Volume 11, number 4
OPTICAL ROTATORY DISPERSION OF AgGaS 2 W.J. ANDERSON, Phil Won YU+ and Y.S. PARK Aerospace Research Laboratories, Wright-Patterson Air Force Base, Ohio 45433, USA Received 21 May 1974
The absorption coefficient of AgGaS2 is presented as a function of temperature and polarization. The band gap is calculated as a function of temperature for a simple direct transition model. The optical rotatory dispersion is calculated for the first time in a crystal along an axis of birefringence. The dispersion curves are fit to a simple oscillator model to give the oscillator energy as a function of temperature.
Previous studies o f AgGaS2, a I I I I - V I 2 compound with a chalcopyrite structure, have discussed the lowest direct energy gap , the structure of the uppermost valence bands , and the luminescence properties . The energy gap versus temperature curve slope has been shown to be positive at low temperatures, changing sign at -~ 100 K . Optical activity was first observed in AgGaS 2 by Hobden . He used AgGaS 2 to demonstrate optical activity for the first time in a non-enantiomorphous crystal. He was able to measure the optical rotation at 0.4974/J because o f an accidental optical isotropy allowing the observation of optical activity without the complications o f birefringence. We have measured the absorption coefficient, c~, of AgGaS 2 as a function o f temperature and polarization. The optical rotatory dispersion was calculated for the first time along a birefringent axis from the transmission spectrum o f ( 1 0 0 ) oriented AgGaS 2 crystal placed between crossed polarizers. The crystals were oriented with X-rays and cut with either a (100) surface for optical rotatory power measurements of a (100) surface for optical absorption measurements. All crystals were checked between crossed polarizers for optical homogeniety. Absorption
spectra were measured using Cary Model 14 spectrophotometer adapted with a liquid helium cold finger for adjusting the temperature of the sample. The left side of fig. 1 is the absorption coefficient of AgGaS 2 as a function o f temperature and polarization. The E II C curves could not be extended above 300 c m - 1 without the sample birefringence causing an appreciable error because o f the -~ 4 ° beam spread o f our spectrophotometer. The right half of fig. 1 contains the square o f the absorption coefficient for E ± C. The curve is linear with energy and yields the direct transition bandgap energy as a function of temperature. In comparison to birefringence, optical activity is a relatively weak effect, thus optical rotatory dispersion has not been measured before along a birefringent axis. Using the nomenclature of Hobden , the fractional transmitted intensity, I/Io, passed by the sample, placed between crossed polarizers, is
+ Permanent address: ,Department of Plrysics, University of Dayton, Ohio 45469, USA. Work performed at the Aerospace Research Laboratories under Contract F3361572-C-2114.
h is the mean refractive index of the two modes, ~ is the rotatory power, )to is the free space wavelength, L is the crystal thickness and n e and n o are the refractive indices of the extraordinary and ordinary polar-
I (G/n)2 sin 2 (½LA), I 0 - (n e - not2 +(G/fi) 2 where G = nC~XO/rr,
A = 27r[(ne-no)2+(G[ff)2 ] I/2/X0,
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(110) ORIENTATION .12ram THICKNESS
_o I,Q. 0 m
PHOTON ENERGY (eV)
Fig. 1. The left-hand side is the absorption coefficient as a function o f temperature and polarization for AgGaS2. The right-hand side is al2 versus energy yielding the band gap energy as a function of temperature for this simple model.
ization modes respectively. It is interesting to note that when I n e - n l >> IG/EI, the positions of the peaks in the 1/10 curve are determined mainly by the birefringence while the amplitude of the peaks depends predominently on the optical activity. This characteristic makes possible calculating the optical activity and birefringence as a function of wavelength. Fig. 2 is the fractional transmitted intensity for a 0.13 mm thickness, 5 K temperature, AgGaS 2 sample from the - 4 t h to the 10th fringe labeling the peak of zero birefringence with zero as shown. The optical activity at 0.4979/1 was 608°/mm measured by rotating the analyzing polarizer until the intensity was extinguished (also indicating zero birefringence). The birefringence at each peak was calculated from
n = 0, 1, 2, ...
and assuming a constant rotatory power of 608°/mm. Except for the region from peak - 1 to +1 the birefringence agreed within a few percent ol~ the published values [6, 7].
The amplitude ratio of each peak to the zeroth peak was then used to calculate the optical rotatory dispersion in fig. 3 by assuming
1/10 ~- (GIFO2/(n e-
A small correction had to be made to compensate for the difference between the absorption coefficients for the two polarization modes. The interference spectrum was measured first by setting the polarizer perpendicular and then parallel to the optic axis. The two measurements were averaged to obtain the peak ratios. The maximum difference in peak amplitude between the two measurements was ~ 10% for the high energy side of the interference spectrum decreasing to zero at the low energy side. Fig. 3 also contains the optical rotatory dispersion curves for 125 K and 300 K measured in the same way. Condon  has reported the development of the theory of optical rotatory dispersion. The optical rotation, 9~, can be represented by 393
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CE 2 E2a_E 2'
where C is a constant. The fit at 5 K gives Eba = 2.70 eV compared to Eba = 2.735 eV determined from the absorption coefficient data. The 125 K data was fit with an Eba = 2.67 eV while the absorption data gives 2.708 eV. A room temperature data fit was not attempted because its range is limited on the high energy side by optical absorption, however, the bandgap does appear to shift slightly to a lower energy. The single oscillator model fit implies that the oscillator energy shifts to lower energy as the temperature increases in contradiction to the absorption coefficient data. The temperature dependence of the optical rotatory power at the point of zero birefringence is compared in fig. 4 to the band gap as measured by the absorption coefficient data from fig. 1. The largest change in rotatory power occurs between 0 - 1 6 0 K. In conclusion, the method for measuring the optical rotatory dispersion discussed in this paper is useful when there is a point of zero birefringence, the birefringence dominates over the optical activity through most of the spectrum, and the absorption coefficients of both polarization modes are approximately the same.
Fig. 2. The absorption o f a AgGaS2 sample 0.13 m m thick placed b e t w e e n crossed polarizers at 4.9 K.
3hcM '-ff E2a_ E2
where M is the molecular weight, p is the density, N is Avogadro's number, h is Planck's constant, c is the speed of light, E is the radiation energy, Eba is the energy of the transition a ~ b and Rba is the rotational strength constant of the a ~ b transition. The solid lines in fig. 3 represent the theoretical fits to the~optica[ rotation data using the equation 394
T E M P E R A T U R E (*K)
Fig. 4. The optical rotatory power and bandgap energy as a function of temperature. The optical rotatory power was measured at the p h o t o n energy of zero birefringence using the sample of fig. 2. The bandgap energy was determined in fig. 1.
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0 300*K '\ 900
OPTICAL ROTATORYDISPERSION Ag GO S 2
0Q. )..n-. 0
.J _(2 I-
~ i .5000
 J .5050
Fig. 3. The optical rotatory dispersion for AgOaS2 sample used in fig. 2.
We would like to thank J. Manthuruthil for growing the crystals used in this experiment.
References  B. Tell and H.M. Kasper, Phys. Rev. 134 (1971) 4455.  B. Tell, J.L. Shay and H.M. Kasper, Phys. Rev. B6 (1972) 3008.
 P.W. Yu and Y.S. Park, J. Appl. Phys. 45 (1974) 823.  P.W. Yu, W.J. Anderson and Y.S. Park, Solid State Commun. 13 (1973) 1833.  M.V. Hobden, Acta. Cryst. A24 (1968) 676.  G.D. Boyd, H. Kasper and J.H. MeFee, J. IEEE Quantum Electron. QE-7 (1971) 563.  C. Schwartz, D.S. Chemla, B. Ayrault and R.C. Smith, Opt. Commun. 5 (1972) 244.  E.U. Condon, Reviews of Modern Physics 9 (1937) 432.