Effect of Oxygen Chemisorption and Photodesorption on the Conductivity of ZnO Powder Layers BY NICO M. BEEKMANS~ Mullard Research Laboratories, Redhill, Surrey Received 25th January, 1977 Chemisorption of oxygen on the surface of the grains of ZnO powder layers mainly controls the photoconductivity. The adsorption of oxygen ions is regarded as a chemical reaction at the interface and involves oxygen from the gas atmosphere and electrons from the metal oxide. The changes in the conductivity of ZnO-layers calculated on this basis are in fair agreement with the experimental results. At low light levels deviations from the theory are observed which result from an “ overdepletion ’’ of the conductivity controlling regions in the powder layer. Considering a ZnO layer as a secondary photoconductor has allowed the calculation of a maximum photosensitivity for such layers.1. INTRODUCTION The electrical conductivity in layers of fine grains of n-type ZnO can be reduced considerably by chemisorption of negatively charged oxygen ions on the surface of \ -- -- I ‘-H FIG. l.-(cz) Cross-section of a powder layer ; shading indicates surface space charge region. (6) Cross-section of a connecting “ neck ” in a powder layer and energy band diagrams corresponding to three cuts across the neck (after Hutson).+ t Presentraddress : Philips Research Laboratories, Eindhoven, The Netherlands. 3132 CONDUCTIVITY OF ZnO the grains. Subsequent illumination with light of suitable wavelength desorbs the oxygen from the surface and restores the conductivity. Effectively such powder layers behave as very sensitive photoconductors, much more sensitive than can be expected from the increase in the bulk free carrier concentration under illumina- ti0n.l.The electronic charge involved in the chemisorption is extracted from the semiconductor. As a result a positively charged depletion layer is formed under the surface to compensate for the negative surface ~ h a r g e . ~ - ~ The effects of depletion regions on the conductivity are illustrated in fig. 1. Attractive forces between the grains, such as Van der Waals forces, cause the formation of contact regions or necks between the grains. For the ZnQ powder used the diameter of these necks can be estimated as - 10 % of the grain diameter.6 By correct matching of grain size, carrier concentration and oxygen pressure, the depletion layers may become thick enough to completely deplete the smallest regions in the powder layer, i.e.the necks between the grains. It is the purpose of this paper to show that the concept of chemisorption on the surface applied to a model of depletion of the necks linking the grains of a powder layer allows the detailed behaviour to be calculated. Section 2 develops the model for the conductivity of a single grain-to-grain contact as a function of geometry, illumination and oxygen pressure. Some experimental results illustrate the feasibility of the model. The effects of percolation is powder layers introduced in section 3 explain the satisfactory agreement between the behaviour of the model for uniform particle sizes and the experimental layers.Using photoconduction theory in section 4 the maximum photosensitivity of ZnO powder layers is calculated. 2. THEORY FOR UNIFORM PARTICLE SIZES In this section a model will be developed for the effects of chemisorption on the conductivity in the neck between two grains of a metal oxide semiconductor. We assume that in oxygen or in air at atmospheric pressure oxygen alone will be adsorbed on the surface of a neck. On the surface a limited number of sites (n, cm-2) are available for adsorption of oxygen. A certain fraction of the oxygen adsorbed may have trapped a free electron from the ZnO. The chemisorption reaction on these sites can be descripted by the scheme :* O,+e; e 0;. (2.2) Positions in the gasphase, at the surface and in the bulk of the semiconductor are indicated by the subscript g, y and s, respectively.Illumination of the semi- conductor with light of suitable wavelength creates electron-hole pairs. Holes generated in the space charge region are attracted to the surface and may discharge an oxygen ion there : (kv} + e; + h$, h$ +OF 3 0,. In this scheme (kv) stands for an absorbed photon with energy hv. We introduce the relative surface occupation r as the fraction of the total surface site concentration (n,) occupied by oxygen ions. As will be shown later the interaction between the gas atmosphere and the ZnO surface is faster than the chemisorption and desorption reactions. Also the creation of an electron-hole pair after absorption * The Kroger and Vink notation will be adopted, see F.A. Kroger, 312e Chemistry of Imperfect CrystaZs (North HollandlAmerican Elsevier 2nd edn, 1974), vol. 2, p. 1.N. M . BEEKMANS 33 of a photon is assumed to be a fast process. Under those conditions the reactions (2.2) and (2.4) are rate determining. Variations of r with time will result from the balance between the adsorption reaction (2.2) and the opposing parallel desorption reactions (2.2) and (2.4), according to : d r - = k'rony-k21'-khy. dt In this rate equation k', k" and k2 are constants, ny and h, stand for respectively the electron and the hole concentration at the surface and To is the concentration of the adsorbed oxygen atoms at the surface. Irradiation of the surface with I W of light consisting of quanta of energy hv creates a number of electron-hole pairs per unit time.The concentration of holes near the surface resulting from this flux is propor- tional to the number of holes generated per unit time : 61 hy cc -- hv (2.5 j where 6 is a conversion efficiency factor which depends on the spatial coordinates in the layer and on the wavelength. An equilibrium between gas atmosphere and the surface according to reaction (2.1) implies : ro cc P&. The negative surface charge caused by the chemisorbed oxygen is compensated by a positive space charge region in the semiconductor. The electron concentration at the surface ny is related to n and to the difference in electrostatic potential # between bulk and surface : where k is the Boltzmann constant and T the absolute temperature.Substitution of the eqn (2.6) to (2.8) in eqn (2.5) and introduction of the constants kl and k3 gives : n, = n exp (-q#lkT), (2.8) - = k1P&nexp(-q4/kT)-T d r dt Integration of Poisson's equation over the thickness L of the space charge region gives the well known relation between L and the surface potential # :' (2.10) where E is the relative dielectric constant and go the permittivity of vacuum. The surface charge per unit area must be equal to the space charge under the same area. This condition gives directly a relation between the relative surface occupation and the surface potential : (2.11) where n, is the number of sites at the surface available for oxygen adsorption. Substitution of eqn (2.11) in eqn (2.9) eliminates the surface potential as a parameter in the latter: (2.12) 1-234 CONDUCTIVITY OF ZnO The reaction equations in this section assume the chemisorption of oxygen as single charged ions.However, the actual ionisation state of the chemisorbed oxygen is still uncertain. 0; ions as well as 0- ions can exist while transitions between the two states are possible.8* For reasons of simplicity the 0- state has arbitrarily been chosen. 2.1 CONDUCTIVITY I N A NECK BETWEEN TWO GRAINS The initial concentration of the free charge carriers in a neck region with a constant cross-section in the direction of the current is n ~ r n - ~ . Suppose that oxygen at the surface of the neck traps some electrons reducing the average concentration in the neck region to n* ~ r n - ~ . The ratio between the volume of the neck region and its surface area will be defined asfcm.Assuming the number of sites at the surface available for oxygen adsorption to be n, cm-2, then the relative surface occupation r is: n-n* nt r=-$ Conversion of carrier concentration into conductivity gives : r = (1-5): (2.13) (2.14) where cr stands for the average conductivity in the partially depleted neck and om for the conductivity in the undepleted neck. The derivation of eqn (2.14) did not require the definition of discrete depletion layers and has as such the advantage that the actual shape of the depletion layers is not important. When applied to a partially depleted neck with limited depletion layers near the surface, om stands for the conductivity of the undepleted channel in the centre of the neck.2.2 RELATIONS BETWEEN PARAMETERS Relations exist between several of the parameters contained in eqn (2.12) which reduce effectively the number of independent variables. Under conditions of equilibrium in darkness (dT/dt = 0 and I = 0), eqn (2.12) yields a relation between kly k2 and r : Y (2.15) where rd stands for the relative surface occupation of the stationary state in darkness, The conductivity of the neck drops to zero when it is just completely depleted. At this moment eqn (2.14) becomes : ?l ra = -f. (2.16) nt Another useful relation can be derived by solving eqn (2.12) for very low values of I' and substitution of eqn (2.14) : 0 = om[ 1--P 7 h2 k 1 1 t f o r a - a,. (2.17) Suppose the rate of adsorption is not slowed down by increasing desorption effectsN.M. BEEKMANS 35 and an opposing surface potential. The conductivity in the neck would then be reduced to zero in a characteristic time (7). For CT = 0, eqn (2.17) becomes : 7 = -* f PO3 (2.18) ntk1 Eqn (2.15), (2.16) and (2.18) enable the calculation of internally consistent sets of values for k l , kZ, r,, z andf. In principle the number of sets of values that satisfy the conditions of the equations mentioned is unlimited. In practice, however, parameters which can be derived from experiments such as the neck ratio (f), characteristic time (2) and rise time of the photoconductivity curve reduce very strongly the range of values for the rate constants and for the surface occupation in darkness. The values used for the material constants in the calculation of the photoconductivity are collected in table 1 .The absolute accuracy of most of the values in the table is not very high. Some parameters can be chosen freely within a certain range. However, the conditions of internal consistency demands then some accuracy for the other parameters. TABLE PA PARAMETERS USED FOR THE CALCULATION OF THE NECK CONDUCTMTY relative surface occupation adsorption rate constant kl desorption rate constant kz photodesorption rate constant k3 characteristic time z ratio between neck volume f density of surface sites nt dielectric constant & temperature T donor concentration n in darkness r d and surface area 4.647~ 10-4 9 . o ~ 10-4 s-1 kzhvlS cm2 1.463 x cm3 bar-* s-l 0.032 s 5 . 6 2 ~ 1W6 cm 1.21 x 1015 cm-2 10 300 K lo1' CM-~ No direct estimation for k3 and 6 has been made.The value of the conversion factor 6 depends on many factors such as geometry, surface condition and position in the layer. The photo assisted desorption reaction (2.4) is so closely related in nature to the spontaneous desorption reaction (2.2) that it seems reasonable to assume k3 to be proportional to k2. This assumption, together with the acceptance of relative illumination levels instead of absolute ones, provides sufficient basis for an estimation of the effects of illumination on the effective conductivity in a neck region. 2.3 COMPARISON BETWEEN THEORY AND EXPERIMENT The change in conductivity with time in a neck at different light levels has been calculated by integration of eqn (2.12) and applying eqn (2.14) on the basis of parameter values listed in table 1 (see fig.2). The neck is assumed to be illuminated for 3 min starting from t = 2 min. Fig. 3 shows an experimental observation of the conductance change with time under illumination* as found in a thin layer (0.5 x 0.5 x 2 x cm3) of fine-grained ZnO powder. The layer has a very low conductance in darkness and is illuminated with U.V. light of various intensities. After an illumination of x3 min duration the conductance returns slowly to its dark con- ductivity level. The general shapes of the curves in fig. 2 and fig. 3 show a close * Details of layer preparation and measuring conditions will be published separately by J. E. Ralph.36 CONDUCTIVITY OF ZnO loo timelmin FIG. 2.-The conductivity change in a neck region with time as calculated for various relative light levels.Between t = 2 min and t = 5 min the neck is illuminated at the relative light level indicated. kl = 1 . 4 6 ~ cm3 bar-* s-l, k2 = 9.00~ s-l, I' = 4 . 6 ~ resemblance. At first sight this seems remarkable since fig. 2 deals with the theoretical conductivity of a single neck, whereas the experimental curves in fig. 3 have reference to a real layer consisting of many grains and with a large variety of geometries of the necks between the grains. However, calculations show that the actual geometry of the neck determines mainly the dark conductivity and only to a limited extent the speed of response and the conductivity under illumination. This is illustrated in fig. 4. The dark conductivities differ by as much as 3 decades but the rise time of the curves and their equilibrium level under illumination are almost the same.I = 0.001x I, I = 0.00 15 X lo timelmin FIG. 3.-Conductance change with time in an experimental ZnO layer. Between t % 0.5 min and t x 4min the sample has been subjected to an illumination strength as indicated. Sample MPIM4, I,, = lo-' W cm-2. In some applications a ZnO layer is illuminated intermittently. Between the light pulses the conductivity of the layer is reset to a low value by means of, for example, a corona discharge.1° For these applications the change in conductivity during aN. M. BEEKMANS 37 I $ - : ’ . ; : 6 :’ : - : 9 L timelmin FIG. 4.-Conductivity in a neck region as a function of time. Necks that differ in their dark conductivities are illuminated between t = 2 min and t = 5 min.Although the dark conductivities of the necks vary over 3 decades, their conductivities under illumination are very nearly the same. kl = 1.46 x cm3 bar-4 s-l, kZ = 9.00~ s-lY I? = 4 . 6 ~ illumination = 1. illumination FIG. 5.-Rate of the conductivity change in a neck region shortly after exposing a neck with a low dark conductivity to a given illumination level. The photosensitivity is calculated for necks with 0 %, 1 %and 3 % overdepletion. kl = 1.46 x 10-19 cm3 b a d s - l , kl = 9.00 x s--l,f= 5.62 x cm.38 CONDUCTIVITY OF ZnO light pulse of given intensity and duration is a criterion for the photosensitivity. The initial conductivity change under illumination can be derived by differentiation of eqn (2.14) and substitution in eqn (2.12).Assuming om % cr we obtain an expression for the rate of conductivity change as a function of illumination : (2.19) The conductivity change per unit of time varies linearly with illumination. In fig. 5 the curve marked 0 % shows the calculated rate of conductivity change for the parameters indicated. Fig. 6 shows the experimental rate of conductance change as can be derived from fig. 3. At high illumination levels the conductance change per unit of time follows closely the predicted slope but at lower light levels the conductance change drops faster than expected. X"X 10121/x I I I I 1 I 16' lo7 16' -I I 10 illumination/W cm-2 J FIG. 6.-Rate of conductance change with time in an experimental ZnO layer shortly after exposing the layer to a given illumination intensity. The broken line shows the theoretical slope for an array of partially depleted necks.The upper curve shows the calculated upper limit for the photo- sensitivity of such a powder layer. Up to now we have considered the necks between the grains as partially depleted. In such a neck a small channel of undepleted ZnO near the centre of the neck provides a path for the electrical current. The width of this channel can be varied by changing the illumination level. Depletion layers in the necks and in the adjacent grains are of equal thickness. Let us consider now an overdepleted neck, i.e. a neck with a diameter less thanN. M . BEEKMANS 39 twice the thickness of the depletion layers in the grains adjacent to the neck.Such an overdepleted neck is characterized by zero conductivity and thicker depletion layers outside the neck than inside. Under sufficiently strong illumination the thickness of the depletion layers both in the neck and in the adjacent grains diminishes and the overdepletion will disappear. Then the thickness of the depletion layers in the neck and in the grains have become equal. Consequently, by changing the neck depletion by illumination from the overdepleted state to the partially depleted state the depletion layer has been reduced in the same shorter time in the neck than in the adjacent grains. The rate at which the thickness of the depletion layer in the neck changes is related to the rate of conductivity change. Hence, we may expect a reduced rate of conductivity change in the overdepleted state.Therefore the extra drop in conductance at low illumination level in fig. 6 suggests that a substantial fraction of the necks in the ZnO layer were overdepleted. Fig. 5 also shows the rate of conduc- tivity change in necks with a radius respectively 1 % and 3 % smaller than the thickness of the depletion layers at equilibrium in darkness. Although eqn (2.19) has been used for the calculations of these curves, it has been derived under conditions which do not include overdepletion. However, it can be shown that the shape of the curves is consistent with the outcome of a more complicated model in which the depletion layers in grain and neck are treated separately. 2.4 EQUILIBRIUM SITUATION Equilibrium in darkness between an oxygen containing atmosphere and a ZnO surface is described by the reactions (2.1) and (2.2).The thermodynamic equilibrium condition for these equations is :11* l2 $luoze+ve = Yo-y* (2.20) In eqn (2.20) we have to use electrochemical potentials (q) instead of chemical potentials ( p ) because the electrons in the semiconductor and the oxygen ions at the surface are separated in space. Consequently, these elements can have different electrostatic potentials. Substitution of the electrochemical potential by chemical and electrostatic potentials converts eqn (2.20) into : +olg 1 0 + 3RT In Po, + pz + RT In n - F+s = p&,+RTln rd-F$y, (2.21) where pz, yo: and ,&- are the standard chemical potentials of the electrons, oxygen and oxygen ions, respectively.These are constants. Further & and 4s stand for the electrostatic potentials at the surface and in the semiconductor, respectively. R is the gas constant and P is Faraday’s constant. Eqn (2.21) is only valid if the relative surface occupation (I?) is less than unity. This condition is fulfilled since we arrived previously at a value for r d of 4.6 x (see table 1). After substitution of +s-4,, = 4, change of constants and some rearrangement eqn (2.21) becomes : ra = KP& n exp [ -q$/kT], (2.22) where K stands for a collection of constants. Comparison of eqn (2.22) with eqn (2.9) applied to the stationary state in darkness (drldt = 0 and I = 0) shows that both equations become identical with K = kl/k2. 2.5 CONDUCTIVITY AS A FUNCTION OF OXYGEN PRESSURE Most studies of the defect properties of ZnO conclude that interstitial zinc ions and electrons act as the dominating defects.The electroneutrality condition together40 CONDUCTIVITY OF ZnO with the law of mass action predicts a % power relation between oxygen pressure and conductivity. This relation combined with eqn (2.14) and (2.22) yields an expression for the average conductivity in a neck at equilibrium in darkness ; kin, * k2.f CJ = ooP&oo -Poz exp [-q+/kT] (2.23) where go stands for the conductivity of ZnO at 1 bar of oxygen (1 bar = lo5 N m-2 = lo5 Pa). The surface potential 4 is a function of the oxygen pressure. Their relation results from the eqn (2.10) and (2.22) : (2.24) Eqn (2.23) together with eqn (2.24) determine the average conductivity against oxygen pressure.A calculated pressure dependence is plotted in fig. 7, while in "7 to' a oxygen pressure/bar FIG. 'I.-Equilibrium conductivity of a neck region as a function of the oxygen pressure. kl = 1.46 x 10-19 cm3 bar-* s-l, kz = 9.00 x s-l, f = 5.62 x 10-411cm. fig. 8 an experimental curve is shown; the latter was measured at 540 K. Above bar the conductivity drops strongly but is not accurately reproducible. This is indicated in the figure with errors bars. At low oxygen pressure the experimental curve follows the predicted +-power law in a reproducible way. I f 12 - 4 I s 3 li4- 3 12 10 -88 IG8 1 2 lo4 16 loo oxygen pressurebar FIG. 8.-Equilibrium conductance of an experimental ZnO layer as a function of the oxygen pressure. NMB sample at 540 K.N.M. BEEKMANS 41 From the time constant for the conductivity change at low oxygen pressures of ~1 h a self diffusion coefficient for zinc of cm2 s-l has been derived. NO values for zinc diffusion at 540 K have been reported but extrapolated literature values for the self diffusion of zinc in ZnO ranges from to cm2 s-1.13-15 The rate of the conductivity change during evacuation of the space above a sample can be enhanced considerably by illumination with U.V. light. After illumination for a short period the conductivity remains nearly constant at a much higher conductivity level. This proves that the rate at which the conductivity increases in darkness is limited by the desorption reaction (2.2) and not by the interaction between surface and gas atmosphere.This was one of the presumptions of section 2.0. 3. EFFECTS OF A DISTRIBUTION IN GRAIN AND NECK SIZE Section 2 dealt mainly with the changes in the average conductivity in a single neck or in layers with uniform particle size. However, experimental layers are built-up from grains of an ill-defined shape and with a certain spread in grain size. The ZnO powder used in the experiments follows closely a log normal distribution with a mean Stokes diameter of 0.64 pm and a standard deviation of 1.46. Although we do not have direct knowledge of the neck size distribution in experimental ZnO layers, it seems fair to assume that the neck size distribution shows some resemblance to the grain size distribution. In this section we assume that the shape of the neck size distribution and the shape of the grain size distribution are the same.Current flow in a ZnO powder layer is possible only if uninterrupted paths for current fiow can be found. Below a certain fraction of conducting necks, the so-called percolation limit, the probability that such paths exist is very low. The conductivity of a powder consisting of a mixture of conducting grains and of non-conducting grains or cavities In this equationp stands for the fraction of the conducting grains in the system while pc is the percolation limit. The power m ranges for the different authors from 1.5 to 2.16-19 According to Scher and Zallen 2o the percolation limit for a three- dimensional array is M 0.1 5 of the occupied volume and for a two-dimensional array M 0.44 of the occupied area.The experimental layers used have a thickness of x 5-8 gains and are therefore not covered by the definition of a three-dimensional layer or by that of a two-dimensional layer. Consequently, the percolation limit for these layers will depend on its thickness. In darkness only a limited fraction of the grains are conductive. Hence, we may expect a strongly non-linear relationship between dark conductivity and layer thickness. This effect is observed experimentally. The necks between the grains can be grouped into three catagories. Firstly, the very large necks, which are always wider than the depletion thickness. Grains interconnected by such necks can always contribute to a conduction path through the layer. Secondly, the moderately size necks, which are almost completely depleted in darkness and consequently have a low dark conductivity.Under illumination the depletion layers in the necks diminish and these necks can then form part of a conducting path through the layer. The third category compreses the necks which are small and heavily overdepleted. These necks will never contribute to the conductivity at the light levels considered. Assuming a conductivity under iUurnination of -80 % of the single crystal value and no dark conductivity, the fraction of the conductiiig and of the light sensitive grains in a layer can be estimated. Fig. 9 shows the resulting neck size distribution based on a space percolation limit of 0.25 and a packing density of 0.55. The fraction42 CONDUCTIVITY OF ZnO of permanently conducting grains in fig.9 is 34 %. Under illumination the fraction of conducting necks increases because of the contribution of the light-sensitive grains (19.5 %). 2.0 T 0.5 0.0 , 0.00 0.05 0. LO neck radiuslpm FIG. 9.-The estimated neck size distribution of the ZnO powder used. A ZnO layer containing up to -34 % conducting necks remains in a low conductive state in darkness. A fraction of light- sensitive grains of -20 % is sufficient to cause a considerable photo effect. Examination of fig. 9 shows that only necks within a small range of radii are light sensitive. Furthermore, the major part of these light sensitive grains have radii smaller than the thickness of the depletion layer in darkness. Therefore, these necks are more or less overdepleted in darkness.As discussed before, overdepletion causes a drop in the photoconductivity, particularly at low light levels. 4. MAXIMUM PHOTOSENSITIVITY In a neck the acceptor or recombination centres are not homogeneously distributed throughout its volume but located on the surface. Nevertheless we may treat such a neck as a simple secondary photoconductor since the diffusion length of the electrons and the holes is more than the neck radius. In a ZnO powder layer reflection of light on the layer, low quantum efficiency, etc. prevent optimal conversion of the incident radiation. Since the influence of all these effects is difficult to estimate, we restrict ourselves to the calculation of an upper limit for the photosensitivity. All effects that reduce the photosensitivity, such as reflection and scattering of photons, are ignored.The quantum efficiency will be taken as one ; the lifetime of the electrons is assumed to be unlimited. Furthermore we assume the ZnO powder layers to be 100 % dense. Light incident on a semiconductor is absorbed according to : A = Zo[l -exp ( - a x ) ] , (4.1) where A is the energy absorbed in a layer with a thickness x, 1, is the incident radiation at the surface ( x = 03, and a the absorption coefficient.N. M. BEEKMANS 43 In a thin sheet of ZnO, electron-hole pairs are generated by the absorption of photons with an energy greater than the band gap of 3.2 eV. The holes recombine at the recombination centres on the surface leaving the electrons free to move. The increase in the free electron concentration results in an increase in the conductivity of the layer.The rate at which the conductivity increases at a depth x is : where Eg is the band gap in eV. Allowing for the geometry and the positions of the electrodes, integration of eqn (4.2) yields the rate of conductance change for a given layer at a certain illumination level. Using the geometry of the experimental layer quoted in section 3 and a mobility of 70 cm2 V-l s-l 21 and an adsorption of 10-4,22 we arrive at the rate of conductance change plotted in fig. 6 . The theoretical maximum rate of conductance change is - 3.5 decades higher than experimentally found, but the calculated curve is based on rather optimistic assumptions. 5. DISCUSSION In section 2 a model has been proposed for the conductivity in a single neck based on the chemisorption and photodesorption of oxygen ions at the surface.Together with the percolation theory this model seems to explain qualitatively nearly all well- established conductivity effects in ZnO powder layers. However, this does not imply that all the underlying assumptions are necessarily correct. For instance, we have ignored the possibility of an intergrain 24 The alignment of the crystal lattices of two adjacent grains is, in general, very poor and will give rise to a barrier in the neck. In section 3 it is shown that the charge density in the space charge region is smaller in an overdepleted neck than in the adjacent grains. This effect will cause also an intergrain barrier either due to the difference in surface potential or due to the creation of a potential barrier inside the neck.In the light-sensitive necks this intergrain barrier exists only in darkness or at low light levels and disappears completely under stronger illumination. 5.1 SURFACE ACTIVATION Photosensitivity has been defined as the rate of conductivity change under illumination. The photosensitivity will be influenced by the method of sample preparation and by the gas atmosphere. Variations in the sample preparation may change the nature of the chemisorbed species. More probable, however, is that certain constituents of the gas phase or of the chemisorbed layer activate or deactivate the chemisorption of the oxygen. For the simple case of 0- adsorption on a fixed number of sites the effects of activation of the surface reaction are relatively easy to understand.The surface reaction can be enhanced or slowed down by some treatment, but in equilibrium the sum of all electrochemical potentials in the surface reaction is zero [eqn (2.20)]. In section 2.4 the equilibrium surface occupation was calculated for this condition. Since the constant Kin eqn (2.22) contains fundamental constants and standardized material constants only, it has to be considered as a characteristic constant for adsorption on ZnO surfaces. The value of this constant is not influenced by any kind of surface activation. The rate constants kl and k2 may change over several decades as a result of surface activation, but the relation K = k1/k2 fixes their ratio. Since rate constant k3 was assumed to be proportional to k2 the photosensitivity of the layer will increase with an increase of the adsorption and desorption rates.44 CONDUCTIVITY OF ZnO The reasoning given above is valid for those types of activation of the chemi- sorption where the activator has an intermediate function only.An example could be: +020 + e; + H20, + 0; + H20, H20g + H207. ( 5 4 It is also possible that the surface adsorption involves another molecule. An example of such a reaction is : go,, + e; + 3H20, + OH;. When eqn (5.2) is valid, the equilibrium surface occupation is no longer a constant but varies with the vapour pressure of water. Nevertheless at a given vapour pressure of water the number of surface sites is fixed. Hence the theory developed in section 2 is fully applicable.Complications may occur when all sites available for adsorption are no longer equal but consist of sites of type I with properties different from sites of type IL2’ This can give rise to effects which the theory presented here cannot account for. For example, suppose chemisorption takes place by fast adsorption on sites of type I, followed by a slow conversion to sites of type 11. Under certain circumstances this will give rise to a peak in the conductivity response to illumination. Such peaks in the conductivity response to illumination. Such peaks in the conductivity plot have been observed by several authors.26* 27 5.2 CONDITIONS FOR MAXIMUM PHOTOSENSITIVITY For the highest photosensitivity a ZnO powder layer must be built up as regularly and uniformly as possible.Ideally, the layer would consist of spherical grains, densely packed in a layer of well-defined thickness, interconnected via necks identical in geometry and operated at an oxygen pressure level which depletes the neck completely in darkness without causing overdepletion. Deviation from this ideal situation deteriorates the photoconductive properties. Overdepletion, for example, reduces the photosensitivity considerably, particularly at low light levels. Since ZnO layers are built up from grains not uniform in size or shape avoidance of overdepletion demands operation at a fairly high conductivity level. Hence, illumination with light of considerable intensity is necessary to change the conductivity at this level substantially. Operating the layer at a lower light level without causing overdepletion is only possible if a material is chosen whose grain size distribution has a smaller standard deviation.6. CONCLUSION The conductivity of a ZnO powder layer appears to be controlled by the neck conductivity, which in turn is controlled by chemisorption of the charged species and can be described as a first order reaction in which oxygen from the surrounding gas atmosphere and electrons extracted from the semi-conductor are involved. Comparison between measurements of the oxygen pressure dependence of the conductivity in ZnO layers and calculation of the thermodynamic equilibrium at the surface has confirmed the feasibility of a model based on surface reactions. The oxygen pressure dependence found experimentally is in agreement with a defect model in which singly charged zinc or oxygen defects and electrons are dominant.The effects predicted by the theory are in fair agreement with the experimental results, particularly at high light levels. Treating the ZnO powder layer as a secondaryN. M. REEKMANS 45 photoconductor has enabled us to calculated. a maximum rate of conductivity change for ZnO powder layers. The rate of conductivity change is for certain applications a criterion for the photosensitivity of the layer. It is shown that a substantial fraction of the necks between the grains would be overdepleted in darkness and at low light levels. Under these conditions the photo- sensitivity of powder layers would be reduced strongly. Maximum photosensitivity in a powder layer requires a regular and densely packed layer of well-defined thickness consisting of equally sized spherical grains and operated at an oxygen pressure which just allows complete depletion in darkness.Powder layers essentially consist of grains with a certain distribution in size and geometry and have an irregular structure. From this point of view powder materials seem not to be the most obvious choice for the realization of a highly sensitive photoconductive layer. The author thanks his colleagues, in particular, Dr. J. E. Ralph, Dr. J. W. Orton, Mr. I. C. P. Millar and Dr. P. S. Clarke for helpful discussions. Most of the experimental data are based on measurements by Mr. I. C. P. Millar on a sample prepared by Mr. M. J. Plummer. D. A. Melnick, J. Chem. Phys., 1957,26,1136. 6. Heiland, E. Mollwo and F. Stockmann, in Solid State Physics, ed. F . Seitz and D. Turnbull (Academic Press, N.Y., 1959), vol. 8, p. 275. S. R. 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