J . Phys. Chem. 1987, 91, 4011-4013 adsorbed phases; agoand asoare those of the standard state. As both phases are ideal we have
hA
= -RT In
BAS
(22)
if the standard state is chosen so that a g o / a s o= 1. The differential free energy of adsorption is obtained from the change of BAS with temperature
= -R d(ln BAS)/d(l/T)
(23)
The differential entropy of adsorption -
is easily derived from AA and The thermodynamic functions of adsorption were calculated for the lower n-alkane molecules which do not have rotational isomers. We have assumed free rotation of the hydrogen atoms of the methyl groups. The statistical thermodynamic calculations require the determination of the adsorption potential for all distances and orientations of the adsorbed molecules. These calculations are not tractable unless simplified expressions are adopted for the adsorption potentials. Therefore, the adsorption thermodynamic characteristics were calculated by using the simplified repulsive atomatom expression (eq 13) deduced from the EHT interaction energy. Moreover, assuming that the translation of the mass center of the molecule parallel to the graphite surface and its rotation around the axis perpendicular to the surface are free, eq 18 reduces to
E.
's
BAS = 4 s
1s e x p [ ( - u / R T )
-11 dz sin 0 d0 d v
(24)
The integration is carried out for all distances and orientations of the molecule with a mean value u(z,e,(p) taken for the adsorption potential in the plane parallel to the graphite surface. Table IV compares the predicted second virial coefficients, the differential energies, and entropies of adsorption of the lower alkanes on graphite, at 0 "C, with the experimental ones measured
4011
by static methods42and by gas chromatography.* Theory accounts well for experiment since the experimental data lie between the theoretical values calculated with an anisotropic graphite polarizability tensor ( P = 0) or an isotropic one ( P = 1). This result does not mean, however, that an intermediate polarizability ratio should be taken for graphite because of the approximations made in selecting the dispersion potential. Nevertheless, an independent and reliable repulsive term can be obtained from the EHT interaction which may be useful as a basis for discussing dispersion potential models and their comparison with experiment.
Conclusion The interaction energies between alkanes and graphite as calculated in the E H T framework are always repulsive because the theory takes no account of the dispersion forces contributions. These calculations are useful to establish the repulsive atom-atom simplified expressions for carbon-carbon and carbon-hydrogen interactions. They may lead also to the prediction of the minimum atom-atom approach distance or van der Waals distance if the parameters of dispersion potential expression are known. The method proposed in this work may be used to calculate the short-range repulsive energy of adsorbate layers or that of other classes of nonpolar molecules with graphite and to evaluate their equilibrium adsorption conformations. A similar approach could be useful to predict the interlayer structure of graphite and its cohesion energy and to explain its equilibrium structure. Acknowledgment. The calculations were performed in FORTRAN language with the computer of the Centre Inter Rigional de Calcul Electronique, Orsay, France. Registry No. Graphite, 7782-42-5; methane, 74-82-8; ethane, 74-84-0; propane, 74-98-6. (42) Avgul, N. N.; Kiselev, A. V. Chemistry and Physics of Carbon; Walker, P. L., Ed.; Marcel Dekker: New York, 1970; Vol. 6, p 1.
Effects of Surface Modlfication on n-CdTe Photoelectrochemical Solar Cells K. C. Mandal, S. Basu,* and D. N. Bose Semiconductor Division, Materials Science Centre, Indian Institute of Technology, Kharagpur 721 302, India (Received: August 11, 1986; In Final Form: March 20, 1987)
Modification of large grain n-CdTe by Ru is shown to considerably improve the properties of n-CdTe photoelectrochemical (PEC) solar cells. The dark I-Vcharacteristic shows a decrease in Jo from 8.6 X to 4.2 X A/cm2 and in ideality factor n from 2.12 to 1.16. Under AM1 illumination V, increased from 0.52 to 0.78 V vs. SCE, J , from 3.4 to 5.2 mA/cm2, and fill factor from 0.42 to 0.51. The minority carrier diffusion length (L,) is shown to increase from 0.1 2 to 0.17 pm after Ru modification. The improvement has been interpreted as being due to removal of interface states within the bandgap as evident by subbandgap and contact potential difference (CPD) measurements.
Introduction Surface modification of semiconductors has been shown to be a powerful technique for improving the properties of photoelectrochemical (PEC) solar cells.' While most of these investigations involved groups 111-V (groups 13-1 5)16 compounds,* Mandal et al.334have shown its application to PEC solar cells using large grain (1) Parkinson, B. A,; Heller, A.; Miller, B. J. Electrochem. Soc. 1979, 126, 954.
(2) Johnston (Jr.) W. D.; Leamy, H. J.; Parkinson, B. A,; Heller, A,; Miller B. J . Elecrrochem. SOC.1980, 127, 90. (3) Mandal, K. C.; Basu, S.;Bose, D. N. Solar Cells 1986, 18, 25. (4) Mandal, K. C.; Basu, S.; Bose, D. N. Proc. Bienn. Cong., Znf. Sol. Energy SOC.1986, 3, 1882.
0022-365418712091-4011$01.50/0
p-CdTe. In this case, along with increased open-circuit voltage V , and fill factor, an improvement in the short-circuit current density J,, was also observed. In the present paper we report the investigation of the surface properties of n-CdTe that are responsible for the observed behavior. Spectral response studies using a monochromator demonstrate a reduction of states within the bandgap which is supported by broad-band subbandgap measurements. Hole diffusion length in n-CdTe was also found to increase from 0.12 to 0.17 pm due to reduction of surface recombination velocity. Finally contact potential difference (CPD) measurements using the Kelvin probe technique have demonstrated for the first time changes in surface Fermi level that were in good agreement with the changes in open-circuit voltage obtained from n-CdTe-electrolyte interfaces. 0 1987 American Chemical Society
4012
The Journal of Physical Chemistry, Vol. 91, No. 15, 1987
Mandal et al. I
I
Wavelength in micron5
Figure 2. Normalized spectral response in the current mode of n-CdTe photoelectrode in 0.025 M Te2-/TeZ2-redox (pH 12.0) before and after Ru modification.
TABLE I: Subbandgap Response on n-CdTe
I
v, V o l t s Figure 1. Solar cell characteristics under AM1 tungsten-halogen illumination: (0)unmodified surface; (A) Ru-modified surface.
subband response, X IO” V CdTe filter GaAs filter InP filter surface treatment ( E , = 1.50 eV) (E, = 1.43 eV) ( E g = 1.34 eV) polished and 37 21 14 etched matte etched 62 35 24 Ru-modified 9 6 3.5 6 h AM1
8.5
6
4
illumination
Results and Discussion The sample exhibited good rectification in the dark. From the forward In J-V characteristic, the ideality factor was found to be 2.12 and the saturation current density 8.6 X IO4 A/cm2. l / c vs. Vplot measured at 10 kHz showed linear variation giving the carrier concentration as 7.2 X 1015cm-3 and a flat band voltage
of -0.97 V vs. SCE. With AMI illumination the solar cell plot shown in Figure 1 gave J , = 3.4 mA/cm2 and V,, = 0.52 V vs. SCE with a fill factor of 0.42. After Ru modification the surface properties underwent a significant change. The forward In J-V characteristic showed a reduction in Jo to 4.2 X A/cm2 and in ideality factor n to 1.16. The l / c vs. Vplot after modification gave V, = -1.20 V vs. S C E and N D = 4.6 X lOI5 ~ m - ~But . the dark voltage increased from 14 to 32 mV. This may be explained as due to metallic ruthenium deposition on CdTe surface as evident from ESCA studies.’ Macroscopic metal-electrolyte junction may cause slight increase in dark voltage. The solar cell plot after modification shown in Figure 1 gave V , = 0.78 V vs. SCE, and J , = 5.2 mA/cm2 with a fill factor of 0.51. Experiments conducted both in the dark and under AM1 illumination showed no measurable weight loss over 320 h. The current remained constant over these periods. The extremely low dark current and voltage were further indications of electrode stability. Moreover, the solution in the cell was analyzed for Cd before and after illumination by using atomic absorption spectroscopy. No change in the Cd content of the solution (
