JOURNAL OF APPLIED PHYSICS VOLUME 36. NUMBER 12 DECEMBER 1965 General Relationship for the Thermal Oxidation of Silicon B. E. DEAL AND A. S. GROVE Fairchild Semiconductor, A Division of Fairchild Camera and Instrument Corporation, Palo Alto, California (Received 10 May 1965; in final form 9 September 1965) The thermal-oxidation kinetics of silicon are examined in detail. Based on a simple model of oxidati?n which takes into account the reactions occurring at the two boundaries of the oxide layer as well as t~e dIf-fusion process, the general relationship x02+:4xo=B(t+r) .is derived. This relationship is ~hown}o be m ~xcellent agreement with oxidation data obtamed over a ;VIde range of temperature (7~ -1300 C), partial pressure (0.1-1.0 atm) and oxide thickness (300-20000 A) for both oxygen and water. oXI~ants. T~e p~rameters A, B, and r are shown to be related to the physico-chemical.constant.s of the o~datlOn reaction m the predicted manner. Such detailed analysis also leads t? .f~rther mfor~tlo~ regardmg the nature of the transported species as well as space-charge effects on the Imtlal phase of OXidatIOn. 1. INTRODUCTION OWING to its great importance in planar silicon-device technology, the formation of silicon dioxide layers by thermal oxidation of single-crystal silicon has been studied very extensively in the past several years,l-15 Now, with the availability of large a~ounts of experimental data, it appears that there IS much contradiction and many peculiarities in the store of knowledge of silicon oxidation. For instance, reported activation energies of rate constants vary between 27 and 100 kcal/mole for oxidation in dry oxygen; pressure dependence of rate constants has been reported as linear as well as logarithmic. While most of the data on silicon oxidation have been evaluated using the parabolic rate law, certain authors have taken recourse to using empirical power-law dependence,14 xon= kt, where both n and k were complex functions of temperature, pressure, and oxide thickness. The problems associated with the latter approach can be illustrated by considering Figs 1 and 2. These figures 1 J. T. Law, J. Phys. Chern. 61, 1200 (1957). 2 M. M. Atalla, Properties of Elementa~ and ComRound Semi-conductors, edited by H. Gatos (Intersclence PublIshers, Inc., New York, 1960), Vol. 5, pp. 16~-181. . 3 J. R. Ligenza and W. G. Spitzer, J. Phys. Chern. Solids 14, 131 (1960). 4 J. R. Ligenza, J. Phys. Che!D' 65, 2011 (1961). . 6 W. G. Spitzer and J. R. Llgenza, J. Phys. Chern. Solids 17, 196 (1961). 6 M. O. Thurston, J. C. C. Tsai, and K. D. Kang, "Diffusion of Impurities into Silicon Through an Oxide Lay~r," Report 896-Final, Ohio State University, Research FoundatIOn, U. S. Army Signal Supply Agency Contract DA-36-039-SC-83874, March 1961. 7 P S Flint "The Rates of Oxidation of Silicon," Paper pre-sented ~t the'Spring Meeting of The Electrochemical Society, Abstract No. 94, Los Angeles, 6-10 May 1962. 8 P. J. Jorgensen, J. Chern. Phys. 37, 874 (1962). 9 J. R. Ligenza, J. Electrochem. Soc. 109, 73 (1962). 10 B. E. Deal, J. Electrochem. Soc. 110, 527 (1963). 11 H. Edagawa, Y. Morita, S. Maekawa, and Y. lnuishi, J. Appl. Phys. (Japan) 2, 765 (1963). 12 N. Karube, K. Yamamoto, and M. Kamiyama, J. App!. Phys. (Japan) 2, 11 (1963). 13 H. C. Evitts, H. W. Cooper, and S. S. Flaschen, J. Electro-chern. Soc. 111, 688 (1964). 14 C. R. Fuller and F. J. Strieter, "Silicon Oxidation," Paper presented at the Spring Meeting of The Electrochemical Society Abstract No. 74, Toronto, 3-7 May 1964. 16 B. E. Deal and M. Sklar, J. Electrochem. Soc. 112, 430 (1965). contain a summary of data obtained in these laboratories which are in good general agreement with the cor-responding data of Fuller and Strieterl4 and of Evitts, Cooper, and FlaschenY (The experimental met~ods are dealt with in detail later.) The plots are logarIthm of oxide thickness vs the logarithm of oxidation time for dry and wet oxygen (9S0C H20) at various tempera-tures. The slope of the lines corresponds to the exponent n in the above power law. These values are indicated at the limiting position of some of the curves. In the case of wet oxygen (Fig. 1), n ranges from 2 for thicker oxides at 1200°C to 1 for the thinner oxide region of the 920°C data. However, for dry oxygen (Fig. 2), the value of n at 1200° approaches 2 as the oxide thickness in-creases above 1.0 ).I.; but at lower temperatures and oxide thicknesses the value of n decreases only to about 1.S and then appears to increase again. Obviously the data cannot be represented by a simple power law. Most of the previous theoretical treatments of the kinetics of the oxidation of metals emphasize only two limiting types of oxidation mechanisms.16 In one, the (I) (I) '" z " !:! :t: ... '" eO.1 ~ 0.1 1.0 10 OXIDATION TIME (hours) FIG. 1. Oxidation of silicon in wet oxygen (95°C H20). 16 N. Cabrera and N. F. Mott, Rept. Progr. Phys.12, 163 (1948). 3770RELATIONSHIP FOR OXIDATION OF Si 3771 oxide thickness is small in comparison to the extent of possible space-charge regions within the oxide, and the oxidation kinetics is strongly influenced by the space charge or by a voltage drop across the oxide film due to contact potential differences. In the other, the rate of diffusion of either the oxidizing species or the metal across the oxide film determines the oxidation kinetics. This latter condition leads to a parabolic relationship, Xo a: tt. These two approaches have been emphasized to such an extent that deviations from parabolic oxida-tion have been attributed incorrectly to space-charge effects. In this paper the oxidation kinetics are examined in greater detail. It is shown that when the reactions occurring at the two boundaries of the oxide layer are taken into account, a general relationship can be ob-tained with parameters which are e~:plicitly related to the physico-chemical constants of the oxidation system. This general relationship is shown to be in excellent agreement with data obtained by various groups of investigators over a wide range of conditions. It is shown that the parameters of this relationship follow the predictions of the model. In addition, further in-formation is obtained regarding the mechanism of oxidation: the nature of the transported species, and the