Electrochemical investigations of a copper—tellurium system and determination of the band gap for α-Cu2Te

Eloctrochimico Acta Vol. 38, No. 13, pp. 169!-1703. Printed in Great Britain.

1593 0

0013~4686/93 56.00 + 0.00 1993. Pergamon Press Ltd.

ELECTROCHEMICAL INVESTIGATIONS OF A COPPER-TELLURIUM SYSTEM AND DETERMINATION OF THE BAND GAP FOR cc-Cu,Te S. N. MOSTAFA,S. R. SELIM,S. A. SOLIMAN and E. G. Chemistry Department,

GADALLA*

Faculty of Science, Al-Azhar University, Nasr City, Cairo, Egypt

(Receiued 13 January 1993; in revisedfirm

17 March 1993)

A&met--The activity of copper in various phases of the copper-tellurium system as a function of the metal to nonmetal ratios has been determind with the help of solid-state coulometric titrations in the temperature region between 350 and 450°C. Homogenous phases of the Cu-Te system have been found between Cu/Te ratios equal to about 2/1.92 [a-phase (Cu,Te)], 1.43/1.39 [p-phase (Cu,Te,)] and 1.32/ 1.30 [y-phase (CuTe)]. Analysis of the experimental data shows that the semiconducting properties of a-Cu,Te and the change of the thermodynamic quantities with composition are due to changes of the thermodynamic quantities of the electrons as a component. The change of the thermodynamic quantities of the electrons are composed of those of the free electrons and electron holes. From the electrochemical measurements, besides partial molar enthaby curves of electrons. the enernetic band gap can be calculated and is about 0.673 eV ior a-cuprous tellurihk.

with metallic copper per gram-atom

INTRODUCTION The copper-tellurium system is one of the silver sulfide group of semiconductors. These substances are well suited for an investigation of small deviations from the exact stoichiometric composition (ie point defect) with the so-called coulometric titration method[l]. They are characterized by the fact that they exhibit mixed conduction, ie partly electronic and partly ionic conduction[2]. From the stoichiometric point of view, they belong to the nonstoichiometric or Bartholide compounds[3]. The Cu/Te ratio can be controlled by means of the solidstate galvaic cell: Pt/Cu/Cu

Br/Cu, _d Te/C,

in which Cu Br is practically an ionic conductor between 350” and 450” when subjected to a polarizing potential of less than 0.3OV[2]. The open circuit potential E of the cell(I) is related to the chemical potential of copper atoms in Cu-Te system, lo,, 7by

PC,”- pzu = - EF = - 2.302RT log a,, ,

6 = (I.W(n,,F),

metal is, (2)

where nTc is the number of gram-atoms of nonmetal. Removal of copper from Cu-Te sample may be described as the removal of copper ions and excess electrons followed by the formation of conduction band electrons and valence band electron holes in order to conform to the condition of internal equilibrium. The present study on the semiconducting and thermodynamic properties of the electrons in Cu-Te system has been carried out with the help of the cell analogous to those made for silver sulfide group semiconductors[S-161 at 360,385,410 and 435°C.

EXPERIMENTAL

(1)

where & is the chemical potential of copper in its pure state; a,, the activity of copper; F the Faraday constant and R the universal gas constant. The activity of copper in various phases of the Cu-Te system as a function of the composition has been determined with the coulometric titrationC4-J. In the Cu-Te system, both ions and electrons are mobile and therefore a uniform Cu/‘l’e ratio IS readily obtained. The decrease in the metal-to-nonmetal ratio with respect to a sample equilibrated

Cuprous telluride was prepared by synthesis from the elements and the solid-state galvanic cell was constructed as described elsewhere[4]. The cuprous telluride was virtually equilibrated with metallic copper by forcing a positive potential of a few millivolts on the platinum electrode of cell(I) for approximately 10 h at 200°C. The weight of Cu,Te samples ranged from 0.045 to 0.070 mg. After titrating a given quantity of copper away from the cuprous telluride sample, a steady potential was obtained within several minutes. All the experiments were conducted in an atmosphere of purified nitrogen in an electrical furnance. Cell(I) was heated between 350 and 450°C and the open circuit potential, E, was measured. RESULTS

* Egyptian Geological Survey and Mining Authority, Cairo, Egypt.

Reproducible results were obtained for addition and substraction of copper up to a potential of 1699

S. N. M~~TAFA et 01.

1700

(.)-410°c

()o-385’C (o)-36O’C

200

0

60

u

540

600

720

660

8x10-3

Fig. 1. The change of E vs. 6 for cuprous telluride at 360,385,410 and 435°C.

0.25OV. At higher potentials, a slow decay of the open circuit potential was observed, because under these conditions cuprous bromide shows noticeable semiconduction in addition to ionic p-type conduction[17]. Figure 1 shows the titration curves for the copper-tellurium system at 360, 385, 410 and 435°C. Upon substracting copper from the phase Cu,Te equilibrated with copper, the potential E of cell(I) rises and levels off at 6 = 0.077 and E = 0.14 V corresponding to a two phase mixture involving a constant activity of copper at 6 > 0.077. In view of increasing electronic conduction in CuBr under more oxidizing conditions[2], measurements were limited to potentials less than about 0.25V, corresponding to 6 = 0.71. According to Fig. 1 two other one-phase regions exhibiting a steep increase of E with increasing 6 are found between 6 = 0.57 and 0.61 and between 6 = 0.68 and 0.70, corresponding approximately to Cu/Te ratios between 1.43 and 1.39 (B-phase (Cu,Te,)) and between 1.32 and 1.30 (y-phase (CuTe)), respectively. The data were analyzed in the same way as the data for Ag,S[6], Ag,Se[S, 9, 181, Cu,S[S, 7, 173 and Cu,Se[lO, 143.

DISCUSSION Cuprous telluride is a compound of a special class of solids called superionic materials. One of the most important features of superionic materials is their anomalously high ionic conductivity, with respect to other solid materials[19]. At 350-45O”C, the copper ions are distributed virtually at random among a large number of nearly equivalent lattice sites according to X-ray investigations[20]. An appreciable homogenity range of the phase Cu,Te with a deficit of copper has already been found by Chikashige[Zl] with the help of thermal analysis and is also indicated by the results of electrical measurements conducted by Reinhold and Briiuninger[22]. The semiconducting properties of cuprous telluride may be accounted for by excess electrons and electron holes. The values in cuprous telluride of ideal composition Cu,Te denoted by x0 and xz must be equal to each other[lO, 14, 163: x0=x;. e

(3)

The obtained values of the electronic point defect concentrations, x0 are given in Table 1.

Fig. 2. Titration curve for cuprous telluride at 410°C.

1701

Investigations of a Cu-Te system Table 1. The characteristic data of electronic defects in a-Cu,_,Te x0 x 10”

mk’x 102’/g

From equation (9)

From equation (10)

360

7.978

0.621

0.614

385

6.978

0.650

0.652

410

7.056

0.674

0.676

435

5.454

2.245 (2.465mJ 2.005 (2.20lmJ 1.887 (2.0721~1,) 1.833 (2.073mJ

0.764

0.760

Aver. = 0.677

Aver. = 0.676

A tentative calculation of the copper deficit with respect to the formula Cu,Te in cuprous telluride coexisting with metallic copper analogous to that made for Cu,Se[lO, 143 and Cu,S[16, 171 is inconclusive because deviations from classical statistics cannot be approximated by correction terms if 6 > 0.10. Although the exact value of the initial ratio of Cu/Te is unknown, the approximation x0 = 2 value of the initial ratio of Cu/re is unknown, the approximation x0 = 2 may be adopted in order to obtain x = 2 in cell(I), for the characterization of phases involving a lower copper content[4]. The deviation from ideal stoichiometric compositions 6 as a function of E has been calculated by using the equation[17] 6=

WeV

WeV

Ref. [14, 161

T/"C

xgexp[(E

- EO)/(RT)x(F)],

(4)

where E" is the emf of cell(I) z 0 for the hypothetical cases that Cu,Te sample on the right-hand side has the ideal composition. The calculated coulometric titration curve at 410°C for cc-phase is included in Fig. 3. It will be seen that the calculated (x) and experimental (0) points are in good agreement, and one may conclude that a-cuprous telluride is in nearly ideal stoichiometric composition when in equilibrium with copper. Figure 4 shows the electronic point defect concentration n, and nb of a-phase as a function of the devi-

by using the following equations[ 161: x Jxf = exp[(uz - u,)/(RT)] = exp[(E’ - E)F/(RT)l

(5) xh/x: = exp[(u, - &(RT)] = exp[(E - E')F/(RT)]. (6) It is evident from Fig. 4 that at the deviation from ideality (6 > 0), the concentration of electron holes is larger than the concentration of conduction band electrons, and increases linearly with increasing deviation for ideality. From the upper part of the curve shown in Fig. 2, the ratio mh+/mcof the effective mass of electron holes to the free electron mass for a-cuprous telluride has been calculated[18]. The calculated values of the effective mass of the electron holes rnt are listed in Table 1. In a completely analogous way as developed by Mostafa et aI.[14,16] in the case of Cu,Se, Cu,S and from statistical thermodynamics the partial molar enthalpies and entropies of the electrons have been evaluated and plotted in Figs 5 and 6. The Figs 7 and 8 show A& and Ak?c, = (AS, and AR,) at 410°C as evaluated from the titration curve and the calculated values according to[ 141:

q = C@,Mx,+ XtJlx se,E- cknm, + %Jlx &I

ation from the ideal composition at 410°C calculated

E

16or

, 1.18

120

0.89

80

(7)

0.59 M 9

M

? 40

0.30

curve for a-cuprous telluride at 410°C [(x) calculated values by equation (4),and (0) measured values].

Fig. 3. Titration

Fig, 4. Electronic and point defect concentrations nc and nb of a-cuprous telluride as a function of the deviation S from

ideal stoichiometry at 410°C.

S. N. MOSTAFAet al.

1702

A, = C(x,Mx,+ xhllx R,

E -

ccGY(x, + -%Jlx A,. (8)

Here s, and fi, are the partial molar entropy and enthalpy of the electrons, L?,,, and kri,,c are these quantities for electrons in the conduction band and s, and R,, are these quantities for the holes. The shapes of the measured curves from the temperature dependence in Figs 5 snd 6 are in good agreement with equations 7 and 8, taking into account that fi,, E and -I?, are independent of the concentration of the free electrons and holes for not too high concentrations, while &, c and -3, are dependent on these concentrations[23]. Determination of the band gap in a-Cu,Te

The width of the band gap Eo between the valence and the conduction bands may evaluated by the following methods : 1. From the argument of the Fermi-Dirac function. When the Fermi energy level E, is exactly halfway between the valence and the conduction bands, the energy band gap is given[24-261 by Eo = 2(E, - Ec) = 2[+KT,

Fig. 6. Enthalpy change upon dissolving one mole of copper in a-cuprous telluride (If,, - HE?) as a function of the deviation

6 from the idea) stoichiometry 410 and 435°C.

at 360, 385,

(9)

where Ec is the energy of the conduction band, K is the Boltzmann constant, [’ is the argument of the Fermi-Dirac function, p,, is the chemical potential of holes and [’ = [(p,,)/(RT)]. The calculated values of Eo by equation (9) and tables of the Fermi-Dirac function computed by McDougall and Stoner[27] are listed in Table 1. 2. From the enthalpy curves. Theoretical considerations show that the difference between the partial enthalpies R,, Eand -R, are related to the band gap Eo according to[23] : E,=k?,,,+ii,-3RT.

(10)

From this, E, can be estimated using the enthalpy curves in Fig. 6. The calculated values of E, by the two ways listed in Table 1 are in good agreement. The average band gap E, is 0.673 eV.

0

20

40

60

3

6x10-3 Fig. 7. The partial molar entropy of electrons (x), AS, = AS,, [calculated values by equation (711 and the relative partial molar entropy (0) [measured values] for a-cuprous telluride at 410°C.

9-

6-

20

40

60

8x10-3 Fig. 5. Entropy changes upon dissolving one mole of copper in or-cuprous telluride (Sc, - S&) as a function of the deviation 6 from ideal stoichiometry at 360, 385, 410 and 435°C.

0

-I

20

40

80

6X10-3

Fig. 8. The partial molar enthalpy of electrons (x), AR, = A&, [calculated values by equation (8) and the relative partial molar enthalpy (0) [measured values] for a-cuprous tellurtde at 410°C.

Investigations of a Cu-Te system In general, one may say that the internal consistency of the electronic and point defect parameters for a-Cu,_,Te as illustrated in Figs 7 and 8 is remarkable and confirms the titration curves and their evaluation. From the present results it may be concluded that a-cuprous telluride is an intrinsic semi-conductor of p-type and the majority defects are ionic, and the disorder type in the a-Cu, _dTe is Frenkel disorder of the copper ions.

REFERENCES 1. C. Wagner, Progress in Solid State Chemistry (Edited by H. Reis and J. D. MeCaldin), Vol. 6, pp 1, Pergamon Press, Oxford (197 1). 2. J. B. Wagner and C. Wagner, J. them. Phys. 26, 1597 (19571

,---.,.

3. A. F. Wells, Structural Inorganic Chemistry, 2nd edition, p. 143. (1950). 4. G. Lorenz and C. Wagner, J. them. Phys. 26, 1607 (1957). 5. C. Wagner, J. them. Phys. 21, 1819 (1953). 6. H. Rickert, V. Sattler and Ch. Wedde, Z. Phys. Chem. Neue Folge 48,329 (1975). 7. S. Mostafa, M. Y. Mourad and S. A. Soliman, Egypt. J. Chcm. 25,521(1982). 8. S. N. Mostafa, S. M. Amer and E. A. M. Eissa, J. electroanal. Chem. 133, 125 (1982). 9. S. N. Mostafa and K. M. Kamel, Z. MetaNkde 73, 249 (1983). 10. S. N. Mostafa and S. A. Soliman, Ber. Bunsenges. Phys. Chem. 87, 1113 (1983).

1703

11. S. N. Mostafaand S. R. Selim, Egypt.J. Chem.27, 119 (1984). 12. S. N. Mostafa and M. Abd-Elmottaleb, Egypt. J. Gem. 27,151(1984). 13. S. N. Mostafa and M. A. Abd-Elreheem, Elecrrochim. Acta 30,635 (1985). 14. S. N. Mostafa, S. R. Selim, S. A. Soliman and F. A. El-lakwah, Ber. Bunsenges., Phys. Chem. 93, 123 (1989). 15. S. N. Mostafa, Ber. Bunsenges., Phys. Chem. 95, 621 (1991). 16. S. N. Mostafa, M. Y. Mourad, S. A. Soliman, 2. Physik. Chem. N. F. 171,231(1991).

17. J. B. Wagner and C. Wagner, J. them. Phys. 26, 1602 (1957). 18. K. Anderko and K. Schubert, 2. Metallkde. 45, 371 (1954). 19. Yu. Ya. Gurevich and A. K. Ivanov, Semiconductors and Semimetals (Edited by R. K. Willardson and Albert C. Beer), Vol. 26, pp. 229. Academic Press, New York (19881. \-20. P. Rahlfs, Z. Phys. Chum. B 31, 157 (1936). 21. M. Chikashige, Z. Anorg. Chem. 54, 50 (1907). 22. H. Reinhold and H. BrHuninger, Z. Phys. Chem. B 41, 397 (1939). 23. H. Rickert, S. N. Mostafa, V. Sattler and Ch. Wedde, 25th Meeting of ISE, p. 319, Brighton, England (1974). 24. A. J. Joffe, Physik der helbleiter, p. 120. Akad. Verlag, Berlin (1960). 25. A. Sommerfeld, Z. Physik 47, 1 (1928). 26. N. F. Mott and H. Jones, Properties of Metals and AfIoys p. 95, Clarendon Press, Oxford (1936). 27. J. McDougall and E. C. Stoner, Roy. Sot. A 237, 67 --I

(1938).