1200
J. T.LAW
his results fit a positive Drude term. We would expect this behavior from the trends seen in Table I. The negative terms are decreasing while the positive terms are increasing with increasing wave length. However, no generalizations should be made until more is known about the effect of helix pitch and diameter. For example, a helical antenna of these dimensions would be expected to be in the normal mode (radiating normal to the helical axis) at the longest wave lengths studied and would be expected to radiate in the axial mode at the shortest wave lengths.15 To what extent this should affect the optical activity is not yet known, but presumably the effects are related. Conclusions We have found that the optical rotation of 1 em. copper helices can be described by a Drude equation. For right handed helices the optical activity along the helical axis has negative Drude terms while the optical activity perpendicular to the heli(15) John D. Kraus. "Antennas," McGraw-Hill Book Co.. Inc., New York, N. Y..1950, p. 176.
Vol. 61
cal axis has positive Drude terms. At long wave lengths the positive terms seem to dominate. The optically active absorption bands are simply related to the length of the wire in the helix. The critical wave lengths along and perpendicular to the helical axes are nearly, but not quite, equal. Except for the dependence on the length of the helix, these phenomena are similar to those found for helical polypeptide~.~A better model for helical polypeptides which should remove this exception would be helices made of alternating lengths of conductor and insulator. The conductor would correspond to the polarizable amide bond and the insulator would correspond to the insulating =CHR group. A quantitative comparison of these results with theories of optical activity of helices4-6 will be made later. Acknowledgment.-We wish to thank Professors Gwinn, Harris, McGarvey, Myers and O'Konski, Dr. Mahan and Mr. Maki. Their loan of equipment and their helpful suggestions made this work feasible.
THE HIGH TEMPERATURE OXIDATION OF SILICON BYJ. T.LAW Bell Telephone Laboratories, Incorporated, Murray Hill,New Jersey Received May 0, 1067
The oxidation kinetics of silicon have been studied over a range of temperatures from 1000 to 1300'K. and at pressures from 10-sto5 X 10-2mm. Under alltheconditions investigated, therate followed a parabolic equation n = ZK(t/n) e, where the rate constant K was markedly pressure dependent. A possible interpretation of this is given in terms of the boundary layer theory. The removal of the oxide film by flashing has been studied as a function of flashing temperature. The rate of evaporation of silicon was found t o be decreased by almost two orders of magnitude in the presence of a 300 A. film.
+
Introduction At present there is considerable interest in the problem of obtaining atomically clean germanium and silicon surfaces. One of the most difficult species to remove from any surface is oxygen, but it is even more difficult to demonstrate conclusively how much chemisorbed oxygen or oxide film is still present after a given treatment. If the oxidation process of silicon has a rate that is determined by the oxide film thickness we then have a tool for measuring fairly directly the amount of oxide remaining after a given treatment. All we need do is measure the rate before and after a certain treatment, and if the oxidation kinetics are known we can then deduce any change in film thickness. Since all surface cleaning techniques depend on high vacuum conditions we would prefer to carry out the oxidation measurements at fairly low oxygen pressures (ca. lo-' mm.). To date no kinetic data are available a t pressures below 200 mm. At atmospheric pressure, McAdam and Geil' measured the thickness of the oxide film as a function of time by an optical method. They found that over the temperature range investigated, 873 to 1273"K., the results could be described by a parabolic rate law (1) D. J. McAdam and G. W. Geil, J . Research NaU. Bur. Standards, 28, 503 (1942).
dn/dt = K / n (1) where n is the number of molecules of oxygen reacted at time t and K is the rate constant. Brodsky and Cubicciotti2 reported data in the temperature range 1220 to 1420°K. and at an oxygen pressure of 200 mm. Under these conditions the oxidation rates could be described by a logarithmic law of the form
n = b log ( 1
+ at)
(2)
where a and b are constants. At the lowest and highest temperatures investigated, the data could be fitted equally well by a parabolic equation. It therefore appears possible that a parabolic law is followed from 873 to 1420°K. Let us consider for a' moment the basis of a paraboIic oxidation law. If the film is sufficiently thick that electric fields across it are small, then the diffusion of reactants through the oxide layer will be controlled by the concentration gradient from the gas-oxide interface to the metal-oxide interface. This gradient is pr?portional to l/n so that the rate of growth, dnldt, 1s also proportional to l/n if the rate-determining step is the diffusion of reactants through the oxide layer. I n the derivation of this equation by Cabrera and MottS it was assumed that local thermo(2) M. (1951).
B. Brodsky and D. Cubicciotti, J. A m . Chem. SOC.,73,3497
(3) N. Cnbrera ancl N. F. Mott, Repts. Proe. Thus., 12, 103 (1048).
-
Sept., 1957
THEHIGHTEMPERATURE OXIDATIONOF SILICON
1201
dynamic equilibrium existed a t the oxide-gas interface. It should therefore be true that if this equilibrium is disturbed, for example by changing the oxygen pressure, the rate of oxidation will also be altered. Similarly, for thin films when the oxidation rate is controlled by the electric field developed across the oxide layer, anything that disturbs the field at the surface (e.g., a change in the number of adsorbed gas ions) will affect the oxidation rate. For these reasons it is obvious that the high pressure measurements reported may not be applicable in the low pressure range in which we are interested. In this paper we will describe some results obtained on silicon between 1000 and 1300OK. and a t mm. oxygen pressures between lo-* and 5 X The measured oxidation rates have also been used as a tool to determine the flashing temperature required to remove an oxide film. Experimental
two arts of the system are1'2 and T z ,then the pressure of a gas and P2 a t equilibrium in these two parts are related by the equations
The rates of oxidation were measured by following the rate of pressure change in a closed system whose volume was made sufficiently large that the pressure change during a run was always small compared with the total pressure of oxygen used. The apparatus consisted essentially of a tube containing a silicon filament, a Pirani gage and valves4 for isolating various parts of the system and for admitting oxygen. The whole system was baked-out under vacuum and pressures below 1 X 10-9 mm. were regularly attained. The silicon filament used was cut from a single crystal of high resistivity material. The purity was sufficiently high that above 650°K. the crystal was intrinsic (i.e., the density of thermally created carriers far exceeded the number due to the presence of impurity levels) so that the logarithm of the conductivity wa8 a linear function of 1/T. Before sealing the filament in the tube it was etched with a mixture of nitric and hydrofluoric acids and well washed with de-ionized water. The geometrical surface area was 8.0 cm.2 and using the previously determined roughness value for germaniun repared in the same ways a total area of 10.4 was ogtained. Spectroscopically pure oxygen was used without further purification. The silicon was heated by passing a large current through it and its temperature determined bv resistivity measurements. The resistivity of intrinsic silicon at high temperatures has been measured by Morin and Maita.6 Since the resistivity of a semi-conductor decreases with increasing temperature it is relatively simple to obtain a uniform temperature along the filament. The amount of end cooling throu h the leads was sufficiently small that no temperature gracbent could be detected with an optical pyrometer. The temperature calibration of the filament was also checked with an optical pyrometer using an emissivity correction determined by Allen,' which varied from 20-40'K. over the temperature range 1000-1300°K. Excellent agreement (within 10'K.) was obtained with the resistivity data. During the evacuation process the filament was heated for several hours at and above 1600°K. The pressure of oxygen in the system was followed with a specially constructed Pirani gage which had a sensitivity of 1 cm. galvanometer deflection for 1 X lO-'mrn. pressure change over the pressure range 10-LlO-1 mm. From the known volume of the system, the changes could be converted readily to molecules :::",? o consumed per cm.* of surface area. In the pressure range investigated the mean free path of the oxygen molecules was not negligibly small compared with the diameter of the tube connecting the Pirani gage and the reaction vessel. For this reason thermomolecular flow corrections were a plied to all pressure measurements. If the diameter o f the connecting tube is d cm. and the temperature of the
Ki KZ n If this is integrated from n = noat t = 0 we get n - no = An = 2K1 ( t / A n ) - 2(no Kn)
(4) D. Alpert, J . AppL Phffs., 24, 860 (1953). The valves used were a modified form of Alpert valves, purohased from Granville Phiiipi Go., Pullman, Washington. (5) J. T.Law, T ~ r JOURXAL, s 60, 648 (1955). (6) F.J. Morin and J. P. Maita, Phya. Row., 96, 28 (1954). (7) F. c). Allen, private oommuniaation.
The isothermal rate law of eq. 1 has usually been applied to the experimental data by assuming the initial conditions that n = 0 a t t = 0. Then n2 = 2Kt (4) In view of the non-isothermal conditions near t = 0 as well as the state of the original surface both with respect to oxide film and roughness factor (the latter will approach unity as the film grows) this is not a satisfactory procedure. If we let n = no at t = 0 integration of (1) gives n - no = An = 2K(t/An) 2n0 (5) Therefore if a plot of An against t/An is linear the validity of the parabolic law is indicated. The slope of the line gives the rate constant K . If both diffusion and the velocity of interface reactions are important in determining the rate, a modified parabolic law is given by9
-
dn/dt =
+
+
(6)
(7)
which has essentially the same form as eq. 5 except for the last term which now includes the rate constant for the surface reaction. One cannot therefore say anything about the importance of surface reactions if an equation such as (7) is obeyed. All the data obtained in the present work gave good straight lines when plotted as An against (t/An).
Results The results obtained can be divided into three groups; (i) the effect of temperature on the rates at constant pressure; (ii) the effect of pressure on the rates at constant temperature; (iii) the effect of flaFihing temperature on the initial oxidation rate. (i) In Fig. 1 some typical oxidation curves are shown for the temperature range 1000-1300°K. at a pressure of 5 X mm. These runs were replotted according to eq. 5 or 7, which predict that tlhn is a linear function of An and good straight lines obtained over quite a wide range of film thickness. The departure from linearity found near t = 0 (or n = 0) is not surprising for several reasons: (a) the ratio of real to apparent area (roughness factor) may change markedly in the thin film region, and (b) the heat evolved when oxygen first reaches the surface will affect the rate of reaction. When the rate of oxidation is low (lOOO-llOO°K.) it is not easy to distinguish unambiguously between a parabolic and a linear rate. The results shown in Fig. 1 at these temperatures could be almost equally well fitted by straight lines. Some of the measurements were carried out for times up to 300 minutes and during this period it was possible to demonstrate that the rate did in fact decrease steadily with increasing time and film thickness. At higher temperatures the curvature is apparent from the figure. (ii) Over the temperature range investigated (1065-1200°K.) the rate of oxidation was found to increase quite rapidly with oxygen pressure. However, the change in pressure did not affect the shape of the curves since a t all temperatures and pressures plots of t/An against An were linear above a film ( 8 ) Knudsen, Ann. Physik. 81, 206 (1910).
(9) C. Wagner and
(1938).
K. Oranewald. Z. physik. Chlm.,
408, 455
J. T. LAW
1202 x 1016
22.51 20.0 17.5
N
15.0
I
9 12.5
8
g 10.0
c 7.5
I
I
I
I
I
I
,
,
I
Vol. 61
pears to be true for films from 100 to 500 A. in thickness. Discussion (i) The Effect of Time and Temperature on the Oxidation Rate.-As described in the previous section, the data obtained could be fitted by a parabolic rate law in agreement with the high pressure data obtained in the same temperature range by McAdam and Gei1.l For comparable times and temperatures our films were about onefifth as thick as those previously reporteds2We will see in the next section that this is purely a result of the lower oxygen pressures that we have used. The rate constants ( K ) of the parabolic law
5.0
dnldt = K / n
(8)
have been calculated from the slopes of plots of t/ An 'against An,. These are listed in Table I for 0 various temperatures at an oxygen pressure of 5 X 0 20 40 60 80 100 120 mm. In the same table values of the rate TIME,t,lN MINUTES, (K') in cm.2 sec.-l are given. These were constant Fig. 1.-The amount of oxygen removed from the gas phase plotted as a function of time a t 1000,1100,1150,1200, obtained from the listed values of K by assuming 1250 and 1300°K. and a t an oxygen pressure of 5 X lo-% that the number of Si02molecules per cm.2 of surmm. face was equal to 7.8 X This corresponds to the assumption that the normal lattice spacing of silicon dioxide calculated from the molal volume, 3.56 A., may be used. This is sufficiently close to the value for silicon, 2.7 A., that no great inaccuracy is introduced. Similarly in Table 11, values of K at 1065, 1125 and 1200°K. are given for various oxygen pressures. 2.5
-
TABLE I PARABOLIC RATECONSTANTS FOR SILICON OXIDATIONAT PO = 5 X 10-2 mm. c
Temp.,
OK.
1000 1050 1100 1150 1200 1250 1300
K', cm.2
4.1 X 9.0 x 3.1 X 4.0 X 1.1 x 1.5 x 3.5 x
8eo. -1
10-la 10-16 10-l6 10-l5 10-14 10-14
10-14
Rate constanK, (moles cm. -2) 8 sec. - 1
2.0 x 4.3 x 1.5 x 1.9 x 5.2 x 7.3 x 1.7 X
1029
102s 1030 1030
1030
1080
loa1
If the data obtained are described by eq. 5 An = 2K(t/An) - 2n0 it is possible to calculate values of no,the film thickness at t = 0. From the results for a pressure of mm. no has values of 5 X 2.8 X lo1' 5X and 3.2 X lo1' a t 1000, 1200 and 13OO0K., respectively. These values are sufficiently large compared to the measured oxidation rates that they cannot refer t o a film thickness at zero time. However, as shown in the Introduction, if an interface reaction of rate constant Kz is important in determining the rate, an eq. 7 of the same form as ( 5 ) is obtained but nois replaced by (no Kz), i.e. An = 2K(t/An) - 2(no + Kz) Thus it is possible that the calculated values of no really refer to (no K z ) . This question of differentiating between an initial film thickness and the possible importance of an interface reaction has been discussed by Moorelo who concludes that an
+
+
(10) W. J. Moore, J . Electrochem. Xoc., 100,302 (1993).
PARABOLIC RATECONSTANTS ( K ) AS 1065'K.
A
TABLE I1 FUNCTION OF OXYQEN PRESSURE AT 1065, 1125 AND 1200'K. 1126'K. 1200°K. 7
R
POP
5.45 x 5.30 X 4.25 X 1.20 x 7.7 x
I203
THEHIGHTEMPERATURE OXIDATIONOF SILICON
Sept., 1957
x 1029 7 . 7 x 1029 3 . 3 x 1029 1 . 0 x 1029 5 . 0 X loz8
10-2
4.1 X 3 . 3 x lo-* 2.08 X 1.5 X
7.9
10-2 10-2 10-8
unequivocal separation is impossible. Even if n = 0 a t t = 0, eq. 7 still has the same form, Le. n = 2K(t/n)
- 2K2
so that the only worthwhile quantity that can be calculated from a plot of t / A n against An is the rate constant K for the diffusion process. The quantity calculated from the intercept could equally well refer t o no,K Zor no Kz. From the rate constants a t a given pressure it is possible to calculate an activation energy AE* from the Arrhenius equation
+
bln K / b T = AE*/RT2
(9)
or K
=
A exp( - A E * / R T )
(10)
This equation is derived from the van't Hoff isochore and therefore can be applied only under conditions of constant activity or constant film thickness. All the rate constants listed in Tables I and 11 were calculated for constant film thickness so that the value of AE* obtained from eq. 9 is thermodynamically correct. Brodsky and Cubicciotti2 applied a logarithmic law to their data n = K" log t
+ C, or d n / d t
=
K"/t
(11)
and obtained rate constants referred not t o constant film thickness but t o constant reaction time, Their value of AE* = 26 kcal. mole-' obtained in this way is therefore not thermodynamically correct. We have recalculated their data applying a parabolic law, and incidentally converted it to our units. The corrected value of AE* is 45 kcal. mole-'. Over the pressure range 1 X loy2to 5 X and temperature range 1000-130OoK. the activation energy obtained in the present work is constant, and equal to 36 kcal. mole-'. Therefore, the effect of lowering the oxygen pressure shows up only in the pre-exponential factor -4. The assumption that the rate of the oxidation process is determined by the same factor throughout the temperature range investigated is confirmed by the constancy of the activation energy over this range. If the process were only parabolic a t the higher temperatures, the plot of log K against 1/T should not give a single straight line. The transition state theoryll has been applied to the oxidation process by Gu1bran~en.I~This assumes that the net rate of the reaction is determined by the number and the average velocity of the particles in an activated state. The rate constant K' is given by (11) 9. Glasstone, K. J. Laidler and H. Eyring, "The Theory of Rate Processes," McGraw-H~ll Book Co., Inc., New York, N. Y., 1941,p. 477. (12) E. A. Gulbransen, TTans. Electrochem. &e., 88, 301 [ lY43).
1 . 7 X loao 1 . 3 X 10" 3 . 6 x 1029 1 . 9 x 1029
K'
=
7
~
Po2
K
POP
5 . 1 X loe2 3 . 4 x 10-2 2.4 X 1 . 3 X lo-'
K
5.2 x 2.6 X 1.2 x 3.2 x
y X z e x p ( A S * / R ) e x p -AE*/RT) (
1030 lOso 10"
1029
(12)
where K' is the parabolic rate constant in units of cme2sec.-l, iiis Boltzmann's constant, h is Planck's constant, h is the distance between diffusion sites, A#* is the entropy of activation and AE* is the energy of activation. Strictly speaking AE* should be a heat of activation AH*, but since PAV" is small the error involved in using the energy is negligible. Values of K' and AE+ can be determined experimentally so that the only unknowns are AS" and A, the jump distance. As the oxide is a more or less disoriented mass, h was assumed equal to (V/N)'/a,where V is the mole volume and N is Avogadro's number, giving h = 3.5 X cm. The calculated values of AS* a t various oxygen pressures and temperatures are listed in Table 111. It can be seen that there is very little dependence on temperature but that with decreasing oxygen pressure the entropy of activation becomes more negative. The tabulated values of the entropy of activation consist of a t least two terms, i.e., AS* = AS1* ASz*, where AS1* refers to the adsorption process and AS* to the diffusion process through the oxide film. Similarly AE* must also consist of two parts as shown in Fig. 3. Since the activation energy for diffusion is constant it is apparent from this figure that an increase in A E A d s leads to a decrease in the measured value of AE*. This assumes that the activation energy for adsorption is small compared to the activation energy for diffusion. As we are dealing with the chemisorption of oxygen it is reasonable that the former of these two quantities is quite small. From the present data which show no change in AE* with oxygen pressure we must assume that A E A is~ essentially ~ constant over this pressure range. At the same time AS2* cannot be affected by pressure changes so that the change in AS* must be ascribed to a change in AS,* or to an increase in the mobility of the adsorbed species with increasing pressure and coverage. This change of -5 e.u. in going from 1 X mm. pressure is quite small when to 5 X one recalls that the entropy of adsorption of an immobile oxygen film is about 35 e.u. Thus only a relatively small increase in the mobility of the adsorbed gas is required to explain the experimental result. The effect of temperature on the rate constants of various pressures is summarized below in Table IV. The units of K' are ems2sec.-l but these can be converted to (molecules cm.-2)2 sec.-l by multiplying by 4.8 X (ii) The Effect of Oxygen Pressure on the Oxidation Rate.-There are several reasons why the rate of oxidation of solid should be affected by Fhanges in the oxygen pressure.
+
1204
J. T.LAW
Vol. 61
must be a function of the rate a t which oxygen is adsorbed at least for low surface coverages. Thus Oxygen pressure mm.OK. A x lo-’ 3.6 x 10-2 2 x lo-’ 1 x 10-2 the rate must go to zero as the oxygen pressure 1300 goes to zero. However, it is equally obvious that -29.0 1250 if the oxidation rate is controlled by the rate of -29.2 1200 adsorption then we should be dealing with a linear -28.6 -30.0 -32.4 -34.4 1150 oxidation law since the rate-determining step is no -29.2 -29.8 -32.2 -34.2 longer transport across the oxide film. 1100 -28.4 -30.0 -32.4 -34.4 1050 For the thin oxide layers (100-1000 A.) that we -29.4 -29.8 -32.2 -34.2 1000 are concerned with in the present work, the trans-28.8 port of ions is essentially controlled by the electric TABLE IV field existing across the oxide film. Engell and Oxyaen pressure K’ (cm.2 eeo.-I) Hauffe16 have shorn that in such cases the field 5 x 10-9 3 . 1 X IO-* exp( -3G000/RT) across the boundary layer is a function of the con1 . 9 X lo-* exp( -36000/RT) 3 . 5 x 10-2 centration of chemisorbed oxygen and hence a func2 . 0 x IO-’ 5.7 X exp( -3GOOO/RT) tion of the oxygen pressure. Thus they showed that 1.0 x 10-2 2.3 X exp( -36000/RT) the parabolic rate constant ( E )is given by K = K OIn Pot + const. (13) Since the transport of ions across the boundary layer is rate determining we have a parabolic oxidation process, but as its magnitude is determined by the electric field it should give an oxygen pressure dependence according to eq. 13. The data obtained in the present work have been plotted according to eq. 13 and at oxygen pressures above 2 X mm. good straight lines obtained. As K must be always positive it is not surprising that 13 breaks down in the lower pressure region. I n fact the equation as derived by Engell and H a d e is only applicable under limited conditions of surface coverage and oxygen pressure so that the degree of linearity obtained must be considered satisDISTANCE -------t factory. Fig. 3.-The potential energy profile for adsorption followed (iii) The Effect of Flashing Temperature on by diffusion through the oxide film. the State of a Silicon Surface.-The technique of (a) If a volatile oxide is formed it is possible that flashing a filament to high temperature is of the rate of diffusion of these evaporating oxide great importance in the removal of oxide fiIms and molecules through the gas phase is the rate-deter- adsorbed material from surfaces. It is very difficult mining step in the over-all oxidation process. Since however, t,o demonstrate conclusively how much the interdiffusion coefficient is inversely propor- material has been removed. The oxidation rate of tional to the gas pressure we would expect that the silicon (and many other solids) is sensitive to the rate would decrease with increasing pressure. This thickness of the oxide film present and this has would be true only for sufficiently high gas pres- been used in the present work to measure the rate sures that the mean free path is small compared of removal of oxide as a function of temperature. with the sample to wall distance. In the oxidation The vapor pressure of silicon has been measured by of germanium this process has been found and dis- BrewerI6 and by Honjg, l7 and evaporation rates have been calculated from their data in terms of cussed at some length.la (b) If the oxide layer formed is a semi-conductor, molecules cm.-2 see.-’ and are shown in Fig. 4 as a then a t the oxide-oxygen interface it is possible to function of temperature. The main difference bechange the concentration of holes and electrons by tween the two curves shown may lie in the fact that varying the oxygen pressure. This is shown by the Brewer assumed that silicon evaporated as atoms fact that the conductivity of the oxide may be while Honig using a mass spectrometer found that a changed in this way. When this occurs the para- considerable quantity evaporated as silicon clusbolic rate constant shows a definite but small ters, and this was taken into account in the calcudependence on oxygen pressure. For example,14 lation of his vapor pressure data. It can be seen the parabolic rate constant for Cu is proportional to that for a relatively clean silicon surface a monop’/7 and for Ni it is proportional to PI/#. This ef- layer will evaporate per second for temperatures in fect has been found to persist up to oxygen pres- the range 1300-1400°K. We are interested in the dependence, if any, of this temperature on the oxide sures of the order of 100 mm. (c) Neither of the two previous mechanisms will film thickness. Giilbransen and AndrewIs studied (15) H. J. Engell and K. Hauffe, Metall.. 6, 285 (1952). explain the pressure dependence found in the pres(le) L. Brewer, “The Chemistry and Metallurgy of Miacellanaous ent work. It is obvious that the rate of oxidation Materials; Thermodynamics.” MoGraw-Hill Book Co., Ino., New (13) J. T. Law and P. 8. Meiga, Trans. Bteclrochem. Soc., 104, 154 York, N. Y.,1950,p. la. TABLEI11
(1957). (14) C.
(1938).
--
AS*, cal. mob-I deg.
Temp.,
Wagner @pcj
v. $.r,@ewald, 2. physik. Cham., B40, 465
(17) R. E. Honig, J . Cham. Phys., 24, 1810 (1954). (18) E. A. Gulbransen and Andrew, Trans. Electroehem. 9ao., 91, 383 (1950).
.
Sept., 1957
THEHIGHTEMPERATURE OXIDATIONOF SILICON
the effect of an oxide film on the vapor pressure of beryllium and found that the vapor pressure was reduced by an amount that was proportional to the square root of the thickness of the film but that the heat of vaporization was unchanged. We have not carried out an exhaustive investigation of the change in evaporation rate with film thickness but from what data we have it appears that there is little if any change in the range 100-500 fL. I n going from a freshly heated surface t o an oxidized one, however, the rate is decreased considerably. From a curve of oxidation rate versus flashing temperature (Fig. 2) it is possible to calculate how much oxide has been removed during a given time interval, by comparing the measured values of dnldt with those obtained during an oxidation rate measurement a t the same temperature and pressure. The results obtained in this way (in molecules evaporating cm.-2 sec. -I) are also plotted in Fig. 4 (broken line). The departure of the results from R linear plot in the high temperature region is due to the fact that once all the oxide has been removed we have no measure for determining how much silicon also has evaporated. Thus eyperimentally the evaporation rate must reach a limiting value which corresponds to the complete removal of the oxide. It seemed reasonable to assume that the low temperature region gave the true evaporation rate for an oxidized surface and we can see that a straight line through this portion is indeed parallel to that obtained by Honig for “clean” silicon in agreement with Gulbransen’s work on beryllium. The rate of evaporation a t any temperature is decreased by a factor of 70 when an oxide film of 100500 A. is present and this may be compared with a decrease of a factor of 10-100 for beryllium under comparable conditions. To summarize then, it is necessary t o heat oxidized silicon to about 1500°K. to remove a few hundred Angstroms of oxide film in a reasonable time. This is considerably higher than what one would predict from the published vapor pressure data but is in substantial agreement with earlier work on beryllium.
1205
5
Fig. 4.-The effect of temperature on the eva oration rate of a cleaned surface (Brewer and Honig) a n 8 of one covered with a 300 A. oxide film.
means that the rate-determining step is the diffusion of some reactant species through the oxide film. Calculations of AS* for the reaction indicate that the entropy of adsorption is decreasing with increasing surface coverage. The rate constant is strongly pressure dependent in the range studied and this is explained in terms of the variation of the surface electrical field with pressure. The rate of evaporation of silicon is found to be lowered by almost two orders of magnitude in the presence of an oxide film but the energy of activation for the process is identical with that obtained Conclusions on clean silicon. The oxidation of silicon from 1000 to 1300°K. Acknowledgment.-The author wishes to express t o his indebtedness to P. S. Meigs, who carried out the and for oxygen pressures in the range 7 X obeys a form of the parabolic law which experimental work presented here, 5 X
