Symmetry of conduction states for GaAs-AlAs type-II superlattices under uniaxial stress

PHYSICAL REVIEW B VOLUME 39, NUMBER 8 15 MARCH 1989-I

Symmetry of conduction states for GaAs-AlAs type-II superlattices under uniaxial stress

P. Lefebvre, B Gil, and H. MathieuGroupe d'Etudes des Serniconducteurs, Universite des Sciences et Techniques du Languedoc,

Place E. Bataan'lion, 34060 Montpellier CEDEX, France

R. PlanelLaboratoire de Microstructures et Microelectronique, 196 Avenue H. Ravera, 92260 Bagneux CEDEX, France

(Received 22 November 1988)

We report the determination of the symmetry of conduction-band states for type-II superlat-tices under on-axis and in-plane uniaxial stress. From their stress dependence, the symmetry ofthe electron states is labeled in terms of X, or X ~ conduction states. In some structures X, isthe conduction ground state and the ordering between X, and X ~ is reversed by in-plane stress.In others, this situation is reversed and an explanation of the results needs to take into accountlattice matching of AlAs slabs to GaAs. The shear tetragonal deformation potential of X statesin AlAs is obtained.

The study of the electronic properties of GaAs-A1Asshort-period superlatices (SPSL's) is of recent interest. '

In contrast to the more classical GaAs-Ga07A103As sys-tem, the "barrier" material A1As is of indirect forbiddengap, with lowest conduction band of X6 symmetry. Therelative ordering and spacing of each pair of extrema (I"sand A' s) in the bulk materials, together with the magni-tude of the valence-band oII'set between GaAs and A1Asacts in such a way that both type-I and type-II SL's cangrown, depending on the relative thickness of the GaAsand A1As slabs. In type-I SL's, both electrons and holesare confined in the GaAs slabs. However, in type-II SL's,the GaAs is the barrier for the electrons and the well ma-terial for the holes. In this latter case, the electron wavefunction is now built up from bulk states of X6 symmetry.An interesting theoretical problem also occurs: At leastthree bulk zone-boundary extrema, X„X,and X~ have tobe considered to calculate the conduction band of the SL.Some tentative calculations in the literature gave resultswhich varied with the theoretical approach used (see a re-cent discussion in Ref. 6). This question has also been ad-dressed experimentally through the problem of exciton lo-calization. The envelope function approach (EFA) al-ways predicts that X,-like states lie at lower energies, dueto the mass anisotropy of X minima. ' On the other hand,Ihm claimed that this situation could be reversed invery-short-period superlattices. Last, taking a precise ac-count of the A1As lattice matching on the GaAs substratemay be of importance in this question. As a matter offact, using the average value E2 =5 eV for the Xdeforma-tion potential of A1As, which we determine in this work,we may estimate the associate splitting between X, andX ~ as —15 meV. This value is opposite to the EFAsplitting, which is thus reduced or inverted, depending onthe SPSL parameters.

In this Rapid Communication an examination of the in-direct luminescence band is made for some type-II SL'sunder uniaxial stress. [110]-and [001l-oriented stresseswere applied on SL's grown by molecular beam epitaxy(MBE) along the [001]direction. The perturbation of the

Xx

Xy

Xx

Xy

Xz 3

[001]UNI AX I AL STRESS

[110]

FIG. 1. Schematic behavior of the three zone-edge-related X6conduction bands under both directions of the stress. Thepresented zero-stress ordering of the conduction minima is con-sistent with the effective-mass approach. 8=EQ(S/I S12),with S;J the elastic constants and E2 the shear tetragonal defor-mation potential of X6 conduction states.

Xs bulk conduction states depends on the orientation ofthe stress axis as shown in Fig. 1; the magnitude of thestress splitting is considerable and can be easily mea-sured. Thus, uniaxial stress is an ideal perturbation toinvestigate the symmetry of zone-boundary electronicstates in type-II SL's. In this paper, we determine for thefirst time the symmetry of the conduction state to whicheach luminescence line is related. The different stress be-havior of the X, and X„~ states may also influence theshape of the luminescence spectra because the lifetimesare expected to be different for X;- and X„~-related tran-sitions.

We first discuss the case of sample 1, a SL with a periodof 9.5 nm, of which 65% is the A1As 1ayer. Some typicalluminescence spectra obtained under [1101 stress are

5550 1989 The American Physical Society

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SYMMETRY OF CONDUCTION STATES FOR GaAs-A1As. . . 5551

displayed in Fig. 2. Consider first the zero stress pattern.The hot direct luminescence band, labeled e, is seen at1800 meV. A reflectance structure was also observed atthis energy. Lower in energy a strong luminescence peak(a) appears; some weak undulations (b,c,d) are also ob-served on its low-energy side, that may be attributed tophonon-assisted transitions from X states, involving threediferent phonon energies. ' When the stress is applied,the intensity of the a transition collapses while the intensi-ty of the phonon-assisted transitions is only weakly depen-dent on the stress. The e line shifts toward high energy,following the general trend for type-I er(1) -HH(1)features; ' the remaining transitions show the opposite be-havior. The stress shift of the a line is small (- —0.4meVkbar ') while the lower band shifts faster (- —4.5meV kbar ' . The [001] stress dependence is ratherdiN'erent: Although hot direct luminescence with a strongpositive shift is observed together with a shift to low ener-

gy of the indirect transitions, no drastic decreasing in theintensity of the a line is observed. The b, c, and 1 lineshave a smaller slope than the a line. Thus, the a line andthe "phonon-assisted" lines do not originate from thesame states. To extract the conduction energy shifts fromthese experimental data, we subtracted the inAuence ofthe stress on valence states and the hydrostatic contribu-tion. A preliminary study of type-I GaAs-A1As samplesconvinced us that the situation for these states is well un-derstood, in a way similar to GaAs-(GaAl)As quantumwells. ' The electron shifts thus obtained for the a line onthe one hand and for the b, c, and d lines on the otherhand match the scheme of Fig. 1, with 8-7.8meVkbar '. As a consequence, we assign the a line tothe zero-phonon transition associated with the X, levels(possibly impurity or defect related); and the b, c, and dlines to phonon-assisted transitions from the X„~ levels,lying at slightly higher energy at zero stress (the phonon

emissions account for lower-energy radiations). The de-

crease of the intensity of the a line under [110]stress thenresults in the change of ordering of the conduction levels

from E(X,) (E(X,~) to the opposite in the range ofstress less than 200 bars. On the other hand, no such sen-

sitivity of the intensity is expected if X, remains theground state under stress, which is actually the case with

[001] stress.It should be pointed out that the X, —X„~ zero-stress

splitting should be in this case, smaller than 1 meV, avalue to be compared to the EFA theoretical value of 20meV without taking mismatch strain effects. Besides,from the experimental value of 8' in this sample, we pro-pose the following value for the Xconduction-band defor-mation potential of A1As E2 =4.S + 0.2 eV.

The same type of experiment has been repeated on a43.4-nm period sample (sample 2) in which the AlAsslabs constitute 60/o of the period. Simple EFA calcula-tions' suggest a X, —X„~ splitting larger than in the caseof sample 1. The luminescence spectra only exhibit oneintense line in this sample; this may be related to poorerquality. The same experiments and data analysis provideconduction shifts shown in Fig. 3 for both stress orienta-tions. Identifying these results with the theoretical sketchof Fig. 1, we deduce 8-8.2~0.2 meVkbar ' and azero-stress splitting between X, and X ~-like states -6.5meV. The weak nonlinearities of the transition energynear the X, -X„~ crossing can be easily reproduced if weintroduce a mixing interaction of & 2 meV between X„X, and X~ states in a valley-orbit mixing-type approach.As possible origins for such a mixing potential we suggestinterface roughness or impurities.

Results shown in Fig. 4 were obtained in an ultrathinshort period SL, with period 1 nm and x 0.6. In contrastto the results of sample 1, no noticeable change of intensi-ties under stress is observed. The shifts of all the transi-

(a) Ga As —41AsP ~9.5 nrnX=0.65

x[[ [i~o]

(b)T=2 K

GaAs-Al AsP=9.5 nmX= 0.65x ll [001]

x50

.5 kbar 40 barsB

400 bars

ar

1700 1750I

1800 1700 1750 1800

ENERG Y (m'eV)

of 1 1 under (a) [110] stress and (b) [0011 stress. The identificacussed in the text. x represents the thickness of A1As measured in units of the period P.

5552 P. LEFEBVRE, B. OIL, H. MATHIEU, AND R. PLANEL

5»

0-

t5CL'

LLIX

54

Ga As. AIAs

-10--P =4.34 nm

X=0 6T=2 K

I

2STRE SS kbar

FIG. 3. Contribution of the shear part of the strain field onthe conduction states for sample 2. Crosses for [1101 stress andpluses for [001] stress.

tion lines are the same. They enable us, using the samedata analysis, to identify the symmetry of the lowest con-duction state as X ~. This is in contradiction with thepredictions of EFA calculations if no lattice mismatch istaken into account. When lattice mismatch is included inan EFA calculation, we find E(X ~) =E(X,) —5 meV inqualitative agreement with the data. Two recent experi-mental works "' reported an W, symmetry from Starkshift" and optically detected magnetic resonance mea-surement. ' In both these works, the authors only limittheir study to one sample, which is not the case here.

In summary, we have presented piezospectroscopicproperties specific to type-II SPSL's. Various periodshave been selected which display: (i) a "nonphonon" linerelated to X, conduction states and phonon assisted transi-tions related to X„', (ii) a [110]-stress-induced reversal ofthe ground-state conduction level from X to X„', (iii)the existence of an analog of the valley orbit interactionbetween X, and X„' produced by a localized potential,and (iv) the need to take into account lattice mismatchbetween GaAs and A1As to explain qualitatively our re-sults. Finally, we also propose the following average valuefor the X6 conduction states deformation potential E2 ofA1As: 5.1~0.7 eV. To conclude, it should be pointed outthat the experimental situation is not yet fully understood:The inAuence of the structure parameters is clearlydemonstrated, but the question of crystal quality is noteasy to separate from it. It may modify the carrier locali-zation and induce valley orbit mixing.

(b)

I-

0- I

0-5STRESS (kbar)

GaAs AIAs

P =1nmX= 0.6 X- $03 bars

LLl

KLkJ

x=LLJ

X

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WKX

STRES

X

20'20 2~&o 2O80ENE RGY ~ey

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1990

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2020 2050 2080ENERGY meV

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F16. 4. Luminescence spectra of the ultrathin short-period SL under (a) [1 10] and (h) [001] stress. Here the intensities do not de-

pend on the magnitude of the stress and all peaks shift with the same slope characteristic of an electronic contribution of X,y origin.

SYMMETRY OF CONDUCTION STATES FOR GaAs-AlAs. . . 5553

We thank C. Benoit a la Guillaume and F. Mollot for fruitful discussions.

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