InP multi-quantum wells

Materials' Science and Engineering, B 21 (1993) 189-193

189

Absorption coefficient and exciton oscillator strengths in InGaAs/InP multi-quantumwells C. Arena and L. Tarricone* Dipartimento di Fisica, viale delle Scienze, 43100 Parma (Italy)

F. Genova and C. Rigo (NELT, via G. Reiss Romoli 274, 10184 Torino (Italy)

Abstract The excitonic properties of InGaAs/InP multi-quantum-wellsystems grown by chemical beam epitaxy have been investigated with absorption measurements in the temperature range 8-300 K and in the spectral region 0.775-1.550 eV. In this region, the excitonic resonances corresponding to n = 1, n = 2 interband transitions, and the steplike behaviour of the two-dimensional density of states have been clearly observed. By fitting the lineshape of the excitonic features with Gaussian functions the most noteworthy parameters are discussed. The energy position of the peak changes as a function of temperature, according to the relation known for the InGaAs energy gap. Moreover, the full width at half maximum is deduced and is discussed in terms of an intrinsic contribution plus a thermal broadening due to the interaction with LO phonons. The integrated area of the excitonic peak examined seems to be temperature independent. On the other hand, the integrated area decreases when the well width increases, because of the shrinkage of the ls exciton wave function. A ratio of the oscillator strengths related to light, and heavy hole excitons equal to 0.6 has been determined, in accordance with the theoretical prediction.

1. Introduction

One of the more remarkable consequences of the two-dimensional confinement provided by quantum well structures is the high enhancement of excitonic absorption. In addition, the application of a moderate electric field results in considerable wavelength shift (quantum Stark effect) and an overall increase in the absorption coefficient. These effects, first extensively studied in GaAs quantum well structures, find applications in optical fibre communication systems. Recently GaAs matched to InP has appeared as a promising system for applications in the near-IR region. In fact, the ground state exciton energy can be tuned within the wavelength region 1.30-1.55 ~m by controlling structural parameters such as well width and composition of the ternary alloy. Since the first report of InGaAs/InP quantum wells grown by low pressure metal-organic chemical vapour deposition (LPMOCVD) [1], the need to increase the structural quality of these materials has led to the use of a number of different growth techniques [2, 3]. Indeed an accurate control of thickness and composition, and

*Author to whom correspondence should be addressed.

(192 I-5107/93/$6.00

an improvement in the interface abruptness can influence significantly the electrical and optical properties of the structures. In particular, chemical beam epitaxy (CBE) emerges as one of the more successful growth techniques [4]. In this work InGaAs/InP quantum well structures grown by CBE have been characterized in detail by optical measurements and the results show the superior quality of CBE.

2. Experimental details

The InGaAs/InP multi-quantum well (MQW) heterostructures, nominally undoped and prepared by CBE were grown by alternating InxGa I _xAs and InP layers onto an S-doped InP substrate. A nominal indium molar fraction x = 0.51 was used. This composition corresponds to lattice mismatch (0.17%) and gives rise to strain effects in the wells, as discussed later. In Table 1 the most important parameters of the MQW structures are reported, where n is the number of periods, Lw is the well width and L b is the barrier width. The MQW region is sandwiched between undoped buffer and cladding InP layers of 0.3 ~ m thickness. Details on the specimen growths are given in ref. 5. The © 1993 - Elsevier Sequoia. All rights reserved

('. Arena et al.

190

/'

Excitonic prol)erties of ht(iaAs/lnl ) '~,lQWsystem~

T A B L E 1. Characteristic parameters of M Q W structures used Sample

n

L. (A)

L b (A)

x~,

qwl91 qw300 qw370 qw371

66 40 12 22

94 63 68 25

80 I O0 250 385

51 5I 5I 5

161

-~

14!--

(

12i--

<

o N p

InP substrate and buffer layers were not removed, because of their transparency near the fundamental edge of the InGaAs. This fact is an advantage since no etching is required to open an optical access through the substrate and so possible stresses to the structure are avoided. In order to perform optical measurements in the temperature range 8-300 K, a close cycle Cryophysics cold-tip cryostat was used. The absorption coefficient spectra of all the samples studied were deduced both from transmission and absorbance measurements. For the transmission measurements, the exciting beam of a halogen lamp, chopped at a frequency of 120 Hz and dispersed by a 0.5 m Spex monochromator, was focused on the M Q W samples. The light transmitted through the samples was detected using a PbS detector and the signals processed by conventional lock-in technique. Wavelength scanning and data acquisition were controlled by an Apple 2E computer. A Varian 2390 spectrophotometer was used to perform absorbance measurements and data were collected on an Olivetti computer.

3. Results and discussion

Transmission and absorbance measurements in the spectral region between the absorption edge of InGaAs and InP have been performed. The absorption curves were calculated from the transmission and/or absorbance experiments according to the relation given in ref. 6, and assuming an equal reflectivity for the two facets (30%). The internal reflections at the InGaAs/InP interfaces were neglected since the refractive index of these materials is quite similar. Figure 1 shows the absorption spectra obtained at 8 K on all the samples. The absorption coefficient spectra exhibit the steplike behaviour characteristic of the two-dimensional density of states and excitonic resonances at the onset of the steps. Besides, the electron-heavy hole n - 2 exciton peak E2hh_~ becomes less well defined as the temperature increases, while electron-light and heavy hole n = l excitonic peaks (EHh-eElhh-~) are clearly observed up to 300 K. Sometimes in the high energy" region of the spectra, the free exciton absorption peak of InP is observed also up to relatively high temperature (200 K). This latter experiment provided clear

lOt--

81 .

~-

.

~

.

.

!

"~-

•

r

qw370

T =8 K

qw191

2L-V 800

1000

1200

1400

! 6(/0

WAVELENGTH(nm) ]Fig. 1. Optical absorption coefficient spectra at T = 9 K as calculated from transmission and absorbance measurements for all the samples. The vertical arrows show the energy position of the main peaks as deduced by theory. In the inset the shrinkage of the 1s exciton with well width decrease is shown.

evidence of the high quality of the present materials. A s expected, the number of excitonic peaks increases with increasing well width. The attribution of the peaks has been possible by comparing the calculated band-toband energy transitions with the experimental values, having considered the influence of the excitonic binding energy [7]. The calculation was carried out by solving the Schr6dinger equation for a particle in a finite potential well within an effective mass approximation. The band non-parabolicity was taken into account by considering the Luttinger parameters; the contribution due to the strain was calculated to be of 6.64 meV. The details of the calculations are given elsewhere [8]. Actually the well is not rectangular in shape but somewhat trapezoidal because of fluctuation of the composition at the interface. In fact, incorporation of As in the barriers and formation of InGaAsP at: the interfaces occurs even using a very fast flux switching system [9]. Moreover, a valence band discontinuity A = 0.55 has been assumed, even though several values of the conduction-valence band offset between InGaAs/InP are reported in literature [7]. However, a satisfactory agreement between theoretical and experimental transition energies is observed for all samples, as shown by vertical arrows in Fig. 1. In

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Excitonic properties of lnGaAs/ lnP MQ W systems

fact, the comparison between the experimental and theoretical results gives an uncertainty of about 1% in the energy peak position. It is also possible to determine from the experimental data the quantum well width to an accuracy of about 10%. Using Gaussian lineshape modelling for the n = 1 hh-e exciton, a semiempirical fit has been performed on the low energy side of the absorption peaks. In addition, a best fit of the absorption spectra over the temperature range studied for sample qwl91 has been made by considering Gaussian functions for the peaks related to the n - - l h h - e and lh-e transitions respectively, superimposed on a more or less broadened twodimensional continuum, as given by the relation reported in ref. 10. In Fig. 2 the energy peak position is given as a function of temperature for all the samples, and it is shown that the temperature dependence of InGaAs bulk gap is followed (solid line). In the inset all the main exciton peak positions of sample qw l 91 are reported as a function of temperature. Figure 3 shows the values of the full width at halfmaximum (FWHM) for temperatures varying between 8 K and room temperature. It may be noted that in general the FWHM gradually increases as the well width decreases. Using the semiempirical law proposed by Chemla [11 ], the experimental data have been fitted (solid lines). Thus the FWHM may be taken to be com-

1.05

I

'1

....

o

1.00

o

....

o

I . . . .

o

I ....

G

a

a

Leo

o i

....

....

....

O0

I'''

0

OO

2hh-e o a o o

O O

oa o °=a

0~

0 as

~

where an appropriate LO phonon energy ha)= 32.2 meV [12] has been assumed. The F 0 parameter is primarily made up of three broadening factors, i.e. composition fluctuations, interface roughness and non-periodicity. The relatively large F 0 value of the structure with thinner wells (qw371) is due to the large influence of monolayer thickness fluctuations at the heterointerfaces. If a comparison is made with the GaAs/GaA1As system, the values F0=4.7 meV, F(300 K) = 9 meV are usually reported for GaAs MQW samples [10], and excitonic absorption peaks are narrower than in InGaAs MQW structures. This fact is probably explained by the increased difficulty encountered in growing ternary compound layers, compared with the binary ones. The effects of dimensionality on the oscillator strength of the n = 1 exciton have been considered. When L w is smaller than the exciton Bohr radius a b (which in the InGaAs system is about 178.4 A [7]), the overlap amplitude of the electron and hole generally increases with the decrease of the well layer thickness L,~. Consequently the oscillator strength of excitons will rapidly increase. In addition, the area of

I . . . .

0~s

~,, .... , ............. ~7~,,

0 Bo

~o

F,, + r , / [ e x p ( h a ) / k T ) - 1]

=

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aa

0.90

r

'''1

I ....

qwlgl

>

posed of two main terms: a constant F 0 plus a contribution F(T) proportional to the density of thermal LO phonons with proportionality constant'F ~, i.e.

i

;o

0.95

191

~;~

~:~

o

[]

Temperature

(K)

,:.

qw300

o

qw370

o

qw371

[]

qwl91

i;i

0.85

0.80

0.v5

,,,,

0

I , , , , 50

I .... 100

I , , ,, [ i i i i ~ 150 200 250

Temperature

300

(K)

Fig. 2. Energy location of the Elhh_ e peak for all the samples as a function of temperature. The solid Line concerns the InGaAs energy gap. In the inset the main peak positions of sample qwl91 are shown.

192

C Arena et aL

/

Excitonic properties of lnGaAs/InP MQ W system.~

the absorption peak is proportional to the oscillator strength. In the inset of Fig. 1, the values of the integrated area are reported as a function of the well width. In agreement with experiments first performed for the GaAs/A1As system [13], it is evident that the area of the heavy exciton peak does not follow the l/L,,

0.055

....

[ .... ~:~

0.050

I ....

I

....

I'''-~

o

qw300

o o

qw370 o

qw371

o

0.045

F ....

dependence (solid line). Finally, m Fig. 4, the therma! behaviour of the integrated area of the main exciton peak (EH, h_~)is shown for all the samples measured and is seen to be almost constant over the temperature range studied. In the inset of Fig. 4, the ratio of the absorption area of the n = 1 light and h e a w excitons, reported as a function of temperature, shows a constant behaviour. The ratio of the oscillator strengths can be expressed as:

c } o /

qwlgl

o

0.040

0

where #th and/-/hh are respectively the reduced mass o f light and heavy exciton, and [[Mc~ liar,and I[M~, nhh are the matrix elements between conduction and light and heavy valence band states. By assuming HM~vllih/ 1[Me,, []hh= ~ [1 4], it can be proven that the experimental value of the ratio fh/fhh = 0.6 is in good agreement with the theoretical prediction.

0

-i

o

0.035

-

D

oooo~¢,

o.o3o _~

D D D

~

O

0.010

0.005

o.ooo r , , , 0

, I .... 50

I .... I .... t I00 150 200 T e m p e r a t u r e (K)

I,,, 250

I

4.

Transmission spectroscopy applied to InGaAs/lnP heterostructures is confirmed as a powerful technique in investigating the M Q W electronic properties which are strongly related to the two-dimensional excitonic features. With a lineshape modelling, parameters related to the structural and compositional quality are deduced, and the shrinkage of the 1s wave function is

300

Fig. 3. The full width at half-maximum (FWHM) of the E l h h e peak as deduced from a Gaussian lineshape of the excitonic peak; the best fits, assuming he) = 32.2 meV are the solid lines.

0.200

,

'

I ....

I ....

[ ....

I ....

I''

''1

O.e

0.175

O00000000QO0000

-

°00o

00

....

~o

I ....

1oo

O

qw370

o

qw371

[]

qwl91

I ....

lso

I ....

eoo

I,

g~

,%

0

o

0

Temperature (K) O

-

0

0

0

O

O

0

-

,

0.025

o

o ,,,I

0.100

qw300

o.~

-

0.125

~:~

I l l l

04 qwl91

d

r

....

00

i

0.150

Conclusions

I

0.000 0

o O D

I,,,,I, 50

100

,,,I,

~

D 13 D El D O O D

D O r-I rl El O D D D r'l 0 0 Vl O

,,

O~0

,

150

,

[

200

,

,

,

,

J

250

,

,

,

t

300

Temperature (K) Fig. 4. Temperature dependence of the integrated area of the E1hh-~absorption peak; in the inset the ratio Area~h/Areahhis plotted.

C. Arena et al.

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Excitonic properties of lnGaAs/InP MQ W systems

shown. A satisfactory agreement between experimental and calculated energy of excitonic transitions supports the quality of this theoretical approach. T h e meaning of the ratio of the oscillator strengths of light and heavy excitons is briefly discussed and the experimental value fh/fhh = 0.6 seems to be consistent with the theoretical one. T h e s e considerations p r o v e also the excellent perf o r m a n c e of CBE.

3 4 5 6 7

Acknowledgments 8 This work has been partially supported by the Progetto Strategico Elettronica dello Stato SolidoCNR. T h e authors wish to thank Professor R. Capelletti for her collaboration in the absorbance experiments and B. Rotelli for her help with the measurements. One of the authors (C.A.) wishes to thank C S E L T which finances her fellowship.

9

10 11 12

References 13 1 M. Razeghi, J. P. Hirtz, U. O. Ziemelis, C. Delalande, B. Etienne and M. Voos, Appl. Phys. Lett., 43 (1983) 585. 2 M. S. Skolnick, L. L. Taylor, S. J. Bass, A. D. Pitt, D. J.

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