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A method for low-concentration phosphorus diffusion by ambient control
Solid-State Electronics Vol. 29, in Great Britain
No. 9, pp. 925928,
0038-I 101/86 $3.00 + 0.00 Pergamon Journals Ltd
1986
Printed
A METHOD FOR LOW-CONCENTRATION PHOSPHORUS DIFFUSION BY AMBIENT CONTROL A. K. GUPTA and M. S. TYAGI Department of Electrical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India (Received 15 April 1985; in revised form 1 January 1986)
Abstract-A method of surface concentration control for phosphorus diffusion by manipulating the growth rate of phosphosilicate glass is described. It is pointed out that the surface concentration in the oxidising ambient can be varied over a wide range by changing (i) the ratio of partial pressures of oxygen and dopant, and (ii) the diffusion temperature. Experimental results for phosphorus diffusion in oxidising ambient using PH, source at various diffusion temperatures are presented.
(ii) C2 (rXo(t),t)/Cl(&(t),t) = m = const, (iii) C, (0,t) = Co = const, and the impurity conservation condition,
1. INTRODUCTION
Low-surface-concentration impurity profiles are required in silicon for the formation of base regions in a number of bipolar devices such as transistors, thyristors and hyperabrupt varactors. Such impurity profiles are rather difficult to produce by commonly used processes of diffusion from chemical vapour sources because of the very low dopant partial pressures involved[l]. Various techniques such as sealedtube diffusion[2], diffusion from doped-oxide sources[3,4], spin-on sources and ion implantation[S] have been developed to achieve more precise control over the impurity concentration below the solidsolubility limit in silicon. An open-tube diffusion process which consists of controlling the dopant partial pressure by introduction of small amounts of water vapour in the diffusion ambient has also been reported for low-concentration boron diffusion in silicon[l]. In this paper an alternative method is presented for manipulating the surface concentration over a wide range by controlling the oxygen content in the diffusion ambient.
(iv) [Or -2
+ d$$)
C,1,,,,
Mathematically, the tical to that for homogeneously-doped For parabolic growth
problem stated above is idenimpurity redistribution in silicon during oxidation[6,7l. of DSG (X0(t) = a), the
impurity
in silicon,
distribution
therefore,
is given
byFi?l C,(z, t) = m
x e-‘*n’4D2erf(6)C, (e-“/J;;)
+ S erf(G ) +
mr8 erf(6)F (3)
2. THEORY The process of impurity diffusion from a Constant source in an oxidising ambient is shown in Fig. 1. Using a two coordinate system, the diffusion equa-
tions in dopo-silicate glass (DSG) and silicon can be written as
aG(x, 0 = at G(Y, t) =
at
a2c,(x,t)
D
I
D
2
8X2
1
x
t > 0 (1)
a2c2cy, 0. ay2
’
co interface
r&(t)O.
The initial and boundary conditions (9 C2(~, r) = C2(n 0) = -Cs,
are,
Original Si -surface, I Initial SiO, layrr
Si -SiO,
interface
Fig. 1. Impurity diffusion in silicon in oxidising ambient. 925
A. K. GUPTAand M. S. TYAGI
926
where F=
-1
+ J;; (r $i/Z!fi,)
B=
1
er2i4D2 erfc(r JZ/*JDJ
-
JQ
erfc(r G/2&)’
’ - @,’
* -
-
JB
-QZr
and r = the silicon to DSG volume ratio. Since CB Q C,, the expression for the impurity concentration at the surface can be written as C,(O, t) = C, * A’//$
(4)
where A’=
mc0
1 + &BeJ2 erf(G)F,’ F, = (1 + mrF).
W
(4’4
Equation (4) predicts a time-invariant surface concentration. It is essentially a consequence of the assumption of parabolic. growth of DSG together with the boundary condition (ii). It can be shown that the deviation from either of the two conditions leads to a variation of surface concentration with time. Equation (4a) describes the dependence of surface concentration on process variables such as ambient, temperature, and composition of DSG (through the D, dependence on DSG composition)[&lO]. The surface concentration can be manipulated by varying Co and/or 6 Co is directly proportional to the dopant partial pressure in the diffusion ambient. For the case of boron diffusion from a BBr, source, the addition of small amounts of water vapour as oxidant (instead of oxygen) has been reported to be an effective method for varying Co over orders of magnitudeHI. For a particular value of Co, 6 depends upon the oxidation rate (hence the temperature and oxygen content in the ambient) and the diffusion coefhcient of dopant in DSG (hence the temperature and DSG composition). It is seen from eqns (4) and (4a) that C, is a very strong function of 6 for S > 1. This offers another effective method of controlling C, since for a given value of Co (hence 0,) 6 can be easily varied by varying the partial pressure of oxygen in the diffusion ambient. For low concentrations the desirable process features are large values of 6 (high growth ;ate of low-doped DSG) and D2 (high diffusion temperature). 3. EXPERIMENTAL
Phosphorus was diffused into
earmarked for characterization of phosphosilicate glass (PSG) grown during diffusion and the other for evaluation of the diffused profile. The PSG parameters of interest are its thickness X0 and the phosphorus concentration at the PSG surface, Co (Fig. 1). The value of X0 was determined by etching a linear step in the PSG using photolithography and by measuring the step height with a Varian A scope, Model 960-4020. The average phosphorus concentration in the PSG was estimated from the etch rate of the PSG inp-etch[9,11]. This etch rate was found to vary from 4.3 A/set for samples diffused at 1250°C to 8.55 A/set for those diffused at 950°C. The average phosphorus concentration thus estimated for each case was taken as an approximate value for Co. This is justified since the phosphorus distribution in PSG grown during the deposition process from a POCIJ source has been observed to be box type[l2]. The diffused profile in silicon was determined by the incremental-sheet-resistivity method[ 131. A circular mesa of 250mil diameter was etched on the diffused sample using photolithography. The depth distribution of the sheet resistivity was determined by taking mesurements on this mesa using a four-point probe (25 mil spacing, K and S make) after successive removal of thin layers (244 A) of silicon by anodic oxidation. The anodic oxidation cell used was similar to the one reported by Ryssel et al. [14]. The electrolyte was 0.08 N solution of KNO, in ethylene glycol with 4% water[4,15,16]. The measured sheet resistivity versus depth data were first smoothed using the cubic spline approximation[l7]. The majority carrier (hence phosphorus) distribution was then computed using the mobility versus impurity concentration expression reported by Antoniadis et al. [18]. The values of A and Dz were computed by numerically solving eqn (3) for A and D2 at two points on the experimental profile. The value of 6 was calculated from eqn (4a) with m = 10. 4. RESULTS
AND DISCUSSION
In Fig. 2 the surface concentrations obtained for diffusions at 950°C have been ,plotted against diffusion time. It is seen that for diffusion times greater than 4 = 00 hr, the surface concentration is almost constant. This indicates that the assumption of parabolic DSG growth as also of boundary condition (ii) are good approximations for diffusion time greater than 4 hr. Since at higher temperatures, the thermal oxide growth in dry O2 tends to be dominantly parabolic, it appears reasonable to assume that for comparable DSG thickness, the PSG growth is parabolic at temperatures greater than 950°C. The sheet resistivity, impurity profile and eqn (3) for calculated values of A and D2 are plotted in Figs. 3 and 4 for the typical diffusion runs at 1150 and 95O”C, respectively. An excellent agreement between the theoretical and experimental profile further
Low-temperature
diffusion by ambient control
921 Samplr no. * -0AS TOmp. . sso*c
10’9
-
-Theory
104
x Eapwimont
6
0
6
IiT ‘E u ii
i
2-
8
1 10’61
’ 10
’ 2
’
’
““1’
4
6
’ 610’
Diffusion
’
’
2
time
’ “1”’ 4
6
10’86- -
0 810’
%
6-
(min) 4
4-
Fig. 2. Variation of surface concentration with diffusion time at 950°C.
i 0
2
justifies the application of the theoretical model described in Sec. 2. The value of A (-A ‘), which is approximately equal to the surface concentration, is plotted against temperature in Fig. 5 with the values of X0, S and F, specified for each point. It is seen that for the same diffusion ambient (and approximately the same PSG composition) the surface concentration varies over two orders of magnitude in the temperature range 95~1250°C. In accordance with eqn (4), the surface concentration is observed to have a strong dependence on 6 and a much weaker dependence on the
2
0 1
4
I Dirtonco form surface (a)
Fig. 4. Sheet resistivity and phosphorus distribution silicon. Diffusion time 15 hr.
ratio of PSG thickness to impurity diffusion length in silicon. Since D, also varies with PSG composition[lO], It is possible to vary 6 over a wide range by changing the ratio of the partial pressures
x,.0.2666
-2
I - 1.66 i, = 13.21
lo-
104
E
_4
3
-2
f .z 0 .10’ 8
-6
_
/
6
-6 -
I
pm
6
-6
_
in
g 8 z cn
F, ‘34.92
6 t 4
/
-4
r,=0.213Spm 8
2
‘2.42
F, -54.16 -2 I
‘“‘zo loo
120130
I
1
1.0
6.0 104/T
I 6.
(K)
Distance from surfacr (w)
Fig. 3. Sheet resistivity and phosphorus distribution in silicon. Diffusion time 3 hr.
Fig. 5. Variation of surface concentration with temperature and F’SG growth rate. Diffusion times are 1,3,6 and 15 hr at 1250, 1150, 1050 and 95OT, respectively.
A. K. GUPTAand M. S. TYAGI
928 1250%
10-i
!-
I
116oT
1050*c
I I 0 Eapwimentol
950%
x Normolired 6643-
7
2-
r
film formation takes place simultaneously with diffusion of phosphorus, and the estimated activation energy of the diffusion coefficient, therefore, may be expected to correspond to the combination of the two processes, while in the latter case it essentially refers to the diffusion of dopant in PSG. The method described above is essentially a variation of the commonly used open-tube diffusion process. Although a gaseous source was used in the experiments, it is possible to extend this method to liquid-dopant sources such as POCl,. Acknowledgement-One of the authors, A. K. Gupta, is grateful to Dr. J. Narain for useful suggestions during the experimental work. REFERENCES
I
'Cl.0
I
1.0
I I 6.0 a2
lO’/T(K)
Fig. 6. Phosphorus diffusion coefficient in PSG.
of oxygen and dopant in the diffusion ambient. It is thus possible to vary the surface concentration, by this process, from very low levels to the solidsolubility limit of the impurity in silicon. The value of S in Fig. 5 is observed to decrease with temperature. For the assumed parabolic growth of PSG (X0 = @), the value of D, has been calculated and plotted in Fig. 6. The estimated values of D1 correspond to PSGs with Pro, concentration varying from 3.0 mole % at 1250°C to 5.4 mole % at 950°C. These data are normalized for PSG containing 4.0mole % Pro, on the basis that D, is directly proportional to the P,Os concentratioin in PSG[lO]. The activation energy of D, thus normalized is determined to be 1.17 eV which is significantly lower than the corresponding value (1.41.6 eV) reported in literature[&lO]. This discrepancy is attributed mainly to the difference in the nature of the experiments. The values reported in the literature correspond to the PSG formed by diffusion of P,Os in thermally grown SiOr while in the present experiments the PSG of approximately uniform composition was grown during the diffusion process. In the former case the PSG
1. R. P. Lever and H. M. Demsky, IBM J. Res. Dev. 1% 40 (1974). 2. R. N. Ghoshtagore, Solid-St. Electron. 15, 1113 (1972). 3. M. L. Barry and P. Olofsen, Solid-St. Technol. 11, 39 (1968). 4. R. N. Ghoshtagore, Solid-St. Electron. 17, 1065 (1974). 5. H. Maes, W. Vandervorst and R. Van Overstraeten, in Impurity Doping Processes in Silicon (Edited by F. F. Y. Wang), p. 444. North-Holland, Amsterdam (1981). 6. A. K. Gupta, On the Phosphorus Diffusion in Silicon in Oxidising and Chloro-oxidising Ambients, Ph.D. thesis, I. I. T. Kanpur, 1984. 7. A. S. Grove, 0. Ixistiko Jr. and C. T. Sah, J. Appl. Phys. 35, 2695 (1964). 8. C. T. Sah, H. Sellow and D. A. Tremere, J. Phys. Chem. Solids 11, 288 (1959). 9. J. M. Eldridge, P. Balk, Trans. Metall. Sot. AZME 242, 539 (1968). 10. R. N. Ghostagore, Solid-St. Electron. 18, 399 (1975). 11. W. A. Pliskin and R. P. Gnall, J. Electrochem. Sot. 111, 872 (1964). 12. I. Franz and W. Langheinrich, Solid-St. Electron. 11, 987 (1968). 13. R. P. Donovan and R. A. Evans, in Silicon Device Processing, U.S. National Bureau of Standards Special Publn. No. 123 (1970). 14. H. Ryssel, K. Sehmid and H. Muller, J. Phy. E: Sci. Znstr. 6, 492 (1973). 15. H. D. Barber, H. B. Lo and J. E. Jones, J. Efectrochem. Sot. 123, 1404 (1976). 16. G. C. Jain, A. Prasad and B. C. Chakravarty, J. Electrochem. Sot. 126, 89 (1979). 17. N. D. Arora, D. J. Roulston and S. G. Chamberlain, Solid-St. Electron. 25, 965 (1982). 18. D. A. Antoniadis, A. G. Gonzalez and R. W. Dutton, J. Efectrochem. Sot. 125, 813 (1978).
No. 9, pp. 925928,
0038-I 101/86 $3.00 + 0.00 Pergamon Journals Ltd
1986
Printed
A METHOD FOR LOW-CONCENTRATION PHOSPHORUS DIFFUSION BY AMBIENT CONTROL A. K. GUPTA and M. S. TYAGI Department of Electrical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India (Received 15 April 1985; in revised form 1 January 1986)
Abstract-A method of surface concentration control for phosphorus diffusion by manipulating the growth rate of phosphosilicate glass is described. It is pointed out that the surface concentration in the oxidising ambient can be varied over a wide range by changing (i) the ratio of partial pressures of oxygen and dopant, and (ii) the diffusion temperature. Experimental results for phosphorus diffusion in oxidising ambient using PH, source at various diffusion temperatures are presented.
(ii) C2 (rXo(t),t)/Cl(&(t),t) = m = const, (iii) C, (0,t) = Co = const, and the impurity conservation condition,
1. INTRODUCTION
Low-surface-concentration impurity profiles are required in silicon for the formation of base regions in a number of bipolar devices such as transistors, thyristors and hyperabrupt varactors. Such impurity profiles are rather difficult to produce by commonly used processes of diffusion from chemical vapour sources because of the very low dopant partial pressures involved[l]. Various techniques such as sealedtube diffusion[2], diffusion from doped-oxide sources[3,4], spin-on sources and ion implantation[S] have been developed to achieve more precise control over the impurity concentration below the solidsolubility limit in silicon. An open-tube diffusion process which consists of controlling the dopant partial pressure by introduction of small amounts of water vapour in the diffusion ambient has also been reported for low-concentration boron diffusion in silicon[l]. In this paper an alternative method is presented for manipulating the surface concentration over a wide range by controlling the oxygen content in the diffusion ambient.
(iv) [Or -2
+ d$$)
C,1,,,,
Mathematically, the tical to that for homogeneously-doped For parabolic growth
problem stated above is idenimpurity redistribution in silicon during oxidation[6,7l. of DSG (X0(t) = a), the
impurity
in silicon,
distribution
therefore,
is given
byFi?l C,(z, t) = m
x e-‘*n’4D2erf(6)C, (e-“/J;;)
+ S erf(G ) +
mr8 erf(6)F (3)
2. THEORY The process of impurity diffusion from a Constant source in an oxidising ambient is shown in Fig. 1. Using a two coordinate system, the diffusion equa-
tions in dopo-silicate glass (DSG) and silicon can be written as
aG(x, 0 = at G(Y, t) =
at
a2c,(x,t)
D
I
D
2
8X2
1
x
t > 0 (1)
a2c2cy, 0. ay2
’
co interface
r&(t)
The initial and boundary conditions (9 C2(~, r) = C2(n 0) = -Cs,
are,
Original Si -surface, I Initial SiO, layrr
Si -SiO,
interface
Fig. 1. Impurity diffusion in silicon in oxidising ambient. 925
A. K. GUPTAand M. S. TYAGI
926
where F=
-1
+ J;; (r $i/Z!fi,)
B=
1
er2i4D2 erfc(r JZ/*JDJ
-
JQ
erfc(r G/2&)’
’ - @,’
* -
-
JB
-QZr
and r = the silicon to DSG volume ratio. Since CB Q C,, the expression for the impurity concentration at the surface can be written as C,(O, t) = C, * A’//$
(4)
where A’=
mc0
1 + &BeJ2 erf(G)F,’ F, = (1 + mrF).
W
(4’4
Equation (4) predicts a time-invariant surface concentration. It is essentially a consequence of the assumption of parabolic. growth of DSG together with the boundary condition (ii). It can be shown that the deviation from either of the two conditions leads to a variation of surface concentration with time. Equation (4a) describes the dependence of surface concentration on process variables such as ambient, temperature, and composition of DSG (through the D, dependence on DSG composition)[&lO]. The surface concentration can be manipulated by varying Co and/or 6 Co is directly proportional to the dopant partial pressure in the diffusion ambient. For the case of boron diffusion from a BBr, source, the addition of small amounts of water vapour as oxidant (instead of oxygen) has been reported to be an effective method for varying Co over orders of magnitudeHI. For a particular value of Co, 6 depends upon the oxidation rate (hence the temperature and oxygen content in the ambient) and the diffusion coefhcient of dopant in DSG (hence the temperature and DSG composition). It is seen from eqns (4) and (4a) that C, is a very strong function of 6 for S > 1. This offers another effective method of controlling C, since for a given value of Co (hence 0,) 6 can be easily varied by varying the partial pressure of oxygen in the diffusion ambient. For low concentrations the desirable process features are large values of 6 (high growth ;ate of low-doped DSG) and D2 (high diffusion temperature). 3. EXPERIMENTAL
Phosphorus was diffused into
earmarked for characterization of phosphosilicate glass (PSG) grown during diffusion and the other for evaluation of the diffused profile. The PSG parameters of interest are its thickness X0 and the phosphorus concentration at the PSG surface, Co (Fig. 1). The value of X0 was determined by etching a linear step in the PSG using photolithography and by measuring the step height with a Varian A scope, Model 960-4020. The average phosphorus concentration in the PSG was estimated from the etch rate of the PSG inp-etch[9,11]. This etch rate was found to vary from 4.3 A/set for samples diffused at 1250°C to 8.55 A/set for those diffused at 950°C. The average phosphorus concentration thus estimated for each case was taken as an approximate value for Co. This is justified since the phosphorus distribution in PSG grown during the deposition process from a POCIJ source has been observed to be box type[l2]. The diffused profile in silicon was determined by the incremental-sheet-resistivity method[ 131. A circular mesa of 250mil diameter was etched on the diffused sample using photolithography. The depth distribution of the sheet resistivity was determined by taking mesurements on this mesa using a four-point probe (25 mil spacing, K and S make) after successive removal of thin layers (244 A) of silicon by anodic oxidation. The anodic oxidation cell used was similar to the one reported by Ryssel et al. [14]. The electrolyte was 0.08 N solution of KNO, in ethylene glycol with 4% water[4,15,16]. The measured sheet resistivity versus depth data were first smoothed using the cubic spline approximation[l7]. The majority carrier (hence phosphorus) distribution was then computed using the mobility versus impurity concentration expression reported by Antoniadis et al. [18]. The values of A and Dz were computed by numerically solving eqn (3) for A and D2 at two points on the experimental profile. The value of 6 was calculated from eqn (4a) with m = 10. 4. RESULTS
AND DISCUSSION
In Fig. 2 the surface concentrations obtained for diffusions at 950°C have been ,plotted against diffusion time. It is seen that for diffusion times greater than 4 = 00 hr, the surface concentration is almost constant. This indicates that the assumption of parabolic DSG growth as also of boundary condition (ii) are good approximations for diffusion time greater than 4 hr. Since at higher temperatures, the thermal oxide growth in dry O2 tends to be dominantly parabolic, it appears reasonable to assume that for comparable DSG thickness, the PSG growth is parabolic at temperatures greater than 950°C. The sheet resistivity, impurity profile and eqn (3) for calculated values of A and D2 are plotted in Figs. 3 and 4 for the typical diffusion runs at 1150 and 95O”C, respectively. An excellent agreement between the theoretical and experimental profile further
Low-temperature
diffusion by ambient control
921 Samplr no. * -0AS TOmp. . sso*c
10’9
-
-Theory
104
x Eapwimont
6
0
6
IiT ‘E u ii
i
2-
8
1 10’61
’ 10
’ 2
’
’
““1’
4
6
’ 610’
Diffusion
’
’
2
time
’ “1”’ 4
6
10’86- -
0 810’
%
6-
(min) 4
4-
Fig. 2. Variation of surface concentration with diffusion time at 950°C.
i 0
2
justifies the application of the theoretical model described in Sec. 2. The value of A (-A ‘), which is approximately equal to the surface concentration, is plotted against temperature in Fig. 5 with the values of X0, S and F, specified for each point. It is seen that for the same diffusion ambient (and approximately the same PSG composition) the surface concentration varies over two orders of magnitude in the temperature range 95~1250°C. In accordance with eqn (4), the surface concentration is observed to have a strong dependence on 6 and a much weaker dependence on the
2
0 1
4
I Dirtonco form surface (a)
Fig. 4. Sheet resistivity and phosphorus distribution silicon. Diffusion time 15 hr.
ratio of PSG thickness to impurity diffusion length in silicon. Since D, also varies with PSG composition[lO], It is possible to vary 6 over a wide range by changing the ratio of the partial pressures
x,.0.2666
-2
I - 1.66 i, = 13.21
lo-
104
E
_4
3
-2
f .z 0 .10’ 8
-6
_
/
6
-6 -
I
pm
6
-6
_
in
g 8 z cn
F, ‘34.92
6 t 4
/
-4
r,=0.213Spm 8
2
‘2.42
F, -54.16 -2 I
‘“‘zo loo
120130
I
1
1.0
6.0 104/T
I 6.
(K)
Distance from surfacr (w)
Fig. 3. Sheet resistivity and phosphorus distribution in silicon. Diffusion time 3 hr.
Fig. 5. Variation of surface concentration with temperature and F’SG growth rate. Diffusion times are 1,3,6 and 15 hr at 1250, 1150, 1050 and 95OT, respectively.
A. K. GUPTAand M. S. TYAGI
928 1250%
10-i
!-
I
116oT
1050*c
I I 0 Eapwimentol
950%
x Normolired 6643-
7
2-
r
film formation takes place simultaneously with diffusion of phosphorus, and the estimated activation energy of the diffusion coefficient, therefore, may be expected to correspond to the combination of the two processes, while in the latter case it essentially refers to the diffusion of dopant in PSG. The method described above is essentially a variation of the commonly used open-tube diffusion process. Although a gaseous source was used in the experiments, it is possible to extend this method to liquid-dopant sources such as POCl,. Acknowledgement-One of the authors, A. K. Gupta, is grateful to Dr. J. Narain for useful suggestions during the experimental work. REFERENCES
I
'Cl.0
I
1.0
I I 6.0 a2
lO’/T(K)
Fig. 6. Phosphorus diffusion coefficient in PSG.
of oxygen and dopant in the diffusion ambient. It is thus possible to vary the surface concentration, by this process, from very low levels to the solidsolubility limit of the impurity in silicon. The value of S in Fig. 5 is observed to decrease with temperature. For the assumed parabolic growth of PSG (X0 = @), the value of D, has been calculated and plotted in Fig. 6. The estimated values of D1 correspond to PSGs with Pro, concentration varying from 3.0 mole % at 1250°C to 5.4 mole % at 950°C. These data are normalized for PSG containing 4.0mole % Pro, on the basis that D, is directly proportional to the P,Os concentratioin in PSG[lO]. The activation energy of D, thus normalized is determined to be 1.17 eV which is significantly lower than the corresponding value (1.41.6 eV) reported in literature[&lO]. This discrepancy is attributed mainly to the difference in the nature of the experiments. The values reported in the literature correspond to the PSG formed by diffusion of P,Os in thermally grown SiOr while in the present experiments the PSG of approximately uniform composition was grown during the diffusion process. In the former case the PSG
1. R. P. Lever and H. M. Demsky, IBM J. Res. Dev. 1% 40 (1974). 2. R. N. Ghoshtagore, Solid-St. Electron. 15, 1113 (1972). 3. M. L. Barry and P. Olofsen, Solid-St. Technol. 11, 39 (1968). 4. R. N. Ghoshtagore, Solid-St. Electron. 17, 1065 (1974). 5. H. Maes, W. Vandervorst and R. Van Overstraeten, in Impurity Doping Processes in Silicon (Edited by F. F. Y. Wang), p. 444. North-Holland, Amsterdam (1981). 6. A. K. Gupta, On the Phosphorus Diffusion in Silicon in Oxidising and Chloro-oxidising Ambients, Ph.D. thesis, I. I. T. Kanpur, 1984. 7. A. S. Grove, 0. Ixistiko Jr. and C. T. Sah, J. Appl. Phys. 35, 2695 (1964). 8. C. T. Sah, H. Sellow and D. A. Tremere, J. Phys. Chem. Solids 11, 288 (1959). 9. J. M. Eldridge, P. Balk, Trans. Metall. Sot. AZME 242, 539 (1968). 10. R. N. Ghostagore, Solid-St. Electron. 18, 399 (1975). 11. W. A. Pliskin and R. P. Gnall, J. Electrochem. Sot. 111, 872 (1964). 12. I. Franz and W. Langheinrich, Solid-St. Electron. 11, 987 (1968). 13. R. P. Donovan and R. A. Evans, in Silicon Device Processing, U.S. National Bureau of Standards Special Publn. No. 123 (1970). 14. H. Ryssel, K. Sehmid and H. Muller, J. Phy. E: Sci. Znstr. 6, 492 (1973). 15. H. D. Barber, H. B. Lo and J. E. Jones, J. Efectrochem. Sot. 123, 1404 (1976). 16. G. C. Jain, A. Prasad and B. C. Chakravarty, J. Electrochem. Sot. 126, 89 (1979). 17. N. D. Arora, D. J. Roulston and S. G. Chamberlain, Solid-St. Electron. 25, 965 (1982). 18. D. A. Antoniadis, A. G. Gonzalez and R. W. Dutton, J. Efectrochem. Sot. 125, 813 (1978).