redox electrolyte interfaces

J. Electroanal. Chem., 188 (1985)287-291

287

Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands Short communication A QUANTITATIVE EXPRESSION FOR PARTIAL FERMI LEVEL PINNING AT S E M I C O N D U C T O R / R E D O X E L E C T R O L Y T E INTERFACES

R.L. VAN ME1RHAEGHEand F. CARDON Rijksunioersiteit Gent, Laboratorium voor Kristallografie en Studie van de Vaste Stof Krijgslaan 281, B- 9000 Gent (Belgium)

W.P. GOMES Rijksuniversiteit Gent, Laboratorium voor Fysische Scheikunde, Krijgslaan 281, B- 9000 Gent (Belgium)

(Received 27th November 1984; in revised form 10th January 1985)

The term Fermi level pinning (FLP) is used to describe an effect which may occur at semiconductor/metal or semiconductor/redox electrolyte Schottky barriers, and whereby electronic states in the forbidden gap at the semiconductor surface equilibrate with the adjacent phase. Specifically for semiconductor/electrolyte junctions, the equilibrium situation in the case of FLP is such that the Fermi level of the redox system and hence also that of the semiconductor is pinned at the energy of the surface state Ess. As the energetic distance between Ess and the band edges at the semiconductor surface is fixed, this implies that the band edges at the surface will shift with the redox potential U, so that also the fiat-band potential Vrb will depend on U and that, in the case of "complete" FLP, the equilibrium band bending will be independent of U. The latter consequence of FLP is obviously important as far as the use of semiconductor/electrolyte junctions for solar energy conversion applications is concerned. The dependence of the flat-band potential, the barrier height or the open-circuit photopotential Voc of semiconductor electrodes on the redox couple added to the electrolyte has recently been studied by several authors [1-6]. A dependence of Vrb on the redox couple may in principle be due either to adsorption of redox components [5] or to FLP. In several cases [4,6] the occurrence of F L P is supported by the observation of a linear relationship between Veb and U. Such a relationship can be generally written as: = eu

+ ct

(1)

in which the coefficient P can in principle take any value between 0 and 1. The case P = 0 is that of an ideal Schottky barrier, the case P = 1 corresponds to complete FLP. The upper limit of the open-circuit photovoltage (Voc)max is equal to Vrb- U and hence, in view of eqn. (1), given by (Voc)max= ( P - 1 ) U

+ ct

0022-0728/85//$03.30

© 1985 ElsevierSequoia S.A.

(2)

288 Thus, for a perfect Schottky barrier, the slope of the linear (Voc)max vs. U relationship is - 1 ; in the case of complete FLP, (Voc)max is independent of U. The data hitherto available for semiconductor/electrolyte Schottky barriers lead to values of P between 0.5 and 0 (so-called partial FLP). E.g., capacitance measurements performed by Bard and co-workers [4] on several semiconductor electrodes in acetonitrile solutions which contained redox electrolytes spanning a wide range of U values lead to a relationship of the type of eqn. (1) for the p-type semiconductors Si, InP, GaAs and WSe2; from Fig. 7 of ref. 4, values for P of 0.46, 0.43 and 0.33 can be deduced for Si, InP and GaAs respectively, whereas in the case of WSe 2, P was found to be zero (i.e. no FLP). For the n-type semiconductors CdS and TiO 2, more complex behaviour was observed than described by eqn. (1). Also for GaAs in aqueous solutions [6], relationship (1) appears to hold, with a value of P = 0.22. Capacitance measurements performed in the past in our laboratories on the n-type semiconductor electrodes ZnO and TiO 2 in aqueous medium were found to be unaffected by the addition of various reducing agents [7]; as, however, in most of these experiments the corresponding oxidizing agent was lacking, it is felt that they do not allow us to draw any clear-cut conclusion on FLP. On the other hand, our recent results [8] on the n-Si electrode in contact with methanolic redox electrolytes, in which the redox potential was varied over more than 0.5 V, demonstrated the absence of FLP in these systems. Consideration of the foregoing facts leads to certain basic questions with respect to F L P at semiconductor/electrolyte interfaces, for which the present contribution is meant to find an answer. These questions pertain to the physical background of the validity of the observed linear relationship (1), to the factors determining the value of the coefficient P and hence to the origin of the difference in pinning behaviour between various semiconductor/redox electrolyte systems. Fermi level pinning has been observed and studied for the last two decades on semiconductor/metal Schottky barriers; for a review of earlier results, see e.g. ref. 9. In many cases, a linear relationship has been found between the barrier height and the work function of the metal, a relationship to which the present eqn. (2) is equivalent. This relationship has been derived theoretically, basing upon the presence of an interfacial layer and of interface states [10-12]. As hitherto in the electrochemical literature, the value of the coefficient P in eqns. (1) and (2) has not been interpreted in structural terms, we thought it to be useful to write a derivation of these equations in a form more appropriate for electrochemists, i.e. flat-band potentials instead of barrier heights and redox potentials as the equivalent for metal work functions. In order to derive eqn. (1), the following assumptions will be made: (i) surface states are present at the semiconductor/electrolyte interface which equilibrate with the redox system; (ii) the surface state density Nss (i.e. their number per unit of surface area and of energy) is constant over that part of the band-gap where the redox Fermi levels of the different redox couples considered are situated before equilibrium. It can be shown that these conditions still lead to linear Mott-Schottky plots with the same slope as in the ideal case [13].

289

electron energ y

0L Ec E F = - eVfb

EF, SHE =0

....

T , _.~ AEg

EF, redox . . . . . = -eU

Ev electrolyte

semiconductor

Fig. 1. Energy scheme of n-type semiconductor/electrolyte interface at flat-band situation.

An energy scheme of an n-type semiconductor/electrolyte interface at flat-band situation is shown in Fig. 1, all energy values being referred to the SHE. The symbols E c, E v, AEg and E F have their usual meaning. The energy E n is such that, if it coincides with the Fermi level of the redox electrolyte EF, redox, no net charge is accumulated in the surface states. It should be remarked that the flat-band situation considered here is a hypothetical one, as in the real flat-band situation the concentration of majority charge carriers at the semiconductor surface is so high that presumably the surface states will equilibrate with the semiconductor and not with the redox electrolyte. However, it is the value of the flat-band potential corresponding to this hypothetical situation which is obtained by extrapolation of M o t t Schottky plots from a potential range where the surface states can be assumed to equilibrate with the redox levels (reverse bias, low majority carrier concentration at the surface), The following energy or potential differences are further defined: A~ = E , - E v ~/= E c -

E F

A~ L = ~ (surface) - q, (electrolyte) The subscript L refers either to the Helmholtz layer or to a series combination of the Helmholtz layer and the native oxide layer. It is assumed that the electrolyte is sufficiently concentrated, so that the G o u y potential drop can be neglected. In the flat-band situation, the charge in the semiconductor is zero, so that the condition for charge neutrality is: QE + Qss = 0

(3)

Qss representing the net charge per unit of surface area in the surface states and QE the compensating charge in the outer Helmholtz layer respectively.

290

The voltage drop over the layer is given (assuming a perfect dielectric) by A~L = 6 L ( Q J ' 0 ~ L )

(4)

with 6 L the thickness and e L the dielectric constant of the layer. For Q~s, the following equation holds, based upon the assumption made that the surface states equilibrate with the redox system:

Qss= eUss( En -- EF,redox)

(5)

where e is the positive elementary charge. The energy difference written as:

E n -

EF,redox can be

En-Er,redox=(En-Ev)-(Ec-Ev)+(Ec-Ev,redox)=A(-AEg+Ec+eU The flat-band potential is related

(6)

to A~L by:

Vfb -- (Vfb) 0 = Aq,L

(7)

Here, (Vfb)0 represents the value of the flat-band potential in the case that A0 L = 0; this corresponds to the situation in which the redox Fermi level coincides with E n (see eqns. 4 and 5). Furthermore, one has (see Fig. 1): Ec = EF + ~1 = - e V f b + n

(8)

From eqns. (7), (4) and (5) it follows that: Vfb = ( Vfb )o + ( SLeUss/(OeL )( E , -- Ev.rcdox)

(9)

Substituting eqns. (6) and (8) into eqn. (9), one obtains: Vfb = ( Vfb)o + ( 6LeUss/%,~.L)( &': -- AEg + 7 / - eVeb + e U )

(10)

Defining x as: (11)

x = 6Le2UsJ%(L

and rearranging eqn. (10), it follows: Vrb(a + x) = (Vfb)o + x U + x ( A , - kEg + ~/)/e

(12)

Furthermore,

A(-AEg+B=En-Ev-(Ec-Ev)+Ee-EF=En-EF (see definitions and Fig. I), so that:

1 1 E, - E v (Vrb)o Vrb - - U+ - - ~-- l + x -1 l + x -1 e l+x

(13)

It can be remarked that eqn. (13) holds for p-type electrodes as well. Comparing eqns. (11) and (13) to eqn. (1), the slope of the Vrb VS. U relationship appears to be: P = (1

+ (0(L/3L e

2

Nss )

-1

(14)

From eqns. (11), (13) and (14), it can be deduced that for N~s = 0 a n d / o r 6 L = 0, x and P are zero and Vro = (Vfb)0. In that limiting case, Vfb is independent of the

291 r e d o x system. T h e o t h e r extreme case, i.e. Nss ~ o0 a n d / o r ~L "-) O0, leads to x ~ oo a n d a linear r e l a t i o n s h i p b e t w e e n Vfb a n d U with a slope of one, c o r r e s p o n d i n g to complete FLP. E q u a t i o n (14) clarifies the role of the layer thickness BE: the larger 8 L, the m o r e p r o n o u n c e d the pinning. A s far as the n a t u r e of the layer is concerned, several possibilities can b e distinguished. In the case of s e m i c o n d u c t o r / e l e c t r o l y t e contacts, a H e l m h o l t z layer is always present. F u r t h e r m o r e , the s e m i c o n d u c t o r itself is u s u a l l y covered b y a native oxide layer after etching, c o n t a c t with air o r water. M o s t l y the thickness o f the native oxide layer is >/2 n m [14]. T h e thickness o f the H e l m h o l t z layer is a b o u t 0.3 nm. Consequently, the presence of a native o x i d e layer will favour F L P . It has to b e stressed however that o u r results o n l y p e r t a i n to a l i m i t e d r a n g e of BE-Values: for large values of ~L ( ~ 5 rim), e q u i l i b r a t i o n of the surface states with the redox system is no longer possible, a n d i n t e r a c t i o n with the charge carriers of the s e m i c o n d u c t o r will prevail. I n the case of G a A s electrodes in a q u e o u s solutions [6], a value of 0.22 has b e e n f o u n d for P. A s s u m i n g that the o n l y layer p r e s e n t is the H e l m h o l t z layer, with EL = 6 a n d ~L = 0.3 nm, a value of Nss = 3 × 1013 c m - 2 eV - ! is c a l c u l a t e d from eqn. (14). T a k i n g on the o t h e r h a n d the values c o r r e s p o n d i n g to the native oxide layer, i.e. EL = 3.6 a n d 8 L = 2 n m [14], a value of Nss = 3 x 1012 c m - 2 eV - I is found. F r o m the w o r k in ref. 3, P is f o u n d to b e 0.46 in the case of p-Si in acetonitrile solutions. U s i n g eqn. (14) with ~L = 3.9 a n d 8L = 2 n m [15] for the native oxide layer, one o b t a i n s N~s = 9 × 1012 c m -2 eV -1. It is c o n c l u d e d that the o b s e r v e d linearity b e t w e e n Vfb a n d U can b e e x p l a i n e d b y a simple model, b a s e d u p o n the e q u i l i b r a t i o n of surface states with r e d o x levels, a n d that the e x p e r i m e n t a l slopes of the Vfb VS. U r e l a t i o n s h i p l e a d to a c c e p t a b l e values for the p a r a m e t e r s involved.

REFERENCES 1 A.J. Bard, A.B. Bocarsly, F.R.F. Fan, E.G. Walton and M.S. Wrighton, J. Am. Chem. Soc., 102 (1980) 3671. 2 J.N. Chazalviel and T.B. Truong, J. Am. Chem. Soc., 103 (1981) 7447. 3 G. Nagasubramanian, B.L. Wheeler, F.R.F. Fan and A.J. Bard, J. Electrochem. Soc., 129 (1982) 1742. 4 G. Nagasubramanian, B.L. Wheeler and A.J. Bard, J. Electrochem. Soc., 130 (1983) 1680. 5 R. Mclntyre and H. Gerischer, Ber. Bunsenges. Phys. Chem., 88 (1984) 963. 6 G. Horowitz, P. Allongue and M. Cachet, J. Electrochem. Soc., 131 (1984) 2563. 7 W.P. Gomes and F. Cardon, Progr. Surf. Sci., 12 (1982) 155. 8 Ph. Brondeel, M. Madou, W.P. Gomes and F. Cardon, Sol. Energy Mater., 7 (1982) 23. 9 S. Kurtin, T.C. McGill and C.A. Mead, Phys. Rev. Len., 22 (1969) 1433. 10 A.M. Cowley and S.M. Sze, J. Appl. Phys., 36 (1965) 3212. 11 S.M. Sze, Physics of Semiconductor Devices, Wiley, New York, 1981. 12 E.H. Rhoderick, Metal-Semiconductor Contacts, Clarendon Press, Oxford, 1978. 13 S.J. Fonash, J. Appl. Phys., 54 (1983) 1966. 14 W.H. Lafl&e, R.L. Van Meirhaeghe and F. Cardon, Solid State Electron., 25 (1982) 389. 15 P.L. Hanselaer, W.H. Lafl6re, R.L. Van Meirhaeghe and F. Cardon, J. Phys. D: Appl. Phys., 15 (1982) L7.