A method for measurement of the optical absorption coefficient of stacked ... method enables us to obtain the thermal conductivity of the thin layer.
Determination of absorption coefficients and thermal conductivity of GaAIAs/GaAs heterostructure using a photothermal method N. Yacoubi, B. Girault, and Jean Fesquet
A method for measurement of the optical absorption coefficient of stacked heterostructures such as GaAlAs on GaAs substrates is described, based on the Fernelius model for an optically absorbing thin layer. This
method enables us to obtain the thermal conductivity of the thin layer. The experimental results are compared with the results given by spectroscopic ellipsometry.
1. Introduction
In recent years photothermal spectroscopy has become one of the most important tools for the study of light absorption in materials that are optically opaque. In a previous paper' we described a nondestructive method of optical absorption coefficient measurement of bulk semiconductor samples based on photoacoustic spectroscopy. Here we present the results of measurements on a heterostructure. Stacked heterostructures
such as GaAlAs on GaAs
substrates are of high technological interest especially for optoelectronic devices. In such devices, precise knowledge of the GaAlAs and GaAs absorption coeffi-
cients near each fundamental absorption edge using nondestructive techniques is of primary importance. For the top GaAlAs layer of the GaAlAs/GaAs structures, measurements are complicated by the fact that GaAs is not transparent in the useful photon energy range and only reflectance-based techniques are available. Among these techniques, spectroscopic ellipsometry with rotating analyzers is the most reliable.2 In this paper we present an improved photothermal technique which allows us to obtain (1) the thermal conductivity, kc, of a 9-,gm thick Gao.4 6Alo.54As top layer;
The authors are with Universite des Sciences et Techniques du
Languedoc, Equipe de Microoptoelectronique de Montpellier (UA au CNRS 3921), F 34060 Montpellier, France. Received 6 March 1986. 0003.6935/86/244622-04$02.00/0. © 1986 Optical Society of America. 4622
APPLIEDOPTICS / Vol. 25, No. 24 / 15 December 1986
(2) the absorption coefficient of the top layer in the 2.05-2.30-eV photon energy range; and (3) the absorption coefficient of the heavily p-doped GaAs substrate in the 1.3-1.44-eV photon energy range. The photothermal data are compared to ellipsometric measurements performed on the same sample. 11. Measurement Method
The outline of the photothermal deflection (mirage effect)3 is schematically represented in Fig. 1. The absorption of the optical exciting beam (heat beam) causes a variation in the temperature of the optically heated region. This temperature variation causes a refractive-index gradient in the oil layer adjacent to the sample surface. By probing this gradient with a second beam (probe beam), one can relate its deflection to optical absorption and to thermal properties of the sample. To obtain a high signal-to-noise ratio, the sample is immersed into carefully filtered cedar oil, which has a refractive index matched to that of the optical sample celland appropriate thermal diffusivity 2 1 (4.8 X 10-8 m
s
).
The cedar oil forms region I; the solid sample composed of the epitaxial GaAlAs layer with a thickness h and the GaAs substrate with a thickness forms region II. The backing forms region III (Fig. 2). The experimental data are reduced using the Fernelius model4 which treats the case of a two-layer sample with different optical and thermal properties. The treatment uses the same level of approximation as Rosencwaig and Gersho.5 The probe beam traveling into the refractive-index gradient is deflected. The probe beam deflection can be related to the optical and thermal properties of the sample under test. Neglecting transients, the general solution giving the temperature
o(x,t) in oil can be written 4 as
,
Il
I /
P robe Beam
SAMPLE
Fig. 1. Schematic view of a photothermal
deflection (mirage effect)
experiment.
1
ABSORPTIONCOEFFICIENT,Pc(M- )
Fig. 3. Theoretical variations of the phase 0, as a function of optical
absorption coefficient of the thin layer. k is the phase of the maximum of the periodic variations of the temperature at the solid-liquid
Y
Probe beam
boundary x = y; kc is the thermal conductivity of the thin layer.
7
X
Heat beam
~~~~~al
is assumed to absorption coefficient fls of the substrate 6 be 5 X 106 m- 1 in this energy range.
The GaAs thermal conductivity ks is assumed to be 44 W - k-1 _ m-1 ,7 and the modulation frequency f = wi
BF
Substrate
Backing
-
3 27r= 152 Hz. We observe that for low values of 1c, 0 =
I-.
-I
~
-lb I
i :h
X_
Fig. 2. Cross-sectional view showing the positions of the solid sample, backing material, and oil.
bo(xt) = [1 - (x - h(lL
-
kL is independent of both 0c and kc, whereas for high values of 0c, p = OH is only dependent on kc. Ak = 'OH L is directly related to kc. Only the real part of the periodic term of 4)0 (x,t) is of physical interest. It is given by the relation TL(x,t) =
h)]00 +0 expLot- L(x - h)] h-
