GaAs structures grown on polar substrates

Microelectronics Journal, 26 (1995) 827-833

0026-2692(95)00043-7

i ¸

Piezoelectric field measurements by photoreflectance in strained InGaAs/ GaAs structures grown on polar substrates P.D. Berger 1 C. Bru 1 Y. Baltagi ~ T. Benyattou ~, M. Berenguer ~, G. Guillot ~ X. Marcadet 2 and J. Nagle 2 I

I

!

l Laboratoire de Physique de la Mati~re, INSA-(URA C N R S 358), Bat. 502, 20, avenue A. Einstein, F-69621 ViUeurbanneCedex, France. Tel: +33 72 43 83 29. Fax: +33 '72 43 85 31. E-mail: bru@insa,insa-lyon.fr 2 Thomson-Laboratoire Central de Recherches, Domaine de Corbeville, F-91404 Orsay Cedex, Fra;~ce. Tel: +33 1 60 19 7096. Fax: +33 1 60 197829

Photoreflectance (PR) measurements were performed on specific structures grown by molecular-beam epitaxy on different substrate orientations: (111)B, (111)B 2 ° off, (111)A and (100). A strained In0.2Ga0.sAs quantum well was grown in the space charge layer of an undoped GaAs layer. On a polar substrate orientation (111), the straininduced piezoelectric field in the quantum well modifies the field in the space charge layer. P k spectra recorded in such structures exhibit Franz Keldysh oscillations from which we can measure the internal electric field. The piezoelectric field is then deduced from a comparison between two structures differing only by the presence of the strained quantum well. Experimental values ranged between 110 kV/cm and 150 kV/cm, and

were used to determine experimentally the piezoelectric constant el4 in In0.zGa0.sAs.

0026-2692/95/$9.50 ~ 1995 Elsevier Science Ltd

827

1. Introduction he g r o w t h o f strained layers o n I I I - V substrates o f high i n d e x surfaces (other than (100)) gives rise to piezoelectric effects due to the zinc blende nature o f the I I I - V c o m p o u n d crystals. T h e o r e t i c a l calculations have s h o w n that v e r y high strain-induced electric fields exist in thin alternating layers o f GaInAs and GaAs in

T

iii

P.D. Berger et al./Piezoelectric field measurements

the (111) crystallographic direction [1]. These built-in electric fields induce modifications of the band structure and of the optical properties of the devices and offer a new parameter for the band gap engineering of novel electronic and optoelectronic devices. In most experimental works, the amplitude of these internal electric fields is generally determined in an indirect way through the study of strained quantum wells in PIN structures by photoluminescence [2], photocurrent spectroscopy [3] or electroreflectance measurements [4]. The piezoelectric field value is deduced from a comparison between the experimental energy of the fundamental optical transition in the quantum well and the results of a modelling of the Stark effect in the quantum well. Such calculations need many assumptions about the strain effects, the valence band anisotropy and the piezoelectric effects. In this paper, we directly measure the straingenerated piezoelectric field by contacfless photoreflectance (PP.) experiments in an In0.2Ga0.sAs quantum well between GaAs barriers grown on different polar substrates. This method was first proposed by Shen et al. [5]. In this paper, we study for the first time the piezoelectric effects on (111)A and (111)B polar substrates.

2. Principle of experiments Special structures called U P + [6] have been designed in order to create a high and wellcontrolled internal electric field in the structure: a narrow non-intentionally doped layer (or undoped layer referred to as U-layer) is grown on a highly doped p+ GaAs layer. Owing to the surface states, the Fermi level is pinned at midgap at the GaAs surface. In the p+ layer, the Fermi level is pinned at the valence band. Thus, if the U-layer thickness L is small compared with the natural extension of the surface space charge layer (SCL), the electric field FSCL in the U-layer is uniform and well defined:

828

rEseLl = IE,,

-

Evbl/L

(1)

where Evs (Evb) is the difference between the Fermi level and the valence band at the surface (in the bulk). If a strained quantum well of thickness d is grown in the middle of the U-layer, a piezoelectric field Fpz is induced by the strain in the quantum well whenever the substrate is of a high index surface. In this case, the measured value F~cL of the field in the U-layer is modified in the following way: (L + d) F~c L -F dFpz =

E~ - Evb

(2)

where the + sign means that the piezoelectric field direction can point either in the direction of or opposite to F~CL. The piezoelectric field Fvz in the quantum well is then determined by the difference between the field F~cL measured in a U P + structure with a strained quantum well and the field FSCL in the structure without the quantum well. The band structures of three U P + samples, each of them containing a strained quantum well in the U-layer, are plotted schematically in Fig. 1. The three samples are grown on substrates of different orientations: (100), (111)A and (111)B. According to the substrate orientation, Fpz is either in the direction of or opposite to Fscr, as illustrated in Fig. 1: on a (111)A substrate, the FscL will be higher than on a (100) substrate, whereas it will be lower on a (111)B substrate. In this work, we have used P R experiments to measure optically the electric field in the U-layer of such samples. The P R technique is an optical modulation spectroscopy technique, which consists of recording the derivative of the optical absorption spectrum with respect to a modulating parameter, in this case the electric field. This gives very sharp features at each optical transition.

Microelectronics Journal, Vol. 26, No. 8

Lorentzian absorption profile, ignoring excitonic effects, and for an electro-optic energy much larger than r [7]: L+d _--

d

I

Ec

z~ ~(E)

forE
o(exp

[ m:he .'fl/j (3a)

Evb -Evs

Ef for E

% / ,

lEg

<111>A

~ E v b Evb -Evsg ~ ~ J

Eg

R (E) oc exp

Ec

L~. ~ ¢/'t''''-

xcos

\

hO ) + ~

(he) ] (3b)

Ef

r-J l Evb -EvsI

>

Ec

I Eg E

where • is a phase factor and h 0 is the electrooptic energy related to the electric field F and to the reduced interband effective mass #It through:

<11 I>B v

1

b Ef

Fig. 1. Schematic band :~tructure of the samples with a strained quantumwell in the undopedtop layer, on different substrateorientations. When the modulating electric field is relatively high, such that the energy gained in the field is much higher than the natural broadening r of the optical transition, the energy ba~Ids are tilted and electrons which attempt to tunnel from the valence to the conduction band see a triangular barrier. If during the tunnelling process they interact with a photon with an energy smaller than the energy gap, the width of the barrier to cross is made smaller and the tunnelling effect can be effective: absorption is then enhanced at energies lower than the barrier. If they interact with photons of energy higher than the band gap, the Franz Keldysh effect gives rise to oscillations in the P R spectrum. This behaviour is described well by a simple form of the lineshape which is valid for a

hO= \

2#11 ,]

(4)

In the condition of high electric fields, the P R spectrum is characterized by an exponential absorption tail below the energy band gap and an exponentially decaying oscillatory behaviour above the band gap, which is known as Franz Keldysh oscillations (FKOs). A plot of (4/3n) (Em -Eg) 3/2 as a function of m (index of the energy extrema) is a straight line whose slope is (h(~)3/2. From this slope, the electric field F can be quantitatively measured if #jj is known. When the internal electric field FSCL is small compared with the modulating field Fac, the FKO period is governed by Fac; but when the internal electric field is much stronger than the modulating field Fac, FSCL is governing the oscillatory behaviour of the spectrum [8]. This is currently the case in the U P + structures studied in this paper. This very interesting property gives the P R technique the ability to measure optically the internal electric field.

829

P.D. Berger et al./Piezoelectric field measurements

The precision obtained in the determination of Fsc/. is linked directly to the number o f oscillations which can be recorded in the spectrum. From eq. (3b), we can see that FKOs exhibit an exponentially decaying character, which is all the more rapid when F is larger: F should be as low as possible, i.e. the semiconducting material has to be very pure. In this respect, the U P + structure used in this study is a very good compromise and also offers high internal electric fields and good material quality in the undoped layer.

3. Experimental The samples used in this study were grown by molecular-beam epitaxy (MBE), and consisted of a 4250 A thick highly doped GaAs:Be layer (1019oCm-3) grown on a GaAs substrate, then a 680 A thick undoped GaAs layer. Four different substrate orientations were studied: (100), (111)B, (111)A and (111)B 2 ° offmisoriented, which is known to allow better quality layers. For each substrate orientation, two samples were grown: one with a 70 A thick In0.2Ga0.8As strained quantum well in the middle o f the U layer, and another simple U P + without any quantum well. The same structures on different substrate orientations were grown all together in the MBE chamber. The growth conditions were optimized for (100) and (111)B 2 ° offorientation. The P R experimental set-up is a conventional one [9] with a 12 m W H e - N e laser as the pump beam and a 150 W quartz tungsten halogen lamp as the probe beam. The p u m p laser beam is chopped at a frequency of 310 Hz and the probe light beam is dispersed through a 0.64 m JobinYvon monochromator. Measurements are performed under an incident angle of the probe beam of 45 °. Reflected light is detected by a Ge or Si photodiode operating in the photovoltaic mode, connected to a current-to-voltage converter. The modulated part of the reflected light (ZXR) is detected by a two-way acquisition module and AR/R spectra versus light wave-

830

length are obtained by numerical division. The sensitivity of our set-up was about 10 -6 in the spectral range between 700 n m and 1800 nm. Spectral resolution was limited to about 7 nm.

4. Results and discussion In Fig. 2, the typical P R spectra recorded at room temperature in each sample are plotted. For each substrate orientation, we have plotted in dashed lines the P R spectrum of the U P + structure with a strained quantum well, and in solid lines the P R spectrum of the structure without the strained quantum well. The spectra were recorded at low pump and probe excitation density in order to minimize the photovoltage effects. For the conventional orientation (100), the two spectra are perfectly superimposed and lead to the same electric field in the space charge layer o f the U-layer. This is consistent with the fact that no piezoelectric effect is expected on a (100) substrate. For all other substrate orientations, we can see that the period of the FKO is modified when a strained quantum well is introduced in

i, 1.3

1.4

1.5

1.6

1.3

1.4

l.S

1.6

1.3

1.4

1.5

1.6

1.5

1.6

',,

r.

1.3

1.4

Energy (eV)

Energy

(eV)

Fig. 2. Room temperature PR spectra recorded in the structures with a quantum well (dashedlines) and without a quantum well (solidlines).

Microelectronics Journal, Vol. 26, No. 8

the U-layer. This signifies a modification of FscL due to the existence of the internal straininduced piezoelectric field in the quantum well. In the case of a (111)A substrate, the FKO period is increased in the presence of the strained quantum well, leading to a higher FSCL. This is consisten,t with a piez,oelectric field in the direction ol~posite to FSCL, as predicted theoretically (see Fig. 1). On the: contrary, in the case of (111)B orientations, the FKO period is decreased, and this leads to a piezoelectric field pointing in the same direction as FscL, as shown in Fig. 1. In order to extract il~Lequantitative value of the piezoelectric field, we have plotted the evolution of 4/37r(Em- Eg) 3/2 as a function of the index extrema m for each of the samples, the slope of which is ( h O ) 3/2 (Fig. 3). The piezoelectric field values are deduced from the comparison between the fields measured in the structures with and without the strained quantum well (QX,~). We used a reduced effective mass #lb

equal to 0.06 m0 in the (111) direction [10], where m0 is the vacuum electron mass. The results are reported in Table 1. These piezoelectric field values are given with a precision of 4-20%, taking into account the precision of the layer thicknesses (10%) and electro-optic energy determination (10%). It is worth noting that the error in the field determination is relatively important, especially in (111)A and (111)B samples, where the number of maxima is relatively low due to a rather large broadening parameter F which is responsible for the rapid damping of FKOs. Indeed, the growth conditions were optimized for (100) and (111)B 2 ° off substrate orientations, and yielded very narrow quantum well photoluminescence peaks at 4 K: the full width at half maximum was 3.7 meV and 6.8 meV, respectively. However, for the structures on (111)B and (111)A, the full width at half maximum increased up to 15 meV and 22 meV due to non-optimized growth conditions for these substrate orientations.

2.0x10 -2

2.0xlO -2

1.5xlO -2

1.5xlO -2

F m 1.0xlO -2

l.OxlO -2

5x10 -3

5xlO -3

A

/I ~I L I ~ I I I

Ox]O ° 0

I

2

3

4

5

6

OxlO °

J

I 0

I I 3 max

I

2

max

I 4

lxl~ 2 1.6x 10-2 8x10-3 1.2x10 "2

6 x l 0 -3

~B

Fm 4x10 -3 2x10 -3 .t~

OxlO ° o

I

8.0x10 -3

~ .a s~ ,4

4.0x10 -3

!

|

|

2

3

4

OxlO °

0

1

2

3

max

4

B

5

Fig. 3. P l o t o f 4 / 3 n (E,~ - Eg) 3/2 as a f u n c t i o n o f m a x i m u m i n d e x m, for t h e e i g h t samples.

831

P.D. Berger et al./Piezoelectric field measurements

TABLE 1 Piezoelectricfieldsin a strained 70 A In0.20Ga0.s0Asquantum well in GaAs Substrate orientation

(111)B

(1111)B2° off

(1111)A

FSCL(without QW) (kV/cm) F~CL(with QW) (kV/cm) Fpz (kV/cm)

46 31 115

35 20 125

41 51 150

e14 (C/m2)

0.058

The values of Table 1 are to be compared with theoretical determinations of the piezoelectric field induced by strain in a layer, the thickness of which is supposed to be less than the critical thickness. Then Fp, can be estimated as a function of the lattice misfit Aa/a, the elastic stiffness tensor elements Cij and the piezoelectric constant of the layer el4 [11]:

Fpz = (2v~e14~ (C11 Cll -[-2C12 .~ \" KK----O'/ +2C12+4C44J(-~)

(5) K0 is the permittivity of free space and x the dielectric constant of the material. The Cij values for In0.2Gao.sAs are linearly extrapolated from the values of the binaries GaAs and the InAs taken in [10]. If we also use a linear extrapolation o f e14 between the two constituent binaries (e14 = 0.14 C/m2), we obtain a theoretical value for Fpz equal to 276 kV/cm. This value appears to be rather high compared with our experimental results as was also the case for other experimental determinations reported in the literature [3, 4]. In order to explain this discrepancy, we can invoke the existence of charges at the quantum well interfaces, as assumed in [4] for InGaAs/ A1GaAs interfaces. It could also be due to the fact that the InGaAs layers are partially relaxed. The indium composition is known within 10% error around the nominal value of 0.20. This value is further confirmed by the energy position

832

0.063

0.076

of the quantum well fundamental transition, which is in good agreement with theoretical determinations. An important source of discrepancy between experimental and theoretical results lies in the poor precision with which the constant el4 is known, even in the binary GaAs: values ranging between 0.12 C/m 2 and 0.16 C/m 2 are found in the literature [12, 13]. So we have used our results to determine experimentally el4 using the measured Fpz in eq. (5). The values are reported in Table 1. The values of el4 obtained for a 20% indium composition are about twice lower than those currently used in such systems, but they are in good agreement with those recently reported in [14]: for the same indium composition on (111)213 orientation, they obtained e14 = 0.07 C/m . In conclusion, we have directly measured in a contactless way the piezoelectric field in a strained In0.2Ga0.sAs quantum well in GaAs, on both orientations (111)B and (111)A. No fitting procedure of the quantum confined Stark effect is necessary to extract the piezoelectric field value, contrary to the usual study of the absorption edge modification in the quantum well by photoluminescence or photocurrent spectroscopies. This direct determination of Fpz may also be used as an experimental determination of the piezoelectric constant, which has not been very precisely known up to now. We find a piezoelectric field value of 130 kV/cm 4- 20% for both substrate orientations.

Microelectronics Journal, Vol. 26, No. 8

References [1] D.L. Smith, Strain-generated electric fields in (111) growth axis strained-layer superlattices, Solid State Commun., 57(12) (1986) 919-921. [2] T.S. Moise, L.J. Guido and R.C. Barker, Magnitude of the piezoelectric field in (111)B InGaAs strainedquantum wells, J. Appl. Phys., 74(7) (1993) 46814684. [3] A. Pabla, J.L. Sanche~,-Rojas,J. Woodhead, R. Grey, J.P.R. David, G.J. Rees, G. Hil, M.A. Pate, P.N. Robson, R.A. Hoog, T.A. Fisher, A.R.K. Willcox, D.M. Wittaker, M.S,. Skolnick and D.J. Mowbray, Tailoring of internal :fieldsin InGaAs/GaAs multiwell structures grown on (111)B GaAs, Appl. Phys. Lett., 63(6) (1993) 752-754. [4] R.L. Tober and T.B. Bahder, Determining the electric field in (111) strained-layer quantum wells, Appl. Phys. Lett., 63(17) (1993) 2369-2371. [5] H. Shen, M. Dutta, W. Chang, R. Moerkirk, D.M. Kim, K.W. Chung, P.P. Ruden, M.I. Nathan and M.A. Stroscio, Direct measurement of piezoelectric field in a (111)B grown InGaAs/GaAs heterostructure by Franz Keldysh oscillations, Appl. Phys. Lett., 60(19) (1992) 2400-2402. [6] C. VanHoff, K. Deneffe,J. De Boeck, D.J. Arent and G. Borghs, Franz Keldysh oscillations originating from a well-controlled electric field in the GaAs depletion region, Atrpl. Phys. Lett., 54 (1989) 608610.

[7] D.E. Aspnes, Band non-parabolicities, broadening, and internal field distributions: the spectroscopy of Franz Keldysh oscillations, Phys. Rev., B10 (1974) 4228-4238. [8] H. Shen and F.H. Pollak, Generalized Franz Keldysh theory of electromodulation, Phys. Rev., B42(11) (1990) 7097. [9] N. Bottka, D.K. Gaskill, R.S. Sillmon, R. Henry and R. Glosser, Modulation spectroscopy for electronic material characterization, J. Electron. Mater., 17(2) (1988) 161-170. [10] O. Madelung, Semiconductors, Landolt and Btrstein, New Series, Vol. 17(a), 1982. [11] E.A. Caridi, T.Y. Chang, K.W. Goossen and L.F. Eastman, Direct demonstration of a misfit straingenerated electric field in a [111] growth axis zincblende heterostructure, Appl. Phys. Lett., 56(7) (1990) 659-661. [12] G. Ark, P. Quadflieg, Piezoelectricity in III-V compounds with a phenomenological analysis of the piezoelectric effect, Phys. Status Solidi, 25 (1968) 323330. [13] A.R. Hutson and D.L. White, Elastic wave propagation in piezoelectric semiconductors, J. Appl. Phys., 33(1) (1962) 40-47. [14] J.L. Sanchez-Rojas, A. Sacedon, F. Gonzalez-Sanz, E. Calleja and E. Munoz, Dependence on the In concentration of the piezoelectric field in (111)B InGaAs/GaAs strained heterostructures, Appl. Phys. Lett., 65(16) (1994) 2042-2044.

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