New Optoelectronic Devices Using GaAs-GaAlAs Epitaxy - CaltechTHESIS

~,

Jn (xc) I

- - '"""'i

n2 (xc)

( b>
Fig. 3-5

Xc

(a) The structure of a PNPN device with a Ga 1_yAlyAs
barrier layer in t he p base. (b) The minority carrier
distribution in t he P base.

-63-

III.4.1

Boundary conditions
In solving for the I-V characteristics of the device, it is

necessary to know th e boundary conditions of the carrier concentrations at all the juncti ons.

Since we are interested in the I-V curves

below the holding poi nt, low level injection conditions are assumed ,
i.e., the injected minority carrier densities are small compared with
the majority carrier densi ties.

In the structure of Fig. 3- 5,

E, E', and Care PN j unc tions , 1 is a PP hetero-junction.

At the

boundaries of the depletion regions of the PN junctions, the excess
minority carrier densities follow the Shockley boundary conditions . ( 3 )
They are
n1 (xe) = nl (e

qVE/kT

- 1)

(3-20)

- 1)

(3-21)

1)

(3-22)

_ qVE.!kT
= p3{e
p3 (x')
- 1)

(3-23}

n2(xc)

n2 (e

p3(x~) = p3(e

qVc/kT
qVc/kT

where n and p are the excess (or injected) electron and hole concentrations, respectively, n and pare the equilibrium values of the electron
and hole densities, the subscripts 1, 2, and 3 denote the three different
base regions, and VE, VC and VE' are the voltage drops across the three PN
junctions E, C, E', respectively.
Since Ga -yAl y As has a wider bandgap than GaAs, the conduction
band edge at the P GaAs - P Ga 1_YAlYAs junction forms a potential barrier
for the electrons and the valence band edge forms a potential barrier f or

-64the holes in the GaAs region (see Fig. 3-6).

From Boltzmann statistics,

the electron densities on both sides of the boundary (x 1 ) are related by
(3-24)
where NCl and NC 2 are the effective densities of states of electrons in
the conduction bands of GaAs and Ga 1 _YAlYAs, respectively, and 6Ec is
the barrier height in the conduction band.

Simi larly, the relation be-

tween the hole densities at the two sides of the boundary is
(3-25)
wher.e ~~Vl'NV 2 are the densities of states of holes in the valance bands
of the two materials, and 6Ev· is the barrier height in the valence band.
Multiplying eq . (3-24) by eq. (3-25) we obtain
(3-26)
Since these two regions are p type, under low-level injection conditions
the hole concentrations are approximately the same as doping concentrations, i.e., p1 {x 1 ) = NAl' p2 (x 1 ) = NA 2 •

6Ev+ 6Ec

in the exponent of

eq.(3-26) is the energy difference, 6Eg ,between the bandgaps of GaAs and
Ga 1_YAlYAs .

Therefore, eq. (3-26 ) becomes

(3-27)
or

-65-

j_-------E
.6Ec J

-------,..,P

GaAs

- - - - - - - , - - - - - - - - - - - Et

n'

6Ev T

Fig. 3-6

The P GaAs- P Ga

1 -y

Al As junction

-66(3-28)
where
( 3-29)
This 6E is the effective height of the potential barrier for the electrons
flowing from region 1 (GaAs) to region 2 (Ga 1 _YAlYAs).
III . 4.2

Solution of the diffusion equation

In order to obtain the carrier and the current distributions in the
p base of the device. it is necessary to solve the diffusion equations
separately in the two materials which compose the base and match the boundary conditions at x = x1 (see Fig. 3-Sa).

For convenience of illustration

the p base region is drawn in Fig. 3-Sb.

In the absence of electric

fields, the diffusion equation for the excess number of electrons is

( 3-30)

L 2

where Ln is the diffusion length of electrons.

The solution of this

equation is
n(x) = c1 e

x/Ln

+ c e

-x/L

(3-31)

where c and c2 are arbitrary constants to be determined by the boundary
conditions . In region 1 the conditions for n(x) at x = xe and x1 are
n(x) = n1 (xe)

at

n(x) = n1 (x 1 )

at

X = xe

(3- 32}

and
X = xl

Applying these two relations to eq. (3-31) we can sol ve for the excess
electron distribution in region

-67x-x

n (x) = --w- [n (x ) sinh~+ n (xe) sinh
1 1

sinh

d-nl

nl

x -x

-t--J
nl

(3-33)

where the subscript 1 indicates region 1, and w is the distance between

x1 and xe.

Similarly, the distribution of excess electrons in region 2 is

x-x
x -x
n2 (x) = -----'-[n 2 (x )sinh ~ + n2 (x1 ) sinh
w2
n2
n2
sinh -Ln2
where w2 is the distance between x1 and xc.

-f-J

(3-34)

The diffusion current of el ectrons, Jn(x), can be obtained by using
the equation
(3-35)
where On is the diffusion constant of electrons.

Substituting eq. (3-33)

and eq. (3-34) into eq. (3-35) we obtain
q Dnl
x -x
x-x
Jnl (x) = _ _..;...;._;__w_ [n (xe) cosh -1 - - n (x ) cosh ~]
1 1
Lnl
nl
Lnl sinh -Lnl

(3-36)

(3-37)

From the condition of continuity of electron current at x = x1 ,

we obtain from eq. (3-36) and eq. (3-37) a relation between n1 (x1 ) and
n (x )
2 1

-68-

onl

w,

sinh - 1
Lnl

nl

--~-w- [cosh -L -

n1 (x 1 )

(3-39)
Substituting the boundary condition
n (x ) = n (x ) e6E/kT

(from eq. {3-28))

into eq. ~3-20) we obtain the solutions fqr n1 (x 1 ) and n2 (x1 ): they are

(3-40)

on2 n2(xc)

n2

ex, )

w2

onl n,(xe)

w1

Ln 2 Slnh -L- L l Slnh -Ln2
nl
= ..,..------~~:;:------c:----....:..:....:..-0
w1 6E/kT
nl coth e
+ ~oth - 2t;;'l
Ln 1
Ln2
Ln2

( 3-41 )

Using the values of n1 (xe) and n2 (xc) from eq.(3-2C) and eq.(3-21), the
above two expressions become
A _

1 n (e
n1 (x 1 ) = c1
n2 (x 1 ) = e6

qVE/kT

A _

- 1) + cn2 (e

qVc/kT

- 1)

E/kT A1 _ qVE I kT
A2 _ qVc/kT
[c- n1 (e
- 1) + c- n2(e
- 1)]

where we have defined

(3-42)
(3-43)

-69_ qDnl
Al = -Lnl
and

_ qDn2
A2 = -Lw
n2 sinh L2
n2

w,

sinh -L nl

qD

qD

Lnl

Lnl

Ln2

n2

= _l!!_ coth - 1- + ~ e -ilE/kT coth -L 2

(3-44)

The distributions of the excess electron density and the electron diffusion current are obtained by substituting eq. (3-42) and eq. (3-43) into
eqs . (3-33),(3-34) and eqs. (3-36),(3-37).
In the N base (region 3 in Fig. 3-Sa) of the device, there is only
one mat erial, N GaAs .

The diffusion equation for minority carriers can

be ea s ily solved.

Using the conditions for hol~s at x~ and x'e
_ qVc/kT
(from eq. (3-22))
- 1)
p3(x~) = P3 (e

p3(x~) = p3(e

qVE./kT
- 1)

(from eq . (3-23))

we obtain the distribution for excess hole concentration
x-x'
qVc/kT
p3{x) = _ ___;___
[sinh ~ p3 (e
- 1)
w3
p3
sinh -L p3
x'-x
+ sinh
p3

+-

(3-45)

and the diffusion current for holes
qD 3
· x'-x
qVE,/kT
Jp(x ) = - - ..1:....=..--w[cosh - eL
- -p3 ( e
- 1)
sinh - 3
P3
Lp3
x-x~ _ ( qVc/kT
cosh - L
p e
- 1)]
p3 3

(3-46)

-70where Lp 3 and Dp 3 are the diffusion length and diffusion constant for
holes in region 3.
!!!.4.3

Transport factors
Using eqs. (3-36), (3-37) and eqs. (3-42), (3-43), one can show

that the electron diffusion currents at x = xe and x = xc are
Jn(xe) = a(e

qVE/kT

- 1) + b(e

qVc/kT

1)

( 3-4 7)

Jn(xc) = A(eqVE/kT- 1) + B(eqVc/kT- 1)

( 3-48)

where
(3-49)

B = -A n (cosh - 2 - __g_ e - tiE/kT)
2 2
Ln 2 C
and A1 , A and Care defined in eq. (3-44).

We now define

= =-~------------~---------------------------

( 3-50)

Dnl Lnl e6 E/kT sinh :l sinh : 2 + cosh :l cosh : 2
0 n2 Ln2
nl
n2
nl
n2

= =-~------------~~---------------------------

0n2 Lnl -6E/kT
wl
w2
wl
w2
onl Ln e
sinh -L - sinh -L - + cosh -L - cosh -L n2
nl
n2
nl

( 3-51)

From eq. (3-47) and eq. (3-48) and the definition of the transport factor
(eq . {3-17)), tN can be regarded as the transport factor for minority
carriers flowing from the emitter to the collector when the emitter june-

-71-

tion is forward biased and the collector junction is reversed biased .
Similarly t 1 can be regarded as the transport factor for minority carriers flowing from the collector to the emitter when the collector
junction is forward biased and the emitter junction is reversed biased.
We shall call tN the normal transport factor and t 1 the inverse trans port factor .
The effect of the barrier height 6E on the transport factors, tN
and t 1 , can be seen very clearly from eq. (3-50) and eq. (3-51) .

small barrier with a hei ght of a few kT can reduce the normal transport
factor, tN, by a very large factor.

If region 1 and region 2 have the

same material and same doping (i .e., NAl = NA 2 ' 6E = 0, Lnl = Ln 2 '
Dnl = Dn 2 ), the expressions for tN and t 1 reduce to the ordinary expres sions of the transport factors. ( 3 ) They are
tN = ti = _......:......_
cosh

( 3- 52)

tn

where w = w1 + w2 and Ln = Lnl = Ln 2 .

For the case of 6E >> kT, Lnl >> wl •

and Ln 2 >> w2 the transport factors become approximately
( 3-53)

(3-54)
In the forward direction (the electrons being transported from the emitter
to the collector) the transport factor is greatly reduced due to the potential barrier.

But in the reverse direction the transport fa ctor i s

-72-

unity since no barrier exists.

In the devices which we fabricated, eq.

(3-53) and eq. (3-54) are nearly true because the widths of the base
regions are usually on the order of 1 ~m or less and the barrier height
is usually much higher than kT.
In the PNP transistor part of the device, there is only one material
(N GaAs) in the base.

From eq. (3-46) the hole currents at the emitter

and the collector junctions are
J (x') = a'(e
P e

p c = A'(e

J (x')

qVE,/kT

qV ,/kT

qV /kT
- 1) + b'(e C
- 1)

- 1) + B'(e

(3-55)

qV /kT

- 1)

(3-56)

where
qD 3
w3 a' = - B' = ~ coth p
Lp 3

Lp 3

( 3-57)

A' = - b' - qDp3
- Lp3

w3

(3-58)

sinh -Lp3

The transport factors are therefore
t..'. = ~ = __1'---N - a'
_ w

(3-59)

b'
I =B'"
= --'--w-3-

(3-60)

cosh c:p3

and

cosh -Lp3

-73-

III.4.4

I-V Characteristics

The total current flowing across the emitter junction E (see Figs.
3-5) is the sum of the electron diffusion current at xe, the hole diffusion current at the edge of the depletion region in the emitter and
the recombination current IR in the depletion region.

Since th i s junc-

tion is a heterojunction and the emitter has a larger band gap than the
base, the hole current injected into the emitter is negligible compared
with the electron current injected into the base.

Therefore the total

current J is
( 3-61 )

where we have used the relation b = tiB.

At the other emitter junction

E' we obtain a similar expression for the total current.

J (x') +I' = a'(e
p e

qV , /kT

- 1) + t'B'(e

qVc/kT

- 1) + IR'

(3-62 )

where JR is the recombination current in the depletion region of the
junction E'.

When qVE, qVE' >> kT, IR and IR are of the form(ll)
, IR

(3-63)

where I 0 and I~ are some constants.
At the collector, the junction is reverse biased because it is operated below the holding point.

If this reverse biased voltage i s suffi-

ciently high, the electrons and the holes entering the junction and the

-74carriers thermally generated in the space charge region will be accelerated by the electric field in this region and collide with the valence
electrons and the lattice, causing avalanche multiplication .

The total

current flowing across the collector junction is, therefore,
(3-64)

where M is the multiplication factor, which is a function of Vc.

IG is

the current generated in the space charge region, which can be due to
thermogeneration, light activation or other means which can generate
electron·· hole pairs.
the gate current.

It also has the effect of the leakage current or

Substituting eq. (3-56) and eq. (3-48) into eq. {3-64 ),

we get
J = M[tNa(e

qV /kT

l)+tNa'(e

qV ,/kT
qVc/kT
- 1) + (B + B')(e
- 1) + IG]
(3-65)

The total voltage drop across the device is the sum of the voltage drops
in the three PN junctions, i.e.,

v = vE + vc + vE •

(3-66)

Now, since there are five unknowns, V, J, VE, Vc, and VE', in the four
equations, eqs. (3-61),(3-62), (3-65), and (3-66), we can eliminate VE,
Vc, and VE' from these equations and get the relation between J and V.
Some numerical calculations of the I-V characteristics will be given in
the next section .

-75-

The injection efficiencies y, y• of the two emitter junctions can
be calculated from eq. (3-61) and eq. (3-62).

= J [a(e

qVE/kT

- 1) + t 1B(e

They are
qVc/kT

- l)]

(3-67)

(3-68)
Combining these two equations with eq. (3-65), we get

(3-69)
where c = ytN and a • = y•tN are the common base current gains of the NPN
and PNP transistors, respectively .

When the denominator on the right

hand side of eq. (3-69) approaches zero, J + oo.

Therefore, switching

wi 11 result if
M(a + a•)

=1

( 3-70)

Since the alphas are proportional to the transport factors, which are
controlled by the potential barrier in the base and can be made very
small, the alphas can be reduced to small values by the barrier.

The

multiplication factor M is a function of the reverse bias voltage VC 7
...

or ·appN~ately the total blocking voltage, and increase with VC'
Therefore, small alphas will result in a greater breakover voltage.

-76III.4.5 Numerical results
In this subsection we present the numerical solutions of the
equations derived in the last subsection.
calculations is shown in Fig. 3-5a.
gions are given in Table 3-1.

The structure used in the

The parameters of the base re-

The energy difference ~Eg

in the band

gaps of the two materials, Ga 1 _YAlyAs and GaAs,in the P base region
depends on the Al content y and is taken as a variable parameter.

The

two emitters are Ga 1_xAlxAs with Al content x = 0.4. 10 and I~ for
the two emitter junctions are taken to be l0- 9A/cm 2 and 3.33 x lo- 10A/cm2 ,
respectively.

The multiplication factor, M, as a function Vc/V
is
80
taken from the calculations of Leguerre et al. ( 9 }
The I-V characteristics of the device are solved using eqs. (3-61},
(3-62}, (3-65), and (3-66).

Fig. 3-7 shows the 1-V curves with different

IG's when ~Eg = 8 kT (corresponding toy= 0.2 in the Ga 1_YAlyAs barrier
layer).

These curves are similar to the usual characteristics of a PNPN

device with different triggering levels.
at IG = 0.01 A/cm 2 with different ~Eg's.

Fig. 3-8 gives the I- V curves
It is clear from thi s figure,

that the breakover voltage increases with the height of the potential
barrier.

As explained before, this is because the transport factor de-

creases as the barrier height is increased.

The holding current Ih

(defined as the current at Vc = 0}, which is the current at th e upper
limit of each curve, also increases with ~Eg.
Ih as a function of ~Eg at IG = 0 .

Fig. 3-9 is the plot of

Ih increases very rapidly with i n-

creasing ~Eg and the larger the ~ Eg, the greater is the rate of increase.

P GaAs

P Ga1_YAlyAs
N GaAs

, alB

~p3 = 300

l1n 2 = 3000

3 X 10 16

1.7

0.5

l1n 1 = 3000

1Ql7

Mobility
(cm2;v-sec)

0.4

(~rn)

Width

(lJm)

Diffusion Length

Table 3-1 Parameters of the base regions used in the numerical calculations

Material

Region

Doping
Concentration
(cm- 3)

........

........

-E

10

IG = 0.05 A/cm2

IG = 0.1 A/cm2

20

as a P.arameter

IG is used

15
25
30
0~~~~
FORWARD VOLTAGE (volts)

10-2

I0- 1

A/cm

!!Eg = 8 kT

Fig. 3-7 Forward 1-V characteristics (below holding point) when !lEg = 8 kT.

::::>

0::
0::

f-

...........

C\J

10

A/cm2

I0 ~~r---r-~

CD

.......

o1

--~

.6E 9 = 2.5 kT

.6Eg = 4 kT

.6Eg = 6 kT

IG = 0.01 A/cm2

Fig. 3-8 1-V characteristics when IG = 0.01 A/cm 2. ~Egis used as a parameter.

n:::
n:::
::)

1-

N' 10

102~---

'-I
\0

-80-

""'
<{

IQ-2L-------~--------~--------~--------~---~

6Eg (kT)

Fig. 3-9 Holding current as a function of 6Eg.

-81-

The plot of the breakover voltage v80 as a function of ~ Eg with IG as
as parameter is shown in Fig. 3-10.

For each IG t 0 the breakover vol-

tage increases with ~ Eg and increases slowly when ~ Eg is large and very
quickly when ~Egis small .

This figure also shows that each curve (with

a particular value of IG) has some minimum value of ~Eg, where v80 drops
very sharply.

If the band gap difference between the P GaAs and the

P Ga -yAl yAs is smaller than this value there is no breakover, and there1
fore, no negative resistance region in the I-V curve. Physically, thi s
is understandable because the alpha of the device becomes higher as the
barrier height is reduced, and when ~Eg is smaller than a certain value
the a 1 ?has, or the gain, will be too high for the device to sustain a
negative re.s istance region.

We have shown experimentally that a PNPN

device having the same dimensions as we discussed here shows an I-V
curve just like those of regular PN diodes if there is no potential
barrier in the base regions.
The excess minority carrier distribution in the base regions
has been calculated at the holding point (VC = 0) for the case when
~Eg =

8 kT and IG = 0.

The curve is shown in Fig. 3-11.

tinuity of the curve at the boundary of P GaAs and P Ga
the effect of the potential barrier.

The discon-

Al As shows
1-y y

-82-

IG = 0.005 A/cm2

{/)

~Eg (kT)

Fig. 3-10 Breakover voltage v80 as a function of ~Eg.
as a parameter

IG is used

I0-7

I0:::: 10-3

>-

8 10

0::::
0::::

0:::: I 0

w 109

0::::
1---

1017

DISTANCE (MICRON)

P Go l-yA lyAs

Fig. 3-11 The minority carrier distribution in the base region

~1~_P Go As

0...

_j

n::

<.9

I N Go3As-I

co

-84-

III.S

Characteristics Near the Lasing Threshold
We have shown in Fig. 3-11, that when a Ga 1 -y Al y As barrier layer

is present in the P base of the device, the number of injected carriers
in region 1 (P GaAs) is higher than those in other regions of the bases.
If we continue to increase the driving current and operate the device
above the holding point, an increasing number of carriers will be injected into this region.

When the number of injected carriers reaches

some threshold value, lasing action, or stimulated recombination, will
take place.

The driving current at this point is the lasing threshold

current and reg1on 1 is the lasing active region.
Near lasing threshold, the carrier density in the active region is
usually higher than the doping concentration.

High level conditions

(n = p >> Npl) have to be used to solve for the carrier and current

distributions in this region.

Under high level conditions the carrier

concentration in region 1 satisfies the ambipolar diffusion equation,(l 2)
namely

(3-71)
where L1 is the ambipolar diffusion length, defined by

(3-72)
where b = on 1;opl' 'no and 'po are the lifetimes of electrons and holes,
respectively.

Subject to the conditions n1 (x) = n1 (xe) at x = xe and

-85-

n1 (x) = n1(x1 ) at x = x 1 , the solution of eq. (3-71) is
{3-73)

In regions 2 and 3 we assume the low level conditions are still
valid .

The distributions of the minority carrier densities are the

same as shown in equations (3-34) and (3-45) .
To solve for the carrier distribution in the base regions , we need
to know the boundary condition for electron densities (the relation between n1( x 1) and n 2( x1 ) ) at the boundary of P GaAs and P Ga 1 _YAlyAs.
Let u~ refer again to Fig . 3-4c, the band diagram of the device near
the lasing threshold.

The electron quasi-Fermi level in the P GaAs

active region is higher than the edge of the conduction band because
of population inversion.

In order to know the electron concentration

in this region we have to use the more accurate Fermi-Dirac function
instead of the Boltzmann function. If ~ is the quasi-Fermi level measured from the bottom of the conduction band of P GaAs at x = x1 , the
electron density at this point is
(3-74)
where F

112

1s the Fermi-Dirac integral .( 3 )

In the P Ga 1_YAlYAs barrier

region, we assume that the barrier is high enough so that the quasiFermi level is lower than the conduction band edge.
sity in this region at x = x1 is, therefore,

The electron den-

-86(3-75)
where Ec 2 is the energy at the bottom of the conduction band of region
2 (P Ga 1 _YAlyAs) and Ef is the Fermi level at x = x1 .

The equilibrium

values of the electron densities in region 1 and region 2 are related by
(3-76)

Substituting this relation into eq. (3-75) we get
( 3-77)

The boundary condition for electron density at x = x1 is thus obtained
by eliminating~ from eq. (3-74) and eq. (3-77).
The electron current in region 1, under high level conditions,
satisfies(l 2)
dn 1
bJ - 2qDnl dX

(3-78)

b + 1

where J is the total current density flowing through the device.

In

the other two regions of the bases (P Ga 1 _YAlyAs and N GaAs) since low
level conditions are still valid, eq. (3-37) and eq. (3-46) are used
to calculate the diffusion currents.

At the two emitter junctions,

since the total current is high when the device is near lasing threshold,
the recombination currents in the depletion regions can be neglected.

-87The minority currents injected into the emitters are also negligible
because the Ga 1_xAlxAs emitters have wider band gaps than GaAs.

At

x = xe the total current is, therefore, equal to the electron current
injected into the base.

Thus
(3-79)

Using thi·s relation with eq. (3-78), we obtain for the total current
(3- 80)
x=x e
At the other emitter, x = x~, we get similarly

= J P(x')

(3-81)

At the collector junction, since it is now forward biased, the multiplication factor M is equal to one.
the total current .

IG is negligible compared with

So
( 3-82)

Jn(xc) and Jp(x~) are the same as shown in equations (3-48), (3-56).
The continuity of electron current at x = x1 requires
(3-83)
Substituting eq . (3-78) into eq. (3-83) we get

2qDn 1 dn 1

~~
1 + b J - 1 + b

crx:- x=x1 = Jn2(x1)

(3-84)

-88Equations (3-80), (3-81), (3-82), (3-84) and the boundary condition of
the electron densities at x = x1 are the necessary conditions one needs
to solve for the carrier distribution inthe base regions.
The ambipolar diffusion equation (eq. (3-71}}, which we used to
solve for the electron distribution in region 1 holds true when the
device is operated at or below lasing threshold.

Above threshold, how-

ever, this equation is only an approximation because it does not include
the stimulated process.

Stimulated recombination of carriers in the

active region is related to the optical power density of the laser light
and is very important when the device is lasing.

If one wants to know

exactly the carrier distribution in the active region, one has to solve
the diffusion equation {eq. (3-71)) with an added term of stimulated
recombination.

However, even without solving the equation, it is still

possible to know approximately the carrier concentration.

Below lasing

threshold, the number of carriers in the active region increases with
the driving current.

When the carrier density reaches some threshold

value, stimulated recombination begins.

Because of the stimulated re-

combination, the number of carriers in the active region will not increase with the current, but will be clamped at the threshold value.
This phenomenon is the so-called gain saturation. (l 3 ) Therefore, above
threshold, the carrier concentration in the active region can be taken
to be the same as the threshold value, and does not change with current.
The threshold carrier concentration depends on the thickness of
the active region and the loss of the laser cavity.
the active layer (region 1) is 0.4 vm thick.

In our PNPN device

If the optical and the

-89-

electrical confinement provided by the confining layers is sufficient
the threshold carrier concentration for lasing can be esti mated to be
about 1 .5 x 1018 cm- 3 .( 14 ) Using this value as n1 (x 1 ) and substituting
it into the equations derived earlier in this section, which are assumed
to be valid at the threshold, one can easily calculate the minority
carrier distribution in the bases and the threshold current density.
When the device is driven above threshold, the number of carriers in
region 1 is clamped.

Since this active region is much narrower than

the carrier diffusion length it is reasonable to assume that the carriers are clamped uniformly.

In this way the carrier density is

assumed constant at the thres hold value, and we don't need to solve
the equations exactly.

In regions 2 and 3, since they are not the

lasing regions, the carrier distribution can be still calculated . u sing ~
the diffusion equations derived earlier.
We have made calculations on a structure having di mensions the
same as those given in Table 3-1 and a band gap difference between
the barrier and the active regions of 8 kT . The minority carrier di stributions in the base at different currents are snown in Fig. 3-12.
It can be seen very clearly that the P Ga 1_YAlYAs potential barrier
confines the carriers in the P GaAs active region.

Because of this

confinement the lasing threshold can be made as small as the threshold
of a regular double heterostructure laser.

The threshold current density calculated in our example is 3.64 kA/cm2 , which is very close to

what we achieved experimentally.

P GoAs

P Ga 1_YAIYAs

0::

DISTANCE (MICRON)

N GoAs

Fig. 3-12 Minority carrier distribution in the base regions at different currents above lasing
threshold

io'5

~ 1016

J = I Jth

0::
0::

w lo'7

0::

~ 1018

0::
f--

i5~ I019 -r""""T----r---r-r---r-~-r--~r------"- ~~~ ~--

\0

-91-

III.6

Experimental Results
The barrier controlled PNPN devices were fabricated using our

horizontal liquid phase epitaxial growth system.

The epitaxial layers

were grown on a (100) oriented N type GaAs substrate with doping concentration n = 3 x 1018 cm- 3 The layers included, from the bottom,
N Ga 1_xAlxAs emitter, P type base, N type base, P Ga 1_xAlxAs emitter,
and last a P+ GaAs layer .

The two emitters had Al content x = 0.4,
and were doped in excess of 10 18 cm- 3 . The base layers were doped to
about 5 x 10 16 cm- 3 .

The last layer, P+ GaAs, was used to achieve a

better ohmic contact.
We have fabricated three types of devices:
barriers, (2)

(1)

with no potential

with a single barrier in the P base. (3)

barriers, one in the P base and one in theN base.

with double

Some of the

parameters and the measured results of these three kinds of de \ ices
are listed in Table 3-2.

The devices with no barriers, which have

only GaAs in the bases, had I-V curves just like those of ordinary PN
diodes and showed no negative resistance regions when the base widths
were about 0.5 ~m .

The diodes with single barrier and double barriers

had breakover voltages varying from 10 to 35 volts. The holding currents were about 10 A/cm 2 and 150 A/cm 2 for the single barrier and the
double barrier devices, respectively.

The results show that when the

bases are thin and contain no potential barriers, the devices have too
much gain and, therefore, cannot function as normal PNPN devices .
gain in the devices with barriers is greatly reduced.

The

The double bar-

rier devices have the lowest gain and this is clearly indicated by the
high value of the holding current.

--

2 lJm

0.2~m

0.3~m

0.2~m

0.3~m

o.5~m

-----·--

X = 0.4

2 ~m

X = 0.4

1. 8 ~m

X = 0.4

2 ~m

X = 0.4

2 ~m

X = 0.3

y = 0.2
1 ~m
y = 0.2
1.6 ~m

y = 0.2
1. 4 ~m
y = 0.2
1 ~m
y = 0.2
1 ~m
--

y = 0.2
llJlll

--

0.5~m

0.5~m

0.6~m

0.5~m

0.5~m

Emitter

p+

1 ~m

O.B~m

o.~m

1 ~m

1 ~m

-200

-150

.... 9

-1 0

controlled PNPN devices.

-35

-15

-10

-1 0

Lasing threshold current density

2 ~m

X = 0.4

2 ~m

X = 0.4

2 ~m

X = 0.4

2 ~m

X = 0.4

2 ~m

X = 0.3

Table 3-2 Layer thicknesses and experi mental results of some barrier

Jh: Hol9ing current, vB 0: Breakover voltage, Jth:

Double 1
Barrier

Single 1
Barrier

· No
Barrier

Base

Emitter

Base

-3

-3

-4

-5

no
1as ing

KA
Gal-xAlls GaAs Ga1_YAlyAs Ga 1-yAl yAs GaAs Ga1-XAl XAs GaAs Jh(-2) VBO (volt) Jth(-2)
an_
nn:
no
1 X = 0.3
1 ~m 1 - 3
5 - 10
2 ~m
2 ~m X = 0.3
lasing
2 ~m
1. 8 ~m

1\,)

1.0

-93-

Fig. 3-13a shows a scanning electron micrograph (SEM) of a s ingle
barrier device.

The P base of this device contains a GaAs layer and a

Ga 0 _8Al 0 _2As barrier layer.

The 20% Al content in the barrier cor-

responds to a band gap difference, 6Eg, of about 8 kT.
obtained for this device is shown in Fig. 3-13b.

The 1-V curve

Since the active

region of the barrier controlled PNPN laser can be made very thin, low
threshold lasing operation can be achieved. We have measured threshold
current density ~ 3 kA/cm 2 at room temperature, which is comparable to
our conventional double heterostructure lasers with the same active
region thickness.
Because of their negative resistance characteristics, the PNPN
devices can be operated in a (current) relaxation oscillation mode
using a circuit arrangement shown in Fig. 3-14.

If the current pul s es

passing through the diodes exceed the lasing threshold current, repetitive laser pulses will be obtained.

The repetition rate and the pul se

duration time can be adjus ted by the external resi s tors and capacitor .
This circuit is, therefore, very useful for a PNPN laser because it
produces laser pul s es without the need for external drives.

If we

neglect the parasitic inductance and the junction capacitance of the
diode, the characteristic times associated with the device in thi s
circuit can be easily shown to be
(3-69)

-94-

Fig. 3-13 (a)

An scanning electron micrograph of the cross

section of a single barrier PNPN device.
1-V curve of this device.

(b)

The

(b)

(a )

5mA

2V

....._ nGoAs substrate

pGoAs
. -pGo 0 .6 Aio.4As
nGoAs
pGo 0 .8 At 0 .2 As
pGoAs
.__ nGo 0 .6 A I o.4As

cr

\0

-96-

rs

Vso V

Fig. 3-14

An oscillation circuit for a PNPN laser diode, and
the I-V characteristic of the diode. rs is the series
resistance of the diode.

-97-

VBO
Td = (r + rs)C .tn Ih (r + r )

(3-70)

TL =

(r + rs)C .tn Ith ~~ + rs)

(3-71)

where Tc is the time to charge the capacitor C through R from the holding
voltage Vh to the breakover voltage v80 , Td is the time to discharge C
through the diode' s resistance rs and the resistance r, and TL is the
total on time of the lasing pulse during the discharge of C.

The fre-

quency of relaxation oscillation is determined by (Tc + Td)- l, but since
Td << Tc' it is Tc that determines the laser pulse repetition rate.
Fig. 3-15a,b are oscillograms of the current and light output of
a double barrier device whose 1-V curve trace is shown in Fig. 3-15c.
The circuit was operated with a bias voltage of 25 V, a charging resistor
R = 420 0, and a capacitor C = 0.2 ~F.

The current pulse level was

changed by adjusting the 10 o trimpot resistor r.
current of this device was Ith = 3.3 A.

The lasing threshold

Note that as the current

increases from below threshold (Fig. 3-15a) to above threshold (Fig.
3-15b) the light pulse (measured from a Sl photomultiplier) increases
in a nonlinear way and also narrows!

A plot of the device emission

spectrum 10% above threshold is shown in Fig. 3-16.
In conclusion, we have found a new way of controlling the characteristics of a PNPN device.

It is achieved by incorporating potential

barriers into the base regions.

We have realized thi s concept with

GaAs - GaAlAs PNPN heterostructure laser diodes.

The barriers are

provided by the wider band gap material Ga 1 _YAlYAs, and the height

CL

0:1
< 3
)>

--.
C7
.._
.._

0,)

.....-

Fig . 3-15 The current and light output oscilloscope traces of a PNPN laser connected in
an electronic circuit shown in Fig. 3-14. (a) Below threshold: 1 - light
pulse, 2 - current pulse; (b) above threshold: note the narrowing and nonlinear
increase of the lasing light pulse relative to the current pulse. (c) is the
I-V curve of this laser.

.._

.....-

co

ID

>-

8900

8925

8950
WAVELENGTH (~d

Fig. 3-16 Lasing spectrum of a barrier controlled PNPN laser

0::

_j

1.0
1.0

1-

o.3A

(/)

1-

-100-

of the barriers can be controlled by the Al content y.

This Ga 1 -y Al y As

barrier not only controls the I-V characteristics of the PNPN operation
but also provides the electrical and optical confinement which is necessary for low threshold laser operation.

Barrier controlled PNPN lasers

with threshold current densities comparable to those of conventional
double heterostructure lasers have been achieved.

-101REFERENCES FOR CHAPTER III
(1)

W. Shockley, Electrons and Holes in Semiconductors, D. Van Nostrand
Inc. (1950)

(2)

J. L. Moll, M. Tanenbaum, J. M. Goldley, and N. Holonyak, 11 p-n-p-n
transistor switches", Proc. IRE, 44, 1174 (1956)

(3)

S. M. Sze, Physics of Semiconductor Devices, John Wiley & Sons ,
Inc., New York (1969)

(4)

W. V. Muench, 11 Gallium arsenide four-layer devices 11 , Solid State
Electron. ~. 827 (1965)

(5)

C. R. Wronski, C. J. Nuese, and H. F. Gossenberger, 11 GaAs vapor
grown Shockley diodes and semiconductor-c0ntrolled rectifiers .. ,
IEEE Trans. Electron Device. ED-19, 691 (1972)

{6)

C. J. Nuese, J. J. Gannon, M. F. Gossenberger, and C. R. Wronski,
.. Electroluminescent Shockley diodes of GaAs and GaAs 1_/x"• J .
Elec. Mater. £, 571 (1973)

(7)

C. P. Lee, A. Gover, S. Margalit, I. Samid; and A. Yariv, .. Barriercontrolled low-threshold PNPN GaAs heterostructure laser", Appl.
Phys. Lett. 30, 535 (1977)

(8)

J. J. Ebers, 11 Four-terminal p-n-p-n transistors .. , Proc. IRE, 40,
1365 (1952)

(9)

R. Leguerre and J. Urgell, .. Approximate values of the multiplication
coefficient in one-sided abrupt junctions .. , Solid State Electron.

li· 857 (1976)
(10)

H. F. Lockwood, K. F. Etzold, T. E. Stockton, and D. P. Marinelli,
11

The GaAs PNPN laser diode", IEEE J. Quantum Electron . QE-10,

567 (1974}

-102(11)

A. S. Grove, Physics and Technology of Semiconductor Devices,
John Wiley & Sons, Inc., New york (1967)

(12)

R. Kokosa, "The potential and carrier distributions of a PNPN
device in the ON state", Proc. IEEE §i, 1389 (1967)

(13)

A. Yariv, Quantum Electronics, 2nd edition, John Wiley & Sons,
Inc., New York (1975)

(14)

M. B. Panish, "Heterostructure injection lasers", Proc. IEEE
64, 1512 (1976)

-103-

CHAPTER IV
GaAs-GaAlAs HETEROSTRUCTURE LASERS ON SEMI-INSULATING SUBSTRATES
IV.l

Introduction
During the last ten years or so GaAs technology has evolved

along two main directions.

One is that of optical devices, the other

in the area of electronic devices.

As described in the previous chapters,

the interest in GaAs as a basic material for optical devices is due
to the following facts:

(1) It is a direct bandgap semiconductor suit-

able for laser operation.

(2) The Ga 1 _xAlxAs ternary system, which

is lattice matched to GaAs, has optical characteristics which are strongly
dependent on x and can be easily grown epitaxially.

(3) It has high

electro-optic, acousto-optic and optical nonlinear coefficients making
it applicable to a variety of switching, modulation and frequency conversion devices.

Using _GaAs-GaAlAs heterostructures, it became possible

to fabricate optical devices such as low threshold single mode lasers,(l- 3 )
waveguides,( 4 ,S) modulators and couplers,(G,?)etc. In parallel, a great
amount of progress has been made on the development of GaAs electronic
devices.

The major reasons for the development are: (1) In GaAs the

conduction electrons have mobilities which are six times larger and a
peak drift velocity which . is bigger by a factor of two than in Si. (B)
This causes the parasitic resistance to be smaller, the transconductance
to be larger, and a shorter transit time of electrons in the high field
region.

(2) The existence of semi-insulating GaAs substrates makes

it possible to fabricate monolithic integrated circuits with low parasitic

-104capacitance, low loss interconnections, and high packing density. (3)
Bulk effects in GaAs makes it suitable for fabricating Gunn oscillators . (g)
Due to the rapidly increasing needs for high speed communication systems
and the saturation of low frequency communication bands there is an increasing demand for microwave devices capable of operation at high frequencies ( > 1 GHz).

The severe limitations of most devices at the high

microwave frequencies make GaAs the most promising material to operate in
this regime.

Today, GaAs field-effect-transistors (FET) capable of

operating at frequencies higher than 10 GHz, for example, can be easily
fabricated on epitaxial layers or on ion-implanted layers. (lO)
Although progress has been made in both the optical devices and
the electronic devices, the integration of these two kinds of devices
has not been achieved.

The difficulty of integration is due to the

fact that most of the optical devices at present are fabricated on highly
conductive substrates.

For example, conventional GaAs lasers use heavily

doped N type substrates.

The P type contact i s applied on the top of

the P type epilayers and the N type contact i s made on the bottom of
the substrate.
junction.

Current flows from one side to the other across the

Monolithic integration of this type of lasers with electronic

devices is almost impossible.

One way of solving this problem is to

fabricate the optical devices on semi-insulating substrates and to confine
the current flow to the thin epilayers on the substrate.

By so doing

one is able not only to achieve the electrical isolation which is needed
for integration, but also to apply conventional planar technology in the
device fabrication.

-105-

In this chapter we describe two different laser structures fabricated on semi- insulating GaAs substrates.

They are the first injection

lasers reported on semi-insulating substrates.

Because of the non-

conductive substrate, current flows laterally along the epilayers.
Instead of a two-dimensional design which is needed for ordinary stripe
geometry lasers, we need to employ a three-dimensional design for lasers
on semi-insulating substrates.

The laser which is described in section

IV.2 is called the crowding effect laser . (ll)

The laser action is based

on carrier confinement via the crowding effect. The second laser, which
is described in section IV.3,is called the lateral injection laser. (l 2 )
The PN junction Jf this laser is not parallel to the epilayers .

Current

flows laterally across the junction.
These newly developed lasers are natural candidates for monolithic
integration with other devices sharing the same crystalline layers.
Section IV.5 describes an experimentall .v demonstrated device - a laser
with aGunn oscillator on a single chip of semi-insulating GaAs. (l 3)
. Other types of integration are suggested.
Fabricating GaAs-GaAlAs injection lasers on semi-insulating
substrates not only revolutionizes the design of conventional injection
lasers but also opens up anew field for integrated optics.
Before we discuss the laser structures it is necessary to describe briefly what semi-insulating GaAs is.

Semi-insulating GaAs is

obtained by adding . chromium (Cr) atoms (deep acceptors) to GaAs .

The

first successful preparation of Cr doped high resistivity GaAs was made
by Cronin and Haisty.< 14 ) The high resistivity of the material is due

-106to the compensation of residual shallow donors and deep donors associated with oxygen impurities by deep Cr acceptors . (lS)

In this way

it is possible to make "semi - insulating" GaAs with resistivity in the
range of 10 8 ohm-em. This resistivity is sufficient to assure good
isolation between devices in an integrated circuit.

The semi-insula-

ting GaAs substrates used in our experiments were purchased from Laser
Diode Laboratory. The resistivity of the wafers is >10 ohm-em, and
the etched pit density is about 3000 cm- 2 . The wafers are about
400 ~m thick, and the surfaces are oriented in the [1 00] direction.

IV.2 GaAs-GaAlAs Heterostructure L ~ sers on Semi-Ins ul at ing Substrates
using Carrier Crowding
As a first step, ordinary GaAs-GaAlAs heterostructures are prepared by epitaxial growth. The layers are parallel to the surface of
the substrate and so is the PN junction .

If we want to maintain this

structure and use the semi - insulating substrate instead of the N type
substrate we have to face the problem of putting metal contacts on the
P type and the N type layers on the same side of the wafer.

One natural

way of solving this problem is to make a structure as the one shown i n
Fig. 4-1.

On the semi-insulating GaAs substrate there are five epita-

xially grown layers forming the double heterostructure.

On the left

hand side the upper four layers are selectively etched away so that
we can put the P type contact on the first layer .

The current injected

through the P type contact flows through the P GaAs layer into the mesa
region.

Due to the sheet resistance of the P GaAs and P GaAlAs layer,

SEMI-INSULATING

hll

GaAs

--+·-CLEAVED
SURFACE
FOR LASER )
( REFLECTION

Fig. 4-1 A schematic drawing of the crowding effect laser.

~~

GaAs (N)
GaAIAs (N)
GaAs
GaAI As (p)
GaAs (P)

0.....,

_.

-108-

the potential drop across the PN junction decreases with distance from
the edge of the mesa.

This causes the injected current to cros s the PN

junction in a narrow stripe adjacent to the edge of the mesa .

This

current crowding yields a narrow effective gain region near th e mesa
edge when the diode is operated with currents above the lasing threshold .
Consequently, in the transverse direction the lasing action takes place
in a small region just as in the case of stripe geometry lasers .

However.

for conventional stripe geometry lasers, two boundaries are needed to
define the lasing active region.
only one boundary is needed.

In the case of crowding effect lasers

The electrical confinement on the other

side is automatically provided by the current crowding effect.

IV.2.1

Crowding effect

The crowding effect, or edge crowding, is a term used in bipolar
transistors. (l 6 ) This phenomenon exists in any transistor to some
degree at high currents .

Because of the transverse IR drop res ultin g

from the base current flowing through the base res i stance, a non - un iform
emitter-base voltage distribution occurs.

The polarity of th e voltage

is such that the emitter-base junction voltage i s largest on the port ions
of the junction nearest the base terminal.

Consequently most of the

injection occurs in these outer portions of the emitter.

With increa-

sing current, the IR drop increases, the effect becomes more pronounced ,
and the active emitter region i s crowded closer and closer to the
external base contact.
The crowding effect which occurs in our lasers can be unders tood

-109-

via Fig. 4-2.

The structure is simplified to include only the impor-

tant layers.

The first two layers in the mesa region are assumed to

be very thin compared to the distance over which the current density
falls off and have a composite sheet resi stance R.

Total current I

injected from the contact flows through the first layer into the mesa
region.

At x > 0 the current divides into two parts. Part of it, i( x)

goes forward and part of it flows up across the PN junction with current
density jy(x).

Because of the sheet resistance of the first two layers

both i(x) and jy(x) decrease with x.

If l is the length of the laser,

the changes in the potential V of the first two layers, and the current
i(x) in a smail distance dx are
dV(x) = -i(x) ~ dx

(4-1)

di(x) = -jy{x)!dx

{4-2)

From these two equations we get the following .differential equations

and

d~~x) = -i(x) ~

(4-3)

dJx(x) = -jy ( Xi

(4-4)

Differentiating eq. (4-3) with x and substituting eq . (4-4) into it
we get
(4-5)

Since the contact covers the whole mesa, we assume that the potential

x= 0

•x

Fig. 4-2 Thi s figure shows that the total current I decomposes into two components
after it enters the mesa region (x>O) . i(x) is the component wh i ch flows
forward in the x direction while jy(x) is the current density which f l ows uoward
i n the y direction.

I_.

_,

_,

-111-

is uniform along x in the layers above the PN junction.

The junction

equation which determines the current density is then
j (x) = j (O) eqV/mkT

(4-6)

Where q is the electronic charge, k is the Boltzmann's constant, m is
a constant, and T is the absolute temperature.
V = 0 at x = 0.

Here we have taken

Substituting eq.(4-6) into eq.(4-5) we get the equation

for V(x)
(4-7)

The solution of this equation is
V(x) = mkT .tn

(~ .;n2

(4-8)

)1/2

(4-9)

xo

Where

= ( mkT

Rjy(O)q

- Substituting eq. (4-8) into eq. (4-3) we get
i(x) = 2mkTt
Rqxo 2- + 12
xo

(4-10)

The current density jy{x} is obtained by substituting eq. (4-8} into
eq. (4-6}

2j (0)
(x) =
(2- + 12 )2

xo

( 4-11}

-112Using the condition i(O) = I we obtain for the parameter x and the

current i(x)
X0

mkT . t
= 12qRI

i(x) =

(4-12)

12I
_25_ + 12
xo

(4-13)

From equations (4-11) and (4-13) one can see clearly that both jy(x)
and i(x) decrease with x and the rates of decrease depend on x0 •
smaller the x0 the faster are the rates of decrease.

The

jy(x) decays to

half of jy(O) at x = (2- 12)x0 and i(x) decays to half of I at x = 12 x0 .
The carrier distribution in the active region can be determined
by solving the diffusion equation

d n -n
- +G=O

dx2

(4-14)

-r

where

(4-15)

is the generation current provided by the injected current density jy{x) .
Here 0 is the effective diffusion constant, -r is the recombination
time and tis the thickness of the active layer.

Using eq. (4-11)

and defining the diffusion length L = D-r we can write eq . (4-14) as

=0
The general solution of this equation is

(4-16)

-113x
/1.
x fexp(- [)
n(x) = c1exp(--L--) + c2exp(- [) + 2 exp(--L--)
B+ x

dx

x fexp(+)
B + X dx

( 4-17)

+ 2 exp(- f)

where

(4-18)
( 4-19)

The two integrals on the right hand side of eq. (4-17) are exponential
integral functions defined by(l 7 )
oo
xk
E1.(x) = ~x x = y + .tn(x) + ,E---,--;."-:---

k=1 k·k!

= -y -

.t n( x ) -

oo (-l}k xk
>.
- k';'l k. k !

(4-20)

(4-21)

Therefore eq. (4-17) becomes
n(x) = c1exp(-[-) + c2exp(- [) - ~ exp(B~x) E 1 (B~x )
+ ~ exp(- B~x) Ei( B~x)

At x ~ oo the current injected into the active layer is zero.
number of carriers n(x) ~ 0.

(4-22)
The excess

At the boundary x = 0, because of the

air-semiconductor interface, there is surface recombination.

If we

take S to be the surface recombination velocity, the boundary condition
for n(x) at x = 0 is
qD ~~~ x=O = qSn(O)

(4-23)

-114-

Applying these two boundary conditions to eo. (4-22) we obtain the
constants c1 and c2 .

They are

c1 = o

(4-24)

A LD
( B)
( B ) SL-0 A
C2 = 2 exp -L- E1 -L- SL+D - 2 exp{- L)Ei (-L-) + B SL+D ( 4 - 25 )

o- We get f Or n ( X ) and C2

B d g = SL
Ta k1ng
a = [an

_ A a ( ) .9.::1.. A -a ( )
A 1
C2 - 2 e E1 a g+1 - 2 e Ei a + a g+1

( 4-27)

Using a as a parameter we can convert equations {4-11) and (4-13) into

(4-28)
i (x) = - - - .I - --

(4-29)

~1+1

La

2 mkT R.
qRI [

{4-30)

Plots of i(x) and jy{x) as functions of distance using a as a
parameter are shown in Fig. 4-3 and Fig. 4-4.

When a

is small, or the

product RI is large, both i(x) and jy{x) are very much crowded near the
edge of the mesa.

When a is large or RI is small the effect of crowding

is weak and currents spread out more, away from x = 0.

If we take

R = 60 ohm, I= 100 rnA and L = 5 ~m, a, from eq. (4-30), is equal to 1.

3.2

X/L

4.8

6.4

8.0

Fig. 4-3 Distribution of the current i(x) as a function of distance. Q is used as a parameter .

00

0'1

1.6

=qRI.L

-- 0.4

_,
_,

0.1

a=

v'2x 0 2mkT J,

....__...

"-

...........

0.6

0.8

1.0

0.6

3.2

X/L

4.8

a=

6.4

=qRI.L

./2x 0 2mkT ~

the junction, as a function of distance. a is used as a parameter.

Fig. 4-4 Distribution of the current density jy(x), which flows upward across

00

0.2

~>-o) \\ \

..........

>-

-Q

1.0

8.0

0'1

_,
_,

-117We can see from Fig. 4-3 that half of the total current flows across
the junction in a small area, within 5 ~m of the mesa edge.
The distributions of the carriers n(x) at different a's are
shown in F1g.4-5.

The effect of crowding on n(x) is similar to that

on i(x) and jy(x).

The smaller the a , or the larger the RI, the

stronger the crowding.

In Fig. 4-5 we have taken g = 10, which corresponds to a surface recombination velocity S = 1.5 x 10 6 em/sec.
Since the crowding effect in our structure depends on the value
RI, one can control this effect by changing the sheet resistance R.
This can be achieved by adjusting either the thickness or the doping
concentrations of the first two layers.

But larger R or stronger

crowding does not mean that the laser is better, because as more
carriers are crowded near the edge of the mesa the larger the effects
of surface recombination and light scattering due to the proximity
of the air interface.

IV.2.2

Device structure and fabrication
The fabrication procedure for a crowding effect laser i s shown

in Fig. 4-6.

On the semi-insulating substrate five layers of GaAs

and GaAlAs layers are grown by liquid phase epitaxy.

The layer

sequence and the parameters for each layer are shown in table 4-1.
The layers form a double heterostructure in the direction perpendicular
to the surface of the substrate.

After the growth the N type contact

Au-Ge is first evaporated over the whole surface of the wafer.
part of this layer is removed photolithographically.

The remaining

"z

l.D

r0

ro

l.D

~~

gL

0)

C\i

co

0.0

r0

l[)

1////

0~

~~ ~

l.{)

r0

~~

ro

.........

1.6

3.2

X/L

CD\ ®\@~ ~

g = 10

4.8

gRI

6.4

g = SL

_ Rxo 2mkT P.
Q=--=--·-

8.0

co

__.
__.

Fig. 4-5 Carrier distribution in the active region as a function of x, a is used as a parameter.

r0

co

l.D

0)

l[)

l.D

co

.q

ro

l[)

l.D
r0

co

.q

\\\ ~

~~ ~~ "'<.0T 1'-1-: / N/'\./\.

~~ ~~ ~~ ~~ ~~ ///A

~r

XI0- 1 XI0- 1 XI0- 2 XI0- 2

CD ® @

-119-

(b)

S.I. Substrate

LPE Growth

(c) .

td)
Au-Ge Evaporation

Etching

II I I

(f)

(e)

Cu Heat Sink
Au-Zn Evaporation

Mounting

Fig. 4-6 Fabrication steps for a crowding effect laser.

P GaAs
P GaAlAs
GaAs
(undoped)
N GaAlAs
N GaAs

1st

2nd

3rd

4th

5th

4-1

Sn

1018

5 X 1015

Sn

Ge

1017

0.4

1017

Ge

2 X 1018

0.4

Dopant

Al
Content

Parameters for each grown layer of a crowding effect laser

Table

0.3

( ~m )

Thickness

Material

Layer

Carrier
Concentration
(cm- 3)

__.

-121metal serves as the mask for the selective etching of the layers .
Etching results in a steplike structure with the edge parallel to [110]
direction .

The etching must be deep enough to reach the P type GaAs

layer since ohmic contact to P GaAlAs is poor.
are H2so 4 :H 202 : H20 (4:1 :1) and HF.

The etchants we used

The first solution etches the

layers down to the P GaAlAs region and the second solution removes
the remaining P GaAlAs selectively without attacking the P GaAs layer .
After the etching, a second evaporation i s performed , in which Au-Zn
is used for the P type contact.

During evaporation, the sample i s

tilted at an angle to the metal source so that the edge of the step
acts as a mask to the evaporation and the metal contacts on the first
layer and on top of the mesa are separated .
The contact alloying was carried -out in H2 atmosphere at 440°C
after the evaporation.
TO~m thic ~nd

diced intOilaser chips.

about 300 ~m long.
- Fig . 4-1 .

The sample was then thinned down to about
Each laser has a cavity

The cross section of the final s tructure is shown in

The laser chips were mounted on a copper heat sink with

two contact leads up. {see Fig . 4-7)

Since the size of the active regio n

is not determined by the area of the contact, one can cut a wide chip
and use a broad top contact for the purpose of smaller resistance
and ease of handling.

IV.2.3 Experimental results
Experimental measurements of the crowding effect lasers were
carried out under pulsed operation.

The current pulses which drove

effect lasers and the lateral injection lasers.

Fig. 4-7 Photograph of a copper heat sink used to mount the crowding

_,

-123the l aser diodes were 100 nsec wide with a repetition rate of 1KHz.
The threshold currents of the crowding effect lasers are
compar able to those of conventional stripe geometry lasers.
typi cal value for a 300 ~m long laser diode i s 150 rnA.

The

The differen-

ti al qu antum efficiency, defined as the ratio of the increase in the
phot on output rate to the increase in the carrier injection r ate, is
about 30%.

These lasers can be driven to very high current and deliver

high output power without breakdown.

Fig. 4-8 is an example of a

typi ca l l aser's light versus current curve .
of thi s laser i s 120 rnA.

The threshold current

The differential quantum efficiency i s 32%.

At 800 ml\ , \'lhid~ is almost seven times the threshold current , the laser
deli ve rs 130 mW output power from o.. e mirror .
The light distribution at the cavity mirror, i.e. the near
fi el d, can be viewed with a microscope equipped with an infrared
image co nve r ter.

Fig . 4-9 shows two photographs of the light distri-

buti on of a crowding effect laser at two different currents:

Fig. 4-9a,

at a cur r ent of 10 rnA, far below threshold, shows a light distribution
extending a long distance (~ 100 ~m) under the mesa; and Fig. 4-9b,
at a current above threshold, shows a much narrower light distribution.
Most of the laser light emanates from a region some 10 - 15 ~m wide
near the edge of the mesa.

These two pictures provide a direct evidence

for the crowding effect.
More detailed measurements of the near fields were made by
scanning the cavity mirror with a rotating mirror. (The set-up will
be described in chapter ~)

Using this method we were able to record

-124 -

140

CEL 4.4
120

-100

3:

__..

>-

t-

(f)

80

t-

t-

60

<..9
_j

40

20

200

400

600

800

CURRENT (mA)
Fig. 4-8

Light intensity vs. driving current curve of a crowding
effect laser . The threshold current is 120 rnA.

-125-

Fig. 4-9

The photographs of the near field radiation patterns
of a crowding effect laser.

(a), with a current of 10 rnA,

way below threshold, shows a light distribution extending
a long distance ( ~100 ~m) under the mesa .

(b), with

a current 250 rnA, which above threshold (240 rnA) shows
much narrower light distribution . Most of the laser li ght
is due to a narrow region near the edge of the mesa.

-126-

(a)

(b)

-127the light distributions on an X-Y recorder and obtain much better
resolution.

Fig. 4-10 and Fig. 4-11 show the measured near fields

of a crowding effect laser at two different current levels.

The

angular distributions of the emitted laser light in the junction
plane, i.e. the far fields, are shown along with the near fields.

In

Fig. 4-10, at a lower current, the near field indicates that there
is only one transverse mode .
points is about 5 ~m.

The distance between the half power

In Fig.4-ll, at a higher current, the width

of the light profile becomes wider and more modes begin to develop.
The modes of the crowding effect lasers are guided along the
cavity with a mechanism different from those of regular dielectric
waveguides .

The transverse confinement of the laser modes is not

due to the refractive index change but,rather, to the monotonic
decrease of the gain as a function of distance from the mesa edge.
This decrease of gain is due to the carrier crowding effect which
we discussed before.

The gain-induced guiding also influences the

lasers• far field radiation patterns.

As shown in Fig. 4-10 and Fig.

4-11, the far field patterns are not symmetric with respect to 0°,
which is normal to the laser mirror, but instead display peaks at
about 10° toward the mesa side.

This gain-induced guiding phenomenon

has been analyzed, and will be discussed in detail in section IV.4.
The spectrum of a typical crowding effect laser is shown in
Fig. 4-12.

The laser light is polarized with the electric field

parallel to the junction plane .

This polarization is similar to that

of a regular heterostructure laser.

a::

UJ

1-

UJ

..J

(!)

1::t

UJ

DISTANCE

-+t 5, 1+-

I= 220 mA

CEL4.3

FAR
FIELD

Fig. 4-10 The recorder traces of the near field and the far field of a crowding effect laser
at a current of 220 rnA. The threshold current of this laser is 180 rnA. The right
hand side of each curve is the mesa side.

.... ,

( /)

1-

NEAR FIELD

co

--'

DISTANCE

-+1

5 J.l 1+-

I= 300 rnA

CEL 4.3

10
20 30
ANGLE (DEGREE)

FAR
FIELD

Fig. 4- 11 The near fi eld and far field of the same laser as in Fig. 4-10 when the current is
increased to 300 rnA.

UJ
0:

..J

t-

->

Ul

..J

"-

I:

I-

UJ
1-

( /)

1-

NEAR FIELD

1.0

.......

0::

_j

r<(

_j

<.9

r-

1--

(/)

I-

)-

8670

WAVELENGTH (A)

8650

8630

Fig. 4-12 The spectrum of a crowding effect laser.

8690

I=210mA
Ith=200mA

CEL 5.1

8610

......

-131-

Since the crowding effect depends on the sheet resistance of
the first two layers, it is possible to control the width of the
injection region ( the active region) by varying the thickness and the
doping concentration of these layers. We have used a carrier concen3
tration of~ 2xlo18cm- in the first layer with a thickness ~ 3 ~m.
The second P GaAlAs layer is more lightly doped.

The crowding effect

in this case is thus controlled by the first layer.

The crowding

effect lasers can also be made with N type layers under the P type
layers, but the doping concentration of the first two layers have to
be much lower in order to get proper crowding effect, because in GaAs
the electron motility is about an order o~ magnitude higher than the
hole mobility.

IV.3 GaAs-GaAlAs Heterostructure Lasers on Semi-Insulating Substrates
using Lateral Injection
The structure of the crowding effect laser is similar to the
conventional double heterostructure lasers, in that the PN junction
is parallel to the epilayers.

The current crowding effect provides

the lateral confinement of the carriers near the edge of the mesa.
However, at the air-semiconductor boundary the carriers in the active
region undergo a nonradiative surface recombination loss which increases the threshold.

The lasing characteristics also suffer from scat-

tering loss due to the etched surface.

Owing to these reasons it

1s difficult to achieve very low threshold crowding effect lasers.
The lateral injection laser, which is described in this section, was

-132conceived with the aim of solving these problems .
The structure of the lateral injection laser, shown in Fig.4-13b,
consists of three double-heterostructure epilayers on a semi-insulating
substrate.

The layers are doped with N type dopants, while the P type

region is obtained by Zn diffusion.

The current flows laterally across

the junction from the P type contact to the N type contact.

Since

GaAlAs has a wider bandgap than that of GaAs, carriers are injected
predominantly across the GaAs PN junction.

The effective area of the

current injection is therefore determined by the thickness of the
GaAs layer.

Since very thin GaAs layers can be easily obtained by

liquid phase epitaxy (LPE), very low threshold lasers can be achieved.
The technique of transverse injection was first used by Namizaki
et al.(lB, 19 ) to make transverse-junction-stripe (TJS) lasers on N+
GaAs substrates.

However, their structure suffered from current

leakage across the (diffused) P GaAlAs-N GaAlAs junction which made
for a rapid increase of the threshold current at higher temperatures.
_ Recently Susaki et al . developed a new TJS structure to eliminate
this current leakage problem. ( 20) However, it requires five epitaxial
layers.

In our structure only three layers are needed and the current

leakage is eliminated because the substrate is semi-insulating.
As shown in Fig. 4-13b, the PN junction in the three different
layers have different junction areas.

In the first GaAlAs layer the

junction lies within the layer and hence has a very large area.
However, owing to the crowding effect, the current which flows into
this layer can not proceed very far to the right.

As a result, most

-133-

GaAIAs (N)
GaAs(N)-.~==========~~~~~~~

GaAIAs (N)

SEMI-INSULATING GaAs

(a)
Fig. 4-13 (a) The cross section of a lateral injection laser after
Zn diffusion. Right hand side of the top layer i s
etched away. The remaining part (on the left) serves as
the diffusion mask.

Au-Ge
GaAIAs (N)
GaAIAs (N)

SEMI-INSULATING GaAs

(b)
Fig. 4-13 (b) The cross section of the final structure of a lateral
injection laser.

-134-

of the current flows across the junction in a small area at the left
corner of the junction .

If we take the first GaAlAs layer and the top

GaAlAs layer to be one layer with effective junction area A , the ratio
of the currents flowing through the GaAs and GaAlAs junction can be
roughly estimated with a method similar to that used to calculate
the leakage current in 11.3.

The current which flows through the

GaAlAs junction, according to the junction equation, is
(4-31)

where J 01 is the saturation current density, m is a constant, and v1
is the voltage across the junction.

Similarly, the current flowing

through the GaAs junction is
(4-32)

where A2 is the junction area, and J 02 and v2 are defined in the same
way as those for the GaAlAs junction.

The ratio of 1 1 and 1 2 is
{4- 33)

The saturation current densities J 01 and J 02 depend on the bandgaps
of GaAlAs and GaAs, respectively.

The ratio is approximately given

by{8)
(4-34)

-135Substituting eq. (4-34) into eq. (4-33), we get

(4-35)

Since the layers are very thin and adjacent to each other, the difference
between v1 and v2 is very small.

If we take 6E g = 0.5 eV (which

corresponds to x ~ 0.4 in the Ga 1_xAlxAs confining layers) and neglect
Vl-V2' eq. (4-35) becomes
I1

Al

= A exp(-20)

For a typical lateral injection laser A1!A 2 ~ 10.

(4-36)

The ratio of the

currents is then
Il
I2

-=

10 exp(- 20)

( 4-37)

Thus, nearly all the current passes through the GaAs junction and no
current leaks through the GaAlAs junction.

IV.3.1

Zn diffusion in Ga 1_xAlxAs
Zn diffusion is a very common method for obtaining P type

regions in the Ga 1_xAlxAs system.

Zn has a high diffusion rate in
GaAlAs and produces sharp diffusion fronts. ( 2l) In our lateral injection
lasers the P type region is obtained by selective Zn diffusion into
the epilayers.

In the experiments we found that the diffusion rates

-136in Ga1 _xAlxAs depend strongly on the Al content x. ( 22 ) The diffusion
rates in the Al containing layers are much larger than in the GaAs
region (the difference increasing with x).

Taking advantage of this

difference, we used the GaAs layer as a diffusion mask in fabricatin g
our lasers. (see Fig. 4-13a)
The GaAs mask has many advantages over the conventional)y used
masks.

In an ordinary mask such as Si0 2 (doped with P) or Si 3N4 ,there

always exists an interfacial stress between the mask and the unde r l ying
crystal because of the nature of the deposition process and the different
thermal expansion rates in Ga 1_xAlxAs and the mask .

This stress con-

tributes to pro blems such as crystal surface damage, unstable masks at
high temperatures, and lateral d1ffusion under the masks. ( 23 ) In
the GaAs mask, due to the near perfect lattice match to GaAlAs, these
problems are largely alleviated.

Futhermore, the GaAs mask is grown

during the same sequence with the other epilayers so that no additional
step of mask deposition is needed .
For determining the diffusion rates in Ga 1-XAl XAs regions with
differing x we have measured the diffusion depth as a function of the
Al content.
epilayer.

We first prepared seven samples each containing a Ga 1_xAl xAs
The Al content x ranges from 0 to 0.71.

has a thickness of about 12 ~m .

Each epilayer

The samples were subsequently sealed

in an evacuated quartz ampoule containing ZnAs 2 as the diffusion
source.

The diffusions were carried out under several conditions

with varying temperatures and durations.

After the diffusion the

samples were cleaved and stained with HF:HN0 3 :H 2o (1:3 :4) to reveal

-137-

the diffusion fronts.

The diffusion depths were measured with a

scanning electron microscope.

Fig. 4-14 shows the diffusion depth

as a function of Al content x in Ga 1-X Al XAs layer for three diffusion
conditions:

670°C, 70 min; 701°C, 55 min; and 639°C, 150 min.

All

three groups of data show that the diffusion depth increases with
Al content when x is less than about 0.5.

The depths at x = 0.47

are about three times the depths in GaAs (x = 0).

When x is higher

(x = 0.62, 0.71) the diffusion fronts become nonuniform and the data
indicate a "slowing down", if not a reversal, in the rate of increase.
The error bars in Fig. 4-14 indicate the variations of the diffusion
depths.
It is well known that Zn diffusion in GaAs is based on the
mechanism of interstitial-substitutional equilibrium in which the
interstitial Zn atoms react with neutral Ga vacanci es to form
substitutional acceptors and holes. ( 24 ) The diffusion constant of
the interstitial mode is much greater than that of the substitutional
mode.

Based on this mechanism, we can explain our experimental

result as follows:

The use of ZnAs 2 as the diffusion source results

in a high As pressure which induces Ga vacancies in GaAs. As the
concentration of the Ga vacancies increases, the Zn atoms are shifted
to the substitutional sites and the fast interstitial diffusion is
suppressed. ( 25 > However, the sitution is different in Ga 1_xAlxAs.
The melting temperature of Ga 1 -XAl X As increases with Al content x, so
it is natural to expect a higher binding energy and therefore less

-138-

670°C
640°C
694°C

70 min
150min
55 min

..--

-:r:

:::i_

.....

Cl..

(/)

:::::>
LL
LL

A~

0.1

0.2

0.3

0.4

0.5

0.6

0. 7

0.8

At CONTENT (X) IN Go 1- x Alx As
Fig. 4-14

Zn diffusion depth as a function of A1 content in Ga 1_xA1xAs .

-139-

lattice vacancies as x increases for a given As pressure.

As the

number of Ga vacancies becomes smaller, the fast interstitial diffusion
becomes more favorable and results in a larger diffusion depth.
This explanation seems to be satisfactory, at least when x < 0.5.
When the Al content is higher (x = 0.62, 0.71) the diffusion fronts
are not uniform.

This might be due to irregular interstitial dif-

fusion,(26) or more likely, to other reasons yet to be understood.

IV.3.2

Device structure and fabrication
The fabrication procedure of the lateral injection laser

is shown in Fig. 4-15.

Four layers are first grown by liquid phase

epitaxy on a semi-insulating substrate.

They are, starting from the

bottom, Ga 1 -X Al XAs, GaAs, Ga 1-y Al YAs, and GaAs (x ~ 0.5, y ~ 0.4)
with thicknesses 4, 0.3,2, and 2.5 ~m. respectively.

The first

three layers are N type and form a double heterostucture in the direction
perpendicular to the plane of the epilayers .

The last GaAs layer is

used as the diffusion mask.
After growth, a straight line parallel to [110] direction
was defined using photolithographic methods.

The GaAs layer on one

side of the line was then etched away using the standard etching
solution H2so 4 :H 2o2 :H 20 {1:8:1).

The Zn diffusion was performed

using ZnAs 2 as the diffusion source in an evacuated quartz ampoule
(~ 10- 6 torr at room temperature) at 660°C for one hour. The cross

-140I

(b)

(a)

Etching

LPE Growth

I·-

------

',

r----- -------'

(d)

(c)

Mask Removal

Z n Diffusion

--------""'

(e)

(f)

--------- "'

Cu Heat Sink

Metal I ization
Fig. 4-15

Mounting

Fabrication steps for a lateral injection laser .

-141section of the layers after diffusion is shown in Fig. 4-13a.

Owing

to the different Zn diffusion rates in GaAs and GaAlAs, the diffusion
depth is much deeper in the unmasked region than in the GaAs mask.
Following diffusi on, the GaAs mask was etched away select ively usi ng
the solution H2o2 + NH 40H at pH= 7.05. ( 27 ) The etchant removed
GaAs only and stopped at the GaAlAs surface. Heat treatment was
subsequently performed at 860°C for 1.5 hours in an H2 atmosphere.
Following that, metal contact of Au-Zn on the P side and Au-Ge on
theN side were applied separately.

The laser chip was moun ted

on a Cu heat sink with the two contact leads pointing up.

The final

structure is schematically shown in Fig. 4-13o.
In conventional stripe geometry lasers, two lines are
required to define the active region.

In our l ateral

injecti p~

lasers only one line is necessary because the active regi on is
automatically defined by the carrier diffusion length.

Therefore

it requires no structural fineness in the lateral direction , which
leads to easy fabrication and excellent reproducibility.
Fig. 4-16a is a scanning electron microgra ph of the cross
section of the layers.

Two diffusion fronts can he seen , which are

due to the two-step diffusion.

The sha llower one is from the first

step diffusion, the deeper one is from the heat treatment.

The

enlarged portion of the PN junction near the GaAs r egion i s shown
1n Fig. 4-16b.

It s hows very clearly that the s lope of the diffusion

-142Fig. 4-16 (a) The SEM micrograph of the cross section of a lateral
injection laser. The right hand side is the Zn diffused
region. The left hand side was masked by a GaAs layer
during the diffusion.
(b) The magnified picture of the diffusion front at the
boundaries of the three epilayers. The shape of the
diffusion front indicates different diffusion rates
in different layers.

-143-

Ga _ AI .4 As(N)0 6 0
GaAs(N)--

Zn DIFFUSED
REGION

(a)

Ga _ Al .4 As(N) ._.
0 6

Zn DIFFUSED
REGION

GaAs(N) --

(b)

-144front changes at the GaAs and the GaAlAs boundaries.
that Zn diffuses faster in GaAlAs than in GaAs.

This indicates

As shown in the

micrograph the diffusion front in the GaAs region is not perpendicular
but tilted at an angle to the plane of the epilayers.

The width

of the PN junction in this region is wider than the thickness of
the GaAs layer.

Because of this, the laser is not a pure homostructure

laser as described in references 18,19 and 20, but a combination
of homostructure and heterostructure.

IV.3.3

Experimental results
After fabrication the sample was thinned down to a thickness

of about 100 ~m and diced into individual laser bars.
had a cavity length of about 300 ~m.

Each laser

The lasers were mounted on Cu

heat sinks similar to the one shown in Fig. 4-7.

The measurements

were carried out with the diodes driven by square current pulses
having 100 nsec widths and a 1 KHz repetition rate.
The properties of lasers having different doping concentrations
in the GaAs active layer were studied.

We found that this concen-

tration strongly affects the lasing characteristics.

Fig. 4-17 shows

the near field and the far field of a laser when the doping concentration is low (~ 1017 cm- 3 , Sn doped). The near field has a half
width (distance between the half power points) of about 5 ~m .
has a small tail penetrating into the N side.

It

As the current

increases (> 1.5 Ith) more modes appear on the N side.

The far

field distribution is similar to that of crowding effect lasers.

>-

0::

_j

I-

-_j

<..9

II

(a)

DISTANCE

0::

_j

I-

~I

II

60

45

FAR FIELD

I \

( b)

(DEGREE)

15

Sn - I

Fig. 4-17 (a) The near field, and (b) the far field of a lateral injection laser with
a lightly doped (~lxlo 17 cm- 3 , Sn doped) GaAs layer. The left hand side of each
picture is the N side while the right hand side is the P side.

2J.Lm

I-

I-

>r-

1 \

I =1,5 I th

Sn - I

(f)

(f)

I-

NEAR FI ELD

15

30

<.1'1

I~

-146-

The light is emitted at an angle with respect to the normal direction
to theN side.

The maximum intensity appears at about 30°.

This

phenomenon can be explained by gain induced guiding and will be
discussed in the next section.

When the N type doping concentration
of the GaAs layer is increased above 1018 cm- 3 the near field
becomes narrower and the peak of the far field moves to the center.
Fig. 4-18, for example, shows the near field and the far field of
a laser with a highly doped GaAs layer(~ 7 x 1018 cm- 3 , Te doped).
The near field is very narrow with a half width of less than 2 ~m.
It corresponds to a single transverse mode and stays stable as the
current increases.

In most of the diodes the near field patterns

remain unchanged as the driving current increases up to the point
of catastrophic breakdown.

The tail in the near field which appears

on the N si de at low doping concentration is absent.

The far field

pattern which is symmetric and centered at 0° resembles the usual
far field of conventional stripe geometry lasers.
The difference in the mode characteristics between la sers having
low doping concentration in the N GaAs region and lase r s having high
doping concentration is due to a difference in wave guiding mechanism.
When the doping concentration of the N side of the GaAs junction is much
lower than that of the P side(~ 1019 cm- 3 , Zn doped), most of the
recombination is due to hole injection.

The laser light generated in

a::

_j

<(

I-

_j

<.9

I-

I-

2J.Lm

r-

15

15

Te- 8

Fig. 4-18 (a) The near field, and (b) The far field of a lateral injection laser
with a heavily doped GaAs layer (~7xlol 8 cm- 3, Te doped)

(b)

30

I \

(a)

45

FAR FIELD

ANGLE (DEGREE)

DISTANCE

a::

_j

<(

I-

-_j

<.9

I-

z-

I-

(f)

(f)

I-

I =1.55 I 1h

Te- 8

I-

NEAR FIELD

'-l

.....

-148the active region is guided along the junction by the mechanism of
gain-loss guiding.

The gain-loss profile in theN side decays with

distance away from the junction.

As will be shown in the next section,

the laser modes guided in such a medium have wavefronts tilted at an
angle to the surface of the cavity mirror.
the wavefronts point toward the N side.

The normal directions of

Consequently, as the laser

light exits from the mirror surface, it propagates toward the N side.
When the doping concentration is increased above 1018 cm- 3 the increased electron injection to the P side causes the gain-loss profile
to become symmetric about the junction plane.

Furthermore, at the

junction region, because of compensation, the effective doping concentration is lower and therefore the index of refraction is higher
than those of the regions away from the junction.( 28 ) The laser modes
are guided along the junction by a combination of gain-loss guiding
and real refractive index guiding.

This results in symmetric far field

patterns centered at 0°.
The N type dopant we used for the GaAs layer was Sn for low doping
and Te for high doping.

The lasers with the lowest threshold currents
have doping concentrations of about 4 x 1018 cm- 3 (Sn doped). The lasing

threshold of a 300 ~m long diode is about 40 rnA.

Fig. 4-19 shows the

measured light intensity curve as a function of the driving current.
The threshold current is 36 rnA.

The curve shows no kinks, or undesired

nonlinearity, as the current is increased up to two times the threshold
value.

The differential quantum efficiency is about 35%.

The near

field and the far field are similar to those shown in Fig. 4-18.

-149-

._r(f)

...._

...._
<(
_j

0:::

10

20

30

40

CURRENT
Fig. 4-19

50

60

70

80

(rnA)

The light output versus driving current curve of a lateral
injection laser. The threshold is 36 rnA.

-150-

The spectrum of the emitted light also varies as theN type doping
concentration in the GaAs layer is changed.

At low doping concentrations

the spectrum shows the existence of a number of longitudinal modes.
When the concentration is higher than about 5 x 1018 cm- 3 (obtained by
Te doping) a single longitudinal mode is observed.

Fig. 4-20, for

example, is the spectrum of one of these lasers.

The oscillation wave-

length is longer than that of one with lower doping concentration, which
might be due to band tailing at high

concentrations .

IV.4 Gain Induced Guiding
In this section we will develop the theory for explaining the
nature of optical modes in a region with a gain profile .

It is well

known that confined Gaussian beams can be supported by a medium with
a quadratic gain profile. ( 29 ) Unlike the case of refractive index
guiding, the wavefronts of such modes are concave, as obse rved in
the direction of wave proppgation. ( 30) Gain induced gui ding phenomenon
has

been found to be operative in several stripe geometry lasers. ( 3l)

The transverse laser modes are determined by the gain-loss profile in
the active region.

All the gain guided modes studied, however, involve

only symmetric gain profiles.

The observed near field and far field

in such cases are not very different from those of the regular index
guided modes.

In the cases of crowding effect lasers and lateral

injection lasers, described earlier in this chapter, the far field
distributions are very different from those of regular lasers.

The

angular distributions of the light output of these lasers are asymmetric
with respect to the normal direction of the cavity mirror (see Fig. 4-10

- 151 -

I = 1.15 I th

._>(f)

._

9060

9070

9080

WAVELENGTH

(,8d

Fig. 4-20 The single mode spectrum of a lateral injection laser.

-152and Fig . 4-17).

This feature can be explained in terms of gain-induced
guiding but with an asymmetric gain-loss profile.< 32 )
For the convenience of illustration we redraw the crowding effect

laser and the lateral injection laser in Fig. 4-21.

In the crowding

effect lasers the gain in the active region is bighest near the edge
of the step and decreases with distance away from the edge due to the
injected carrier crowding near the step edge.

In the case of lateral

injection lasers, when the doping concentration of the N GaAs region
is much lower than the Zn diffused P GaAs region, most of the recombination is due to hole injection.

The injected carrier (hole) concen-

tration and the gain profile, when ,asing, decay exponentially with
distance away from the junction into the N region.
In solving the wave equation in these two structures we assume
the complex dielectric constant in the guiding region at x > 0 to be
E(x) = Er + i(Ae-x/d - B)

(4-38)

where £r is the real part of the dielectric constant.

It is taken to

be constant since for x > 0 the medium is homogeneous.

The imaginary

part of eq. (4-38) corresponds to the gain or the loss in the medium.
The gain is assumed to be an exponentially decaying function with d
as the characteristic length.

The constant B accounts for the loss in

the medium.

Taking the electric field as E(x)ei(Bz-wt) we can write
the wave equation v2E + (w 2 /c 2 )~£ (r) = 0 as
d2E +f w2 [£ + i(Ae-x/d- B)]- 82\E = 0
dl c 2 r

(4-39)

-153-

Au-Ge

E====3~GaAs (N)

Au-Zn

1 - - - - - - - - r - GoAl As (N)
Go As
GoAl As( P)
Go As( P)
SEMI-INSULATING GaAs

(a)
-~•~

t-l

X=O

X>O
Au-Ge
~-GaAIAs(N)

~~~~~~~~~============~-GaAs(N)

,.._-GaAIAs( N)

~-----------------~

SEMI-INSULATING GaAs

(b)
Fig. 4-21

The schematic drawings of the cross sections of (a) a
crowding effect laser, and (b) a lateral injection laser .

-154where S is the propagation constant in the z direction (normal to the
plane of the figure), w is the angular frequency and cis the speed
of light in vacuum.

The dependence of the field on y (the direction

perpendicular to the epilayers) can be treated independently using
regular refractive index guiding and will not be considered here.
a guided wave E(x) must be zero as x goes to infinity.

For

We also take

E(O) = 0 since there is a large refractive index difference between
GaAs and air in the case of crowding effect lasers and a strong absorption in the heavily doped P type GaAs region in the case of lateral
injection lasers .

The boundary conditions for a guided wave are thus

E = 0 at x = 0 and x + oo

(4-40)

Substituting

into eq. (4-39) we can convert eq. (4-39) into a Bessel equation

(4-42)
The solution of this equation is
E = DJ._}t)

where D is an arbitrary constant and

(4-44)

-155-

The other independent solution Yv(~) (Bessel function of the second
kind) is not allowed since the solution needs to be bounded at ~ = 0
(i.e .• x + ~).

The eigenvalues v are determined by the boundary con-

dition at x = o. i.e .•
(4-45)

Here we have used the relation ~ = 2 ~ , where A is the wavelength in
free space.

Since Jv(~) is a complex function of x we can write it

as
(4-46)

where the index k indicates the mode number, rk(x) is the amplitude
and ek(x) is the phase term.

The electric field of the kth mode is

then
( 4-47)

(4-48)

or

where ek,r , Bk,i are the real part and the imaginary part of Bk
respectively.

The wavefronts of the modes are now described b.v
(4-49)

Because of e(x), the wavefronts of the modes are x dependent and no
longer planar and perpendicular to the z direction.

The eigenvalues

-156-

of a are obtained from eq. (4-44)

2] l/2

\) 2

a = _k_ + (e:

[ 4d2

- i B)__!!?_._

(4-50)

c2

Since e:r is dominant on the right hand side, ek can be expanded by
taking the first two terms of the Taylor series

(4-51)

where vk 'r and vk , ,. are the real part and the imaginary part of vk .
Using the relations IE= n and

~C =a, we get
(4-52)

where n is the refractive index of the medium and a is the loss coefficient in the medium.

The imaginary part of ak is the net gain (or

loss) of the kth mode, which is

= vk,r vk,i C - a

(4-53)

4d n w

The net gain is now separated into two parts.

The first term is the

gain coefficient and the second term is the loss coefficient.
gk is positive the mode possesses net gain.

When

When it is negative

the mode is lossy.
As shown in eq. (4-46) the profile of the kth mode at a constant
phase plane is described by rk(x).

Fig. 4-22 is the numerical plot

LL

_j

T\

II\ I\

T\

DISTANCE (X/d)

Fig. 4-22 Plots of the three modes calculated for a waveguide with 4n~: lO+lOi.
The amplitudes of all the modes are normalized to 1.

00

0.333

0.667

1.01

10

_,

0'1
'-.I

-158of the modes \'/hen 4n ~ lfA = 10 + 1 Oi .

The zeros of J) 10 + 1Oi)

were solved numerically and lie at values of 5.71+8.83i, 2.57+7.93i
and 0.034+7.17i.

There are thus three modes,

An interesting

feature of the mode profiles is that there are no zero crossings
for the higher order modes.

This is different from the situation

in which the modes are guided by a real refractive index where the
reflective boundaries produce standing waves in the waveguide and thus
always give rise to zero crossings for the higher order modes.

The

wavefronts of these modes shown in Fig. 4-22 are determined by
eq. {4-49) and are plotted in Fig. 4-23.
as the guiding medium.

Here we have taken GaAs

The wavelength A is taken to be 0.88 ~m

and index of refraction 3.6.

As shown in the plot, the wavefronts

are not perpendicular to the z axis.

The normal direction of these

wavefronts point toward x > 0 (lossy side).

Therefore, as the modes

are emitted from the laser cavity they propagate toward the x > 0
side.

This satisfactorily explains why we observe the asymmetric

far field distributions with peaks

off to one side in our lasers.

For the particular case 4n ~ lfA ~ . lO+lOi,
if we take d = 6A and A= 2.714 x 10- 3 the angles between the normals
(see Fig. 4-10 and Fig. 4-17)

of the wavefronts and the z axis are about 6.5°.

The gain of each

mode can be readily calculated from eq. (4-53).

If we take the loss

constant a in the medium to be 125 cm-l, the mode gains in our example
are 50.87 cm-l, -54.026 cm-l and -124.063 cm- 1 for the oth, 1st and
2nd order mode respectively.

Only the oth order mode has net gain.

The other two modes are lossy.

This result is understandable since

._...

::i.

DISTANCE ( X/d)

Fig. 4-23 Plots of the wavefronts of the three modes shown in Fig. 4-22.

0.361

E o.542

0.722

0.903 ~~---r-------r-----r---------,------,--------.

c.n

1.0

......

-160-

the oth order mode concentrates the intensity near x = 0 and consequently experiences the highest gain.

IV.S Monolithic Integration of Injection Lasers with Electronic Devices
As mentioned in the introduction to this chapter the difficulty
of integrating injection lasers with electronic devices on a single
chip of GaAs is due to the fact that all GaAs lasers reported today
have been fabricated on N+ GaAs substrates.

Because of the highly

conductive substrates, electrical isolation, which is necessary for
integration, is difficult to achieve.

The idea of fabricating GaAs

lasers on semi-insulating substrates was conceived with the aim of
solving this problem.

Using the non-conductive substrate we can perform

the electrical integration on epilayers without worrying about the
current leakage through the substrate and the parasitic interactions
between the devices and the substrate.

Furthermore, we can take

advantage of the already developed GaAs planar technology to perform
the integration.
In this section several examples of integration are discussed.
The integration of a crowding effect laser and a Gunn oscillator,
which we have demonstrated,(l 3 ) is discussed in IV.S.l. The
possible integration of lasers with metal-semiconductor field-effect
transistors (MESFET) is discussed in IV . 5.2.

-161IV.5.1

Integration of a crowding effect laser with a Gunn oscillator
on a semi-insulating substrate
GaAs injection lasers are of great interest as transmitters for

high bit-rate fiber optical communication systems.

One of the most

attractive features of GaAs laser is the capability of high speed
modulation into the GHz range. ( 33 ) A number of modulation schemes
have been proposed and investigated.
the lasers with external circuits.

However, all the schemes modulate
Because of high speed operation,

special care has to be taken in wiring, connections, packing etc. to
eliminate undesired

parasitic capacitances and inductances.

Monolithic

integration, wh:ch does not suffer from these problems, is therefore
much more attractive.

However, monolithic integration was difficult

and not seriously attempted till our success with the fabrication of
lasers on semi-insulating substrates.
The first realization of this kind of integration was obtained
by fabricating a crowding effect laser and a Gunn oscillator on a piece
of semi-insulating substrate.

The cross section of the structure is

schematically shown in Fig. 4-24.

The laser and the Gunn device are

integrated in series, so that the high frequency oscillating current
pulses from the Gunn device pass through the laser and modulate the
light output.

The advantage of using a Gunn device lies in the fact

that it can supply fast current pulses of constant waveforms without
any shaping, and it can be easily fabricated.
The structure of the crowding effect laser used for this integrated
device is similar to the one described in section IV.2 except that the

GUNN DEVICE

Fig. 4-24 The schematic drawing of the integrated Gunn-Laser
device. The electrode on the left side of the Gunn
device was not used. The vo ltage was applied between
the electrode to the right and the P type contact
on top of the mesa.

SEMI-INSULATING GaAs

GaAs-. GaAIAs(N)
GaAs(N).-._ _ _ _ _ _ _ _ _ _ _ _ _ _ __

GaAs{P)_. GaAIAs(P

.......

-163-

N type layers lie below the P type layers.

The reason for doing this

is that only N type GaAs displays the Gunn effect. (B)
Gunn oscillation was first discovered by Gunn in 1963. ( 34 )
He found that when the applied electric field across a short N type
sample of

GaAs or InP exceeded a critical threshold value of several

thousand volts per centimeter, coherent microwave output was generated.
The frequency of oscillation was approximately equal to the reciprocal
of the carrier transit time across the length of the sample.

Later,

Kromer pointed out that this oscillation was due to a differential
negative resistance in the material. ( 3S) The mechanism responsible
for the differer.tial negative resistance i s a field-induced transfer
of conduction-band electrons from a low-energy, high mobility valley
to a higher energy, low-mobility valley.

When this negative resistance

appears (at certain high fields) current oscillation occurs.

Of the

semiconductor materials displaying Gunn effect, N type GaAs i s the
most widely understood and used .
The fabrication procedure of our integrated "laser-Gunn" device
is the same as that described in IV . 2.2.

After theN type contact

(Au-Ge) was evaporated,a stripe 140 ~m was opened in the metal using
photolithographic methods .

The N GaAs layer under the window serves

as the drift region of the Gunn oscillator.

The cross section of

the final structure is shown in Fig. 4-24.
If the voltage across the two electrodes of the Gunn device
is higher than some critical value,Gunn oscillation occurs.

The

-164oscillating current pulses flow through the PN junction in the mesa
region and modulate the light .

If the range of the current oscillation

is higher than the lasing threshold current, the laser light will be
modulated.

If the threshold current of the laser lies in the range

of the current oscillation the laser will be turned on and off repetitively at the oscillation frequency.

The frequency of oscillation depends

on the distance between the electrodes of the Gunn device and is higher
when the distance is smaller.
The sheet resistance of the N type GaAs layer is an important
parameter for this device because it determines the threshold of the
Gunn oscillatio~ and the effect of current. crowding in the laser.
We have chosen a doping concentratiun ~ 1016cm- 3 for this layer and
a thickness~ 3~m.

For a 300 ~m long device the typical threshold

current for Gunn oscillation is about 200 rnA and the lasing threshold
is about 160 rnA.
We have operated this integrated Gunn diode-laser as a two
terminal device.

The voltage was applied across the P type contact

on top of the mesa and the cathode of the Gunn device.

The laser

{which serves as one of the Gunn oscillator's electrodes) and the
Gunn device are thus integrated crystallographically since they use
the same epitaxial layer for the series connection.
Fig. 4-25 shows a typical oscillogram of the current pulse and
the light pulse.
pulse.

Trace 1 is the light pulse and trace 2 is the current

Oscillation can be seen on top of both pulses.

In this case even

the minima of the current exceed the lasing threshold current (~ 170 rnA)

Fi g. 4-25 The oscillogram of the current and the light output of an i ntegrated
Gunn-Laser device. (1) is the light pulse, and (2) i s the current Pulse.
The expanded traces of (1) and (2) are shown by (3) and (4) respecti vely .
The ti me scale is 100 nsec/div for (l) and (2) and 2 nsec/di v for (3) and (4) .

(}1

0'1

.......

-166and the laser is not turned off.

Because of the nonlinear light

current characteristics of lasers, the modulation dep t h of the laser
output(~

70%) is much larger than that of the current(~ 15%) .

Traces 3 and 4 are expanded traces of the light and the current,
respectively.

The frequency of oscillaion is about 0.75 GHz.

1 GHz modulation has been achieved with a smaller separation between
the Gunn electrodes .
For three-terminal operation it is possible to add a Schottky

gate on the Gunn device and use the gate to trigger the Gunn os cillation.
In thi s way a single short laser pulse can be achieved.

IV.5 . 2 Integration of injection lasers with MESFET' s
In the past few years, the GaAs metal-semiconductor field-effect
transistor (FET) has become the most attractive high s peed microwave
transistor.

This is due to its capability of high gain, low noise

and high speed performance . (lO)

GaAs MESFET's are usually fabricated

on N type epilayers or ion-implanted layers on semi - insulating s ubstrates .
Integrating a MESFET with a crowding effect laser or a lateral
injection laser on a common semi-insulating substrate can be easi ly
conceived. ( 36 ) Fig. 4-26 shows two examples of the integration.
The upper one in the figure is an integrated device consistinq of a
lateral injection laser and a MESFET, and the lower one shows the
integration of a crowding effect laser with a MESFET .

The fabrication

procedure of these devices will consist of epitaxial growth, selective

-167-

SCHOTTKY GATE

SEMI-INSULATING GaAs

SCHOTTKY GATE
GoAl As(P)

GaAs-.·==============~

GoAl As (N)

SEMI-INSULATING GaAs

Fig. 4-26

These are two examples of the integration of a
GaAs-GaAlAs laser with a Schottky gate FET. The
upper one uses a lateral injection laser and
the lower one uses a crowding effect laser.

-168-

etching, selective diffusion and metallization.

The current passing

through the FET is modulated by the signals from the Schottky gate
and the laser light is, in turn, modulated by the current.
Since the laser and the FET are integrated on a single chip
of GaAs crystal, it is possible to operate it at very high speed.
Using today•s know-how in GaAs microwave devices and the technology
which we developed of fabricating GaAs lasers on semi-insulating
substrates, considerable integration of high speed electronics and
lasers can be expected in the near future.

-169REFERENCES FOR CHAPTER IV
(1)

T. Tsukada, "GaAs-Ga1 _xAlxAs buried-heterostructure injection
lasers", J. Appl. Phys. 45, 4899 (1974)

(2)

H. Namizaki, "Transverse-junction-s tripe lasers with a GaAs p-n
homojunction", IEEE J . Quantum Electron. QE-11, 427 (1975)

(3)

K. Aiki, M. Nakamura, T. Kuroda, J. Umeda, R. Ito, N. Chinone,
and M. Maeda, "Transverse mode stablized Al XGa 1 -X As injection lasers
with channeled-substrate-planar structure", IEEE J. Quantum Electron.
QE-14, 89 (1978)

(4)

S. Somekh, E. Garmire, A. Yariv, H. L. Garvin, and R. G. Hunsperger,
"Channel optical waveguides and directional couplers in GaAsinbedded and ridged", Appl. Opt • .J.l, 327 ( 1971)

(5)

F. L. Leonberger, J. P. Donnelly, and C. 0. Bozler, "Low loss GaAs
p+n-n+ three- dimensional optical waveguides ", Appl. Phys. Lett .
28, 616 (1976)

(6)

+ - +

F. L. Leonberger, J . P. Donnelly, and C. 0. Bozler, "GaAs p n n
directional coupler switch", Appl. Phys. Lett. 29, 652 (1976)

(7)

F. K. Reinhart, J. C. Shelton, and R. A. Logan, "Densely packed
electrooptic Al 1-yGayAs-Al XGa 1-XAs rib waveguide modulators and
switches", Topical Meeting on Integrated and Guided Wave Optics,
paper MD2-l, Salt Lake City, Utah (1978)

(8)

S.M. Sze, Physics of Semiconductor Devices, John Wiley & Sons Inc.,
New York (1969)

(9)

J. A. Copeland and S. Knight, "Applications utilizing bulk negative
resitance", in Semiconductors and Semimetals Vol .7, edited by
R. K. Willardson and A. C. Beer, Academic Press (1971)

-170(10}

C. A. Liechti, "Microwave field-effect transistors-1976", IEFE
Trans. Microwave Theory Tech. MIT-24, 279 (1976}

(11}

C. P. Lee, S. Marga1it, and A. Yariv, "Double-heterostructure
GaAs-GaAlAs injection lasers on semi-insulating substrates using
carrier crowding", Appl. Phys. Lett. _R,281 (1977}

(12}

C. P. Lee, S. Margalit, I. Ury, and A. Yariv, "GaAs-GaAlAs injection
lasers on semi-insulating substrates using laterally diffused
junctions", Appl. Phys. Lett. 32, 410 (1978)

(13)

C. P. Lee, S. Margalit, I. Ury, and A. Yariv, "I ntegration of an
injection laser with a Gunn oscillator on a semi-insulating GaAs
substrate", Appl. Phys. Lett. 32, 806 (1978)

(14}

G. R. Cronin and R. W. Haisty, "The preparation of semi-insulating
GaAs by chromi urn doping", J. El ectrochem. Soc. ffi, 874 ( 1964)

(15}

R. Zucca, " Electrical compensation in semi-insulating GaAs",
J. Appl. Phys. 48, 1987 (1977}

(16}

See for example, Pritchard, Electrical Characteristics of Transistors,
McGraw Hi 11 ( 1967}

(17}

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions,
Dover Publications, Inc., New York (1970}

(18)

H. Namizak1, H. Kan, M. Ishii, and A. Ito, "Transverse-junctionstripe-geometry double-heterostructure lasers with very low
threshold current", J. Appl. Phys. 45, 2785 (1974)

(19}

H. Namizaki, H. Kan, M. Ishii, and A. Ito, "Characteristics of
the junction-stripe-geometry double heterostructure lasers",
Japan J. Appl. Phys. Jl, 1618 (1974)

-171(20)

W. Susaki, T. Tanaka, H. Kan, and M. Ishii, "New structures of
GaAlAs lateral-injection laser for low-thres hold and s ingle mo de
operation", IEEE J. Quantum Electron. QE-13, 587 (1977)

(21)

L. R. Weisberg, "Diffusion in GaAs", Trans. TMS-AIME 230, 291 (1 964)

(22)

C. P. Lee, S. Margalit, and A. Yariv, "Dependence of Zn diffusion
on the Al content in Ga 1- xAl xAs", Solid State Electron.(to be
published)

(23)

B. J . Baliga and S. K. Ghandhi, "Lateral diffusion of Zinc and
Tin in GaAs " , IEEE Trans. Electron Device . ED-21, 410 (1974)

(24)

D. Kendall, in Semiconductors and Semimetals Vol .4, edited by
R. K. Willardson and A. C. Beer, Academic Press (1968)

(25)

I . L. Chang and G. L. Pearson, "Diffusion mechanism of Zn in GaAs

and GaP based on isoconcentration diffusion experiments", J. Appl.
Phys. 35, 1960 (1964}
(26)

H. Rupprecht and C. Z. Lemay, "Diffusion of Zn into GaAs under
the pres sure of excess arsenic vapor" ,J . Appl . Phys . 35,1970 ( 1964 )

(27}

R. A. Logan and F. K. Reinhart, "Optical waveguides in GaAs-GaAlAs
epitaxial layers", J. Appl. Phys . 44, 4172 (1973}

(28)

E. Garmire , D. F. Lovelace, and G. H. B. Thon.pson, "Diffused
two-dimensional optical waveguides in GaAs", Appl. Phys. Lett .
26, 239 (1975)

(29}

H. Kogelnik, "On -the propagation of Gaussian beam of liaht throuoh
lens like media including those with loss or qain variation"

(30)

Appl. Optic. i· 1562 (1965)
D. Marcuse, Light Transmi ss ion Optic~, Van Nostrand, New York (1972}

-172(31)

D. D. Cook and F. R. Nash,

11

Gain-induced guiding and astigmatic

output beam of GaAs lasers", J. Appl. Phys. 46, 1660 (1975)
(32)

c. P . Lee, S. Margalit, and A. Yariv, "vJaveguiding in an exponentially decaying gain medium", Optics Comm . .£§._, 1 (1978)

(33)

G. Arnold and P. Russer, "Modulation behavior of s emiconductor
injection lasers", Appl. Phys. 14, 255 (1977)

(34)

J. B. Gunn, "Microwave oscillation of current in III-V s emiconductors", So 1 i d State Comm. 1. 88 (1963)

(35)

H. Kromer, "Theory of the Gunn effect", Proc. IEEE, 52, 1736
( 1964)

(36)

C. P. Lee, S. Margalit, and A. Yariv, "GaAs-Ga.A.lAs heterostructure
lasers on semi-insulating substrates", IEEE Trans . Electron
Device. (to be published)

-173-

CHAPTER V
EXPERIMENTAL TECHNIQUES
V.l

Introduction
During the course of studying the various GaAs-GaAlAs laser de-

vices described in the previous chapters, many experimental techniques
have been involved .

They can be generally divided into three cate-

gories: material preparation, device processing, and device characterization and measurements.
All the structures described previously are prepared by a liquid
phase epitaxial (LPE) growth system in our laboratory.
are generally smooth and of good quality.

The grown layers

The thicknesses of the layers

can be controlled to within a tolerance which is on the order of 0.1 ~m .
Good devices depend on the ability to grow good quality layers.

Thus,

material preparation is probably the most important step in the device
fabrication.

Details of the epita xial growth are gi ven in the next sec-

tion.
The device processing includes cleaning, diffusion, photolithography, chemical etching, metallization, packaging, etc.

Part of these

procedures have been described in the previous chapters .

In this chapter

we will use the double heterostructure laser as an example of the fabrication procedure.
The characterization of a laser device includes threshold determination, spectrum measurement, and near- and far-field measurements.
Since the wavel ength of the GaAs laser is around 8500~, infrared
detectors have to be used in these measurements.

Details of these

-174-

techniques are given in Section V-3.
V.2

GaAs-GaAlAs Liquid Phase Epitaxy
Epitaxy, derived from the Greek word "epi" meaning "on", and

the word "taxis" meaning "arrangement", describes a technique of growing
a thin crystalline layer on a parent substrate in which the crystallographic orientation of the layer is determined by that of the parent
substrate.

This technique has been used very widely in the fabrication

of various types of semiconductor devices.

For GaAs-GaAlAs heterostruc-

ture devices the epitaxial growth is especially important, because the
multilayer structure cannot be achieved by techniques such as diffusion
or ion implantation.
During the last ten years or so three kinds of epitaxial growth
techniques for the GaAs-GaAlAs system have been developed.

They are

(1) vapor phase epitaxy (VPE) in which the material for growth is in
the form of chemical compounds in the vapor phase, and in which GaAs or
GaAlAs is deposited on the substrate by chemical reaction; (2) liquid
phase epitaxy (LPE) in whi ch the epitaxial layer is precipitated on the
substrate from a saturated liquid solution; (3) molecular beam epitaxy
(MBE) in which the constituents of the growth in the form of an atomic
beam impinge upon the surface of the substrate in an ultrahigh vacuum
system.

Among these three techniques liquid phase epitaxy is by far the

most popular and most reliable method for preparing high quality epilayers for optoelectronic devices.

All the devices described in the

previous chapters were fabricated in our laboratory using this technique.

-175In order to control the material composition of the epitaxial
layers grown from the liquid phase, the composition-temperature relations for the Al-Ga-As system must be known.

A number of studies
reporting phase diagrams for GaAs-GaAlAs are available(l- 3 ). Theresulting phase diagrams that describe the liquid and solid compositions
that are in equilibrium at a given temperature are used to establish
the necessary compositions of the liquid to be used for the growth of
a given Ga 1-XAl XAs layer.
V.2.l

Growth system
The liquid phase epitaxial growth system used by the author is

shown in Fig. 5-l.

This is a so-called horizontal sliding boat system
which was first developed by Panish et al. ( 4 ) In this system all the
epitaxial layers can be grown during a single growth cycle without any
intervening handling steps.

The system consists of three major parts:

a furnace, a quartz tube, and a graphite boat.
A photograph of the boat is shown in Fig. 5-2.
three pieces of graphite.

The upper piece has a number of wells which

contain the growth solutions.

Under this piece is a long slider on

which the substrates are seated.
bottom slab of graphite.

It consists of

The horizontal sliding bar rests on a

The top surface of the sliding bar forms the

floor for the solution wells.

A small quartz tube is used to hold this

boat in position relative to the furnace.

This holding tube is sealed

at the end which is in the furnace, and a thermocouple is inserted into
the tube from the other end.

The temperature of the boat is monitored

..,....

......

Fig. 5-l The liquid phase epitaxial growth system us ed in this work

SUBSTRATE

~ /

~ ~

SOLUTIONS

DUMMY WAFE'K

~~v ~

77777//J/L//L7L7Z7///L/L//Z/

tTHERMOCOUP~E

ROD

t""ULLII~I:i

QUARTZ

H2

LSLIDER

DVI-\1

GRAPHITE

7/77/T/ZT/ZIT/ZZZT/ZT/ZZZZlZZZIZZTfl7777J7777777Z/T/ZT/ZZT/ZT/ZTLT/lT/ZT/l?Z1ZT/ZZZI.

~ 800°C

-....1
0\

--'

-177-

·' ~"·

.....

VI

"'0

QJ
VI

::J

+->

ro

.J:l
QJ

+->

§::_lr.

E. ..

t::

~ ~

..
'·

....,"
'·

.....
.... "'

1t

LO

-178by this thermocouple during the entire growth cycle.

The slider, which

holds the growth substrates, can be moved relative to the solutions by
a quartz rod so that the substrate can be translated from one well position to another under the various solutions .

As illustrated in Fig. 5-1,

the boat is placed into a quartz tube in a windowless resistance furnace.
In order to assure a uniform growth on the substrate, the temperature
profile along the furnace is kept very uniform.

In a 25-inch long

range near the center of the furnace, where the boat is located, the temperature variation is less than 0.5°C.
Elimination of oxygen in the growth system is one of the key factors
in achieving good quality crystals.

The GaAs substrates and the solu-

tions, especially those which contain Al, can be easily oxidized at high
temperatures.

The oxidation prevents wetting between the substrate and

the Ga solution, and results in irregular growth.

In our system the whole

quartz processing tube is airtight and kept in high purity hydrogen atmosphere with a constant flow of palladium-diffused hydrogen.

The oxygen

content in the system is monitored by an oxygen monitor.

In normal con-

ditions, the oxygen content in our system is less than 0.1 ppm.
V.2.2

Growth procedure
GaAs-GaAlAs LPE growth is usually carried out using Ga as a sol-

vent.

Other materials such as GaAs, Al, and dopants are added to the

Ga to form the required liquid solution.

If this solution is super-

saturated with arsenic at an appropriate temperature ( ~ 800°C) and is
brought in contact with a GaAs substrate, a solid epitaxial layer will be
precipitated on the surface of the substrate.

The supersaturation is

-179-

usually achieved by cooling the solution, and the growth rate of the
epilayer depends on the rate of cooling.
The entire growth cycle consists of several steps.
is to bake the solvent-Ga.

The first step

In the case of a four-layer double hetero-

structure as an example, we put Ga in the first four wells of the boat
with each well containing four grams of Ga, and then insert the boat
inside the quartz tube and heat it in the furnace at 800°C for about
three or four hours.

This baking step is very important for the growth,

especially for GaAlAs because it cleans the Ga and drives out the residual oxygen which is dissolved in the Ga.

After baking, the boat is taken

out of the quartz tube and other materials are added to the Ga solvents.
For a double heterostructure, the first layer is N GaAlAs, so GaAs, Al
and Sn are put in the first well.

The second layer is the GaAs active

layer which is usually not intentionally doped, so only GaAs i s added to
saturate the Ga melt.

The third layer, P GaAlAs, is similar to the first

layer except for being P type, so instead of Sn we add Ge as the dopant.
The last layer is P+ GaAs, so we add GaAs and Ge in the fourth well.
Sn and Ge are the dopants we usually use for N type and P type
layers, respectively.

The aluminum concentration in the liquid is de-

termined on the basis of the desired concentrations in the solid using
the solidus and liquidus phase data. ( 3 • 5 ) GaAs is used to saturate the
solutions at the growth temperature.

At the same time we put these mate-

rials in the Ga melts, two pieces of GaAs substrate are placed on the
graphite slider.
below.

The reason for using two substrates will be explained

In most instances the substrates are (100) N type GaAs doped in

-180the range n = 1018 to 1019 cm- 3 with silicon or tellurium.

They are

cleaned and etched with H2so4 :H 2o2 :H 20 (4:1 :1) to remove possible surface
damage .

The size of each substrate is 1.5 mm x 14 .5 nm.

After the boat is loaded and in se rted back into the quartz tube,
the whole system is flushed with hydrogen for about two or three hours
before it is heated up .

Heating the system from room temperature to the

growth temperature, ~8 00°C, takes about 40 minutes.

After it reaches

this temperature we usually l eave it there for three or four hours so
that complete thermal equilibri um can be reached inside the solutions.
We then set up a cooling ra te to lower the temperature of the furnace,
and use the quartz pulling ro d to bring the GaAs substrates into contact
with the different solutions succ es~;vely from the first solution to the
last.

As the temperature dro ps, the saturated material in the solutions

precipitates on the substrates t o form the epitaxial layers.

The cooling

rate determines the growth rate and i s usually set at 0.1°/min to 1°/min.
For embedded epitaxy, since the growth rate is higher than that of the
usual growth, a much lower cooling rate was used.
The two GaAs substrates which are put on the slider are used in the
growth for different purposes.

The first one, which is closer to the

solutions in the starting position, is called the 11 dummy 11 wafer (see Fig.
5-l}.

The second one is the 11 actual 11 wafer, on which we need to grow

the layers.

The dummy wafer is introduced under each solution before the

second wafer.

Therefore, it brings the solutions into equilibrium with

respect to arsenic concentration before the growth takes place on the
actual substrate .

This technique was first used by Dawson,(G) and is

-181called 11 near equilibrium 11 growth.

With this technique the layer thickness

and the growth rate can be easily controlled because the growth starts
on the 11 actual 11 wafer from an almost equilibrium solution.

At tempera-

tures near 800°C the GaAs epilayer grows with a rate of about 1 ~m for
every one degree of cooling.

The Ga 1-X Al XAs layer grows at a slower rate,

and the higher the Al content the slower it grows.
growth rate is about 0.5 ~m/°C.

When x = 0.4 the

The thickness of each layer is thus con-

trolled by the temperature drop during the growth.

Figure 5-3 shows a

typical growth cycle of a GaAs-GaAlAs double heterostructure and the corresponding layer thicknesses.

A photograph of a typical wafer after a

four-layer growth is shown in Fig. 5-4.

Except for a few small spots and

for the areas near the edges, the surface of the growth is usually smooth
and mirror-like.
V.3

Laser Diode Fabrication
In this section we use the case of a regular double heterostructure

laser as an example to describe the fabrication procedures of a laser
diode.

The compositions, dimensions and sequence of the layers are the

same as those shown in Fig. 1-3.

After the layers are grown, the sample

is taken out of the growth system and then cleaned with hot methanol and
hydrochloric acid to remove the residual Ga drops which remain on the
surface of the wafer.

The sample is then rinsed in distilled water and

blown dry with high purity nitrogen.

Following that, it is placed into

a vacuum chamber and P type contact metal is evaporated on the surface of
the top epilayer.

The metal used for P type contact is usually either a

Cr-Au or a Au-Zn alloy.

Cr-Au requires two steps of evaporation: a thin

1-

41

a.

S41

10

::::1

41
S-

Put in GaAs, Al ,and dopants

4 hours
6T =

Fig. 5-3 A typical growth cycle of a four-lay~r double heterostructure laser

Time

Cooling rate
4 = 0.3 /min.

0: Dummy piece under the 1st solution
1: Actual piece under the lstsolution, dummy piece ·under the 2nd solution
growth of N Ga 0. 6Al 0. 4As layer ( 2~m )
2: Actual piece under the 2nd solution, dummy pieta under the lrd solution
growth of GaAs active layer ( 0.2~m )
3: Actual piece under the 3rd solution, dummy piece under the 4th solution
growth of P Ga 0 . 6Al 0 . 4Ast~ayer ( 2~m)
4: Actual piece under the 4 solution
growth of P GaAs layer ( l~m)

~ 4 hours ---71
6T = 40

Start cooling

7'
--------..
i - - 1'

Put in Ga

co

__.

Fig. 5-4 A typical top view of a wafer after a four-layer epitaxial growth.
The dimension of the wafer is 7 X 14 mm2.

_..

co

-184layer of Cr <~ 500~) is evaporated first, and then a thick Au layer

(~ 3000~) is evaporated .
~500°C

During evaporation, the wafer is hea t ed at

(for Cr) and then ~200°C (for Au) for better adhesi on and better

ohmic contact.

Au-Zn alloy, containing 95% Au and 5% Zn, is evaporated

on the wafer in a single step.

The sample is subsequently heated in H2

atmosphere at 500°C for 5 minutes.

After the P type contact is prepared,

the n side (substrate) of the wafer is lapped until the total wafer thic kness is about 100 ~m.

The lapped surface is cleaned briefly in

H2so4 :H 2o2 :H20 (4:1 :1) and rinsed with water, and then theN type metal
contact is applied on it. We have used electrodeless plating of Au-Sn
and evaporation of Au-Ge to deposit this · conta~t layer .

When the former

is used, the P side of the wafer is masked with a plating resist L~d then
the wafer is immersed for about 30 seconds in an electrodeless plating
solution which deposits gold and a small amount of tin on the lapped surface.

The plating-resist mask is then removed and the wafer is placed

on a hot stage with a hydrogen atmosphere, heated to 450°C, and cooled
rapidly.

When Au-Ge alloy (86% Au and 14% Ge) is used, the sample is

placed in a vacuum system and the metal layer is evaporated on the lapped
surface.

Following that, the contact is thermally alloyed at 430°C for

one minute.

Alloying the metal contact with the semiconductor is an im-

portant step in making good ohmic contact .

Recently we found that alloy- ·

1ng of Au-Ge on N type GaAs can also be achieved using a Q-switched ruby
laser. ( 7) The short laser pulse (15 nsec) raises the temperature of the
contact instantaneously above the eutectic point and makes it alloy.

The

resulting contact has more uniform surface quality and lower contact resistance (~ 7 x l0- 5n-cm 2 ) compared with that of conventional thermal

-185-

alloying techniques.
After the contacts are applied, the sample is cleaved into bars in
the [110] direction.

The bars are 300-500 ~m wide with the smooth

cleaved edges comprising the partially reflecting mirrors for the laser
cavities.

The bars are cut into slices ~100 ~m wide with a microsaw.

Each slice is thus an individual laser.

The lasers are then mounted on

copper heat sinks for subsequent testing.
V.4

Optical Measurements
Threshold current, differential quantum efficiency and spectrum

V.4.1

After a laser is fabricated, several optical measurements are performed.

The first one is the determination of the threshold current and

the differential quantum efficiency.

Threshold current is usually found

by plotting the curve of light intensity versus driving current, as those
shown in Figs. 2-11, 4-8, and 4-19.

The current at the point where the

curve has a dramatic change in slope, viz., when the light output starts
to go up rapidly with current, is the threshold current.

The light inten-

sity was measured with a Sl photomultiplier.
The differential quantum efficiency of a laser is defined by( 8)

{5-l)

where P is the power output at current I, hv is the photon energy, q is

the electronic charge, and Ith is the threshold current.

The power output

was measured with a calibrated si licon photodetector, and nd' as defined

-186in eq. (5-l) was taken as the slope of the light-current curve.
The spectra of our lasers were measured with a Czerny-Turner
scanning spectrometer (SPEX #1600).

The laser light was focused onto

the input slit of the spectrometer and the signals from the output slit
were picked up by a water-cooled GaAs photomultiplier.

The grating in

the spectrometer was s lowly rotated by a driving motor and the signals
from the photomultiplier were integrated by a boxcar integrator, and
then recorded on a strip chart recorder.
V.4.2

Near field measurements
The laser light mode profile in the direction perpendicular to

the cavity is usually obtained by measuring the light distribution at
one of the cavity mirrors.

This mirror illumination is called the near

field pattern of the laser.

The experimental setup used by us

form this measurement is shown in Fig. 5-5.

to per-

The near-field pattern at a

cleaved end of a laser was imaged by means of a microscope objective
onto a 20 ~m wide slit placed in front of a Sl photomultiplier located
0.35 meters from the imaging objective.

The microscope objective used

in the setup had a magnification factor of 43:1, a focal length of 4 mm,
and a numerical aperture (N.A.) of 0.85.

The resolution, as determined

by Rayleigh criterion,(g) was
1.22A = 1.22 X 0.85
S -_ 2'1U\2 X 0.85

= 0.65 ~m
where we have taken the wavelength A to be 0.85 ~m.

(5-2)

CURRENT
SOURCE

,,

PHOTO- MULTIPLIER

--~ SLIT

I I
I I
I I
I I

GALVANOMETER
MIRROR

Fig. 5-5 Set-up for measuring lasers' near field patterns.

RECORDER

x. I

VARIABLE
DC POWER
SUPPLY

----------

----------

CYLINDRICAL
LENS

------------

MICROSCOPE
OBJECTIVE

_,

........

(X)

-188The magnification of the whole system, as the ratio of the image distance and the focal length of the objective, was 87.5.

Since the

diameter of the Rayleigh disk imaged onto the slit was about 57 ~m
( ~ 87.5

x 0.65 ~m) the system resolution was determined by eq. (5-2) as

opposed to the width of the slit which was 20 ~m.
The mode profiles were obtained by scanning, via a galvanometer
mirror, the imaged patterns over the slit of the photomultiplier .

The

galvanometer mirror wa s driven by a variable D.C. power supply which was
manually controlled.

The output of the photomultiplier went to a boxcar

integrator and the integrated signal was recorded on an X-Y recorder
whose X base was driven by the same D.C. voltage which drove the galvanometer mirror.
V.4.3

Far field measurements
The far field radiation pattern of a laser is the spatial distri-

bution of the laser light at a distance much greater than the dimension
of the light source, i.e., the near field.

From the far field pattern

one can tell how the light propagates after it is emitted from the la ser
cavity.

For example, Fig. 4-17, the far field of a lateral injection

laser, tells us that the laser light propagates to one side instead of
being emitted perpendicular to t he front mirror.

Al so , owing to the

finite dimension of the near field, the far field tells us how the light
is diffracted and the divergence of the beam.
Far fields are usually gi ven as functions of the angle between
the observation direction and the normal of the front mirror.

The exper-

imental setup used to perform the far field measurements is shown in
Fig. 5-6.

The laser was put at the center of a rotating table where

RECORDER

..,... /

Fig. 5-6 Set-up for measuring lasers' far field patterns

DC POWER
SUPPLY

POTENTIOMETER

CURRENT
SOURCE

..,... .....

ROTATING TABLE

BOX CAR
INTEGRATOR

SLIT

PHOTOMULTIPLIER

lO

co

__.

-190-

angles could be accurately measured.

The photomultiplier was placed be-

hind a slit 8 em away from the diode.

A D.C. power supply and a poten-

tiometer, which was attached to the table, were used to convert the
angle of rotation into voltage which served as the X drive of an X-Y
recorder.

The output of the photomultiplier was integrated by a boxcar

integrator and then coupled to the Y drive of the recorder. The measured
angular distribution of light had a resolution determined by the angle
spanned by the slit opening with respect to the light source.

The slit

width used in our measurements was 1 mm, which corresponds to a resolution of 0.7°.

-191REFERENCES FOR CHAPTER V
1.

M. B. Panish and S. Sumski, "Ga-Al-As phase, thermodynamic and optical properties", J. Phys. Chern. Solids 30, 129 (1969)

2.

M. Ilegems and G. L. Pearson, "Derivation of the Ga-Al-As ternary
phase diagram with applications to liquid phase epitaxy", in 1968
Proc. Symp. Gallium Arsenide, London (1969)

3.

M. B. Panish and M. Ilegems, "Phase equilibria in ternary III-V systerns", in Progress in Solid State Chemistry,]_, (Pergamon Press,
1 972)

4.

M. B. Panish, S. Sumski, and I. Hayashi, "Preparation of multilayer
LPE heterostructures with crystalline solid solutions of Al XGa 1-XAs
heterostructure lasers," Met . Trans.~. 795 (1971)

5.

K. Garno, T. Inada, I. Samid, C. P. Lee, and J. W. Mayer, "Analysis
of Ga 1 Al As-GaAs heteroepitaxial layers by proton backscattering ",

-x x

in Ion Beam Surface Layer Analysis l (Plenum Press, New York, 1976)
6.

L. R. Dawson, "Near-equilibrium LPE growth of GaAs-Ga 1_xAlxAs double
heterostructures", J. Cryst. Growth?]_, 86 (1974)

7.

0. Fekete, C. P. Lee, S. Margalit, D. M. Pepper, and A. Yariv, "Qswitched ruby laser alloying of ohmic contacts in GaAs epilayers",
to be published

8.

A. Yariv, Introduction to Optical Electronics (Holt, Reinhart and
Winston, Inc., New York, 1971)

9.

F. A. Jenkins and H. E. White, Fundamentals of Optics, 3rd Ed.
(McGraw-Hill, New York, 1957)