We measured the optical dispersion of the interband Faraday rotation of GaSe near the absorption edge at the temperature of 298°K. From our data it is possible to confirm that a direct allowed electronic transition takes place between the valence and the conduction bands in GaSe. © 1980 American Institute of Physics.72105341534

Donatti D.A.

Villaverde A.B.

English

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GaSe Faraday rotation near the absorption edge
A. Balbin Villaverde and D. A. Donatti 
 
Citation: The Journal of Chemical Physics 72, 5341 (1980); doi: 10.1063/1.439025 
View online: http://dx.doi.org/10.1063/1.439025 
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GaSe Faraday rotation near the absorption edge 
A. 8albin Villaverde and D. A. Donatti 
Universidade Estadual de Campinas. Instituto de Fisica "Gleb Wataghin." 13100 - Campinas - SP. Brazil 
(Received 13 November 1979; accepted 5 February 1980) 
We measured the optical dispersion of the interband Faraday rotation of GaSe near the absorption edge 
at the temperature of 298 oK. From our data it is possible to confirm that a direct allowed electronic 
transition takes place between the valence and the conduction bands in GaSe. 
We measured the Faraday rotation of a thin sample 
of GaSe as a function of the wavelength, near the ab-
sorption edge, at a temperature of 298 "K. A pulsed 
magnetic field with a pulse duration of the order 5 msec 
was used. The system characteristics, as well as the 
calibration procedure of the magnetic field, are de-
scribed elsewhere. I We used as a light source for the 
Faraday rotation measurements a argon pumped 
Rhodamine 6G dye laser. The laser wavelength, mea-
sured with a precision better than 0.1 nm, was varied 
from 649.4 nm up to 625.6 nm. This last value cor-
responds to an upper limit in the laser photon energy 
of 98. 5% of the GaSe energy gap. The sample of a 
thickness of 215 ,urn was studied with the laser light 
polarization perpendicular to its c axis. 
We carried out two sets of measurements correspond-
ing to the values of the magnetic field peak of 60 and 
30 kG, respectively. We found that the rotation angles 
were proportional to the strength of the applied mag-
netic field within experimental errors for the whole 
spectral range; so, we averaged the values obtained 
for the two series of measurements. The Faraday ro-
tation of GaSe was found to be positive. Our results 
are summarized in Table I. Because the Verdet con-
stant of the sample depends on its temperature (by 
shifting the energy gap), we kept the temperature stable 
within ± 2 "K. By using the value given by Tatsuyama 
et al. 2 for the variation of the energy gap E, with tem-
perature 
* = - 5 X 10-4 eV /"K, (1) 
we find that an uncertainty of ± 2 "K in the temperature 
produces a shift in E, of the order ± 0.001 eV, which 
is unimportant in our experiment. 
In Fig. 1 we plotted the measured Verdet constant 
of GaSe, multiplied it by the index of refraction, as a 
function of inCident photon energy; the corresponding 
values of the index of refraction were taken from the 
Akhundov et al. measurements. 3 We estimated an ex-
perimental error for the Verdet constant measurements 
of the order ± 5%. 
By measuring the frequency dependence of the inter-
band Faraday rotation of a semiconductor, it is possible 
to obtain information about the value of its energy gap 
and the nature of the optical transition: direct or in-
direct, that takes place. According to Boswarva et al. 4 
we have for a direct allowed optical transition the rela-
tion 
(2) 
where n is the index of refraction of the sample, V is 
its Verdet constant (min G- t em-I), K is a constant, and 
the variable x is defined by 
x=E/E" (3) 
where E is the incident photon energy and E, is the 
energy gap. The function F 2(x) is given by 
F 2(x) = (l/x) [(1-xr Il2 - (1 +xt1l2] -1. (4) 
This last function applies when the contributions of the 
lower bands are taken into account. On the other hand, 
when it is assumed that only one valence band contrib-
utes to the magneto-optical rotation, we have the rela-
tion, as shown by Roth, 5 
nV=KFt(x), (5) 
where the function F t (x) is given by 
FI (x)= (l/x) [(I-xr I/2 - (1 +xtI/2] 
- (4/x 2)[2 - (1_x)1I2 _ (1 +x)1I2]. (6) 
The two functions are very similar and both approach 
1/2 • (l-xf when E-E,. However, for any value of x, 
the function F t (x) is always smaller than F2(x). 
For indirect allowed electronic transitions between 
valence and conduction bands, the phonon contribution 
must be included. Assuming one phonon emission and 
absorption process, Kolodziejczak et al. G found the 
relation 
L ') ( 1 1 1 1 - x' ) 
nV=KF3", = ~ln 1~+,ln-1--' +1 K, (7) x -x x +x 
While Boswarva et at. « obtained the result 
1..1) ( 1 1 1 1 1 - x' ) 
nV=KF4", = 2'ln 1-x'2 +2x' n 1+X' +1 K, (8) 
TABLE 1. Optical dispersion of the Verdet constant of GaSe. 
Wavelength 
(j.lm) 
0.6494 
0.6459 
0.6420 
0.6381 
0.6356 
0.6328 
0.6306 
0.6287 
0.6275 
0.6265 
Photon energy 
(eV) 
1. 909 
1.9195 
1. 931 
1. 943 
1. 9505 
1.959 
1. 966 
1.972 
1.976 
1.979 
Verdet constant 
(min G -\ cm -\) 
0.595 
0.615 
0.65 
0.70 
0.74 
0.8°5 
0.91 
1. 045 
1. 15 
1.285 
J. Chem. Phys. 72(10),15 May 1980 0021·9606/80/105341-02$01 .00 © 1980 American I nstitute of Physics 5341 
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5342 A. B. Villaverde and D. A. Donatti: GaSe Faraday rotation 
4.00 
3.50 
'e 3.00 u 
'" .. ::I 2.50 c 
... 
, 
c: 
'i§ 
2.00 
> c: 
1.50 
1.00 
1.90 1.92 1.94 1.96 1.98 
ENERGY (eV) 
FIG. 1. GaSe Verdet constant, multiplied by its index of re-
fraction, as a function of the incident photon energy. 
where x' = E/(EI + E pb ) and Epb is the phonon energy. 
These two last functions are quite different from Fl or 
F 2, in that they rise more slowly and do not go to in-
finity as E goes to E1 • 
Our Faraday rotation data, as a function of the inci-
dent photon energy, were fitted to Eqs. (3), (5), (7), 
and (8). We found that when functions F3 and F, are 
used the fitting is very poor; whereas, a much better 
agreement is obtained by using the functions Fl or F 2• 
For function Fl we get the parameter values 
K=0.720minG- 1 cm-1 and E,=2.02eV; (9) 
and by uSing function F 2, 
K = 0.520 minG-1 cm- 1 and EI = 2. 01 eV. (10) 
Thus we can conclude from the observed frequency de-
pendence of the GaSe Faraday rotation that an electronic 
direct allowed transition takes place between the valence 
and conduction bands. Nevertheless, from our experi-
mental data it is not possible to decide if functions Fl 
or F2 give us a better description of the interband Fara-
day rotation effect in GaSe. 
We also plotted in Fig. 1 (solid line) the theoretical 
curve represented by Eq. (3). A similar curve is ob-
tained by using the function Fl instead of F 2• It can be 
seen from the graph that the fitting is not quite satis-
factory, the difference between the theoretical curve 
and the data points is slightly bigger than the assumed 
experimental error. Such a discrepancy can be ex-
plained in the following way: from optical absorption 
spectra data (Akhundov et al. 3) and magneto-optical 
absorption (Brebner et al. 7), it is known that there is 
an exciton absorption line in GaSe very near to the 
fundamental absorption edge (about 30 mV below of it) 
and the contribution of this excitonic transition to the 
Faraday rotation should be taken into account in order 
to get a better agreement between theory and experi-
mental data. 
The constant K in Eqs. (2) and (5) is given by the re-
lation, according to Boswarva et al. , 3 
(11) 
in cgs units, where e is the electron charge (in esu 
units), c is the light velocity in a vacuum, If is the 
Planck's constant divided by 21T, rno is the mass of the 
free electron, Jl is the reduced effective mass for elec-
trons and holes, Eg is the energy gap, y is the Zeeman 
splitting parameter 
Y = JlB (gc + gv)/2n;, (12) 
with JlB the Bohr magneton and gc and gv the g factors 
of the conduction and valence bands, respectively; and 
IP~v 12 is the square of the matrix element of - m(a/ax) 
between the valence and the conduction states at k= 0. 
By using the values for GaSe given by Nishina et al. , 8 
we get 
(13) 
and the values of the parameters K and Eg given in 
Eqs. (9) and (10), we obtain the two possible values of 
1 P~v 12, 
(14) 
or 
Ip ~v 12 = 3. 3 X 10- 39 cgs units, (15) 
respectively. These are of the same order of magnitude 
as reported by Balkanski et al. 9 for the II-VI com-
pounds, such as znS, ZnSe, CdS, and ZnTe, 
1 p~~ 12 = 1. 53 X 10- 38 cgs units. (16) 
Likewise, the value we obtained for the energy gap E, 
is in complete agreement with the values reported from 
optical absorption experiments at room temperature. 
For instance, according to Tatsuyama et al. , 2 Eg 
= 2. 01 eV at 282 OK. 
We express our gratitude to Horiclea Sampaio for 
growing the GaSe samples. We also acknowledge the 
financial support of Centro Tecnologico Aeroespacial 
and the FundaC;ao de Amparo a Pesquisa do Estado de 
Sao Paulo. 
IA. Balbin Villaverde, D. A. Donatti, and D. G. Bozinis, J. 
Phys. C 11, 495 (1978). 
2C. Tatsuyama, C. Hamaguchi, H. Tomita, and J. Nakai, Jpn. 
J. Appl. Phys. 10, 1968 (1971). 
3G . A. Akhundov, N. A. Gasanova, and M. A. Nizametdinova, 
Phys. status Solidi 15, K109 (1966). 
41. M. Boswarva, R. H. Howard, and A. B. Lidiard, Proc. 
R. Soc. London Ser. A 269, 125 (1962). 
5L . M. Roth, Phys. Rev. 133, A542 (1964). 
6J. Kolodziejczak, B. Lax, and Y. Nishina, Phys. Rev. 128, 
2655 (1962). 
7J. L. Brebner, J. Halpern, and E. Mooser, Helv. Phys. Acta 
40, 385 (1967). 
By. Nishina, S. Kurita, and S. Sugano, J. Phys. Soc. Jpn. 21, 
1609 (1966). 
9M . Balkanski, E. A mzallag , and D. Langer, J. Phys. Chern. 
Solids 27, 299 (1966). 
J. Chern. Phys., Vol. 72, No. 10, 15 May 1980 
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Gase Faraday Rotation Near The Absorption Edge

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Gase Faraday Rotation Near The Absorption Edge

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