects
/end of interface

/backcontact
name: Backcontact
BandBending: Flat-band
ref:
constant reflection
abs:
constant absorption
int_ref: 0
constant internal reflection
/end of backcontact

/layer
name: vacuum/air
width: 1E-6 cm
layer thickness
incoherent:
false
incoherent calculation
n:
optical coefficient n
k:
optical coefficient k
/end of layer

/end of all layers

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