Manifestations of the quantum size effect in the electrochemical behaviour of thin bismuth films

J. Electroanal. Chem., 196 (1985) 157-165 Elsevier Sequoia S.A., Lausanne - Printed

157 in The Netherlands

MANIFESTATIONS OF THE QUANTUM SIZE EFFECT IN THE ELECTROCHEMICAL BEHAVIOUR OF THIN BISMUTH FILMS

A.M. SKUNDIN,

A.Z. ZAIDENBERG,

A.N. Frumkrn Institute of Electrochemisity, (Received

A.M. BRODSKY

and V.S. BAGOTZKY

Academy of Sciences of the U.S.S.R.,

Moscow (U.S.S.R.)

17th April 1985)

ABSTRACT

The photoemtssion current (j) and the differential capacitance of the double layer (C) on 20-200 nm thick bismuth films have been measured. The current j as a function of potential(E) follows the 5/2 law for films of thickness exceeding 80 nm and for bulk bismuth. The current j as a function of E for thin films exhibits steps whose width increases as the thickness decreases. The absolute values of j and C also decrease for thinner films. These effects are manifestations of the quantum size effect in the energy spectrum of charge carriers in bismuth. Estimations of the degree of metalhzation of the bismuth surface are presented.

INTRODUCTION

Over the last two decades, the electrochemical properties of thin films have aroused great interest [l-8]. These properties were found to differ markedly from those of bulk samples. Since these differences depend on the characteristic size (the thickness of the film), they belong to the general category of size effects. All the size effects noted up to now for the electrochemical behaviour of thin films may be regarded as classical, in that none of them is related to phenomena concerning size quantization of the energy spectrum of charge carriers. The quantum size effect (QSE) shows up in films with thickness comparable to the DeBroglie wavelength (X B) of the charge carriers and originates from quantization of the transverse motion of quasi-particles in films: the component of the quasi-momentum normal to the film can assume only a discrete set of values. This leads to splitting of the energy zones into discrete two-dimensional subzones [9-121. This size quantization can induce new phenomena caused by changes in the energy spectrum of the films. These phenomena are likely to occur in two cases [lo]: (i) when the system of subzones is shifted with respect to the Fermi level, as is the case, for instance, with varying film thickness; (ii) when the energy of the electrons varies relative to the subzone system; for instance, in a strong external electric field, due to photon absorption, in the tunnelling process, etc. The QSE theory predicts strong oscillations in the density of

158

the states in the first case, and step-wise variation of the density of the states in the second [lo]. In metallic, semiconductor and semimetal films, QSE is usually studied by non-electrochemical methods. However, in metallic films the observation of QSE is and hampered by the short wavelength, X, - 0.1 nm [9,11]. In semiconductors semimetals with a small effective mass (m* = lop2 m,, where m, is the mass of a free electron), the effective wavelength of the electrons can be macroscopically large = 100 nm). Preparation of uniform films of this thickness is not hard to achieve. (Aa A prominent feature of QSE is the attenuation of the observed oscillations with increasing temperature; that is why QSE is usually studied at low temperatures. Yet, there exists ample experimental evidence that in films with sufficiently perfect structures one may observe QSE manifestations at higher temperatures too, including room temperature [10,12]. Such results were obtained for Bi films [13-161, Cd,As, [17], Sb [18] and InSb [19]. Weak, high-temperature attenuation of oscillations in Bi and Sb films is considered theoretically in refs. 10 and 20. Thin bismuth films are the most convenient and interesting for observing QSE by electrochemical methods. Bismuth is a semimetal with unique electron properties: low bulk concentration of charge carriers (lop5 electrons per atom), low effective mass of electrons (- 10e2 m,), high dielectric permeability of the lattice (- 100) and high diamagnetic susceptibility (- 10m5) [21]. The electrochemical behaviour of bulk bismuth has been thoroughly studied, and the structure of the electric double layer [22], the kinetics of the electrode processes [23] and the photoemission of electrons into electrolytes (241 displayed no principal deviations from the corresponding properties of conventional s-p metals. This absence of any specific electrochemical behaviour in bulk bismuth suggests metallization of its surface [24]. Metallization of the surface of bismuth in a vacuum was studied in refs. 25 and 26. There are voluminous papers dealing with the thermodynamic, magnetic and optical properties of thin bismuth films [lo-121. However, there are no results on the electrochemical properties of films. The aim of the present paper is to study the electrochemical and photoemission properties of thin bismuth films in the range of thicknesses (of the order of 80 nm) where QSE can be expected. Studies of the properties of thin films should clarify specific features of the electrochemistry of bulk bismuth and should enable quantitative estimation of the degree of metallization of the surface. EXPERIMENTAL

Thin films were produced by thermal evaporation of 99.999% pure bismuth in a vacuum (residual pressure 1 mPa), on a mica support heated to 340-350 K. This technique is known to produce mosaic films composed of planar crystallites with a trigonal axis normal to the support plane [lo]. The thickness of the film was determined to within f 5 nm accuracy by gravimetric methods. Plane samples of uniform thickness and wedge-shaped samples were used. Electric contacts were made by the deposition of a 200 nm thick electroconducting layer on the non-fidu-

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Fig. 1. Schematic structure of samples with thin bismuth films (not to scale). Top: films of uniform thickness; bottom: wedge-shaped films. (1) Mica; (2) fiducial surface of the film; (3) current lead; (4) F’TFE lacquer.

cial part of the film through a mask, which was then isolated by PTFE lacquer. The schematic design of the thin-film samples is shown in Fig. 1. In photoemission measurements, stationary illumination of the electrodes by a DRSh-1000 mercury-vapour lamp with a 365 nm interference light-filter was used. To improve the accuracy of the photocurrent measurement against the background of in-dark current, the latter was partially compensated for. N,O was used as an electron acceptor. Most measurements were carried out in 0.5 A4 KCl, 0.2 A4 NaF and 0.2 M Na,SO,, with a saturated calomel electrode as the reference. The differential capacitance was measured by the galvanostatic pulse method [27,28] with 5-10 ~LS pulses. In this method, capacitance is given by the initial slope of the potential as a function of time. The curve observed on the oscilloscope screen showed a simultaneous jump of the potential, corresponding to the iR drop on the integrated resistance including that of the film. Usually, it did not exceed 0.5 k0. It should be noted that one can work with thin bismuth films only in a certain range of potentials and pH of solution: the best stability is achieved in the pH range of 5-7 and at potentials from - 0.5 to - 1.4 V (vs. SCE). Prolonged operation at potentials greater than -0.5 V leads to film oxidation; at potentials less than - 1.4 V, cathodic incorporation of alkaline metals [29] may occur. Besides, intense evolution of hydrogen leads to destruction and spalling of the film. Destruction and spalling of the films results in a steep rise in ohmic resistance, which is a good means of checking film life times. The capacitances of the films of various thicknesses were measured by pressing the capillary with the solution to the wedge surface at different points. Steady-state polarization curves of hydrogen evolution were measured at a potential scan rate of 0.01 V/s. During polarization measurements, the iR drop was simultaneously controlled by switching off the current. The polarization curves were plotted with iR corrections. Sample surface conditions were controlled by voltammetric techniques.

160

Fig. 2. Cyclic voltammetric curves for the 63 nm thick bismuth film in 0.2 M NaF at a scan rate of 0.02 V/s. Upper limit of Ihe potential scan (in V vs. SCE): (1) -0.23, (2) - 0.20, (3) + 3.0. (Curve 3 is from ref. 30.)

EXPERIMENTAL

RESULTS

Cyclic voltammetric curves recorded for the 63 nm thick film of bismuth in 0.2 M NaF are shown in Fig. 2. The same results were obtained for films of different thickness (from 20 to 200 nm) and for bulk bismuth. The latter results agree with the previously published ones [30]. Hence, the surface properties (in particular, the oxygen adsorption properties) of films produced by thermal evaporation do not differ from those of bulk bismuth. The photocurrent j vs. E plots (in j 04, E coordinates dictated by the 5/2 law) for 20, 29 and 170 nm thick bismuth films are shown in Fig. 3. For the thickest film one observes good agreement with the 5/2 law, in accordance with the results obtained for bulk bismuth [24]. A similar result is found for all films with thickness exceeding 80 nm. For thinner films the phot~~ssion properties possess two features not inherent in bulk samples. Firstly, the phot~u~ent is no longer a smooth function of the applied voltage, but becomes increasingly stepped as the film becomes thinner. Secondly, at sufficiently negative potentials the photocurrent decreases steeply as the film thickness decreases, i.e. the slopes of approximating straight lines in the j0.4-E plot (shown in Fig. 3 by dashed lines) decrease gradually. The thickness dependence of the photocurrent at E = - 1.3 V is shown in Fig. 4.

161

2-

Fig. 3. Photocurrent vs. potential in J o 4- E coordinates films, and for the 25 nm gold film (4).

for 20 nm (l), 29 nm (2) and 170 nm (3) bismuth

The fact that the above two features occur together is a specific property of bismuth films. As a reference test, we also studied gold and antimony films. For gold films the 5/2 law was found to hold true for all the thicknesses studied (Fig. 3) and the photocurrent did not depend on the film thickness. For antimony films also, the photocurrent did not show any thickness dependence (Fig. 4), although on the j0.4-E plot the steps appeared for films thinner than 30 nm. Still thinner antimony films proved to be rather unstable and we could not study their properties. The differential capacitance of two wedge-shaped samples of bismuth film as a function of film thickness is shown in Fig. 5 (for E = -0.6 V). It can be seen that for thicknesses exceeding 80 nm the differential capacitance measured does not depend on the thickness and is close to that of the double layer on bulk bismuth. For thicknesses less than 80 nm the differential capacitance drops steeply (at 28 nm being only about 20 mF/m*) by an order in magnitude below that for bulk bismuth. Typical polarization curves of the cathode process in 0.3 M NH,Cl on bismuth films are shown in Fig. 6. The polarization curves for “thick” samples (thickness > 80 nm) coincide with that of hydrogen evolution on bulk bismuth. As the film thickness is decreased, the polarization curves change fundamentally: the slope

0-

160 I

/nm

Fig. 4. Photocurrent vs. film thickness at E = - 1.3 V for bismuth (1) and antimony (2) films.

Fig. 5. Relative differential capacitance vs. film thickness for two wedge-shaped sampIes at E = -0.6 V. C, is the differential capacitance of the bulk bismuth electrode (ZOOmF/m*).

KG-

A-l n-2 o-3

1027 *,,

_

KP-

-t 10-l

-1.2

11’ -1.4

$1 -1.6

f -1.6

c -20

E ,‘Vbec)

Fig. 6. Cathodic hydrogen evolution polarization curves for 30 nm (l), 60 nm (2) and 240 nm (3) bismuth films and bulk bismuth (4) in 0.3 A4 NH,Cl.

dE/d log i rises steeply for thinner films. As a result, at small over-potentials the current density increases and at high overpotentials the current density decreases as films are made thinner and thinner.

DISCUSSION

The results of the experiments reported demonstrate that the electrochemical and photoelectrochemical properties of bismuth films with thicknesses greater than 100 nm show virtually no difference from those of bulk bismuth. Significant structural changes (in particular, m~festations of the ~s~n~n~ty of films) occur in films thinner than 20 run [lo]. Hence, significant changes in the properties of films with

163

thickness L varying from 20 to 100 nm (i.e. at L ( A,) are most likely due to manifestations of the size quantization. In bismuth films, the most striking quantum size effect is a stepwise dependence of the photocurrent of external photoemission on the potential, related to the stepwise density of energy levels in thin films. Using the energy spectrum of electrons in bismuth (a simple double-band model proposed by Lax [31]) the relation

is obtained where 8s is the energy gap between the conduction and valence bands and parameters Q,, Q,. and Q, characterize the interaction between bands at the L-point of the Brillouin zone (x-direction is oriented along the trigonal axis). Extrapolating this spectrum into the region of 8’2 8’ yields the following equation for the width of steps along the potential axis: AE=

Q&r/L

(2)

Q, can be estimated from the results shown in Fig. 3. For the 20 nm film, Q, = 1.4 X lo6 m s-‘, which agrees with the value of Q, for bulk bismuth [32]. Another manifestation of the size quantization is a decrease in the differential capacitance and in the photocurrent as the film thickness is decreased down to values of a few tens of nanometers (Figs. 4 and 5). According to the theory of photoemission of electrons into electrolyte solutions [33], the photocurrent is proportional to the electron density near the Fermi surface. This suggests that the experimentally observed drop in photocurrent as the film thickness decreases is most likely due to a change in the charge carrier concentration. On the other hand, variations of the differential capacitance of the bismuth electrode should also be related to changes in the electron density. Indeed, from the QSE theory it follows that as the density of electrons and the charge carrier mobility are lowered the film thickness decreases, whereas the Fermi energy rises and the electron work function decreases [9,34]. In thin bismuth films, on the boundary with the electrolyte the QSE is observed in strong external electric fields (in the Helmholtz layer, fields up to 10” V/m are known to be attainable). Shift of the potential to more negative values is f@owed by injection of electrons into the conduction zone, i.e. by metallization. This would result in increasing energy of electrons with respect to the bottom of the conduction zone, which, in this particular case, is related to the surface concentration of electrons via the equation [35]:

(In bulk bismuth the Fermi energy is known to be about 0.02 eV (see, for instance, ref. 21) with respect to the bottom of the conduction zone, implying that the conduction zone is virtually unpopulated.)

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The surface concentration of charge carriers can be estimated from the measured capacitance (Fig, 5) which for the 40 nm film equals approximately 40 mF/m* and depends weakly on the potential. The zero charge potential of bismuth equals - 0.63 V [22]. In the range of potentials from - 0.7 to - 1.4 V the surface density of ions equals p, = CAE/e = 10’7-10’8 m-*. The corresponding bulk charge density equals at least 1025-1027 rnm3, i.e. it exceeds that in bulk bismuth by at least one to two this value into eqn. (3) and using the orders of magnitude *. By substituting magnitude of Q, determined from the results of photoemission studies, one obtains A&‘= 0.1-1.0 eV. In this film the surplus charge carriers are rather uniformly distributed over the film, with the probability density given by solution of the corresponding Schrodinger equation (if the film thickness is comparable with ha). Hence, as the potential is shifted in the negative direction the conduction zone in thin films will indeed become more populated, thus enhancing photoemission from this zone. The results on cathodic hydrogen evolution on thin bismuth films are the most difficult to interpret. The rise in the dE/d log i slopes is not related to the increasing resistance of thin films, as the latter has already been taken into account while plotting the data in Fig. 6. Besides, from Fig. 6 it follows that at low polarizations the current density in thin films is somewhat higher than that in thicker films and/or bulk samples. Hence, one is tempted to conclude rather that the mechanism of the hydrogen evolution process changes. Presumably, the QSE-induced reduction of the work function of thin films, as well as the effect of the jump of the potential on the degree of metallization of the surface of bismuth contributes to that. Neither effect can be ruled out. REFERENCES

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l One has to bear in mind that along with electrons the surface can attract holes as well, which will result in partial compensation of electron charge.

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