Chemical Processes at Clean { loTO] ZnO Surfaces Part 1 .-Thermal Production of Surface Defects BY MINO GREEN" AND IMENTS R. LAUKS Department of Electrical Engineering, Imperial College, Exhibition Road, London SW7 2BT Received 24th November, 1977 Oxygen loss from single crystal ZnO { lOiO} surfaces has been investigated using the method of thermally programmed desorption (t.p.d.). The t.p.d. parameters (peak area, shape, width at half height and temperature of the maximum) have been analysed in terms of O2 and Zn loss kinetics from the outermost surface atoms of the crystal only. A reaction mechanism is proposed in which both positive surface oxygen vacancies and neutral surface step sites are formed, and in which the reaction kinetics are dependent upon the fractional concentration of both kinds of surface defect (6 and O,,).The maximum value of 8 is 4 % and 6,, is -20 %. There have been many studies of the chemical and physical properties of zinc oxide surfaces, and the present position has been thoroughly reviewed. 1-3 However, these studies have left a great deal unresolved, and if the objective is to obtain a deeper knowledge of the elementary processes occurring at the surface of the solid, then it is necessary that well-defined single crystal surfaces should be the starting point of any investigation. A well-defined surface is taken to mean one for which the surface composition, surface crystallography and surface state type and levels is known. Of the few papers on clean (lOT0) ZnO single crystal surfaces 4-8 bearing on this study, those by Gopel 7* are the most relevant.It is reported that clean (lOT0) surfaces are unreconstructed but do have split LEED spots, typical of terraces, and that surface vacancies of oxygen are formed. This paper, the first in a series of studies on well-defined ZnO single crystal needles in which -99.9 % of the exposed surface is the non-polar (IOiO), is concerned with determining the extent and kinetics of surface defect (oxygen vacancies) formation. The technique employed is thermally programmed desorption (t.p.d.). Halpern and Germain have used t.p.d. to investigate various oxides and it was their work which led to our adopting this technique, though the analysis of the data has had to be very much extended. Work carried out on Q16/018 exchange and N20 decomposition is reported in Parts 2 and 3.1° EXPERIMENTAL ZnO CRYSTALS AND SURFACE CLEANING PROCEDURE The ZnO used in this study consisted of a mass of single crystal needles of radius-to-length ranging between (5 pm to 10 mm) to (250 pm to 14 mm), most of them being in the smaller range.The needles have a regular hexagonal cross-section normal to the c-axis; the exposed planes parallel to the c-axis were found (by an X-ray rocking method) to be (1OiO) and are termed the prism planes. The hexagonal end faces of the needles, the polar planes, 2724M . GREEN AND I . R . LAUKS 2725 constitute xO.1 % of the exposed surface area. Scanning electron microscopy shows no gross surface defects. The crystals were of high purity, the greatest impurity concentrations being Ca(l), Fe(0.5), Mg(0.4), Si(5) and A1(1.5), the bracketted numbers being parts per million.The “ as-grown ” crystals had resistivities E 10 Q cm. The surface area of the crystal masses used in this study was ~ 2 5 0 cm2, as determined by gas adsorption using Kr and the B.E.T. method of analysis. The surface cleaning procedure and analysis of surface impurity concentration have been described e1sewhere.l APPARATUS The apparatus is shown in block form in fig. 1. It consists of three chambers : the gas source chamber ; the reaction chamber plus leak valves 1 and 2 ; and the analysis chamber plus pump. The essential features of the apparatus are as follows. SOURCE CHAMBER This was a metal system except for the Pyrex glass gas flasks containing O2 or N20 (research grade) and the thermistor gauge, capable of being pumped down with sorption and ion-pump to z 5 x lo-’ Torr.The high pressure thermistor gauge l2 was previously calibrated (for O2 or N20) using a McLeod gauge. Leakvalve2 Leakvalvel (conductance (conductance K2,tm3s?) K Jcm’s“) a ThiVtllktOr gLKIge Ion purrp Mass 1 (speed Skrn’s ‘1 spectmeter 1 Ion wmp I ! I Analysts chamber Reaction chamber Source chamber (volume v,/cm3) (volume v,/cm’ (volume v,lcm’) (pressure f./torr) (pressure P,/ torr) (pressure P.ltwr) FIG. 1.-Schematic diagram of the apparatus. REACTION CHAMBER This was an all-quartz vessel (shown in fig. 2) and connected to the leak valves via stainless steel connectors. The O-rings were prebaked Viton. Leak valve 1 (Vacuum Accessories) was stainless steel with a bellows mounted micro-grooved pin construction.The conductance calibration was checked in the usual way for both O2 and N,O and was accurately known down to cm3 s-l. Leak valve 2 (Nupro) was a stainless steel 10 turn needle valve with calibrated conductance in the range 10-2-5.5 x lo-’ cm3 s-l. ANALYSIS CHAMBER AND ION-PUMP These were all stainless steel. The ion-pump speed was calibrated over the pressure range 10-8-10-6 Torr (-constant to 7 %) and found to be (1.25k0.05) lo3 cm3 s-l for 0 2 and (1.5Of0.05) lo3 cm3 s-l for N2. A mass spectrometer (A.E.1.-MS10) was used for analysis. The calibration was frequently checked and found to correspond to the makers’ quoted values, namely 48 pA Torr-l for N2 and 28 pA Torr-I for 02. The entire system was baked before a run, However, it was found that the freshly baked analysis chamber walls had a finite pumping speed and so it was necessary to allow2726 ZnO SURFACES the system to stand for several hours in order to saturate this unwanted effect.The back- ground spectrum of the analysis plus reaction chambers was HzO+ (8 x CO+/N; (8.8 x The background spectrum of the reaction chamber was obtained by measuring the decrease in pressures with leak valve 2 closed and calculating the reaction chamber pressures which produced the difference in the two sets of readings : the valves so obtained were HzO+ (1.7~ lo-’), CO+/N; (3 x and CO; (4.5~ The background spectrum of the source chamber, to which another mass spectrometer was attached, was HzO+ (4x CO+/NZ.(1.5 x O2 (4x and CO, (1 x Bracketted quantities above are pressures in Torr. and CO; (1.3 x L. v 2 (z F o - ring anion--+ H 1 cm. u - Temperature distance programmer 2 FIG. 2.-Schematic diagram of the reaction chamber. - ___ FURNACE AND REACTION CHAMBER Fig. 2 shows the arrangement of reaction chamber, furnace aiid thermocouples, together with coiitroller and recorder. The total volume of the chamber, including that of the leak valves was 5.80 cm3. The tube furnace was wound so as to achieve a flat temperature profile (k2 K) at furnace temperatures in the range 300-1100 K, as shown in the figure. The furnace was powered by a temperature programmer (Stanton Redcroft) capable of linear heating, or cooling, rates of 0.017 to 1.7Ks-l, or thermostatic control up to 1300K.T/C 3 was the programmer sensing element. T/C 1 and T/C 2 measured the temperature around the ZnO crystal mass, and were given good thermal contact to the outer silica walls by means of a silver paste. At a heating rate of 0.4 I<; s-I, T2 was 5 K greater than TI : at lower rates temperature differences were 2 K and at a rate of 1.7 K s-’ the difference was 8 K. T/C 1 was taken as the temperature of the ZnO mass, since the thermocouple well was immersed in the dense mass of ZnO needles. SYSTEM RESPONSE The various system parameters such as pressures, volumes, conductances and pump speed are referred to in fig. 1. Over a wide range of operating conditions the time lagM . GREEN AND I . R. LAUKS 2727 between a pressure change in the reaction chamber and that measured in the analysis chamber reduces to the simple expression l3 For our values, Vr = 5.8 cni3, V, = 1100 cm3 and S = 1250 cm3 s-l and a typical K2 value of 3 x 10-1 gives z = 20 s.Under conditions of t.p.d. used extensively in this work leak valve 2 is wide open and z is 11.2 s. This means that a gas wave, called " a peak ", will be distorted by the system response. An analysis l3 shows the true peak height to be reduced - 5 % and the maximum temperature of the peak to be increased -2 K (this is partly cancelled by the thermal lag mentioned above). TYPICAL T.P.D. RUN A run consists of two parts : first pretreatment of the clean ZnO crystal mass followed by quenching ; and secondly a t.p.d. in which the evolution of oxygen as a function of time is followed.Pretreatment consists of initially heating the ZnO mass in vacuum at - 1100 K for 15 min. This serves to remove any carbon recontamination which may have occurred on standing and leaves the ZnO surface depleted in oxygen. The ZnO is then cooled to the specific pretreatment temperature required (in the range 850-1000 K) and exposed to a particular I40 120 100 080 063 040 M 020 300 360 ;GO 340 timelmin FIG. 3.-Oxygen t.p.d.s after various pretreatments at 963 K for 1 h in oxygen. Poz = (a) 0.360, (b) 0.194, (c) 0.062, ( d ) 0.370, (e) 0.051, (f) 0.045, (9) 0.039.2728 ZnO SURFACES O2 pressure (under flow conditions) in the range 0-0.5 Torr for 1 h. After this time leak valve 1 is closed and 2 is turned fully open and the furnace is switched off. It takes about 1 min to cool to 750 K.These conditions are such as to constitute quenching of the surface, corresponding to the chosen temperature and pressure of pretreatment. The t.p.d. run is next carried out starting from some known low temperature, e.g. 700 K, with the linear heating rate p set, for all runs reported here, at 0.4 IS s-'. p is set to become zero at 1100 K. A range of t.p.d. curves is shown in fig. 3 of the next section. O2 was the only species detected by the mass spectrometer and H20, CO, COr, etc., remained at the initial background level through a t.p.d. run. RESULTS Fig. 3 shows a typical set of t.p.d. peaks for various conditions of pretreatment. Almost invariably a single well-defined peak occurs, in which case the peak shape, defined as the ratio of the areas either side of a vertical drawn through the maximum of the peak, is found to be (1.86+0.2) : 1.Occasionally a doublet is observed, and this feature is discussed later. 0*04< Po2 /Torr FIG. 4.-Oxygen t.p.d. peak area, Ae, and fractional surface oxygen vacancy concentration, 8, against oxygen pretreatment pressure, Po2, at various tempzratures of pretreatment : (0) 993, ( 0 ) 979, (+) 963, (0) 923, m) 888 K ; the solid lines are the best fits through experimental points, the broken lines are theoretically computed isotherms. The area of a peak is a measure of the net amount of O2 evolved from the ZnO, and is expressed in atoms of oxygen evolved per surface lattice oxygen atom, i.e. as the fraction At?. A0 depended upon the O2 pretreatment conditions of temperature and pressure, and these results are summarised in fig.4.M. GREEN AND I . R. LAUKS 2729 The interrelation between t.p.d. features is shown in fig. 5 and 6. Thus fig. 5 shows the relation between maximum peak temperature, Tp, and peak area, AO, for a comprehensive set of runs, while fig. 6 shows Tp against AT., the peak width at half height. 0-035 0.030 I 0 0020 d 0 015 0 010 0 GO5 920 940 960 980 1000 1020 1040 TP/K FIG. 5.-Experimental variation of peak area, AO, with peak maximum temperature, Tp. The solid line is the theoretically computed variation. 920 940 960 980 1000 1020 1040 1060 TPIK FIG. 6.-Experimental variation of peak width at half height, AT+ with peak maximum temperature, Tp. The solid line is the theoretically computed variation.2730 ZnO SURFACES range 0.017 to 0.4 K s-l.There is no variation in the above characteristic parameters as /3 is varied over the DISCUSSION SOURCE OF EVOLVED OXYGEN When ZnO is heated to 1100 K the observed oxygen loss or gain is, in all iniportaiit senses in this study, only a loss or gain from the outermost layer of the crystal, i.e. from the surface lattice. This is to be expected from the existing thermodynamic data on ZnO taken together with our surface-to-volume ratio. The equilibrium oxygen vacancy concentration is given by l4 [Yo] = 1.1 x lo2’ P;: exp (-2,25/kT)/~m-~ (1) where the energy is in eV and Poz is the oxygen pressure in Torr. Using this relation and assuming complete equilibrium through a crystal, which in fact is highly unrealistic, we can compare the difference in the amount of oxygen (atoms) which should come from crystals pretreated at 0.36 Torr and crystals pretreated at 0.039 Torr corresponding to (a) and (9) in fig.3. For our experimental ZnO volume of 0.08 cm3 and for a temperature of 963 K, AIVo] is 1.3 x 10l2, while the difference in the amounts of oxygen obtained by t.p.d. experiments is 3.7 x 10”. There is direct experimental verification of the negative predictions made using eqn (1) based on 016/018 isotope exchange. Briefly, since this is discussed fully in Part 2,1° a known amount of 0 l 8 is incorporated into the ZnO. Some of this 0l8 is subsequently abstracted from the ZnO, by t.p.d., and the amount by which it has become diluted with 0l6 measured. The observed dilution is only consistent with equilibration with the surface lattice.Finally, the isotope exchange experiments show that the oxygen of a t.p.d. cannot be associated with oxygen adsorbed on a passive surface. Thus if we were simply dealing with chemisorbed oxygen, where there was no exchange with the surface lattice, we would expect, upon desorption, to obtain exactly that amount of OI8 which had been adsorbed. This is shown not to be the case, 0 l 8 being distributed among the atoms of the surface lattice. SURFACE LATTICE STOICHIOMETRY When ZnO is pretreated in O2 at the lowest temperature (888 K) and highest oxygen pressure (0.44 Torr) shown in fig. 4, it has its highest oxygen content and, by inference, its lowest oxygen surface vacancy concentration. The 888 K isotherm is almost saturated at the higher pressures and likewise the 0.44 Torr isobar is almost flat at the low temperature end: it is deduced that we are therefore close, in this pretreatment condition, to maximum oxygen content of the surface.By extra- polation, it is estimated that, in the limit, another = 15 % oxygen would be taken up. Such a surface would be relatively free of vacancies (i.e. 5 10l2 cm-2) and when subjected to t.p.d. would yield net oxygen loss corresponding to -4 % surface vacancies (i.e. -2.4 x 1013 cm-2). This conclusion is supported by the resistivity against temperature and pressure measurements carried out by Arghiropoulos and Teichner l5 on sintered ZnO powders. The above observations allow us, within fairly narrow limits, to estimate the fractional surface lattice vacancy concentration shown as 8 on fig.4. The scatter in the isotherms is attributed (see later) to variations in surface heterogeneity associated with the history of pretreatment.M. GREEN A N D I . R . LAUKS 273 1 REACTION MECHANISMS In proposing a reaction scheme it was necessary to note that a peak could not be formulated for the 0-4 % oxygen loss from a surface lattice, without at the same time having some limiting mechanism. For this we propose a parallel zinc loss (experi- mentally observed), and consequently the observed oxygen at the mass spectrometer is the difference in the amounts of oxygen and zinc lost from the ZnO. Two possible reaction schemes are formulated, the first of which, the vacancy-pair mechanism, follows immediately.Oxygen evolution : K t "0: $ "A . . .o- k2 slow k3 TV,+ . . . 0- +s(n)O: + O,(g) +T,+ . . . +2'pe- "6 . . . "V,+ + 2'v; and parallel zinc loss : k4 +SPe- + zn(g)+'O: k5 224s) + 02(g) + 2ZnO(s). (3) (4) The symbolism used above is the system due to Kroger and Vink16 : is oxygen on an oxygen site in the surface lattice layer (superscript s) ; is a vacant surface lattice oxygen site with effective charge + 1 ; . . . 0- is a surface (i.e. on top of the surface lattice) 0- adsorbed species adjacent to a TVof species ; s(n)Oj: is a surface lattice oxygen next to an oxygen vacancy; . . . is a nearest neighbour pair of vacancies; spe- is a quasi-free electron in the conduction band confined to a surface space charge region within the ZnO. The second mechanism differs from the above in the oxygen evolution branch after the first pseudo-equilibrium step, eqn (2), i.e.k; 'V; . . . 0- -+ 'VA + 'Pe- + O(ads) O(ads)+"V,f . . . 0- -+ 02(g)+'V~+spe-. slow k; Here O(ads) symbolises an adsorbed oxygen atom, which is taken to move a limited distance over the surface to react with a surface oxygen ion. Since t.p.d. kinetics alone do not allow a choice to be made between the two postulated mechanisms, but Gopel's work,8 in which no desorbed oxygen atoms are observed, and 016/0'8 exchange studies (Part 2) appear to point to the first of the above schemes, the rest of this discussion is confined to the vacancy-pair mechanism. The first step, eqn (2), is taken to precede the rate determining step and is in pseudo-equilibrium. The rate determining step, eqn (3), is the abstraction of a nearest neighbour lattice oxygen by the surface 0- to yield O2 gas, leaving a charged surface lattice oxygen vacancy pair and two compensating space charge electrons. The succeeding step, eqn (4), is rapid decomposition of the vacancy pair. The parallel zinc loss reaction is written in the form shown because it is assumed that only sZn; adjacent to VV,* can be lost to the gas phase and that the resulting missing ZnO has simply lowered the surface lattice by one layer at that two atom site, hence the creation of a "0: in eqn (9, see fig.10. Finally the zinc vapour condenses on the2732 ZnO SURFACES cooler parts of the In a large reaction mass-spectrometer reaction vessel, as Zn(s), where it reacts with oxygen to give ZnO.chamber O2 and Zn can be determined separately in a line-of-sight ' before surface reaction as has been shown by GopeL8 REACTION KINETICS The observed net rate of O2 evolution in a t.p.d. is given by and, for the evolved zinc, which is rapidly oxidised as condensed zinc atoms, whence eqn (9) can be rewritten as k, c" V,' ] rPe-] = 2 k5 Po, [Zn( s)] 2, (10) The net rate of formation is given by and with the pre-rate determining step in pseudo-equilibrium, i.e., p,'. . . o-] c"03 Kl = and the rapid post rate determining step giving we obtain k3rVO+ . . . 'V;] = k2[3'2 . . . O-]~'")O~], which by reference to eqn (11) shows, as it should, that dpV,'] - 2dPo2 dt dt * --- Since ["V,'] does not exceed 4 %, ["03 can be taken as constant and equal to the number of surface oxygen atoms in the (1OiO) ZnO surface.Rewriting eqn (15) using the fractional vacancy concentration, 8 = ["V,']/c"O,"], we obtain RATE EQUATIONS Eqn (17) can be written d0 + + - = j 2 - j 4 . dt Using a; for the activity of species i in phase a and adopting absolute rate theory, (19) kT h t j , = F4 -a+,, a:- exp ( - A f i * / k T )M . GREEN AND I . R . LAUKS 2733 where I;, k, T and h have their usual meaning and AFY* is the standard molecular free energy of formation of the activated complex in the slow step, eqn (5). Since the surface electron activity is related to the bulk electron activity in the ZnO, where 4' is the surface potential as defined in fig. 7 and e is the electronic charge. Eqn (19) becomes (20) a:- = a:- e-&'IkT Now A&':* can be written as the free energy difference between transition and initial state, namely which simplifies to where P4(O < p4 < 1) is related to the fractional charge on the transition state, z = -e, and AfiG8=o, is the standard free energy when the space charge potential is zero.AC' = AF:&=0)+(84- l)z$'-e@ (23) Substituting eqn (23) in eqn (21) gives Charge free Space charge bulk I region - 1- I FIG. 7.-Energy level diagram for ZnO including surface space charge region. Thus, as has been shown by Green,17 it is variations in bulk electron activity and not surface activity which is compensated by q5s changes which affect the reaction rate. But @ does affect the free energy of the charged species on the surface, e.g. the surface vacancies.For the forward reaction where a:(,,, is taken as unity. 0,2734 ZnO SURFACES Combining eqn (24) and (25) in eqn (17) SPACE CHARGE, #'AGAINST 8 The surface oxygen vacancy is a shallow singly charged donor state ~ 0 . 0 5 eV below the conduction band edge,8 hence VV,' is the state of the oxygen vacancy taken throughout this work. Since any PV,'] of the order of 10l2 cm-' or more will give rise to a degenerate carrier distribution at the surface and will also cause the surface state energy level to broaden into a band overlapping the conduction band edge, we use degenerate statistics throughout and may ignore the effects of variations in c& on the position of the Fermi level at the surface (with respect to E,, cf., fig. 7). Furthermore, at- is taken in this work to be constant and close to an at- value corresponding to EF near the conduction band edge.Using the semiconductor relations given by Seiwatz and Green for a degenerate space charge region, we obtain Taking pz = Q4 = 3, which is the situation corresponding to a symmetrical barrier, and is what is generally done in the absence of detailed knowledge, substituting eqn (27) into eqn (24) and also substituting for K,, i.e. - z p = eos = -3.25 0°*8[eV. (27) Kl = exp (- AFy[kT) (28) This rate equation can be restated in terms of enthalpies of activation by incor- porating the entropy term into the pre-exponential, which is now primed, to give 1- r H Y * ---620°*8] dtl - = x ' e x p - r p * 1,2 + kT 3.258°*8 d t Y'8 exp- (30) SURFACE HETEROGENEITY Eqn (30) predicts a peak in the oxygen t.p.d.with the correct shape and half width, but does not yield the observed Tp against A0 variation. We therefore need to seek a second term that alters the enthalpy of activation as a function of 0. We postulate oxygen loss from a heterogeneous surface where the extent of heterogeneity is dependent upon 8 ; that this heterogeneity is most likely surface steps is discussed later. We call this term g(0). The rate eqn (30) now becomesM . GREEN AND I . R. LAUKS 273 5 since (d6/dT) = P-'(de/dt). Eqn (31), and similar equations, are solved by numer- ical methods1 Y' = 8 x 10ls s-', AH?,; = 3.47, AH:* = 3.83 eV. These are to be compared in the case of AH?,; with 3.52k0.1 and 3.61 eV obtained by Gopel and Halpern and Germain respectively.Gopel reports a value of 3.47k0.1 eV for AH:*. In order to obtain the best value for g(6), eqn (31), with one trial function of g(0) against 6 inserted, is solved by an iterative technique. A family of curves, d0/dT against T, for different values of O0 is obtained. These are compared with the experimental set of t.p.d. curves. This procedure is repeated with different values of the g(0) against 8 function until the fit is good. The values of the kinetic parameters obtained were, X' = 5.2 x 5 0 i 2 - 0.08 004- 0 20 1 - I 0 16 0 0.01 0.02 0.03 0.04 8 FIG. 8.-Change in the activation energy of the surface oxygen loss reaction due to surface heterogeneity. (a) g(8) (t.p.d.); (b) g(8) (steady state); (c) 8ss(o) = 0 at e0 = 0, kTln {1+8ss exp (0.35 eV/kT) + I]) ; (d) Oss(o) = 0 at Bo = 0, kT In { 1 + BSs[exp (0.25 eV/kT) - 11 ).The g(0) function is shown in fig. 8, and from it a family of theoretical t.p.d. peaks has been computed for different values of 807 the vacancy concentration at the start of a t.p.d. run as set by the pre-treatment. This is shownin fig. 9. Acomparison of these curves with the experimental t.p.d. data is made by observing the agreement between the peak characteristics, namely peak shape, A0 and AT+ against Tp. The A6 against Tp relationship, shown in fig. 5 has predicted the correct variation, namely a decrease in Tp of over 100 K with decreasing A6. The experimental AT+ against Tp relationship is compared with the predicted relation in fig. 6. Peak shape for a large sample of experimental t.p.d.s is in the ratio (1.8640.2) : 1 and for the theoreti- cally generated peaks the ratio is (2.08 kO.2) : 1, showing agreement within experi- mental error.STEP SITES The likely physical origin of the g(0) term in the rate expression emerges upon closer examination of the reaction mechanism. When a zinc atom is lost froin the surface lattice according to the reaction svVf,+spe- + zn(g)+SOi2736 ZnO SURFACES 3 TIK FIG. 9.-Theoretically computed oxygen t.p.d.s. (a) do = 0, Ad = 0.025 ; (b) 60 = 0.01, A8 = 0.01475; (c) 4, = 0.015, Ae = 0.01 ; (d) do = 0.035, Ad = 5x (e) 60 = 0.0425, Ae = 4.9 x lo-' ; (f) Bo = 0.0428, A0 = 3.3 x lo-' ; (9) 60 = 0.0438, A6 = 1.1 x ; (h) do = 0.038, Ad = 2~ ci> eo = 0.0405, A0 = 4.6~ 10-4; (k) do = ( i ) eo = 0.0395, Ad = 9 .8 ~ 0.041, A0 = 2.9 x t Surface atoms ('AX, Bulk atoms ( bAc) FIG. 10.-Schematic diagram of the surface zinc loss reaction from the 1070 surface.M . GREEN AND I . R. LAUKS 2737 not only is a sub-surface lattice oxygen atom revealed but the surface oxygen atom next to the evaporated zinc is now in a new environment, i.e. at a step site (4. schematic diagram of the zinc loss reaction of fig. 10). It is likely that the enthalpy of activation of oxygen loss from such a site will be less than that for a perfect surface lattice oxygen site. It is proposed that the equilibrium constant of step 1 of the reaction sequence is thus different for a step site oxygen atom; i.e. an oxygen atom at a lattice step is more likely to move onto the surface. T/K FIG. 11.-Theoretically computed oxygen t.p.d.s with different values of initial surface vacancy concentration, Bo : (a), (6) and (c) = 0, (d) = 0.015 and surface step site concentration, Bsso : (a) 0.05, (b) 0.017, (c) 0, (d) 0.017.Now if a fraction O,, of all surface lattice oxygen sites are at steps, i.e. (1-O,,) is the fraction of perfect lattice sites, and AE is the extent by which the free energy of formation of 'V; . . . 0- is reduced when formed from a step site oxygen atom, eqn (3 1) becomes, Y'O - [A=* - 1 .620°.'] kT exp- This equation can be solved by iterative techniques using different initial values of 60 and O,,,, i.e., values of vacancy concentration and step site concentration at the start of the t.p.d., as set by the pretreatment conditions, and a trial value of AE, to obtain2738 ZnO SURFACES a family of dO/dT against T t.p.d. curves.Fig. 11 shows such a set of curves (for AE = 0.25 eV). In the case where 8, = 0 and O,,, = 0, a peak is obtained whose maximum, Tp, occurs at 1040 K, and whose area, A@, is -0.025, identical with the peak obtained by solution of the rate equation using the g(8) function. The values against 8 for the kT In [l +O,,[exp (0.25/kT)- l)] term, with 0,,, = 0 and 0, = 0 obtained from the iterative technique are shown in fig. 8. There is a close corres- pondence between it and the optimum g(8) function obtained earlier. For compari- son the expression with AE = 0.35 eV is also shown. In effect, then, g(0) can be replaced by the more specific relation shown above, with the arbitrarily found relation between OSs and 8, and AE = 0.3 eV.The set of t.p.d. peaks computed earlier with the g(8) function (fig. 9) which were a very close fit to experiment, can equally well be computed using the full rate expression shown in eqn (32) with the condition that Oo = 0 and 8,,, = 0. (It is shown elsewhere l 3 that kTln (1 +Qss[exp (AE/kT)- l]} is relatively insensitive to variations in T over the temperature range of the t.p.d. peak, and that 8,, = f ( 0 ) , so that the full expression can be treated to a good approximation as a function of 8 alone, i.e. equivalent to g(0)). Throughout the above discussion it has been assumed that at O0 = 0, g(0) and 8,, = 0. However, it is possible that, for some pretreatment conditions, 8,, is not zero at 8, = 0. The effect of a non-zero O,,, on the computed t.p.d.is shown in fig. 11. As 8,,, increases the observed peak shifts to lower temperatures, broadens and increases in area. Notice that with the simpler theory a maximum peak area of A8 = 0.025 is observed, whereas when O,,, is allowed to take non-zero values A8 can approach 0.04, i.e. the maximum experimentally estimated value of the vacancy concentration. The change in Tp and AT+ with changing 8,,, may well explain the scatter on the A8 and AT+ against Tp curves (fig. 5 and 6). Furthermore, the only induced heterogeneity considered is the step site but, of course, variations on this theme are possible, indeed likely. A more detailed theoretical study is planned, but the above is regarded as a reasonable step on the way to a detailed understanding. For the condition 8, = 0.02 and O,,, = 0 the computed rate expression yields a doublet in the t.p.d., cf.fig. 10. Such a doublet is occasionally observed in the experimentally obtained t.p.d. peaks, cf. fig. 3. e AND e,, AS A FUNCTION OF PRETREATMENT The area under the experimental peak yields the vacancy concentration pre- vailing at the steady-state pretreatment conditions, as is shown on fig. 4. In considering the relation of 8 to Poz we obtain, Inserting those variations of the rate constants arising from changes in enthalpy with 8 and g(e), as indicated in fig. 12, eqn (33) becomes, where ge(8) now defines the variation in the activation enthalpy of oxygen loss due to step sites at equilibrium. K is the overall equilibrium constant for the reaction and C is a temperature dependent constant.Note that when 8 and s,(@ are small eqn (34) reduced to the form 2'0; + 2"; + O,(g) + 2'Pe- (35) p0, = i q e 2 . (36)M . GREEN AND I . R. LAUKS 2739 I 1 c1 U 9 0 Q reaction coordinate FIG. 12.-Potential energy diagram for (a) the surface oxygen loss reaction, and (6) the surface zinc loss reaction.2740 zllo SURFACES At T, a steady state temperature, when Po, = 0 and 8 = 0.04, eqn (34) gives 1 c = -exp-[ 1 4.87eo.* - g,(e = 0.04) 0.04 kT (37) and eqn (34) can now be evaluated for various values of 8 over the range 0 to 0.04. The necessary ge(8) against 8 function is obtained by adjusting ge(8) for one chosen isotherm until the correct shape is obtained. Kis then chosen to give the correct mag- nitude to the isotherm.This g,(8) is then used, without change, to generate all the other isotherms and K values. The comparison of the isotherms so obtained with the experimental isotherms is shown in fig. 4. The K values obtained are used in the expression d l n K AH" d(l/T) k where AHo is the standard enthalpy of oxygen gas loss from the ZnO surface, eqn (35). The variation of In K with 1/T is shown in fig. 13, for which a value of AHo = (1.94 k 0.24) eV is obtained. This is to be compared with a value of 2.35 eV obtained by Boreskov, Popovskii and Sazanov.20 The ge(@ function required to reproduce the experimentally observed S-shaped isotherm is shown in fig. 9. This function has the same general form as the g(8) function required for the temperature transient kinetic data.The physical reason for the observed S-shape of the isotherm is that at high 8 (low Po,) there is an enhanced rate of surface oxygen loss from the step sites, and the steady state value of 8 at this low Po, is greater than that predicted by eqn (36). Using this value of ge(8) and the relationship ge(8) = kT In { 1 + B,,[exp (AEIkT) - 11) at T = 1000 K and AE = 0.30, values of 8,, against 8 can be obtained. At 8 = 0 to 0.01, 8,, z 0 ; as 8 increases 8,, increases and approaches a constant value of 8,, = 0.28 as 8 approaches 0.04. This value of 8,, is to be compared with that obtained by Gopel and Ne~enfeldt.~ From observation of LEED reflex splitting they report the formation of regular step arrays on a vacuum treated (1 100 K, 4 min) {lOTO) ZnO surface.These 2.6 x cm high steps occur perpendicular to the c-axis with an average spacing of 41 x cm. This leads to a value for OSs of xO.125. - = -- CONCLUSION The main conclusions from this work are : that an initially stoichiometric and near ideal {lOTO) ZnO surface at 900 K, when subjected to a linear temperature rise up to 1100 K, will lose x20 % ZnO (as 0, and Zn). The difference in the loss rates yields a peak in O2 t.p.d. and results in a final surface containing x 4 % TV., and ~ 2 0 % step sites. Surfaces with lower 8 and O,, can be obtained in a controllable manner. The oxygen loss rate has been shown to depend upon both 8 and OSs. A quantitative knowledge of both 8 and 8,, constitutes a considerable improvement in the definition of the nature of the solid surface and should advance our detailed understanding of chemical reactions on ZnO. A yet more detailed analysis, in which other types of surface defect are considered, should eventually be carried out, when coupled with more extensive experimental data. Clearly the techniques discussed above may be applied to other oxide systems. l C. G. Scott and C. E. Reed, Surface Physics of Phosphors and Semiconductors, ed. C . G. Scott and C. E. Reed (Academic Press, London, 1975), p. 411. P. Roussel and S. J. Teichner, Catalysis Rev., 1972, 6, 133.M. GREEN AND I . R. LAUKS 2741 G. Heiland, E. Mollwo and F. Stockmann, Solid State Physics, ed. F. Seitz and D. Turnbull (Academic Press, New York, 1959), vol. 8, p. 193. S. C. Chang and P. Mark, Surface Sci., 1974, 45,721. A. R. Lubinsky, C. B. Duke, S. C. Chang, B. W. Lee and P. Mark, J. Vac. Sci. Techn., 1976, 13, 189. W. Gopel, Ber. Bunsenges phys. Chem., 1976, 80,481. ' W. Gopel and G. Neuenfeldt, Surface Sci., 1976, 55, 362. W. Gopel, Surface Sci., 1977, 62, 165. B. Halpern and J. E. Germain, J. Catalysis, 1975, 37, 44. l o M. Green, and I. R. Lauks, to be published. l 1 M. Green and I. R. Lauks, Surface Sci., 1978, 71, 735. l 2 M. Green and M. J. Lee, J. Sci. Inst., 1966,43,948. l3 I. Lauks, Ph.D. Thesis (University of London, 1977). l4 F. A. Kroger, The Chemistry of Imperfect Crystals (North-Holland, Amsterdam, 1974), vol. 2. l 5 B. M. Arghiropoulos and S. J. Teichner, J. CataZysis, 1964, 3, 477. l6 F. A. Kroger and H. J. Vink, Solid State Physics, ed. F. Seitz and D. Turnbull (Academic Press, New York, 1956), vol. 3, p. 307. l7 M. Green, J. Chem. Phys., 1959,31,200. R. Seiwatz and M. Green, J. Appl. Phys., 1958,29,1034. E . Kreyszig, Advanced Engineering Mathematics (John Wiley, New York, 3rd edn, 1972). 'O G. K. Boreskov, V. V. Popovskii and V. A. Sazanov, Proc. 4th Int. Congr. Catalysis (Moscow 1968), 1971, vol. 1, p. 439. (PAPER 7/2070)