GaSb/InGaSb strained-layer quantum wells by MOCVD

Solid-Stare Electronics Vol. 35, No. 10, pp. 1385-1390, 1992 0038-l 101/92 $5.00 + 0.00 Printed in Great Britain Pergamon Press Ltd

GaSb/InGaSb STRAINED-LAYER QUANTUM WELLS BY MOCVD

C. H. Su, Y. K. Su and F. S. JUANG

Department of Electrical Engineering, National Cheng Kung University, Tainan, Taiwan, Republic of China

(Received I7 March 1992)

Abstract-The characteristics of GaSb/InGaSb strained quantum wells were studied. The variation of critical layer thickness with In content was calculated using energy balance and mechanical equilibrium models, respectively. The variation of a bulk In,Ga, _,Sb energy-gap was deduced from experimental data. Then the transition energies in the GaSb/In,Ga,_.Sb single quantum well were calculated using a model which takes into account the elastic strain and quantum well effects. The transition energies from conduction bands to light holes at 12 K were found to be higher than the GaSb energy-gap with In composition below 0.3. Thus, the light hole band cannot be confined in the quantum wells with In composition between 0 and 0.3. The photoluminescence (PL) spectra of quantum well structures with different well widths were presented. The transition energies obtained from the PL spectra were compared with theoretical predictions.

NOTATION

strain in the layer (100) plane Poisson’s ratio strained layer thickness critical thickness quantum well width bandgap of unstrained bulk material strained band gap from the condition band to mj = & l/2 hole strained band gap from the conduction band to rn, = + 312 hole spin-orbit splitting energy (J = 3/2 to l/2) bulk epilayer lattice constant for In,Ga, _,Sb substrate lattice constant elastic stiffness coefficient for the epilayer pressure coefficients hydrostatic deformation potential shear deformation potential or valence band [OOl] axial deformation potential hydrostatic strain contribution shear strain contribution Luttinger parameters

1. INTRODUCTION

Strained quantum wells (SQWs) and strained-layer superlattices show promise for opto-electronic applications. In addition to being able to tailor the operation wavelength over a wider range, with a greater flexibility on the choice of substrate, using strain and quantization enables the light- and heavy- hole energies to be tailored independently[ I]. Another advantage is the benefit for many engineering applications, including faster complementary logic and efficient, stable long-wavelength lasers[2]. The strained GaAs/GaSb quantum well band structures were considered and grown with metal-organic chemical vapor deposition (MOCVD) by Chidley et

a1.[3]. Recently, Mailhiot and Smith have proposed

that InAs/In,Ga, _,Sb strained-layer superlattice (SLS) is a candidate for far-i.r. applications with diode tunneling currents smaller than and optical absorption coefficient as good as those of the Hg,Cd,_.Te alloy in the lO-12pm region[4-61. Chow et aZ.[7] have reported the growth of InAs/InGaSb SLS by MBE. Bulk layers of both GaSb and InGaSb have been deposited by MOCVD[9-161 but few two-dimensional (2-D) structures and theory calculations for GaSb/InGaSb materials have been reported, except for those of Haywood et a1.[8]. In this paper, we report detailed calculations of transition energies for GaSb/ In,Ga,_,Sb quantum wells, with which the experimental results were compared.

2. EXPERIMENTS

All the samples were grown under a pressure of 170 torr and substrate temperature 600°C. The V/III ratio was about 5.7. The flowrates of TEGa(lO”C) and TMIn(20”C) and TMSb( - 19S”C) were 2, 1.2 and 3.8 seem for the growth of In,,,Ga,,, Sb wells. For the growth of the GaSb barrier, the TMSb flowrate must be changed to 2.7 seem to fix the V/III ratio near 5.7. The flowrate settings on the mass flow controllers and the actuations of the epiflod were automatically controlled by a computer during the growth. The growth rates were 1.67A s-’ for GaSb and 2.54 A s- ’ for InGaSb, respectively. Growth inter- ruptions of 60 s (stop growth) were used between the growth of each heterostructure layer. During inter- rupt periods, only TMSb flows into the main gas line but TMIn or TEGa flows to the vent gas line. The main structure for GsSb/InGaSb SQWs consisted of a 0.1 pm undoped GaSb buffer layer, a 100-270 A

1385

C. H. Su ef al 1386

0.60

.oc I I I

I 0.05 0.10 0.15 0.20

INDIUM SOLID COMPOSITION (x)

Fig. 1. Variation of In,Ga, ,Sb energy gap with In solid composition. Our data (deduced from 12.6 K PL peaks) are identified as full circles and compared with theoretical curves in this work (---) for 12.6 and 300 K. The dashed lines were calculated directly using the theory reported by Auvergne et a1.[18]. Also shown are the 300 K experimental

data (identified as 0) from Bougnot ef a1.[17].

undoped In,,,,Ga,,,, Sb well and a 0.2 pm undoped GaSb cap layer.

3. RESULTS AND DISCUSSIONS

In Fig. 1 the 12.6 K energy bandgap variation (deduced from photoluminescence measurements) vs solid composition (deduced from X-ray diffraction) is presented. The energy gaps measured at 12.6 K in this work are identified as full circles. From these measured data, the relationship between the 12.6 K energy-gap (&,) and In composition (x) was calculated to be:

E@(x) = 0.421x2 - 0.978.~ + 0.730 eV

(300 K, Bougnot et d.), (2)

which was the bottom solid line in Fig. 1. Bougnot et al. determined the energy gaps from optical absorption edge measurement on In,Ga, ,Sb alloys. The temperature coefficient p(x) vs In composition between 12.6 and 300 K was then calculated from eqns (1) and (2) to be:

E@(x) =0.171x2 -0.745x + 0.809 eV p(.u)=(8.690x2-8.136.~ -2.773) x 10m4eV K ’

(12.6 K, this work), (1) (this work), (3)

0.0 0.2 0.4 0.6 0.8


Fig. 2. Theoretical values of critical thickness vs In solid compositions. Curve (a) is the result from the People and Bean energy balance model and curve (b) is the result from the Matthews and Blakeslee mechanical equilibrium model.

which was the top solid line plotted in Fig. 1. From the 300 K experimental data grown at 760 torr reported by Bougnot et a1.[17] (identified as open squares), the relationship between the 300 K energy- gap and In composition was calculated to be:

Table I. Bulk material parameters used for calculations

GaSb InSb In,Ga, ,Sb Ref.

A 6.09593 6.41931 lO”dyncm~’ 8.84 6.70 10”dyncm~2 4.03 3.65 10e6eVbarm’ 14.5 IS.0

eV 0.77 0.81 0.74’ 0.82* 0.75 0.81

eV -8.3 -1.7 eV -2.0’ - 2.0’

- I.8 - I.8 II.8 4.03 35.08 15.64 0.042 0.0145 0.0505 0.0152

0.38344x + 6.09593 -2.14x + 8.84 -0.38x + 4.03

0.5x + 14.5

0.08x + 0.74

2.0

-0.0275x + 0.042 -0.0353x + 0.0505

[21 [251 [251 I261 [271 USI [21 [21 I21 v71 [301 [301 I21

1291 ” mmkl 0.267 0.263 - 0.00422~ + 0.267 ~291

’ Hydrostatic deformation potential. b Shear deformation potential. rl , r2 are Luttinger parameters. *Used in this work.

GaSbiInGaSb strained-layer quantum wells 1387

3 0.60

z;

8 i: 0.40 g Z

.Z b 0.20 ; -12K . . unstrain_

I - - - 300K

0.00 m 0.0 0.2 0.4 0.6 0.8 1.0


Fig. 3. Strain-induced shifts of the energy bandgaps (C-LH and C-HH) in In,Ga, _,Sb alloys as a function of In solid compositions for 12 K (-) and 300 K (-- -), respectively, without quantum size effects. Also shown are the bandgaps

of unstrained bulk In,Ga, _ .Sb alloys.

assuming the variation of energy-gap temperature is linear. The variation of energy-gap temperature can be represented as:

E,,(x, T) = P(x)(T - 12.6) + E,,(x, 12.6 K) eV.

(4)

Also shown in Fig. 1 are the 12.6 and 300 K theoretical curves (dashed lines) reported by Auvergne et a1.[18]. The energy gaps of In,Ga, _,Sb alloys in their study were determined from piezoreflectance measurements. The 12.6 K dashed line was calculated from the 300 K energy-gap as:

Eti(x)=0.415(l -~)~+0.139(1 -x)+O.l72eV

(300 K, Auvergne et al.), (5)

directly using the temperature coefficient /I(x) = 0.95x - 3.7 eV K- ’ which is different from our work. The 12.6 K dashed line using Auvergne’s parameters predicted the GaSb energy gap at 0 K to be 0.83 eV, which is slightly larger than the general value of 0.81 eV adopted by Casey and Panish[l9].

3.1. Critical thickness

Figure 2 shows the critical thickness values h, as a function of In solid composition. Curves (a) are calculated from the People and Bean energy- balance model[20,21] which gives the critical thick-

ness as:

k=(~)&ln($$). (6)

where a(x) is the lattice constant of the In,Ga, _,Sb epilayer, e,, the net strain in the layer plane and d the Poisson ratio given as[20];

G2

O=c,,+ (7)

Curve (b) in Fig. 2 was obtained from the Matthews and Blakeslee mechanical equilibrium model[22,23] which gives the critical thickness as:

h _a(x) ’ c

In Jzh,+l [ 1 .

47re,, (1 + 0) 4x1 (8) The unstrained alloy lattice constants and elastic

constants C, for In,Ga, _,Sb are linear interpolations of those for InSb and GaSb (as shown in Table 1). The temperature dependence of the lattice constants were neglected.

3.2. Energy bandgap shif with compressive strain

The effect of the compressive strain is to uniformly increase both the bandgap and split the (J = 3/2, mi = f 3/2)-hole and (J = 312, m, = + l/2)-hole de- generacy at the r point. The strained bandgaps Eoh and Eti from the conduction band to the mj = + 312 (heavy hole along z-axial) and m, = + l/2 holes (light hole along z-axial), respectively, are[ 11:

Egh=EgO+AEH+f6Es, (9)

E,,=E,,+AE,+f(A-@ES)

- f[9(f 6ES)2 + 6E,A + A2]“2, (10)

where AEH is the total hydrostatic strain contribution, 6E, the shear strain contribution and EBo the composition-dependent bandgap of unstrained bulk material. For In,Ga, _,Sb at 12.6 K, EBo was obtained from equation (1). The spin-orbit splitting energy A is a linear interpolation of those for InSb and GaSb (see Table 1). The band offsets (AE,:AE,) were assumed to be 50: 50 in our calculations.

CB G&b

I ‘T--- cl

C I

Fig. 4. Band diagram of GaSb/InGaSb single quantum well.

1388 C. H. SU et al.

0.55 F 0.0 0.2 0.4 0.6


Fig. 5. Calculated curves of 12 K transition energy Esh (-) and Ear (- --) as a function of x for strained

GaSb/In,Ga, -.Sb SQWs with L, = 270 A.

Figure 3 shows the shifts of the transition energies:

Es1 and Esh with elastic strain in In,Ga, _,Sb alloys as a function of In solid composition (x) for 12 (solid lines) and 300 K (dashed lines), respectively. Also known in Fig. 3 are the 12 and 300K bandgaps of unstrained bulk In,Ga, _,Sb alloys which are deduced from eqn (4). The strain-induced mixing of the valence bands places the light hole band below the heavy hole valence band. At 12 K tempera-

0.80 , I

0.40 m 0.0 0.2 0.4 0.6


Fig. 6. Calculated curves of 300 K transition energies Esr, (-) and EoI (---) as a function of x for strained GaSb/In,Ga, _,Sb SQWs with Lz = 270 A. The &, is ob-

served differently from Fig. 5.

0.72

t 0.68 ’ I I I J

0 100 200 300 400

WELL WIDTH (A)

Fig. 7. Calculated curves of 12 K transition energies Es,, as a function of well width for strained GaSb/In,,,Ga, s, Sb

SQWs.

ture, the strain-induced shift of the light hole valence band may be greater than the difference in the unstrained valence band manifolds with In composition below 0.3 (e.g. AE,)[24]. The bandgap rep- resentation of a GaSb/InGaSb strained single quantum well is shown in Fig. 4. As seen from Fig. 3, the transition energy Ed (12 K) is higher than the GaSb energy-gap with In solid composition between 0 and 0.3. Thus, the light-hole band cannot be confined in the quantum wells when the In solid composition is 0.19. Hence we will not consider the Ed energy in the calculations of quantized levels at the low temperature of 12 K in the strained GaSb/In,Ga, _ .Sb quantum well structures when In solid composition is below 0.3.

The theoretical curves of transition energy Egh (solid line) and Eg, (dashed line) at 12 K as a function of x for strained GaSb/In,Ga,_XSb SQWs with L, = 270 8, are shown in Fig. 5.

Figure 6 shows the 300 K transition energy EB1 (dashed line) and EBh (solid line) as a function of x for strained GaSb/In,Ga,_XSb SQWs. The transition energy Ed is observed at 300 K which does not appear at 12 K when In composition is below 0.3, as shown in Fig. 5. The reason has been explained above.

The theoretical curves of transition energies at 12 and 300 K as a function of well width for strained GaSb/Int,,sGa,,,,Sb SQWs are shown in Figs 7 and 8, respectively. There are two transition energy levels EBh, and Egh2 when the well width is larger than 170 8, for GaSb/In,Ga,_.Sb SQWs at 12 K. Other transition energies Ed, and Ed2 are observed at 300 K, differently from those at 12 K.

GaSb/InGaSb strained-layer quantum wells 1389

0.76

x=0.19

I I I 0.60 L 0 100 200 300 400

WEU WIDTH (A)

Fig. 8. Calculated curves of 300 K transition energies EBh (-) and &,, (- - -) as a function of well width for strained GaSb/In,,,Ga,,,, Sb SQWs. The EBh is obtained differently

from Fig. 7.

3.3. Photoluminescence results

Figure 9 shows the PL spectra of: (a) GaSb/ In,,,,Ga,,B,Sb SQW with L, = 270 A; (b) undoped GaSb wafer; (c) In,,,,Ga,,B, Sb bulk material 0.8 pm thick; and (d) SQW with L, = 110 A. The data were

200 mW (6.4 W cm-‘). The PL signal of bulk In- GaSb epilayer, spectra (c), is much weaker due to the high dislocation density in the mismatched interface. The corresponding energy gap of In,,,,Gar,,,Sb is 677.4 meV (18,305 A). In spectra (a), the emission peak at X-A” = 805.0 meV is attributed to the GaSb neutral-acceptor-to-bound-exciton-transition, Do-A = 780.1 meV donor-to-native-acceptor transition[28] in GaSb and 747.9 meV the exciton bound to the lC-1HH transition associated with the InGaSb strained SQW with L, = 270 A. the contribution of peaks X-A ’ and D “-A arising from the GaSb barrier or cap layers is obvious when compared with spectra (b) of the GaSb wafer, which are typical of the GaSb material. In spectra (d), the 766.0 meV luminescence is the exciton bound to the lC-1HH InGaSb confined transition with L, = 110 A.

The experimental data of two lC-1HH transition energies and 768.8 meV emission energy with respect to different L, were noted in Fig. 7 for comparison with the theoretical curve. The lC-1HH transition energies in spectra (a) and (d) of Fig. 9 have never been observed in any of the bulk GaSb layers[28] as compared with spectra (b) of the GaSb wafer and are due to quantum well transitions. The values of lC-1H energies are in agreement with the theoretical curve.

If the excitation power decreases from 200 to 40 mW the intensity of the lC-1HH transition energy in the SQW structure with L, = 270 A becomes I .4 times greater than the extrinsic luminescence (DO-A) in the GaSb barrier layer, as shown in Fig. 10. This indicates the carrier collection is efficient in the

obtained at 12.6 K using an excitation power of quantum well.

I I

14500 15750 17000 18250 1:

WAVELENGTH (A)

12.6 K

200 mW mev

6724

iO0

Fig. 9. 12.6 K photoluminescence for: (a) SQW with Lz = 270 A; (b) undoped GaSb wafer; (c) bulk In0,,,G%,8, Sb epilayer; and (d) SQW with ~5.~ = 110 A. The excitation power is 200 mW (6.4 W cm -*).

1390 C. H. Su et al.

12.6 K 4omw

*

(d t

14500 15375 16250 17125 1E

WAVELENGTH (A)

.lH National Science Council, Republic of China, under con- !S tract NSC80-0417-EOO6-02.

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-I

10( )O 9.

10. Fig. 10. 12.6 K photoluminescence for: (a) SQW with L, = 270 A; (b) undoped GaSb wafer; and (c) SQW with L, = 110 A. The excitation power is 40 mW (1.3 W cm -‘).

Figure 10 shows another emission peak at 768.8 meV which is not obvious in Fig. 9(a). This is the transition from higher sub-bands due to 2C-2HH transition energy. The values of 2C-2HH transition energies are also in agreement with the theoretical curve.

4. CONCLUSIONS

The variation of critical layer thickness with In content was calculated using energy balance and mechanical equilibrium models, respectively. The variation of bulk In,Ga, _,Sb energy-gap has been deduced from experimental data. Then the transition energies in the GaSb/In,Ga, -,Sb single quantum well were calculated using a mode1 which takes into account the elastic strain and quantum well effects. The transition energies from conduction bands to heavy holes at 12 K were found to be higher than the GaSb energy-gap when In solid composition is below 0.3. Thus, the light-hole band cannot be confined in the quantum wells when the In solid composition is between 0 and 0.3. The shifts of transition energies as a function of In solid composition and well widths for 300 and 12 K, respectively, were calculated. The photoluminescence spectra for QW structures with different well widths are shown and compared with the theoretical predictions.

Acknowledgements-The authors wish to express their

27. R. Zallen and W. Paul, Phys. Rev. 155, 703 (967). 28. S. C. Chen and Y. K. Su, J. appl. Phys. 66, 350 (1989). 29. S. Datta, Quantum Phenomena, Chap. 6. Addison-

thanks to Dr M. Yokoyama and Dr C. T. Lee for their Wesley, Reading, MA (1989). useful discussions. This project was supported by the 30. P. Lawaetz, Phys. Rev. 4, 3460 (1971).

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GaSb/InGaSb strained-layer quantum wells by MOCVD