Electronic structure of (111)-GaAsPAlGaAs strained-layer quantum wells

surface science ELSEVIER

Surface Science 387 (1997) 371-382

Electronic structure of (111)-GaAsP/A1GaAs strained-layer quantum wells Xiong Zhang a,,, Mitsuteru Ishikawa b, Hiroyuki Yaguchi b, Kentaro Onabe

b

a Centerfor Optoelectronics, Department of Electrical Engineering, National Universityof Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore b Department of AppliedPhysics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113, Japan

Received 24 December 1996;accepted for publication 14 May 1997

Abstract

The GaAsl_xPx/AlyGal_yAs (x=0.07~.14, y=0.3) strained-layer multiple quantum wells grown by metal-organic vapor phase epitaxy on GaAs-(111 )B substrates have been characterized by X-ray diffraction and photoreflectance (PR) spectroscopy. By fitting the experimental results with the calculation which was based on the deformation potential theory modified by the strain-induced piezoelectric field, the energy band offset ratio for the conduction band at the heterointerface of GaAsl_xPx/AlyGal_yAs was quantitatively determined to be Q, = 0.61 --0.03. This value was found to be nearly independent of the phosphorous composition x in the whole region that has been investigated in this study. Moreover, several anomalous phenomena observed with the PR measurement as well as the possible physical origins have also been discussed. Q 1997 Elsevier Science B.V. Keywords: Quantum well; Photoreflectance spectroscopy; Piezoelctric effect; X-ray diffraction

1. Introduction

Recently the possibility o f tailoring the electronic and optical properties o f strained-layer q u a n t u m wells ( S L Q W s ) or superlattices (SLSs) that are c o m p o s e d o f I I I - V or I I - V I zincblendetype c o m p o u n d semiconductors according to variation in g r o w t h axis, has attracted m u c h attention [ 1-19]. This mainly originates f r o m the theoretical prediction that extremely large internal electric fields are generated by piezoelectric effect when S L Q W s or SLSs are g r o w n f r o m these piezoelectrically active semiconductors on non-(100) substrates [ 1 ]. These strong built-in piezoelectric fields * Corresponding author. Fax: 65 779 1103; e-mail: [email protected] 0039-6028/97/$17.00 © 1997 Elsevier ScienceB.V. All rights reserved. PII S0039-6028 (97) 00401-9

will change the shape o f the q u a n t u m well potentials, the s u b b a n d energy levels, and the wave functions, thereby substantially modifying the electronic structures and the optical properties o f the ( 111)-oriented S L Q W s or SLSs. W o r k to date for the study o f the non-(100)oriented S L Q W s or SLSs has been mainly perf o r m e d with the ( l l l ) - o r i e n t e d I n G a A s / G a A s S L Q W s or SLSs. However, for the I n G a A s / G a A s S L Q W s , it is impossible to adjust the strain or the internal piezoelectric field without changing the energy b a n d offset at the heterointerface or the well depth, since b o t h the strain and the energy b a n d offset are uniquely determined by the indium composition. This p r o b l e m m a y be solved by employing the ( l l l ) - G a A s P / A 1 G a A s S L Q W s [8]. For such a strained system, the strain and hence the

372

X. Zhang et aL / Surface Science 387 (1997) 371 382

strain-induced internal electric field is completely determined by the phosphorus composition in GaAsP well (ignoring the slight lattice mismatch between GaAs substrate and A1GaAs barriers), whereas the energy band offset at the heterointerface is primarily determined by the aluminium composition in A1GaAs barrier layers. Consequently, the strain and thus the straininduced internal electric field can be adjusted independently of the energy band offset by changing the phosphorus and aluminium compositions, respectively. This fact indicates that the (111)GaAsP/A1GaAs SLQWs may be one of the most potentially competitive candidates for optoelectronic device applications. In a previous paper [8], we reported a detailed study of the (111)-GaAsP/A1GaAs SLQWs by photoluminescence (PL) spectroscopy. However, except the lowest n = 1 electron to heavy-hole excitonic transition (le-lhh), the higher ( n > l ) heavy-hole-related excitonic transitions as well as the light-hole related excitonic transitions ( le-llh, etc.) were hardly detected in the PL spectra. For getting complete knowledge about the electronic structures of SLQWs, photoreflectance (PR) spectroscopy has been demonstrated to be a very sensitive, nondestructive, and convenient technique [20-25]. The most important advantage that can be achieved with PR is, however, that extremely rich information about the energy band structures of SLQWs, can be easily obtained even at room temperature. This paper is organized as follows: in Section 2 a brief review of the theoretical background for deducing the electronic structures of the (111)GaAsP/A1GaAs SLQWs is presented. Particular attention is paid on the modification of the energy band structures of the (111)-GaAsP/A1GaAs SLQWs by the strain-induced internal piezoelectric field. In Section 3, the experimental results of X-ray diffraction and PR spectroscopy for the ( 111 )-GaAsP/A1GaAs strained-layer multiple quantum wells (SLMQWs) are demonstrated and analyzed with the theories described in Section 2. The quantitative determination procedure of the energy band offsets and some interesting phenomena observed for these (lll)-SLMQWs are

discussed in Section 4. Finally the conclusions of this article are given in Section 5.

2. Theoretic methods

In this section, the effects of the strain-induced piezoelectric field on the electronic structures of the (111 )-oriented SLQWs are reviewed. Special emphasis is placed on the comparison of the strainmodified energy band structures between the (001)- and the (lll)-oriented SLQWs. The theoretical background for PR is also briefly discussed. 2.1. Strain-induced piezoelectric field As mentioned above, for SLQWs grown from zincblende-type semiconductors along a non-[ 100] direction, lattice-mismatch strain induces polarization fields via the piezoelectric effect, which in turn generate internal electric fields. The strain-induced polarization field, Pi, is given by Pi=2e14e~k

( i , j , k cyclic),

(1)

where e14 is the piezoelectric constant and eik is an off-diagonal strain component of the strain tensor. Note that the diagonal strain components (exx, eyy and ezz) do not generate a polarization vector, the widely studied (lO0)-oriented SLQWs where only the diagonal strain components are nonzero will thus not give rise to strain-induced polarization field. In the case of the (111 )-oriented SLQWs, the components of the strain tensor are related by exx =eyy =ezz =e±

and

exy =eyz =e~z =ell.

(2)

Therefore, the components of the polarization vector are equal and the direction of the polarization vector is along the [111] growth axis. The sign of the polarization vector in a constituent material of the (111)-oriented SLQWs, however, depends upon whether its lattice constant is larger or smaller than that of the substrate and upon the sign of the piezoelectric coefficient. Generally, for a III-V compound semiconductor having a lattice constant larger than that of the substrate or suffer-

X. Zhang et al. / Surface Science 387 (1997) 371-382

ing a biaxial compressive strain in the ( i l l ) oriented SLQWs, the polarization vector points from the A (cation) to the B (anion) face. In contrast, for a III-V compound semiconductor with a lattice constant smaller than that of the substrate or suffering a biaxial tensile strain in the (111)-oriented SLQWs, the polarization vector points from the B to the A face. The strain-induced polarization field Pz generates electric field E~ given by [17]

(3)

D i = eoEi + eoZEi + 2el4ejk,

where Z is the susceptibility and D~ is the electric displacement. If there are no external charges, Dz vanishes, and the electric field reduces to 2el4ejk

E~ -

(4)

e0e where e = 1 + Z is the relative dielectric constant of the constituent material. For the ( 111 )-oriented SLQWs, the strain-tensor components are expressed as [19]

4G4

e, =

6,

(5)

373

Table 1 Lattice, elastic, piezoelectric a n d relative dielectric constants, energy b a n d gaps, d e f o r m a t i o n potentials, L u t t i n g e r p a r a m e t e r s a n d effective m a s s e s for G a A s , A l A s a n d G a P

Lattice c o n s t a n t (,~) C u ( 10 l° N m -2) Cla ( 10 l° N m -z) C44 ( 10 l° N m -z) el4 (C m -2) e Eg (eV) a~ (eV) av (eV) d (eV) Ao (eV) Vl ~2 ~3 m * (m0) m * h (100) (rn0) m * h (111) (m0) m * (100) (mo) m ~ ( 111 ) (mo) "Ref. bRef. °Ref. aRef. °Ref.

GaAs

AlAs

GaP

5.6533 a 1.223 b 0.571 b 0.600 b -0.16 ° 13.18 c 1.424 c -7.17 b 1.16 b -4.5 b 0.34 b 7.65e 2.41~ 3.28 ~ 0.067 ~ 0.62 c 0.917 b 0.087 c 0.070 b

5.6605 ~ 1.250 b 0.534 b 0.542 b -0.225 ~ 10.06 c 2.168 ~ -5.64 b 2.47 b -3.4 c 0.28 b 4.04~ 0.78~ 1.57 ~ 0.150 ° 0.76 ~ 1.111 b 0.150 ~ 0.139 b

5.4512 a 1.439 b 0.652 b 0.714 b --0.10 ~ 11.1 a 2.74 a --7.14 b 1.70 b -4.6 u 0.08 b 4-20~ 0-98° 1.66 ° 0.17 a 0.79 a 1.136 b 0.14 d 0.133 b

[37]. [27]. [30]. [38]. [31].

C l i -}- 2 C i 2 + 4 C 4 4

Cii -k 2 C i z

Cll +2Clz

6

2.2. Band structure modification due to strain effect

( i , j = x , y , z; ivLj).

-I-4C44

(6) Here Cli, C12and C44 represent the elastic stiffness constants, and ~ is the lattice mismatch between the epitaxial layer and substrate and can be written as

6-

as --ao -

-

(7)

ao

where ao and a s are the lattice constants of the epitaxial layer and substrate, respectively. The material parameters for calculating the straininduced internal piezoelectric field in the (11 !)GaAsl_xPx/AlrGal_yAs SLQWs are summarized in Table 1.

A standard approach for determining the electronic structure is to calculate the eigen energies and wave functions with an envelope-function model [26]. In an effective-mass approximation, this calculation is reduced to numerically solving a one-dimensional Schr6dinger equation for a finite square quantum well. We first consider the strain-induced band-edge shifts for both conduction band and valence bands. Then we give a quantitative description of the electronic band structures by taking into account the internal built-in piezoelectric fields in the (111)-oriented SLQWs. According to the deformation potential theory [27], the strain-induced energy band-edge shifts for the conduction band, 6Ec, and for the heavyhole and the light-hole related valence bands,

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X. Zhang et al. / Surface Science 387 (1997) 371-382

6Evh and 6Evl, at the F point can be expressed as At2 6Eo = a c - - , £2

(8)

6Evh=AEv-½Ao +~AEm + ~1/ A 20 + AoAE111 + 42(AEl11)2,

(9)

6Evl = A E v --1A 0 - - 1 A E l l l 1 20 -[- A o A E l l 1 + 9 ( A E l 1 1 ) 2, + ~¢/A

(10)

with At2

zxE~=av - - ,

(11)

AE111 = 4~3dei~,

(12)

12

At2 -

t2

Tr (6) = (exx + eyy + ezz) = 3eii,

( 13 )

where a c and av are the hydrostatic deformation potentials for the conduction band and valence bands, respectively, d is the shear deformation potential; and Ao is the s p i m o r b i t splitting energy. As a first-order perturbation of the strain Hamiltonian, the strain-induced modification of band structures can be simply written as

6Ec = 3aceu, C]Evh =

3a ve u + ~/3d~ij ,

6E~l = 3aveu -- ~/3deij.

(14)

(15) (16)

The energy discontinuities or energy band offsets at the heterointerface for conduction band, AE c, heavy-hole subband, AE~h, and light-hole subband, AEvl, however, can not yet b e uniquely determined only by employing Eqs. (14)-(16) and the energy difference in band gaps between the two constituent materials AEg. This is due to the fact that the energy band offset ratios both for conduction band and heavy-hole- and light-hole subbands, Q~ = AE~/(AE~ + AEv0, Qvh = AEvh/ (AEo + AE~h), and Qvl = AEvl/(AEo + AEvl), are still unknown. In fact, the knowledge of the energy band offsets at a semiconductor heterointerface is quite limited and disputed even up to date. It is especially true for the strained-layer quantum structures because of the experimental difficulties

and the absence of reliable theoretical predictions. For illustrative purpose, a tentative compositionindependent value of the band offset ratio at the heterointerface of GaAsP/A1GaAs, Qo = 0.61, or Qv1=0.39 was used in calculating the excitonic transition energy. The material parameters necessary for this calculation are also listed in Table 1. N o w we consider the influence of the internal piezoelectric fields on the electronic structures of the (111 )-oriented SLQWs. When a perpendicular electric field is applied across the quantum wells, the band edges both for the conduction band and the valence bands are tilted, and the wave functions of the electrons and holes are separated due to the so-called quantum-confined Stark effect (QCSE) [28]. The decrease of the overlap integral between the wave functions of the electrons and the holes reduces the oscillator strength and thus the excitonic transition intensity. Meanwhile, the confined energy levels shift to the b o t t o m of the quantum well because of the tilting of the band edges. As a result, the effective energy band gap is decreased, corresponding to a red shift of the excitonic transition peaks in PL or PR spectra. The eigen energy shifts can be calculated by using an "effective wellwidth model" developed by Miller et al. [28]. In this model, an actual quantum well with a finite barrier under a uniform static field is approximated by an imaginary quantum well that has an infinitely deep well with an "effective well width". This "effective well width" is obtained by giving the exactly same solutions of the eigen functions and eigen energies as that for the actual quantum well with a finite barrier in the absence of electric field. With such a approximation, the Schr6dinger equation under an electric field perpendicular to the quantum well layers can be written as h

d2 --

2m* dz z

gt(z) - ( E + eF± z) ~e(z) = 0

(17)

with the boundary conditions of gt(+½Lz)=0. For a certain value of F±, the eigen energies and wave functions can be derived numerically to any desired accuracy by using the series expansion of the Airy functions [28]. In order to calculate the energy discontinuities at the heterointerface as well as the quantum

X. Zhang et al. / Surface Science 387 (1997) 371-382

confined energy levels for the (111)-GaAs l_xPx/ AlyGal_yAs SLQWs, the information about the energy band gaps of the constituent GaAsl_xPx and AlyGal_yAs alloys is essential. The energy band gap of GaAsl_~P~ at 300 K, Eg(x), as a function of the phosphorous composition, x can be expressed as [29] Eg(x) = 1.424+ 1.15x+ 0.176x 2.

(18)

On the other hand, the experimental relationship between the energy band gap of AlyGal_yAs Eg(y) and the aluminium composition y at 300 K is also known as [30]

Eg(y)=l.424+l.247y

(0
Eg(y)=l.9+0.125y+0.143y 2

(19)

(0.45
2.3. Valence-bandanisotropy An important difference between the quantum well structures grown along (100) direction and those grown along < 111 > direction is concerned with the valance-band anisotropy that results in different effective hole masses for these two kinds of quantum structures. This difference will significantly influence the quantization shifts in energy levels, the magnitude of optical matrix elements and the state densities in quantum wells. Expressed in terms of Luttinger parameters, 71, 72, and, 73, the effective masses both for the light hole (lh) and the heavy hole (hh) in vicinity of the zone center ( k = 0 ) can be written as mo

m *lh - - hh 71 ±272 /,no * - - mlh hh 71 ! 2 y 3

for (100),

(21)

for (111),

(22)

375

hole effective mass was found to be nearly independent of the crystal orientation. In other words, the light hole-related transition energy is lightly affected by the crystal orientation. All the material parameters of ternary III-V compound semiconductors except for the energy band gap, can be obtained by linear interpolation of the values for the corresponding binary materials listed in Table 1.

2.4. Photoreflectance (PR) spectroscopy With PR spectroscopy, the modulation is accomplished by exerting a periodic perturbation (here the photon-related electric field) to the complex dielectric function through the production of photoexcited carriers on the surface of the material. Under a weak-field approximation which is generally true and of fundamental importance for PR spectroscopy, according to the Aspnes's theory [32], the differential change in reflectivity, AR/R, can be expressed as AR R

=Re(Cei°(E--Eg + i F ) - " ) ,

(23)

where C and 0 are amplitude and phase factors, respectively, which vary slowly with E. Eg is the energy band gap at the critical point, /" is the homogeneous broadening parameter and n is a parameter determined by the dimensionality of the interband transition.

3. Measurement results

respectively. Here mo is the free-electron mass. Employing the Luttinger parameters obtained by Lawaetz [31 ], the effective masses along the (100) and <111) directions for GaAs, AlAs and GaP are calculated and summarized in Table 1. The heavy hole effective mass along the < 111 > axis was found to be approximately 1.5 times as large as that along the <100> axis. In contrast, the light

As demonstrated in Section 2, the strain-induced intrinsic piezoelectric fields serve to modify the energy band structure, and thus exert profound influence on the electronic and optical properties of the (111)-oriented SLQWs. In this section, a detailed description of the structural and optical characterization by means of X-ray diffraction and PR spectroscopy is given for the ( l l l ) GaAsP/A1GaAs SLMQWs.

376

X. Zhang et aL/ Surface Science 387 (1997) 371 382

3.1. Structural characterization

neously. Fundamental to our discussion below is Bragg's law:

All of our (111)-GaAsl_xPx/AlyGal_yAs SLMQW samples used in this study were grown by metal-organic vapor phase epitaxy (MOVPE), as described in detail in Ref. [8]. Fig. 1 shows the schematic structure of the (lll)-GaAsl_~Px/ AlyGaa_/ks (x=0.07-0.14, y=0.3) SLMQWs. For estimating the well width and barrier thickness for these (111)-oriented SLMQWs, one of the most convenient and extensively adopted method is to measure the growth rate of MOVPE from the observation of the cross-sectional scanning electron microscope (SEM) images of the samples. This method, however, can only provide a rough estimation of the layer thickness because the measurement accuracy of the growth rate is usually limited due to a lot of uncertain factors occurred in the MOVPE growth process. X-ray diffraction technique proves to be a very powerful and nondestructive characterization tool for knowing the structural information of semiconductor quantum wells and superlattices. In fact, by means of X-ray diffraction one cannot only obtain the accurate knowledge about the layer thickness as well as the precise magnitude of the elastic strain and the composition, but also examine the crystalline quality of the samples simulta-

n2 = 2d sin 0,

GaAsP well AIGaAs barrier

(24)

where n is the reflection order, 2 is the wavelength of the incident X-rays, 0 is the angle between the incident X-rays and the diffracting plane, and d is the spacing distance between the diffraction planes, which can be written as a

d=

~/h 2 + k 2 + 12

(25)

for the diffraction from the (hkl) plane. Here a is the lattice constant of the substrate. The GaAsl_xPx well width and the AlyGal_yAs barrier thickness as well as the phosphorous composition in the (lll)-GaAsl_xPx/ AlyGal_yAs SLMQWs were determined from the measurement of the difference in diffracting angles between the SLMQWs-related and the GaAs( 111)B substrate-related diffracting peaks, A0. The measurements were performed using the highresolution double crystal X-ray diffraction from symmetric (333)-plane with the substrate-related diffracting angle being set to be A0 = 0. For example, Fig. 2b shows the measured double crystal X-ray diffraction rocking curve for the (333) plane of the ( 111 )-GaAso.86Po.14/ Alo.3Ga0.TAs SLMQWs. It is clear that besides the dominant GaAs-(lll)B substrate-related diffracting peak, a series of comparatively weak and broad diffracting peaks which are attributed to the diffraction from the SLMQWs, are also prominent. This assignment is consistent very well with the computer simulation result (Fig. 2a), which was obtained according to the theory developed by Fewster and Curling [33 ]. By fitting the simulation with the measurement, the well width and the barrier thickness as well as the phosphorous composition can be determined accurately. Furthermore, the prominent diffracting peaks from the SLMQWs indicate that the quality of the sample is quite high, as confirmed by the observed mirror-like surface morphology.

3.2. Optical characterization by PR Fig. 1. Schematic structure of the ( l l l ) - G a A s 1 xPff AlyGai yAs (x=0.07-0.14, y=0.3) SLMQWs grown by LP-MOVPE.

The PR experimental setup in this study is schematically displayed in Fig. 3. To modulate the

X.. Zhang et aL / Surface Science 387 (1997) 371-382

GaAs(333) (111)-GaAso 86Po14/Aio3Gao7As SLMQW Lz= 150A, Lb = 1190 A

E

(a) Calculation "~

X100

"¢-

.a_a A L A _ L L _ L

= (b) Experiment

,

0

I

400

,

I

,

800

I

,

1200

A0 (arcsec) Fig. 2. Calculated (a) and measured (b) double crystal X-ray diffraction rocking curve for the (333) plane of the (111 )-GaAs0.86Po.14/Alo.3Ga0.vAs SLMQWs.

488 nm

Halogen

Mirror 2

Lamp

Mirror 3

Per real

I Lock-in Amplifier Filter

I

-=1

~

IDigita'V°l~eterl I

Fig. 3. The schematic PR experimental setup used in this study. The normalized signal AR/R is derived from the digital dividing of the a.c. signal by the d.c. signal.

built-in electric field at the surface of the SLMQWs, the 488-nm emission line from an Ar-ion laser was used as the p u m p beam which was chopped at a frequency of O m = 340 Hz. The probe light was a monochromatic beam which was obtained from a 300-W b r o a d - b a n d halogen lamp and dispersed through a 0.5-m monochromator. The slit width of this m o n o c h r o m a t o r was set to

377

1 m m , corresponding to an energy resolution of 2.5 meV. The reflected light from the sample was detected by an I n G a A s photodiode detector. The light focused onto the detector contains two kinds of signals: the d.c. or average value which is proportional to the d.c. reflectance R of the sample, and the a.c. signal or modulated value which is proportional to the change in reflectance AR, varying with the frequency £2m. The d.c. signal was detected by a digital voltmeter, while the a.c. signal or modulated value was measured with a lock-in amplifier. The normalized signal AR/R was derived from the digital dividing of the a.c. signal by the d.c. signal, giving rise to a first-derivativelike spectrum. A c o m m o n problem associated with the PR measurement is how to obstruct the stray light which m a y induce spurious result to the P R spectrum from being detected. One of the unwanted light-signals is the scattered p u m p light which has the same frequency as the signal of interest and thus can be easily detected. Another is due to the PL emission generated by the p u m p light, which sometimes is even greater in intensity than the signal of interest. This problem m a y be solved by utilizing one set of long band pass filters in front of the detector, and/or by reducing the intensity of the p u m p laser beam. The former method is, however, not very appropriate for the filtering of the PL signal, and the latter works at the expense of a p o o r signal-to-noise ratio. For these reasons, the intensity of the p m n p laser beam was usually suppressed as low as possible in our PR measurement, The measuring temperature was in a wide region of 4.2-300 K . We have measured the PR spectra for a number of ( l l l ) - G a A s l _ x P x / A l y G a l , y A s ( x = 0 . 0 7 0.14, y = 0 . 3 ) S L M Q W s at different temperatures and under varied excitation powers. Fig. 4 shows the PR spectrum at 300 K for the ( 111)-GaAso.93P0.ov/Alo.3Goao.TAs S L M Q W s with the well width of L~ = 110 A, and the barrier layer thickness of Lb = 1110 A. To suppress the influence of the scattered p u m p laser beam and the PL signal on the PR spectrum, the excitation power was chosen to be as low as 0.02 mW. As can be clearly seen from this figure, there are two significant spectral structures around 1.435 and 1.850 eV,

X. Zhang et aL /Surface Science 387 (1997) 371 382

378 i

I

I

I

I

I

(111 )-GaAs~_,P×/AlyGal_yAs SLMQW

T=300 K

x=0.07, y=0.3, Lz=110 A, Lb=1110 A le-lhh GaAs

r "~

i

le-1

h

IL

IT'

AIGaAs 2e-2hh

,

,

,

,

,

1.4

1.5

1.6

1.7

1.8

,

19

,.

20

Photon Energy (eV) Fig. 4. The PR spectrum at 300 K for the (111 )-GaAs0~93Po.07/Alo.3Gao.vAs SLMQWs with the well width of L= = 110 A, and the barrier layer thickness of Lb = 1110 A.

respectively. Compared with the PL spectrum for identical sample, the two dominant PR signals can be immediately recognized to be G a A s - ( l l l ) B substrate- and AlyGal_rAs barrier-layer-related band-edge optical transitions, respectively. From the position of the AlyGal_yAs barrier-layerrelated transition, the aluminium composition y was determined to be 0.3 which is in good agreement with the result obtained from X-ray measurement. Another feature with the PR spectrum shown in Fig. 4 is that besides the two dominant signals, one set of relatively weak but unambiguous PR structures can also be distinctly resolved on the high-energy side of the GaAs-(111)B-substraterelated signal. From the line-shape analysis of the experimental data with the first-derivativeLorentzian dielectric functions, we can readily understand that these spectral features should be attributed to the optical modulation of the excitonic transitions rather than the modulation of the band-to-band transitions. The arrows labeled menhh (or me-nlh) in this figure indicate the anticipated energy positions for the excitonic interband transitions between the mth conduction subband and the nth heavy-hole- (or light-hole-) related valence subband. The anticipated energy position which corresponds to the experimental results obtained in the PR measurement, was derived

from line shape analysis with the least-squares method [34]. The PR spectra for the other ( 111)-GaAsl -xPx/AlyGat-yAs SLMQW samples which have different phosphorous compositions or layer thickness are similar to that shown in Fig. 4. Fig. 5, for example, shows the PR spectrum at 3 0 0 K for the (lll)-GaAsl_xPx/AlyGal_yAs SLMQWs with the structural parameters of x = 0.14, y =0.3, L~ = 150 A, L b = 1190 A, which is also characterized by a series of intense excitonic transitions, as denoted by labeled arrows. The plentiful spectral structures in the PR spectra provide us a lot of useful information about the interband excitonic transitions, which plays a crucial role in the determination of the energy band offsets at the heterointerface. This is just the reason why we have utilized PR spectroscopy to characterize the ( 111)-oriented SLMQWs in this study.

4. Analysis and discussion As can be clearly seen in Figs. 4 and 5, besides the normal "parity-allowed" excitonic transitions, such as l e - l h h , l e - l l h , 2e-2hh, etc., some "parityforbidden" excitonic transitions like l e - 2 h h and le-21h, are also evident in these PR spectra. There

7

1 T=300 K

T--r~--l" 1 T-'-~1 (I11)-GaAsv~P./AlyGavyASSLMQW x=0.14, y=0.3, L,=150 A, Lb=1190 k

GaAs "C---t

le-21h

I le-llh

!e-2hh

lie)h" t

/

2e-2'h [I

/ 3e-3hh

AIGaAs

n-

__L 1.4

1.5

1.6

1 1.7

1.8

&_____L___ 1.9

2.0

Photon Energy (eV) Fig. 5. The PR spectrum at 300 K for the ( 111 )-GaAs?.86Po.14/A10.3Ga0.TAs SLMQWs with the well width of Lz = 150 A, and the barrier layer thickness of Lb= 1190 A.

X. Zhang et al. / Surface Science 387 (1997) 371-382

are mainly two reasons which should be responsible for this phenomenon. The first one is due to the so-called "band-mixing" effect [35]. This effect leads to a mixing of heavy-hole and light-hole wave functions and produces the valence subband states with different indices to have both heavyhole and light-hole characters. Therefore, the normal parity selection rule (n = m for the quantum well with infinite barrier height or n + m = 0, 2, 4 .... for the quantum well with finite barrier height) is broken down and "parity-forbidden" excitonic transitions are expected to be observed. This bandmixing effect is, however, usually very weak and apparently applicable to any kind of quantum wells and superlattices. The second reason or more important reason is the presence of the straininduced internal piezoelectric field in the (111)oriented S L M Q W structures. This built-in electric field causes an asymmetric potential and thus thoroughly break the normal parity selection rule down. Here the photon-associated field of the incident pump light was not taken into account, since it was in general much smaller than the strain-induced piezoelectric field. These "parityforbidden" transitions, however, have never been observed in the PL spectra for the ( l l l ) GaAsP/A1GaAs S L M Q W samples. In fact, even the parity-allowed n = 1 light-hole related excitonic transition ( l e - l l h ) was hardly resolved in the PL spectra, as reported in Ref. [8]. The calculation of excitonic transition energies was performed based on the envelop-function approach by assuming an energy band-offset ratio for the conduction-band, Qo=0.61, as mentioned in Section 2. Nonparabolicity effect of the conduction-band and exciton binding energy were included in the calculation. It was noted that the number of observed excitonic transition peaks in a PR spectrum seemed to be always smaller than that of the theoretically predicted transitions, no matter what value of the band-offset ratio may be used in the calculation. In fact, several anticipated "parity-forbidden" transitions and higher-order transitions were not observed in the PR spectra. The physical origin for this discrepancy is still not very clear up to date, however, segregation effect of atoms at the heterointerface may be a possible reason [23]. This effect confuses the boundary

379

between quantum well and barrier layer and thus deduces the real well width as well as well depth. As a result, the quantum confined effect will be weaken in some extent and the number of practically observed optical transitions will be smaller than the predicted one. Based on such a consideration and a careful comparison between the experimental and calculated results, we determined the energy band-offset ratio for the conduction-band Qc at the heterointefface of GaAsl_ ~PJAlyGal_ ~ s in the ( l l l ) - G a A s l _ ~ P J A l y G a l _ y A s SLMQWs to be Qo = 0.61 ___0.03. This value was found to be nearly independent of the phosphorous composition x in the whole region investigated (0.07
X. Zhang et aL/ Surface Science 387 (1997) 371-382

380 !

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(1 11 )-GaAso.93Po.o~AIo.3Gao.TAsSLMQW Lz=110 A, Lb=l 110 P=0.02 mW GaAs QW

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Fig. 6. The temperature-dependent P R spectra for the same sample as that shown in Fig. 4. The measuring temperature was varied from 11 to 300 K.

due to the quickly growing noise, the QW-related excitonic transitions in the PR spectra for our (111 )-GaAs l_xP~/AlyGa l_yAs SLMQWs become hardly resolved as soon as the temperature was decreased below 200 K. This poor resolution at low temperature may be mainly resulted by the unwanted PL signal which tended to become stronger when the temperature was decreased. To suppress the PL-induced noise, reducing the intensity of the pump laser light is usually a simple and effective countermeasure. However, this countermeasure suffers from the compensation that the useful PR signal will be suppressed simultaneously. In fact, during our measurement, the power of pump light had been decreased as low as 0.02 mW, which implies that the line-width of the QW-related excitonic transitions may not be accurately determined from these temperature-dependent PR spectra for the (lll)-GaAs~_xPJAlyGal_~As SLMQWs, and we have to adopt or develop other

method to give a quantitative characterization of the interface roughness. This is an actually challenging work for us in the future. Moreover, in order to clarify whether the straininduced internal piezoelectric field exerts a significant influence on the energy positions of excitonic transitions in PR spectrum as it does in PL spectrum, we have investigated the p u m p - l i g h t power-dependence of the PR spectra for our (lll)-GaASl_xPx/AlyGal_yAs SLMQWs. Fig. 7 demonstrates the PR spectra for the same sample as that shown in Figs. 4 and 6. The p u m p - l i g h t power used was varied in the region between 0.01 and 0.3 mW. It was found that no any apparent blue-shift of the excitonic transitions emerged when the pump light power was increased from 0.01 to 0.3 mW. This result can be interpreted according to the substance of P R modulation mechanism. Because even the maximum pump power adopted in the PR measurement, that is, 0.3 mW, is much smaller than the excitation power employed in the PL measurements[8]. The latter was in general of the magnitude order of several tens of milliwatts. In other words, although the electric field induced by the photo-excited carriers in the PR measurement could indeed modulate the surface built-in field and give rise to PR spectrum, it was, however, too weak to exert a prominent opposite effect on the strong strain-induced internal piezoelectric field. Therefore, profound energy-shift of the excitonic transitions may not be observed in PR measurement.: As mentioned i n the foregoing discussion, increasing pump light power may result in an evident attenuation in the PR signal due to the rapid multiplication of unwanted PL. In fact, as can be seen in Fig. 7, the PR features obtained at the pump light power of 0.3 mW which corresponds to case d in this figure, is approximately three times weaker than those PR features measured at the pump powers of 0.03 m W (case b) and 0.1 m W (case c). It was also noted that the relative intensity of PR signals exhibited a drastic reduction as the pump light power was suppressed < 0.01 mW, as shown clearly in Fig. 7a. The major reason for this phenomenon is that under such a weak pumping condition, the intrinsic electric noise associated with the PR measuring system

X.. Zhang et aL / Surface Science 387 (1997) 371-382 I

I

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(1 11 )-GaAso.93Po.07/Alo.aGao.zAs SLMQW

Lz= 110 ~,, k b = 1 1 1 0 A T=11 K

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(a)

0.01mW

(b)

O.03mW

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381

to be Qc=0.61 _+0.03. This value was found to be nearly independent of the phosphorous composition x in the whole region that we investigated. Furthermore, several interesting phenomena observed in the PR measurement of the ( 111)-GaASl_xPx/AlyGal_yAs SLMQWs as well as the possible physical origins have also been discussed.

References

rr rr

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(c)

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(d)

0.3mW

[1] [2] [3] [4] [5] [6]

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1.6

1.7

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Photon E n e r g y (eV) Fig. 7. The PR spectra of the same sample as that shown in Figs. 4 and 6 with the pump-light-power varied in the region between 0.01 and 0.3 mW.

will become dominant and submerge the PR signals. Therefore, we have performed the PR measurement in this study by using the pump light power usually varied in the region between 0.02 and 0.04 mW.

5. Conclusions

In this article, the effects of the strain-induced piezoelectric field on the electronic structures of the ( 111 )-GaAsl -xPx/AlyGal_yAs SLMQWs have been described in detail according to the deformation potential theory modified by QCSE. The structural and the optical characterization by X-ray diffraction and PR spectroscopy for these SLMQWs have been demonstrated and analyzed i n t e n s i v e l y . By fitting t h e e x p e r i m e n t a l results w i t h the calculation, we have quantitatively determined t h e e n e r g y b a n d offset r a t i o f o r c o n d u c t i o n b a n d at t h e h e t e r o i n t e r f a c e o f G a A s l _ x P x / A l y G a l _ y A s

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