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Characterization of Ga1-xInxSb thin layers grown on GaAs substrate by infrared reflectivity
A. Mezerreg, C. Llinares, N. Rezzoug, B. Mbow
To cite this version:
A. Mezerreg, C. Llinares, N. Rezzoug, B. Mbow. Characterization of Ga1-xInxSb thin layers grown on GaAs substrate by infrared reflectivity. Journal de Physique III, EDP Sciences, 1993, 3 (9), pp.1819- 1824. �10.1051/jp3:1993241�. �jpa-00249044�
J. Phys. III Franc-e 3 (1993) 1819-1824 SEPTEMBER 1993, PAGE 1819
Classification Physic-s Ahstiacts
72.20 32.20F 72.80E
Characterization of Ga,_~ln~sb thin layers grown on GaAs
substrate by infrared reflectivity
A. Mezerreg, C. Llinares, N. Rezzoug and B. Mbow
Centre d'Electronique de Montpellier, URA CNRS 391, Universitd Montpellierll, Sciences et Techniques du Languedoc, 34095 Montpellier Cedex 05, France
(Receii>ed lo November1992, revised 31 March 1993, accepted 20 April /993)
Rdsumk. Des me~ures de r£flectivit£ infra-rouge sont faites sur des couches de GanmIn,~_~osb
£pitaxi£es sur substrat de GaAs semi-isolant avec une densit6 de porteurs allant de lo'? cm~~ h 10'~ cm~ ~. Les paramdtres 61ectriques et optiques de la couche sont d£termin£s simultan£ment en
ajustant [es donn£es exp£rimentales par le moddle th£orique approprid. Les densit£s et mobilitds obtenues sont comparables h celles donn£es par les mesures d'effet Hall, et les parambtres optiques
sont en bon accord avec [es valeurs donn£es dans la litt£rature.
Abstract. Infrared reflectivity measurement are made on Gaj,~oInj,~j~Sb thin layers grown on
semi-insulating GaAs substrate with free-carrier density varying from lo'? cm~~ to 10'~ cm~~.
Electrical and optical parameters of the layers are determined simultaneously by fitting appropriate
theoretical model with experimental data. Densities and mobilities obtained are of the order of the
ones given by Hall measurements and optical parameters are in good agreement with those given in the literature.
1. Introduction.
Infrared reflectivity is currently used to investigate optical and electrical properties of III-V semiconductors [1-5]. In previous publications we reported results of some III-V semiconduc- tors characterization by infrared reflectivity spectra analysis. We found that for binary compounds, such as Gasb substrates [6] Gasb epitaxial layers on Gasb or semi-insulating (SI) GaAs substrates [7], quatemary alloys Ga, _,In,As,Sbj
_,
and Gaj _,Al,As,Sbj
_,
thin layers
grown on Gasb substrates [8], the results given by the optical method were in good agreement
with those given by electrical measurements or given in literature. In this work, we report results concerning both electrical and optical parameters of thin layers of Gaj _,In,Sb ternary compounds grown on GaAs (SI) substrates.
2. Theory.
2. VIBRATIONAL MODE oF Gaj _,In,Sb. Gay _,In,Sb behave with a single vibrational mode
for.i~ 0.30 and with two-mode for.<~ 0.30 [9]. Each mode is observable on infrared
1820 JOURNAL DE PHYSIQUE III N° 9
reflectivity spectrum as a peak. So, for Gaj _,In,Sb there is one peak for -1~ 0.30 and two peaks for ~i
~ 0.30.
2.2 REFLECTIVITY. For our fitting procedure we used the well known reflection model [7], assuming an abrupt junction and an uniform layer of constant thickness. Reflection is calculated in terms of the layer thickness and complex refractive indices of the layer and the substrate, whose relation to permittivity may be written as
~ ~
? ~
fi~
=
P(w
= t.~ + ~j
~
~ /"' ~" ~~ II)
wqo~ w'- iw y~ w (w + ilT~)
where
w and p~ are the frequency and the high frequency dielectric constant respectively,
(s~, w~o~, y~) are the oscillator strength, transverse optical phonon frequency and damping
constant for the j-th lattice oscillator respectively, and w~, T~ are plasma frequency and free- carrier scattering time, related to density n and mobility p of free carriers [6].
In equation (1) 7(w) is expressed by the sum of the lattice and free-carrier (last term) contributions. For the substrate which is a binary compound there is only one oscillator with
strength given by .I
= p~ p~ =
(w/o/w(o p~. For the temary compound Gaj _,In,Sb,
p~ and effective mass are approximated by following linear relationships
~~ " (l »t) ~mGasb + X~mlnsb (2)
and
m * " ( fi ill$JSb + ""llI$Sb ~~~
2.3 MiNlmizATioN. In our fitting technique, we used the method of maximum neighbour-
hood given by Marquardt [10]. This method performs an optimized interpolation between the
Taylor series method and the gradient method and is based upon an adequate representation, in
a maximum neighbourhood, of the non linear model by a first order truncation of a Taylor
serie. Marquardt Algorithm minimizes the sum of squares difference ~Pby finding a trial vector B~'+ '~ at (I + )-th iteration from that of the I-th iteration by :
~(,+ll_~(>) ~~(,l (4)
where 6~'~ is the step vector at the r-th iteration, calculated by solving the linear equation (A* + AI) 6*
=
g* (5)
where I is the unity matrix, A * is the correlation matrix and A is a parameter which can be varied in order to obtain ~P~' + ' '
~ ~P ~'' g * depends on the derivatives and difference between theoretical and experimental reflectivities (see Refs. [6, 10] for more details).
3. Experiments.
The layers are grown by MOVPE (metal-organic vapour phase epitaxy) in our laboratory, using a vertical reactor at atmospheric pressure. Layers are doped with Te. Reflectivity
measurements are done with an FFT infrared spectrometer IFS II 3 V Bruker, using a Genzel
interferometer allowing to cover a large range of frequency by easily selecting spletters which
are of small dimensions and are disposed on a carrousel in the focal plan. Spectra are recorded with a resolution of 2 cm~ ' and 4 cm~ ' at the angle of incidence of about 6°.
N° 9 CHARACTERIZATION OF Ga~ ,In,Sb BY lR REFLECTIVITY 1821
4. Analysis.
We have characterized Te doped epitaxial layers of Gaj ,In,Sb grown on GaAs (SI) substrate,
with thickness of about 2~m and with carrier densities varying from 10'~cm~~ to
10'~ cm~ ~ For all samples treated the peak corresponding to Gasb like-mode is well apparent, but the one corresponding to Insb like-mode is hardly noticeable.
Layer parameters depend on its composition. So, if >. is taken as a fitting parameter,
iterations will strongly slow down and will compromise convergence. To avoid this, >. is fixed
at a value which is measured with a good precision (~ 2 iii) by microprobe (EDS Energy
Dispersive Spectroscopy), all others parameters on which dielectric constant depend are adjusted (s~, w~o~, y~, w~, T~, t). Substrate was semi-insulating, Hall effect (Van der Pauw
technique [I I]) measurements are made on samples after taking their reflectivity spectra.
We started the fitting procedure by assigning some reasonable values to the parameters ; such values can be found for the oscillator strength and optical frequency by inspecting position and amplitude of peaks in the spectra. The iteration procedure converges when enough precision concerning the various parameters (~0.01iii), is reached. To obtain the best solution, after three or four trys of computation started with different values of parameters, we
chose the solution that give a smallest value for the sum of squares difference ~P and a best
accord between experimental and theoretical curves. Figure shows an example of theoretical
curves obtained for sample 2 together with experimental curve. Dispersion on corresponding
densities and mobilities are An
~ 0.3 x 10'~ cm~ ~, AR
~ ?25 cm~ v~ ' s~ ', and
errors on
chosing a solution or another are less than 6 §b on density and less than 20 ill on mobility.
3 2
~' 4
3 ~
il ,//
_./
4
15O 2&J 4X
Frequency
Try n° n cm-~
~ cm2 v-' s-' ~P
4.9 x 10'7 309 3.8 x 10-~
2 5.I x 10'7 155 3.2 x 10-~
3 5.2 x 10'7 084 2.8 x 10-~
4 4.9 x 10'7 II1 2.7 x 10-~
Fig. I. E~ample of variou; re;ult, and corre;ponding curve~ given by lea,t-,quare, fit for ,ample ?.
1822 jOURNAL DE PHYSIQUE III N° 9
Some reflectivity spectra and the corresponding theoretical curves, given by a least-squares fit,
are shown in figure 2. Table I summarizes our results densities of free-carrier obtained by the
optical technique are in good agreement with those given by electrical measurements, relative difference (An/n
= jn~ -n~j/n~) is always less than 21iii, nevertheless we note large
w ~)
mmme2 Mmme3
E E
,o
30
SO loo 150 200 250 300 350 400
F~uency [Cm"'
lc) (C~
aampie4 sample8
E E
Frequency cm Fmquency cm"
Fig. 2. Reflectivity spectra ofGajjmInj,~j,Sb layers grown on GaAs (SI) substrate (- experiments, least-squares fit).
Table I. Electrical parameters of the layers.
sample nH nR @H ~R t tR
(x 1017 10'7 v-i s-i) v-i s-i) j~m) (~m)
4.4 4.7 360 391 2.3 2.37
2 4.5 4.9 007 11 2.1 2
3 6.6 7.8 800 050 2 2.03
4 8.5 9.9 000 355 2.I 1.95
5 10.5 12.I 300 793 2 1.85
6 11 13 2 000 2 733 2.3 2.3
7 17 20.7 2 200 2 873 2 2.07
8 20 22 2 627 3 156 2 1.93
N° 9 CHARACTERIZATION OF Ga, _,In,Sb BY IR REFLECTIVITY 1823
discrepancies between mobilities. Mobility has a tendency to increase when t§e concentration of electrons increases, this seems to be compatible with results reported by Gazanly et al. [12]
who found that for n-type Gaj _,In,Sb free carrier scattering time grow when electrons density
increases from 10'~ cm~ ~ to 10'~ cm~ The small values of mobility can be attributed to
layers mismatch on GaAs substrate which leads to bad crystallinity. It is also possible that these small values are due to the existence of a compensated layer (especially for smallest densities). The values of optical parameters are reported in table II together with the values
given by Brodsky et al. [9] for the same composition x
=
0.30. Optical frequencies are close to those of binary compounds corresponding to each mode and are in good agreement with those given in reference [9] : w~oj l 75 cm ' to 180 cm ' (w~o (Insb)
= 185 cm '), w~oi
220 cm~ ' (w~o(Gasb
=
225.5 cm~ '). The oscillator strengths are in relative agreement with the peaks amplitudes of the modes, but we note a dispersion on damping constants.
Table II. Optic-al parameters of the layei~s.
~~~'P~~ W
TO (Cm St Y (Cm )
W ~~~ (Cm~ Sj l'2 (Cm~
l 173 0. 4.7 222 1.2 5.23
2 175 0.22 4.4 221 1.39 4.3
3 176 0.27 4.8 217 1.39 3.1
4 182 0.12 7.7 218 1.03 6.7
5 180 0.08 3 219 0.77 3.9
6 175 0.29 3.7 218 1.29 4.9
7 188 0.03 2.8 220 0.66 2.9
8 176 0,14 3 220 0.9 3,
Brodsky 175 0.16 4.4 221 1.33 4.2
et al.
Conclusion.
Gaomlno~osb Te doped thin layers grown on GaAs jSI) substrate are characterized using
infrared reflectivity. Both free-carrier parameters (density and mobility) and lattice parameters
are determined simultaneously by fitting appropriate theoretical model to experimental
reflectivity data. Values obtained for electrical parameters are comparable to those given by
Hall measurements and optical parameters are in good agreement with published values for the
same composition. These results and those published previously [6-8] confirm the efficiency of this optical technique in characterizing a wide range of III-V semiconductors, and especially
temary and quatemary compounds. This characterization does not require any preliminary study of the compound to investigate its vibrational parameters and those are simultaneously
determined with electrical parameters by using an efficient algorithm in the minimization
procedure. This technique, furthermore does not involve any contact with the sample, which is not the case with electrical technique where the sample is usually damaged.
1824 jOURNAL DE PHYSIQUE III N° 9
References
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[2] Perkowitz S. and Breecher J., Iiili.ared Ph_v.v. 13 (1973) 321-326.
[3] Palik E. D., Holm R. T. and Jibson J. W., Thin Solid Film 47 (1977) 167-176.
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[5] Pickering C.. I. Elec.fi.oil. Mall. IS 11 986) 51.
[6] Mezerreg A., Llinares C. and Montaner A., Ph».v. Stattt.v Solidi (hi169 (1992) 121.
[7] Mezerreg A.. Llinares C., Ph».<. Snafu.v Solidi (hi170 (1992) 129.
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[9] Brodsky M. H., Lucovsky G., Chen M. F. and Plaskett T. S., Phy.v. Ret'. B 2 (1970) 3303.
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