- Email: [email protected]
The growth of ultrathin oxides of silicon by low temperature wet oxidation technique
Materials Research Bulletin, Vol. 34, Nos. 10/11, pp. 1797–1803, 1999 Copyright © 2000 Elsevier Science Ltd Printed in the USA. All rights reserved 0025-5408/99/$–see front matter
PII S0025-5408(99)00158-0
THE GROWTH OF ULTRATHIN OXIDES OF SILICON BY LOW TEMPERATURE WET OXIDATION TECHNIQUE
Vishwanath Krishna Bhat1, M. Pattabiraman1, K.N. Bhat2, and A. Subrahmanyam1* 1 Department of Physics, Indian Institute of Technology, Madras 600036, India 2 Department of Electrical Engineering, Indian Institute of Technology, Madras 600036, India (Communicated by C.N.R. Rao) (Received September 7, 1998; Accepted November 5, 1998)
ABSTRACT In the present investigation, ultrathin oxides of silicon (⬍250 Å) were grown on p-type (100) oriented monocrystalline silicon, employing a low-temperature wet oxidation technique. The effect of furnace temperature (600 and 700°C), water vapor pressure (0.3–1.0 atm), and oxidation time (15–180 min) on the rate of oxide growth was studied. The oxidation rates observed in the present investigation were fitted to the theoretical model proposed by da Silva and Stosic (Semicond. Sci. Technol. 12, 1038, 1997). © 2000 Elsevier Science Ltd KEYWORDS: A. oxides, A. electronic materials, A. semiconductors INTRODUCTION With the recent rapid advances in submicron technology of the silicon devices, ultrathin (⬍100 Å) oxides of silicon grown with low thermal budgets have gained considerable importance. Presently, these ultrathin oxides are being used in highly efficient metal insulator semiconductor inversion layer (MISIL) solar cells [1], MOS transistors with tunnel emitter [2], and scaled oxide–nitride– oxide (ONO) multilayer dielectrics [3]. An understanding of the growth mechanism and kinetics of thermal oxides of large thickness (⬎250 Å) has been achieved by several investigations [4,5], and the Deal and Grove model [6] has laid the foundation for theoretical studies. Ultrathin oxides grown with low thermal budgets require considerable attention. These ultrathin oxides are, in general, grown by dry and wet oxidation
*To whom correspondence should be addressed. E-mail: [email protected]. 1797
1798
V.K. BHAT et al.
Vol. 34, Nos. 10/11
FIG. 1 Experimental setup of the low-temperature wet oxidation technique.
techniques (a) by lowering the growth temperature [7], (b) by diluting the oxygen gas with nitrogen [8], and (c) by reducing the oxidant pressure of the growth ambient [9]. Most of the studies have concentrated on dry oxidation, where the process generates weak dangling bonds near the Si/SiO2 interface [10]. It is well known that, although wet oxidation incorporates hydrogen and passivates the dangling bonds, the excess amount of water related species makes the oxides prone to stress-induced degradation due to electron trapping [11]. The aim of the present study was to grow ultrathin oxides of silicon by a low temperature wet oxidation technique by varying the water vapor pressure, the oxidation (furnace) temperature, and the oxidation time. The data on the oxidation rates were fitted successfully to a theoretical model proposed by da Silva and Stosic [12]. EXPERIMENTAL Ultrathin oxides of silicon were grown on lap-polished monocrystalline p-type silicon wafers (M/s Bayer Chemie, Germany) by the float zone (FZ) technique. They were (100) oriented and exhibited a resistivity of 0.5–1.0 ohm-cm. Samples cut to an area of 1 cm ⫻ 1 cm were degreased in boiling trichloroethylene (TCE) and acetone and thoroughly rinsed in deionized (DI) water. A thin chemical oxide was then formed by boiling the wafers in nitric acid (HNO3) for 10 min. Just before loading the wafers into the oxidation furnace, the native oxide and the chemical oxide formed were removed by dipping the wafers into dilute hydrofluoric (HF) acid and then thoroughly washing them in running DI water. A schematic of the oxidation system is given in Figure 1. It consists of a horizontal quartz tube with an inlet and an outlet. Pure nitrogen carrier gas was bubbled through the deionized water in a quartz bubbler. The carrier gas flow rate was maintained at 7.0 L/h. The water temperature in the quartz bubbler was varied, to vary the vapor pressure of the water [13].
Vol. 34, Nos. 10/11
SILICON OXIDE FILMS
1799
FIG. 2 Oxide thickness vs. water vapor pressure for 600°C oxidation temperature and 60 min oxidation time.
Oxidation was carried out at two different furnace temperatures, 600 and 700°C, and for different durations in the range of 15–180 min. The oxide layer thickness was measured at several regions on the wafer, using a Gaertner L116B ellipsometer using a He:Ne laser ( ⫽ 632 nm). The refractive index of the grown oxide layer was assumed to be 1.46. Accuracy within ⫾5% was achieved with this method of measurement. The reproducibility in the growth and in the measurement was ascertained by repeating the experiment several times under nearly identical conditions. RESULTS AND DISCUSSION As mentioned earlier, the growth of thin oxides by low temperature wet oxidation technique depends upon (a) the vapor pressure of water, (b) the furnace temperature, and (c) the time of oxidation. Figure 2 presents the thickness of the oxide grown as a function of vapor pressure of water when the furnace was at 600°C and the oxidation time was 60 min. Figure 3 gives similar data for a furnace temperature of 700°C and oxidation times of 30 and 60 min. In both cases, the oxide thicknesses are comparable for the water vapor pressure below 0.3 atm. In the case of a furnace temperature of 700°C, the oxidation thickness increased sharply as the vapor pressure of water approached 1.0 atm for both 30 and 60 min oxidation times. It may be noted from Figures 2 and 3 that the initial oxidation rates for these oxidation times were different. Figure 4 gives the oxide thickness (Å) as a function of oxidation time (in minutes) for oxides grown at a constant temperature of 600°C and two different water vapor pressures (0.3
1800
V.K. BHAT et al.
Vol. 34, Nos. 10/11
FIG. 3 Oxide thickness vs. water vapor pressure for 700°C oxidation temperature and oxidation times of 30 and 60 min.
atm and 1.0 atm). (The solid squares and solid circles represent the data obtained experimentally; the line and the dotted line correspond to the theoretical fitting discussed in the following section.) These results clearly show that controlled thin oxides with a thickness in the range 25–50 Å can be grown when the water vapor pressure is kept in the range of about 0.3–1.0 atm at 600°C. It is well known that the initial growth of oxides is complicated. There are theoretical models [14 –16] to explain the growth of thin oxides. It may be noted that the Deal and Grove linear-parabolic model [6], which is derived by considering diffusion of oxidizing species through an already existing oxide layer, does not explain the initial oxidation phenomena for oxide films with thicknesses less than 250 Å (anomalous oxidation region). In a recent paper, da Silva and Stosic [12] have proposed a model to simulate the early stages of growth of thin SiO2 films. The model is based on the assumption that the Si/SiO2 system is composed of three regions: (a) the oxidized region of thickness x formed by SiO2, (b) an intermediate transition region of thickness S representing the oxidation consisting of SimOn (m ⱕ 3, n ⬍ 2), and (c) the bulk crystalline silicon. The growth kinetics of the oxidation region (SiaOb) may be assumed to have a fractal geometry (based on the earlier studies showing that the silicon dioxide surface is highly irregular), suggesting that the Si/SiO2 interface probably has a complex fractal (self-affine) structure [17]. The oxidation kinetics for such a system is given as
Vol. 34, Nos. 10/11
SILICON OXIDE FILMS
1801
FIG. 4 Oxide thickness vs. time for 600°C oxidation temperature and 0.3 and 1.0 atm water vapor pressures. Solid circles and solid squares represent the data obtained experimentally. The solid and dotted lines correspond to the theoretical fitting. (dx/dt) ⫽ KCL ␣⫺2 (兹2Dt ⫺ x)
(1)
where D is the diffusion constant of oxygen, K is the chemical reaction rate constant (depends upon the temperature, pressure, and surface conditions), C is the proportionality constant, L is the linear dimension of the sample, and ␣ ⱕ 2 is the fractal dimension of the transition layer. Eq. 1 may be approximated as Xox(t) ⫽ S ⫹ at b
(2)
where S is the transition region thickness, t is the time of oxidation, and a and b are the fitting parameters, which depend upon the external parameters such as pressure, temperature, atmospheric ambient, and the intrinsic nature of the growth process. Eq. 2 predicts the widely known linear-parabolic growth regimes. This equation has been fitted to a wide variety of data including dry and wet oxidations; however, the oxide grown by low temperature wet oxidation technique is being fitted for the first time in the present communication. It may be noted that the exponent b (eq. 2) is extremely sensitive to the initial choice of the interface thickness S (the value of a also depends upon S). It is shown that the experimental data obtained in our wet oxidation process at 600°C follow eq. 2 if appropriate fitting parameters S, a, and b are chosen. These results are presented in Figure 4 (the solid line and dotted line correspond to the theoretical fitting). It can be seen from the solid line that a linear fit with y ⫽ 18.5 Å, a ⫽ 0.257, and b ⫽ 1.0 (linear variation) agrees well with the experimental results for 1.0 atm oxidation. Further, it is very interesting to note (from the
1802
V.K. BHAT et al.
Vol. 34, Nos. 10/11
TABLE 1 Fitting Parameters for the Equation Xox(t) ⫽ S ⫹ atb for the Experimental Data on the Oxidation Thickness for 600°C, 0.3 atm of Water Vapor Pressure S
a
b
1.0 2.0 3.0 4.0 5.0 8.0 9.0 10.0 11.0 13.0 14.0 15.0
13.27 12.45 11.64 10.83 10.05 7.76 7.04 6.33 5.64 4.35 3.75 3.18
0.18 0.19 0.20 0.21 0.22 0.25 0.26 0.27 0.29 0.32 0.35 0.37
dashed line) that, with keeping the oxidation temperature constant at 600°C and decreasing the water vapor pressure to 0.3 atm, the exponent b should be reduced to 0.48, to fit into the experimental data, resulting in a near parabolic variation. The S, however, takes the value same as before, viz., 18.5 Å (Fig. 4). It is possible to fit the observed experimental data for different values of S, as presented in Table 1 (for 600°C, 0.3 atm of water vapor pressure); however, a proper judgement of S can only give realistic values of the fitting parameters a and b; the sensitivity of a and b may be seen from the Table 1.
CONCLUSIONS Ultrathin oxides of silicon were grown by the wet oxidation technique at furnace temperatures of 600 –700°C by varying the water pressure 0.01–1.0 atm. It was shown that the oxidation rate depends strongly on the water vapor pressure at a given temperature. Fitting the experimental data to the fractal geometry theory developed by da Silva and Stosic [12], it was shown that the growth rate changes from linear to parabolic as the water vapor pressure is decreased from 1.0 to 0.3 atm. Thus, it was shown for the first time that the oxidation rate of ultrathin oxides grown at 600°C in the presence of water vapor obeys their theoretical model.
ACKNOWLEDGMENTS On of the authors, Vishwanath Krishna Bhat, acknowledges the support (Senior Research fellowship) of the Council of Scientific and Industrial Research (CSIR), India, in carrying out this work.
Vol. 34, Nos. 10/11
SILICON OXIDE FILMS
1803
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.
A.G. Aberle, B. Kuhlmann, R. Meyer, A. Hubner, C. Hampe, and R. Hezel, Prog. Photovolt. 4, 193 (1996). K.M. Chu and D.L. Pulfrey, IEEE Trans. Electron Devices ED-35, 188 (1988). K. Kobayashi, H. Migatake, M. Migatake, M. Hirayama, T. Higab, and H. Abe, J. Electrochem. Soc. 139, 1693 (1992). C.J. Sofield and A.M. Stoneham, Semicond. Sci. Technol. 10, 215 (1995). E.A. Irene, Critical Reviews in Solid State and Materials Science, p. 175, CRC Press, Boca Raton, FL (1988). B.E. Deal and A.S. Grove, J. Appl. Phys. 36, 3770 (1965). A.M. Goodman and J.M. Breece, J. Electrochem. Soc. 117, 982 (1970). Y. Kramigaki and Y. Itoh, J. Appl. Phys. 48, 2891 (1977). A.C. Adams, T.E. Smith, and C.C. Chang, J. Electrochem. Soc. 127, 1788 (1980). P. Hahn and M. Henzler, J. Vac. Sci. Technol. A 2, 574 (1984). R. Razouk and B.E. Deal, J. Electrochem. Soc. 126, 1573 (1979). E.F. da Silva, Jr. and B.D. Stosic, Semicond. Sci. Technol. 12, 1038 (1997). D.R. Lide, Handbook of Chemistry and Physics, p. 6, CRC Press, Florida (1995). K. Ohishi, and T. Hattori, Jpn. J. Appl. Phys. 33, L 675 (1994). T. Aiba, K. Yamauchi, Y. Shimizu, N. Tate, M. Katayama, and T. Hattori, Jpn. J. Appl. Phys. 34, 707 (1995). K.-Y. Peng, L.-C. Wang, and J.C. Slattery, J. Vac. Sci. Technol. B 14, 3317 (1996). M.A.F. Gomes, E.F. da Silva, Jr., and J.A. Aguiar, Semicond. Sci. Technol. 10, 1037 (1995).
PII S0025-5408(99)00158-0
THE GROWTH OF ULTRATHIN OXIDES OF SILICON BY LOW TEMPERATURE WET OXIDATION TECHNIQUE
Vishwanath Krishna Bhat1, M. Pattabiraman1, K.N. Bhat2, and A. Subrahmanyam1* 1 Department of Physics, Indian Institute of Technology, Madras 600036, India 2 Department of Electrical Engineering, Indian Institute of Technology, Madras 600036, India (Communicated by C.N.R. Rao) (Received September 7, 1998; Accepted November 5, 1998)
ABSTRACT In the present investigation, ultrathin oxides of silicon (⬍250 Å) were grown on p-type (100) oriented monocrystalline silicon, employing a low-temperature wet oxidation technique. The effect of furnace temperature (600 and 700°C), water vapor pressure (0.3–1.0 atm), and oxidation time (15–180 min) on the rate of oxide growth was studied. The oxidation rates observed in the present investigation were fitted to the theoretical model proposed by da Silva and Stosic (Semicond. Sci. Technol. 12, 1038, 1997). © 2000 Elsevier Science Ltd KEYWORDS: A. oxides, A. electronic materials, A. semiconductors INTRODUCTION With the recent rapid advances in submicron technology of the silicon devices, ultrathin (⬍100 Å) oxides of silicon grown with low thermal budgets have gained considerable importance. Presently, these ultrathin oxides are being used in highly efficient metal insulator semiconductor inversion layer (MISIL) solar cells [1], MOS transistors with tunnel emitter [2], and scaled oxide–nitride– oxide (ONO) multilayer dielectrics [3]. An understanding of the growth mechanism and kinetics of thermal oxides of large thickness (⬎250 Å) has been achieved by several investigations [4,5], and the Deal and Grove model [6] has laid the foundation for theoretical studies. Ultrathin oxides grown with low thermal budgets require considerable attention. These ultrathin oxides are, in general, grown by dry and wet oxidation
*To whom correspondence should be addressed. E-mail: [email protected]. 1797
1798
V.K. BHAT et al.
Vol. 34, Nos. 10/11
FIG. 1 Experimental setup of the low-temperature wet oxidation technique.
techniques (a) by lowering the growth temperature [7], (b) by diluting the oxygen gas with nitrogen [8], and (c) by reducing the oxidant pressure of the growth ambient [9]. Most of the studies have concentrated on dry oxidation, where the process generates weak dangling bonds near the Si/SiO2 interface [10]. It is well known that, although wet oxidation incorporates hydrogen and passivates the dangling bonds, the excess amount of water related species makes the oxides prone to stress-induced degradation due to electron trapping [11]. The aim of the present study was to grow ultrathin oxides of silicon by a low temperature wet oxidation technique by varying the water vapor pressure, the oxidation (furnace) temperature, and the oxidation time. The data on the oxidation rates were fitted successfully to a theoretical model proposed by da Silva and Stosic [12]. EXPERIMENTAL Ultrathin oxides of silicon were grown on lap-polished monocrystalline p-type silicon wafers (M/s Bayer Chemie, Germany) by the float zone (FZ) technique. They were (100) oriented and exhibited a resistivity of 0.5–1.0 ohm-cm. Samples cut to an area of 1 cm ⫻ 1 cm were degreased in boiling trichloroethylene (TCE) and acetone and thoroughly rinsed in deionized (DI) water. A thin chemical oxide was then formed by boiling the wafers in nitric acid (HNO3) for 10 min. Just before loading the wafers into the oxidation furnace, the native oxide and the chemical oxide formed were removed by dipping the wafers into dilute hydrofluoric (HF) acid and then thoroughly washing them in running DI water. A schematic of the oxidation system is given in Figure 1. It consists of a horizontal quartz tube with an inlet and an outlet. Pure nitrogen carrier gas was bubbled through the deionized water in a quartz bubbler. The carrier gas flow rate was maintained at 7.0 L/h. The water temperature in the quartz bubbler was varied, to vary the vapor pressure of the water [13].
Vol. 34, Nos. 10/11
SILICON OXIDE FILMS
1799
FIG. 2 Oxide thickness vs. water vapor pressure for 600°C oxidation temperature and 60 min oxidation time.
Oxidation was carried out at two different furnace temperatures, 600 and 700°C, and for different durations in the range of 15–180 min. The oxide layer thickness was measured at several regions on the wafer, using a Gaertner L116B ellipsometer using a He:Ne laser ( ⫽ 632 nm). The refractive index of the grown oxide layer was assumed to be 1.46. Accuracy within ⫾5% was achieved with this method of measurement. The reproducibility in the growth and in the measurement was ascertained by repeating the experiment several times under nearly identical conditions. RESULTS AND DISCUSSION As mentioned earlier, the growth of thin oxides by low temperature wet oxidation technique depends upon (a) the vapor pressure of water, (b) the furnace temperature, and (c) the time of oxidation. Figure 2 presents the thickness of the oxide grown as a function of vapor pressure of water when the furnace was at 600°C and the oxidation time was 60 min. Figure 3 gives similar data for a furnace temperature of 700°C and oxidation times of 30 and 60 min. In both cases, the oxide thicknesses are comparable for the water vapor pressure below 0.3 atm. In the case of a furnace temperature of 700°C, the oxidation thickness increased sharply as the vapor pressure of water approached 1.0 atm for both 30 and 60 min oxidation times. It may be noted from Figures 2 and 3 that the initial oxidation rates for these oxidation times were different. Figure 4 gives the oxide thickness (Å) as a function of oxidation time (in minutes) for oxides grown at a constant temperature of 600°C and two different water vapor pressures (0.3
1800
V.K. BHAT et al.
Vol. 34, Nos. 10/11
FIG. 3 Oxide thickness vs. water vapor pressure for 700°C oxidation temperature and oxidation times of 30 and 60 min.
atm and 1.0 atm). (The solid squares and solid circles represent the data obtained experimentally; the line and the dotted line correspond to the theoretical fitting discussed in the following section.) These results clearly show that controlled thin oxides with a thickness in the range 25–50 Å can be grown when the water vapor pressure is kept in the range of about 0.3–1.0 atm at 600°C. It is well known that the initial growth of oxides is complicated. There are theoretical models [14 –16] to explain the growth of thin oxides. It may be noted that the Deal and Grove linear-parabolic model [6], which is derived by considering diffusion of oxidizing species through an already existing oxide layer, does not explain the initial oxidation phenomena for oxide films with thicknesses less than 250 Å (anomalous oxidation region). In a recent paper, da Silva and Stosic [12] have proposed a model to simulate the early stages of growth of thin SiO2 films. The model is based on the assumption that the Si/SiO2 system is composed of three regions: (a) the oxidized region of thickness x formed by SiO2, (b) an intermediate transition region of thickness S representing the oxidation consisting of SimOn (m ⱕ 3, n ⬍ 2), and (c) the bulk crystalline silicon. The growth kinetics of the oxidation region (SiaOb) may be assumed to have a fractal geometry (based on the earlier studies showing that the silicon dioxide surface is highly irregular), suggesting that the Si/SiO2 interface probably has a complex fractal (self-affine) structure [17]. The oxidation kinetics for such a system is given as
Vol. 34, Nos. 10/11
SILICON OXIDE FILMS
1801
FIG. 4 Oxide thickness vs. time for 600°C oxidation temperature and 0.3 and 1.0 atm water vapor pressures. Solid circles and solid squares represent the data obtained experimentally. The solid and dotted lines correspond to the theoretical fitting. (dx/dt) ⫽ KCL ␣⫺2 (兹2Dt ⫺ x)
(1)
where D is the diffusion constant of oxygen, K is the chemical reaction rate constant (depends upon the temperature, pressure, and surface conditions), C is the proportionality constant, L is the linear dimension of the sample, and ␣ ⱕ 2 is the fractal dimension of the transition layer. Eq. 1 may be approximated as Xox(t) ⫽ S ⫹ at b
(2)
where S is the transition region thickness, t is the time of oxidation, and a and b are the fitting parameters, which depend upon the external parameters such as pressure, temperature, atmospheric ambient, and the intrinsic nature of the growth process. Eq. 2 predicts the widely known linear-parabolic growth regimes. This equation has been fitted to a wide variety of data including dry and wet oxidations; however, the oxide grown by low temperature wet oxidation technique is being fitted for the first time in the present communication. It may be noted that the exponent b (eq. 2) is extremely sensitive to the initial choice of the interface thickness S (the value of a also depends upon S). It is shown that the experimental data obtained in our wet oxidation process at 600°C follow eq. 2 if appropriate fitting parameters S, a, and b are chosen. These results are presented in Figure 4 (the solid line and dotted line correspond to the theoretical fitting). It can be seen from the solid line that a linear fit with y ⫽ 18.5 Å, a ⫽ 0.257, and b ⫽ 1.0 (linear variation) agrees well with the experimental results for 1.0 atm oxidation. Further, it is very interesting to note (from the
1802
V.K. BHAT et al.
Vol. 34, Nos. 10/11
TABLE 1 Fitting Parameters for the Equation Xox(t) ⫽ S ⫹ atb for the Experimental Data on the Oxidation Thickness for 600°C, 0.3 atm of Water Vapor Pressure S
a
b
1.0 2.0 3.0 4.0 5.0 8.0 9.0 10.0 11.0 13.0 14.0 15.0
13.27 12.45 11.64 10.83 10.05 7.76 7.04 6.33 5.64 4.35 3.75 3.18
0.18 0.19 0.20 0.21 0.22 0.25 0.26 0.27 0.29 0.32 0.35 0.37
dashed line) that, with keeping the oxidation temperature constant at 600°C and decreasing the water vapor pressure to 0.3 atm, the exponent b should be reduced to 0.48, to fit into the experimental data, resulting in a near parabolic variation. The S, however, takes the value same as before, viz., 18.5 Å (Fig. 4). It is possible to fit the observed experimental data for different values of S, as presented in Table 1 (for 600°C, 0.3 atm of water vapor pressure); however, a proper judgement of S can only give realistic values of the fitting parameters a and b; the sensitivity of a and b may be seen from the Table 1.
CONCLUSIONS Ultrathin oxides of silicon were grown by the wet oxidation technique at furnace temperatures of 600 –700°C by varying the water pressure 0.01–1.0 atm. It was shown that the oxidation rate depends strongly on the water vapor pressure at a given temperature. Fitting the experimental data to the fractal geometry theory developed by da Silva and Stosic [12], it was shown that the growth rate changes from linear to parabolic as the water vapor pressure is decreased from 1.0 to 0.3 atm. Thus, it was shown for the first time that the oxidation rate of ultrathin oxides grown at 600°C in the presence of water vapor obeys their theoretical model.
ACKNOWLEDGMENTS On of the authors, Vishwanath Krishna Bhat, acknowledges the support (Senior Research fellowship) of the Council of Scientific and Industrial Research (CSIR), India, in carrying out this work.
Vol. 34, Nos. 10/11
SILICON OXIDE FILMS
1803
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.
A.G. Aberle, B. Kuhlmann, R. Meyer, A. Hubner, C. Hampe, and R. Hezel, Prog. Photovolt. 4, 193 (1996). K.M. Chu and D.L. Pulfrey, IEEE Trans. Electron Devices ED-35, 188 (1988). K. Kobayashi, H. Migatake, M. Migatake, M. Hirayama, T. Higab, and H. Abe, J. Electrochem. Soc. 139, 1693 (1992). C.J. Sofield and A.M. Stoneham, Semicond. Sci. Technol. 10, 215 (1995). E.A. Irene, Critical Reviews in Solid State and Materials Science, p. 175, CRC Press, Boca Raton, FL (1988). B.E. Deal and A.S. Grove, J. Appl. Phys. 36, 3770 (1965). A.M. Goodman and J.M. Breece, J. Electrochem. Soc. 117, 982 (1970). Y. Kramigaki and Y. Itoh, J. Appl. Phys. 48, 2891 (1977). A.C. Adams, T.E. Smith, and C.C. Chang, J. Electrochem. Soc. 127, 1788 (1980). P. Hahn and M. Henzler, J. Vac. Sci. Technol. A 2, 574 (1984). R. Razouk and B.E. Deal, J. Electrochem. Soc. 126, 1573 (1979). E.F. da Silva, Jr. and B.D. Stosic, Semicond. Sci. Technol. 12, 1038 (1997). D.R. Lide, Handbook of Chemistry and Physics, p. 6, CRC Press, Florida (1995). K. Ohishi, and T. Hattori, Jpn. J. Appl. Phys. 33, L 675 (1994). T. Aiba, K. Yamauchi, Y. Shimizu, N. Tate, M. Katayama, and T. Hattori, Jpn. J. Appl. Phys. 34, 707 (1995). K.-Y. Peng, L.-C. Wang, and J.C. Slattery, J. Vac. Sci. Technol. B 14, 3317 (1996). M.A.F. Gomes, E.F. da Silva, Jr., and J.A. Aguiar, Semicond. Sci. Technol. 10, 1037 (1995).