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A reassessment of intervalence band absorption in 1.6μm (GaIn)(AsP)/InP
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1987 Semicond. Sci. Technol. 2 761
(http://iopscience.iop.org/0268-1242/2/12/001)
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Semicond. Sci. Technol. 2 ( 1 987) 761 -764.Printed in theUK
A R Adams, K C Heasman and J Hilton
Department of Physics, University of Surrey, Guildford, Surrey, UK
Received 9 June 1987
paper w e re-evaluate the influence of intervalence band absorption
on the temperature sensitivity of 1.6 pm (Galn)(AsP)/lnP lasers and emphasise its
general importance in semiconductorlasers
operating a t several times their
threshold current.
Abstract. In this
1. Introduction
Thetemperature
sensitivity of (GaIn)(AsP)/InPlasers
fabricated to operate nearI .6 pm where opticalfibres have
their minimum absorptioncontinues
to be apractical
problem. For example. if as is conventional. we write the
threshold current density in the form
Jth(TZ)=Jrh(TI)
e x d ( T 2 - Tl)/TO]
(1)
then when temperatures TI and T , are
near
room
temperature To is typically 50-70 K [ l ] . This compares
with a value of To= 150 K [21 at lower temperatures and
values of To= 200 K in GaAlAs/GaAs lasers up to about
350 K [31. Since this effect appears almost independent of
the laser
structure
or
the
growth
mechanism
used.
theoretical explanations in terms of thefundamental
properties of the semiconductor band structure, such as
Auger recombination [4] intervalence
and
band
absorption [ 2 ] have been sought. This approach has been
supported experimentallyby measurements using hydrostaticpressure [ 5 , 6 ] which showthatthe
To problem
improves as the direct band gapis increased with pressure
andhas led to suggestions how thebandstructurefor
long-wavelength lasers might be improved in strained layer
systems 17, S]. However, recent careful calculations of the
magnitude of Auger
recombination
rates
and
of
intervalence band absorption have led authors to discount
these mechanisms. Takeshima [91 considered both Auger
recombination and IVBA and concluded that neither could
explain theobservedtemperature
sensitivity of lasers.
Most recently, Childs and co-workers [IO] concentrated
on IVBA calculating its magnitude using a pseudopotential
band structure and matrix elements evaluated along 21 kspace
directions
through
the
Brillouin zone.
They
calculatedthatat1.6pmtheabsorption
coefficient for
IVBA, a= 39 c m - ' for 1 x lo18c m - ) holes atroom
temperature, i.e. a= 39 x 10 - I 8 cm2. This is in very good
agreement with the
magnitude
of a determined
experimentally from laser characteristics [ 2 , 5 ] which
require anabsorption coefficient in theactive region of
about 100 cm-' at the threshold carrier density, which is
0268-1242/87/120761 + 0 4 $02.50 @ 1987 Ltd
IOP Publishing
typically NI,= 2 to 3 x 10l8c m - ) . However. Childs and
co-workers concluded that the temperature sensitivity of
I V B A ( I / a ) da/dT=0.45 96 K - ' at 300 K which they
derived is insufficient to explain the observed temperature
sensitivity of lasers. I n this paper we make use of the
results of Childs and co-workers but show that when the
rate of change of Nthwith temperature is takeninto
account, I V B A can
account
almost
entirely
for
the
temperature sensitivity of 1.6 pm devices.
Unlike Auger recombination. I V B A directly affects the
quantum differential efficiency. vd. of lasers. Here we
considerthe light output of devicesworking at several
timestheirthreshold
currentandshowthat
it is the
influence of IVBA on ?ld thataffects their temperature
stability rather than thestability of the threshold current.
2. Temperature
current density
dependence
of
the
threshold
Childsandco-workersfoundthatthe
intervalence band
absorption coefficient depended approximately linearly on
the hole density over the range considered. i.e. p = 7.5 x
IO1' to 3 x I O l 8 cm -). Therefore, since an increase in a
due to an increase in temperature requires an increase in
threshold carrier density to overcome the extra loss. this in
turn increases the absorption and the process
iterates. If
we write the I V B A absorption coefficient under threshold
conditions as
aac = aNlh
(2)
where we take Nth as the electron and hole densities in the
active region in units of 10I8cm
then
-).
d a-d a a c-NI,,dT dT dT
+ a-.dN,,,
(3)
If the absolute magnitude of a is large the second term of
equation (3) can be very important. Indeed, wewill show
that the value of To= 150 K expected for a lossless laser is
761
A R Adams et a/
reduced to 120 K when a= 39 x 10 - l 8 cm2 even when
d a / d T is zero.
The radiative currentdensity may be written as [2]
1
where
We
took
the
following typical
values
for
the
laser
parameters; laserlength L = 300 x
cm,thickness of
the activeregion d = 0 . 2 x l o p 4cm, confinement factor
r =0.636, reflectively of endfacetsR=0.42andloss
external to the active region constant and equal to aex=
20 cm- l .
From [2], it was assumed that the peak
gain of the
laser is linearly related to the carrier density
so that we
may write
20
40
IVBA,[X
where A , = 1.75 x 10-l6 cm2 at 300 K and varies with
temperatureas derived in [2]andthegainrequiredto
reach transparency, ai,,= 200 cm - l at 300 K and was
varied with temperature in such a way as togive a value of
To= 150 K with aac=O[2].
The gain required to overcomelosses
80
60
(10”~ c m 2 ~
Figure 1. The effect of the magnitude and temperature
dependence of intervalence band absorption on To the
temperature sensitivity of the threshold current calculated at
300 K. a is the absorption coefficient for an injected hole
density of 1 0l8cm-3. The values on the curves are
( I / a ) d a / d T ( % K - ’ ) . The arrow indicates the a value from
[IO].
1
These values resulted in NthN 2 x 10l8cm-3 near 300 K
for a=39 x 10-18cm2.
From equations (2), (6) and (7) we may write
of which only a and its temperature dependence remain
adjustable parameters.
From Nth and a we determine a,, from (2) and hence
vd from (5) and then J R from (4). Finally we introduce a
loss current, J A , due to Auger recombination andwrite
JR Jth=
+J A
(9)
where
J A = edA
Nh
:
(10)
A , theAuger
where e is the electronic chargeand
coefficient, is kept as an adjustable parameter.
3. R e s u l t s
The results of the influence of intervalence
band
absorption
on
the
temperature
dependence
of the
thresholdcurrent
of 1.6pm(GaIn)(AsP)/InPlasers
is
762
Auger coefflclent , A
c m 6 S”
)
Figure 2. The variation of TOdue to a temperature
independent Auger coefficient and intervalence band
absorption with a temperature variation at 300 K of
( l / a )da/dT=0.45% K” [lo].The values on the curve are
a ( I O ’ 8 cm’).
lntervalence band absorption in 1.6 p m lasers
clearly that a loss mechanism proportional to the carrier
concentrationdoesnot
need to be at all temperature
sensitive to influence To. The full curve in figure 1 shows
how To varieswith a if ( l / a ) ,da/dT=0.45 % K - I as
given in [ 101. We see that when a = 3 9 c m - ' for 1 x 10I8
holes cm -3, the value determinedin [ 101 for 1.6 pm lasers,
TOis decreased to 90 K. Increasing a to 60cm-', probably within theaccuracy
of thecomplexabsorption
calculations,decreases
To to 70 K avalue
observed
experimentally.
Although we can see that IVBA as calculated in [ 101
alone can count for most of the temperature sensitivity of
1.6pm
lasers,
since it causes N,, to
change
with
the
temperature, IVBA will also influence Auger
recominationratethroughequation
(10). To emphasise
this point we haveconsidered a situation in which the
Auger coefficient A is assumedto be independent of
temperature. The results are shown
in figure 2 where we
1 x lo1* holes, To is
see that when a is 39 cm"for
reduced from 90 to 73 K for a temperature independent
Auger coefficient of 5 x
cm6 S - l .
loo/
50
.
0
I
1
150
2b0
240
Temperature ,T (K)
1
300
Figure 3. Temperature dependence of the threshold current
and differential quantum efficiency for 1.6p m
(Galn)(AsP)/lnP lasers. Solid symbols, threshold current data
[21; open symbols, differential quantum efficiency data [2];
full curves, a= 60 x 1 C'* cm2 broken curves
a= 39 x 1O"* cm2 a t 3 0 0 K and varied with temperature as
given in [ 101.
summarised in
figure
1. The
threshold
current
was
calculatedat290and320
K and To determined using
equation (1). Figure 1 showsthevariation
of To with
intervalence band absorption a the absorption coefficient
for 10l8 cm - 3 holes in the valence band. For a = 0, T =
150 K, the assumed value fora loss free laser. The various
curves show the variation of To with a for different values
of the temperature dependence of a. It is interesting to see
how IVBA decreases To even whenda/dT=O,showing
0.9
0.8
I
300
I
310
Ternperature,T [ K )
I
320
1
Figure 4. ( a )The influence of IVBA on the light-current characteristic of 1.6pm (Galn) (AsP)/lnPlasers operating a t
currents five times the threshold current.Full curve T = 2 9 0 K, aac= O ;broken curves T=320 K, cg, = O ;chain
curve T= 3 2 0 K. a a c = 100 cm"; (To = 6 5 K, L = 300pm, R= 0.42, r =0.636, aex
= 2 0 cm "1. ( b )The temperature
dependence of the normalised light output at five times the threshold current
as a function of theintervalence band
absorption coefficient at3 0 0 K. The values on the curve are aac(cm").
763
A R Adams et a/
So far we have only considered temperatures around
roomtemperature, where lasersarenormallyoperated.
However, when studyingthe T o problemauthorshave
presented results over amuch
wider range.Wehave
thereforecalculated I,, and v d from150to320
K for
comparison with experiment.Figure 3 showsthe results
for a= 39 and 60 x 10 - l 8 cm2 at 300 K and varying with
temperature as given graphically in [ 101. The experimental
results are taken from [2]. The absolute
value of qd for
a=60 x 10-l8 c m 2 is in excellent agreement with
experiment over the entire temperature range as might be
expected. The
calculated
threshold
current
increases
somewhat less quickly than is normally observed and may
reflect the increasing influence of Auger recombination.
Finally we would like to consider the influence of IVBA
on lasers operating at several times their threshold current.
This is becoming of increasing practical importance as the
technologies of growthandfabricationimprove.The
situation is illustrated diagrammatically in figure 4(a)
which indicates how, at five times threshold, the absolute
light outputdependsmore sensitively on v d than on Ith,
Returningtoour lasermodel we plot in figure 4(b) the
light output as a functionof temperature, normalised toits
value at 290 K for a device held at a constant operating
current five times thethresholdat290
K. Thecurves
produced are for constant a,, so they are not the curves a
laser would follow when heated and a,, increases. The top
curve aac=O is derivedfor
T 0 = 6 5K ,a e , = 2 0 c m - ’
assumingthat
q d remainstemperatureindependentas
would be expected tothe first approximation if Auger
recombination alone is responsible for the T oproblem. We
see that heating the laser from 290 to 320 K then reduces
the light output by 14 % while including a very modest
value of a,, = 20 cm - l reduces the output by double this
and a more realistic value of a,,= 100 cm - l reduces the
light output by 42 %. Clearly IVBA is particularly
importantforlasersoperatingat
several
times
their
threshold current and may even need to be considered in
GaAs devices.
764
4. Conclusion
Takingthecalculated
values forthemagnitudeand
temperature dependence of intervalence band absorption
(IVBA)
in 1.6 pm (GaIn)(AsP)/InP lasers calculatedin [ lOJ
we have shown thatit can accountfor most of the observed
temperature sensitivity of the
threshold
current
and
quantum differential efficiency. Itwasalsoshownthat
IVBA can strongly influence the Auger recombination rate
at lasing threshold. Finally it wasshownthat
IVBA is
particularly important in devices operated at several times
their threshold current.
Acknowledgments
One of us (KCH) wishes tothankSERCand
Philips
Research Laboratories, Redhill, for financial support.
References
[ 1 Horikoshi Y 1982 GaInAsPAllow Semiconductors ed.
T P Pearsall (New York: Wiley) ch 15
[2] Asada M, Adams A R, Stubkjaer K E, Suematsu Y, Itaya
Y and Arai S 198 1 I E E E J . Quantum Electron. JQE 17
61 1
[3] Kojima
K,
Noda
S, Mitsunaga
K,
Kyuma
K
and
Nakayama T 1985 Appl. Phq’s. Lett. 47 570
[4] Dutta N K and Nelson R J 1982 J . Appl. Phys. 53 74
[ 5 ] Patel D. Adams A R, Greene P D and Henshall G D 1982
Electron. Lett. 18 9 19
[6]MozerA,Hausser
S and Pilkuhn M 1985 I E E E J .
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[ 7 ] Adams A R 1986 Electron. Lett. 22 249
G P
[8] E P O’Reilly, K C Heasman,ARAdamsand
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[9] Takeshima M 1984 J . Appl. Phys. 56 69 1
[ l o ] Childs G N, Brand S andAbramRA1986
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