phys. stat. sol. (b) 187, 149 (1995) ..... A. GOLDMAN, J. TEJEDA, N. J. SHEVCHIK, and M. CARDONA, Phys. Rev. B 10, 4388 (1974). (Received May 26, 1994; ...
J. GONZALEZ et al.: Hydrostatic Deformation Potentials and Phase Transitions
149
phys. stat. sol. (b) 187, 149 (1995) Subject classification: 71.25 and 78.20; 64.70; S8.16 Centro de Estudios de Semicondutores, Facultad de Ciencias, Universidad de Los Andex, MPrida
Hydrostatic Deformation Potentials and Phase Transitions in CuGa(SxSe,JZ Alloys at High Pressure BY J. GONZALEZ, E. CALDERON, and F. CAPET~) The optical absorption edge of CuGa(S,Se, -x)2 single crystals is measured as a function of hydrostatic pressure, covering the full stability range (0 to 30 GPa) of the chalcopyrite phase. For 0 2 x 5 1, a linear increase of the direct energy gap with pressure is found. The corresponding gap deformation potential is calculated to be -4.5 eV for x = 0, - 5.2 eV for x = 0.5, and -4.4 eV for x = 1. From changes in the light transmission characteristic of the samples under pressure, structural first-order phase transitions are observed.
1. Introduction
In recent years, the I-111-VI, chalcopyrite semiconductors have received considerable interest because they show promise for practical applications in non-linear optics, light emitting diodes, photovoltaic optical detectors, and solar cells [l]. The system CuGa(S,Se, -x)2 which shows a single phase solid solution over the whole composition range and a continuous variation of structure and electronic properties [2 to 41, has received considerable attention. A large amount of experimental and theoretical work has been carried out in order to gain a better understanding of their electronic, electrical, and optical properties at normal pressures [5 to 81. However, only a limited number of high-pressure studies have been performed on these compounds [9 to 171. No systematic data have been published on the change in their energy band structures with hydrostatic pressure. Recent in situ X-ray measurements [ 151 show that the CuGa(S,Se, - J 2 samples, as the other chalcopyrites, undergo a phase transition from the low-pressure body-centered tetragonal structure (point group I42 m, with two formula units per unit cell) which has fourfold coordination of the atoms, to a high-pressure structure with sixfold coordination, which is of rocksalt type. This transition is similar in nature to the corresponding one in the IV, 111-V, and 11-VI families, i.e. it is strongly of first order with martensitic character and accompanied by a large (16%) volume decrease. Hence, in the present work we have studied the optical absorption coefficients of CuGa(S,Se, -x)2 single crystals as a function of pressure up to 30 GPa. From the data, the pressure dependence of the energy gaps (dE$dP) and the hydrostatic deformation potentials (ag)were obtained. From the change in the light-transmission characteristic under pressure, evidence of first-order structural transitions in these compounds, similar to those observed in X-ray measurements, was found. I)
Merida 5101, Venezuela.
’) Permanent address: Laboratoire de Dynamique et Structure des Mattriaux Molkculaires, URA
CNRS 801, UFR de Physique, BPt. P5, USTL, F-59655 Villenueve dAscq, France.
J. GONZALEZ, E. C A L D E R ~and N , F. CAPET
150
2. Experimental
CuGa(S,Se, -J2 samples were grown by the chemical vapor transport method as described elsewhere [2]. The X-ray analysis of Debye-Scherrer powder photographs indicates the presence of a single phase with the chalcopyrite structure (Ia2d). All these samples, as observed by thermal probe, were p-type conducting. The samples used were 20 pm thick with transverse dimensions of about 150 pm. They were prepared by mechanical lapping and polishing on both sides of the platelets and later broken into small pieces of the required dimensions for the pressure chamber. Optical absorption measurements were performed in a gasketed diamond anvil cell (DAC) with a 4 : 1 methanol-ethanol mixture as the hydrostatic pressure medium. This mixture retains fluidity up to 10 GPa. The pressure was determined to within f O . l GPa by using the R1 line shift of a 10 pm ruby chip placed close to the sample. The maximum pressure gradient across the gasket hole was less than 0.1 GPa as checked by measuring the pressure distribution with several ruby chips. The transmittance T = I / I , was measured by the sample-in-sample-out method, I is the intensity transmitted through the sample and I, the light from a quartz-iodine tungsten lamp, is measured through the pressure transmitting medium in the cell, near the sample, by moving the DAC perpendicularly to the beam. In order to prevent errors due to light diffusion in the cell, we used a two-pinhole system. The first one is used to make a small light spot in the cell (@ x 30pm). The second one, placed between the cell and the spectrometer, ensures that only light coming directly from the central part of the spot area is analyzed. This method reduces stray light (Tmi,,)down to 8.0 x At low energy, far below the absorption edge of the sample, a non-zero and constant value for the apparent absorption coefficient is found. This is a general case in optical measurements on transparent crystal samples and comes from various reasons: imperfections of the crystal, diffusion at the interfaces, etc. In the low frequency region, where the samples are known to be transparent, the apparent transmittance is corrected by a constant factor a to fit the theoretical transmittance for IX = 0. This factor is experimentally determined for each pressure and sample by measuring the low energy constant transmittance region. The non-polarized transmitted light was analyzed by a simple Spex monochromator (0.25 m) yielding a linear dispersion of 1 nm mm- in the first order. The second-order radiation diffracted from the 1200 lines mm-’ grating was eliminated by using adequate filters. The radiation was detected by a photomultiplier whose signal was processed with a photon counting system. Finally, the absorption coefficient c1 is calculated from the transmittance given by
if old & 1, then
and c1
1 d
= - [2 In (1 - R )
- In (a(T - Tmi,,))]
Hydrostatic Deformation Potentials and Phase Transitions in CuGa(S,Se, -J2
151
with
where n is the refractive index of the sample, no the refractive index of the methanol-ethanol pressure-transmitting medium. T is the experimental transmittance, a the correction factor, and a' the thickness of the sample. It should be noted that the correction due to the stray light (Tmi,)has been taken into account in the high energy, low transmittance region. The refractive index of methanol-ethanol n,(P) has been extrapolated from the results of [18] with the Clausius-Mossotti law. For the calculation, values of n as a function of wavelength reported by Boyd et al. [19] at 300K were used. We neglected the n versus P variation because in the I-111-VI, compounds the coefficient dn/dP is very low. Final errors in the absorption coefficient c1 due to errors in the determination of the refractive index of methanol-ethanol and the samples and in the experimental transmittance are less than 2% for 100cm-' < c1 < 2500 cm-l; these limits being set by the thickness of the sample.
3. Results and Discussion The variation of the direct band gap under pressure for x = 0,0.5, and 1 of CuGa(S,Se, -,) up to their respective phase transition, is measured. Some representative absorption spectra for x = 1 and 0.5 at different pressures are shown in Fig. 1 and 2, respectively. Similar spectra were recorded for x = 0. An analysis of the spectra for all the materials showed that the absorption at the fundamental edge can be described by the relation A a = - (hv - E nhv
(4)
ENERGY (eV)
-
Fig. 1. Shift in the absorption edge with hydrostatic pressure for CuGaS, (1) P = 0, (2) 0.2, ( 3 ) 1.0, (4) 2.0, (5) 2.5, (6) 4.0, (7) 4.5, (8) 9.0 GPa
152
J. GONZ~LEZ, E. CALDERON, and F. CAPET
ENERGY ( e V -)
Fig. 2. Shift in the absorption edge with hydrostatic pressure for CuGa(S,Se,-.), for x = 0.5 (1) P = 0.6, (2) 1.1, (3) 1.9, (4) 2.5, (5) 5.0, (6) 8.0, (7) 10.1, (8) 12.8, (9) 15.7, (10) 16.3 GPa 3.1
I
CuGa (S1-,Sex) 2 x.1.0
t-
->,
2.9 2.7
a
a
(3
> (3 a 2.5
w
This corresponds to an allowed direct transition between parabolic bands without electron-hole interaction. This behavior is in agreement with all previous measurements at normal pressures [l]. The resulting pressure dependence of the energy gap values, obtained by (4) are shown in Fig. 3 for x = 1 and 0.5. For every concentration x, we observed a blue shift of the direct band gap with pressure. For most semiconductors, the variation of the direct band gap under pressure can be described by a quadratic expression of the form EJP)
=
E,(O)
+ U P+ b P 2 .
(5)
2.3
2.1
0
I
5
I
10
PRESSURE (GPO)-
Fig. 3. Pressure dependence of the direct energy gap in CuGa(S,Se,-.), for x = 1 and 0.5
Hydrostatic Deformation Potentials and Phase Transitions in CuGa(S,Se,
153
-J2
Table 1 Linear and quadratic coeficients describing the dependence of the direct energy gap of CuGa(S,Se, -J2, ZnSe, and ZnS compounds. The values of the deformation potential (a,), bulk modulus (B,,), and transition pressure ( P , ) are also given x
Zn Se ") CuGaSc, CuGaS2 ZnS")
E,(O) a (ev) lo-' (eV GPa-')
2.69 0 1.66 0.5 2.13 1 2.50 3.64
7.2 5.0 5.1 4.5 6.7
b (eV GPa-,)
- 1.5 0 -0.7 0 - 1.31
(ev)
B, @Pa)
-4.8 -4.5 -5.2 -4.4 -5.0
66.7 91 103 96 77.1
ug
Ho P, (X-ray) P, (optical) (GPa) (GPa) 4 4
4 4 4
13.5 14.5") 15.7") lgb) 15.0
13.6 17.0 18.0
") See [20]. ') See [15].
Table 1 gives the results of the least-squares fit of the data to such a polynomial. For comparison the values for the 11-VI analogues of CuGaS, and CuGaSe, are also shown. Murnaghan's equation of state has been used to perform the transformation from pressure to volume parameters, taking for the isothermal bulk modulus B = B , + BbP. The values of B , and B, are listed in Table 1 and are obtained from in situ X-ray experiments under high pressure [15]. In this manner, the experimental variation of the band gap E, with the relative variation of the volume V can be calculated. This is shown in Fig. 4 for samples with x = 1 and 0.5. A least-squares fit to the experimental data is performed with
where ag is the hydrostatic deformation potential for the band gap, sometimes called acoustic deformation potential. The ug values are given in Table 1 for x = 0, 0.5, and 1. The values of ZnS and ZnSe are also included for comparison. As can be observed, in the case of CuGa(S,Se,_,), compounds the direct energy gap increases with increasing pressure, similar to the binary analogues, but the rate of change of E, with pressure (dE,/dP) is smaller. It has been suggested that the p-d hybridization of the uppermost valence bands of the I-111-VI, compounds is responsible for this anomaly [21, 221. This type of hybridization has been also observed in [23] for the copper halides. On the other hand, as pointed out by Jaffe and Zunger [7] the p-d hybridization has a simple molecular-orbital interpretation. The outer valence p orbitals on the anion form in a cubic field a threefold degenerate state, rls(p). The five fold degenerate d orbitals on the cation (separated by an energy AEPdfrom the anion p states) transform in cubic field into a threefold degenerate r,5(d) combination and into a twofold degenerate T,,(d) combination. The states of the same symmetry T,,(p) and T,,(d) can interact, forming a lower bonding state and an upper antibonding state. Perturbation theory suggests that the two states, T,,(p) and r15(d), will repel each other by an amount inversely proportional to AEpdand directly proportional to the p-d coupling matrix element I(p I I/' I d>l2.This leads to a substantial upward repulsion of T,,(p) and a reduction in the band gap in the I-111-VI, compounds, as compared to their 11-VI analogues by amounts of up to 1.6eV. Under pressure, the reduction in the length of the I-VI bonds increases the p-d hybridization of the valence bands and causes a reduction in the energy gap with pressure.
J. GONZALEZ, E. CALDER~N, and F. CAPET
154 3.1
t
>,
Y
2-9
2.7
a
a (3
>(3
cc
2.5
w
2.3
2.'
-0.12
-0.09
-0.06
-0.03
Fig. 4. Volume dependence of the direct energy gap in CuGa(S,Se,
0
-JZ
for x
=
1 and 0.5
A quantitative estimate of (dE,/dP),-,, the variation of the energy gap due to the variation of the p-d hybridization under pressure, can be obtained using
where ( d E g ~ d P ) l ~ l l lis~ vthe 1 2experimental value of the pressure coefficient of the energy gap in the I-111-VI, compounds, (dE,/dP),,-,, represents the pressure coefficient of their 11-VI semiconductor analogues, in other words, freezing the d orbitals gives for the I-111-VI, compounds almost the same energy gap variation under pressure as for the binary analogues. Using the values reported in Table 1 for (dE$dP),,,,,,, (dEJdP),,,, (dEgldP)CuGaSe2, and (dE,ldP)z,s, we obtain
lslp-d =
-2.2 x
eV GPa-'
both for CuGaS, and CuGaSe,. Equation (7) has also been used for the copper halides where both terms nearly cancel [23].
Hydrostatic Deformation Potentials and Phase Transitions in CuGa(S,Se,
-J2
155
This means that in the CuGa(S,Se,-,), system the energy gap reduction under pressure due to the p-d hybridization is nearly constant. Since the d-like character over the series of these compounds [7] is of the order of 35% (CuGaS,) and 36% (CuGaSe,), this fact is not surprising. From Table 1 we also see that when the experimental E , is plotted versus the relative change in the volume, it exhibits an almost linear dependence, The deformation potential values of the CuGa(S,Se, -J2 compounds are similar to the 11-VI analogues. Table 1 also shows the relative anion independence, in the case of CuGa(S,Se, -,.) of the pressure coefficient of the energy gaps and the acoustic deformation potentials. Pressure-induced phase transitions in covalent semiconductors are caused by the necessity of the relatively open tetrahedral structure to become close-packed under compression. The resulting volume decrease is typically 15 to 20%. For group IV and weakly ionic 111-V materials, the lowest pressure transition is generally to a sixfold coordinated p-tin structure that exhibits metallic conductivity and can be superconducting. With increasing ionicity in 111-V and 11-VI compounds, the lowest pressure transition is to a semiconducting NaC1-type structure. After releasing pressure, metastable phases sometimes occur. Considerable progress in understanding these transitions has resulted from recent density functional treatments. Since tetrahedral coordination prevails in the chalcopyrite compounds, they may be expected, just as in their 11-IV zinc blende analogues, to transform under pressure to a higher-coordinated structure. From recent high pressure X-ray studies on CuGa(S,Se,-,), compounds [15], it has been shown that the chalcopyrite structure becomes unstable under pressure and transforms to the NaC1-type structure. The transition pressure (P,)is listed in Table 1.When decreasing the pressure to zero the samples completely revert to the chalcopyrite phase. In the present optical study, for pressures higher than a certain value denoted by P , all the samples become opaque (transmission less than 0.03% in the spectral range 0.7 to 2.8 eV). We presume that a first-order phase transformation to a metallic (or narrow gap semiconductor) structure has occurred. The values of P , (optical) are also listed in Table 1. Within the experimental uncertainty the values of P, obtained by optical and X-ray measurements are not very different. The pressure P , given in Table 1 does not necessarily correspond to the “equilibrium” transition pressures; usually, a large volume reduction of the order of 15% and a large hysteresis are associated with the first pressure induced phase transition of tetrahedrally bonded semiconductors. Hence, there may be a significant amount of “superpressing”, which depends on the magnitude of the non-isotropic stress component acting on the sample [16]. 4. Concluding Remarks
The direct energy gap of CuGa(S,Se, -,), single crystals exhibits a linear increase under pressure and the corresponding acoustic deformation potential is not very different from the values of ZnS and ZnSe, the 11-VI analogues. The pressure coefficient of the energy gap is smaller as compared to their respective 11-VI analogues. This anomalous effect is attributed to the increase in the p-d hybridization of the valence bands which causes a reduction in the energy gap with pressure. The values of (dE,/dP),-d are nearly constant for these materials. Under high pressure the CuGa(S,Se, - ,) compounds undergo a phase transition to the NaCl structure, which is opaque in the range 0.7 to 2.8 eV. The values obtained by optical and X-ray measurements for the transition pressures (P,) are not very different.
156
J. GONZALEZ et al.: Hydrostatic Deformation Potentials and Phase Transitions
Acknowledgements
This work was supported by CONICIT-BID under grant NM-09. One of us (J. G.) is grateful to Consejo de Desarrollo Cientifico y Tecnologico (CDCHT) of the Universidad de Los Andes, the CEFI-PCP Materials (France), and CONICIT (Venezuela)for financial support. References [I] See for example, Proc. 7th Internat. Conf. Ternary and Multinary Compounds, Ed. S. K. DEB and A. ZUNGER,Materials Research Society, Pittsburgh 1986. J. C. WOOLLEY, and J. GONZALEZ, Japan. J. appl. Phys. 19, Suppl. 19-3, 123 [2] R. G. GOODCHILD, (1980). 131 M. QUINTERO, K. YOODEE, and J. C. WOOLLEY. Canad. J. Phys. 64,45 (1986). S. ENDO,and H. NAKANISHI, Japan. J. appl. Phys. 29, 484 (1990). [4] H. MATSUSHITA, B. HENNION, J. GONZALEZ, and S. M. WASIM,Phys. Rev. B 47, 8269 (1993). [5] R. FOURET, [6] S. M. WASIM,Solar Cells 16,289 (1986). 171 1. E. JAFFEand A. ZUNGER, Phys. Rev. B 29, 1882 (1984) (and references therein). and G. SANCHEZ PBREZ,J. appl. Phys. 51, 6634 (1983). 181 C. RINCON,J. GONZALEZ, A. JAYARAMAN,V. NAVAYANAMURTI, H. M. KASPER,M. A. CHIN,and R. G. MAINES, Phys. Rev. B 14. 3516 (1976). \ , A. JAYARAMAN, P. D. DERNIER, H. M. KASPER,and R. G. MAINES,High Temp.-High Press. 9,97 (1977). D. OLEGO,A. JAYARAMAN, and M. CARDONA, Phys. Rev. B 22. 3877 (1980). C. CARLONE, A. WERNER, H. D. HOCHHEIMER, and A. JAYARAMAN, Phys. Rev. B 23, 3826 (1981). M. BETTINIand W. B. HOLZAPFEL, Solid State Commun. 16, 27 (1975). S. B. QADRI,E. F. SKELTON, A. W. WEBB,S. A. WOLF,W. T. ELAN,and Z. REK,Mater. Res. SOC. Symp. Proc. 22, 25 (1984). J. GONZALEZ, E. MOYA,T. TINOCO,A. POLIAN,and J. P. ITIE,to be published. J. GONZALEZ, B. J. FERNANDEZ, J. M. BESSON, and A. POLIAN,Phys. Rev. B 46, 15092 (1992). J. GONZALEZ and C. RINCON,J. appl. Phys. 54, 2031 (1989). M.GAUTHIER, A. POLIAN,J. M. BESSON,and A. CHEVY,Phys. Rev. B 40, 3837 (1989). G. D. BOYD,H. KASPER,and J. H. McFcc, IEEE J. Quantum Electronics 7, 563 (1971). S. VES: V. SCHWARZ, N. E. CHRISTENSEN, K. SYASSEN, and M. CARDONA, Phys. Rev. B 42, 9113 (1990). and L. M. SCHIAVONE, Phys. Rev. B 5, 5003 (1972). J. L. SHAY,B. TELL,H. M. KARPER, W. BRAUN,A. GOLDMAN, and M. CARDONA, Phys. Rev. B 10, 5069 (1974). A. GOLDMAN, J. TEJEDA,N. J. SHEVCHIK, and M. CARDONA, Phys. Rev. B 10, 4388 (1974). (Received May 26, 1994; in revised form August 10, 1994)
