Photoelectrochemical-determination-of-minority-carrier-diffusion-length-and-energy-band-gap-in-heavi

Pergrmon J. Phys. Chem. Sotid.~ Vol. 55. Nb. 5, pp. 4434 I, 1994 Copydghl 67 1994 Elscvitr Science Ltd Fnnted in Great Britain. All righu rc~ervcd 0022-3697/W 57.00 + D.W

PHOTOELECTROCHEMICAL DETERMINATION OF

MINORITY-CARRIER DIFFUSION LENGTH AND

ENERGY BAND GAP IN HEAVILY DOPED

SEMICONDUCTORS-II. INTERBAND OPTICAL

TRANSITIONS IN DEGENERATE n-Cd0

I. D. MAKUTA,~ S, K. POZNYAK and A. I. KULAK

Byelorussian State University, Institute of Physics-Chemical Problems, 220080 Minsk, Republic of Belarus

(Received 2 September 1993; ocwpted 15 D.xH&v- 1993)

Ahstrati-A new photoelectrochemical (PEG) method proposed in Part I of this paper (Makuta I. D. and Kulak A. I., J. Phys. Chem. Soli& 55, 211, 1994) is applied for determining bandgap energy (I$) in degenerate n-Cd0 As follows from obtained results, it gives reliable E, values (unlike the conventlonal Butler method) when the photocurrent is limited by interfacial kinetics. Moreover, some modifications of Butler’s method are shown to be required even if PEC behaviour of the serniconductor~lectrolyte junction is described by the Schottky-barrier-like model. As found for rr-W03, it allows u3 to avoid the potential and electrolyte dependence of EB values which has no physical meaning and originates from the unfitness of simplifying assumptions used as a rule.

Keywor&: Photoelectrochemistry, energy gap determination, degenerate semiconductor, cadmium oxide.

INTRODUCTION

A new photoelectrochemical (PEC) method has been proposed in Part I of this paper [l] for determining

some physical and electrochemical parameters of

heavily-doped semiconductors (SC) when photo- response is limited by the interfacial kinetics. The

necessity of developing that method was caused by

the unfitness of the commonly used Gartner model [Z]

in such conditions occurring frequently for real electrochemical systems. In Part I, the following

relationship has been presented

$lw [K(l + W/L) - q]-’ = A,L (Rw - Eg)“n, (1)

derived for PEC determination of bandgap energy {E,) from Wilson’s model [3] and a well-known

expression [4] for absorption coefficient (a) near the

SC band edge

a = A,(ho)-‘(AU - &)““, (2)

where q is the quantum efficiency of photocurrent, hw the photon energy, K the parameter defined as the relation S,/[S, + S,) between the velocities of surface recombination (S,) and minority-carrier transfer (S,), W the thickness of depletion region, L the _ TAuthor to whom correspondence should be addressed. minority-carrier diffusion length, A, the constant and

n depends on whether the transition is direct (n = 2)

or indirect (n = l/2). In the present paper, the comparison between the

proposed approach and conventional PEC method

(developed by Butler [4] from Gartner’s model) is performed having used our experimental data for

degenerate n-CdO. Moreover, with results reported

for n-WQ electrodes [4], some modifications of Butler’s method are shown to be required when

relations between IV, L and CL differ from those accepted usually (viz. rW

EXPERIMENTAL

The detailed consideration of experimental tech- niques, preparation procedures and PEC behaviour

of n-Cd0 is given in our previous works [l, 5,6].

Here we would only note that as samples were used

polycrystalline sintered compacts with the diffirent

degrees of degeneracy evaluated in terms of reduced Fermi energy A& = (F - E,),fkT (where F is the

Fermi level and E, is the conduction band bottom). All PEC measurements were carried out under poten- tiostatic conditions in conventional three electrode cell {Pt counter electrode, Ag/AgCl reference electrode, 0.2 M NaSCN supporting electrolyte).

447 448 I. D. MAKUTA ef al.

RESULTS AND DISCUSSION

It has been shown earlier [5,6] that the reverse

(anodic) biasing results in the formation of depletion

layer within subsurface region of n-Cd0 electrodes,

and that the mechanism of photocurrent generation

in degenerate n-Cd0 coincides in principle with

that inherent to non-degenerate semiconductors.

Naturally, it makes quite reasonable sense to apply

the traditional apparatus of photoelectrochemistry

for determining bandgap energy and the nature of interband transitions. The conventional PEC method

uses the expression

$lo = &(W + L)(hw - &)‘:a (3)

derived from eqn (2) and Butler-Gartner equation [4]

q = [l - exp(-aW)/(aL + l)] (4)

in the form q = a (W + L ) which corresponds to the

fulfilment of boundary conditions a W cc 1 and aL << 1.

The values of Eg determined from eqn (3) for

n-Cd0 electrodes with the different degrees of degen-

eracy are given in Table 1 (and partially, in our report

[5]). As follows from these results, there are three interband optical transitions in Cd0 with energy gaps