- Email: [email protected]
Comment on Hill and Coleman's single high frequency approximation for interface state density determination
%7
Notes tive of the function and has the advantage that it requires less function evaluation per iterative step as compared to the Newton method. Thus, using eqns (2) and (3) one can easily calculate the concentration N as a function of distance x. The computer program used to determine the concentration profile from sheet resistance data, using eqns (2) and (3), is available from the authors on request. EXPERMENTALaRESUL.TS As discussed earlier, n+-diffused samples on p-substrates with (100)orientation were used to measure the profile of the diffused layer. For the profiling work, repeated anodization was carried out at a preset voltage of 60V corresponding to silicon oxide removed between successive runs of 280+ 5 A. About 40 layers of the silicon were stripped during the measurement process. The resulting surface resistivity data were then processed through the computer profiling program discussed earlier. The results are shown in Fig. 2 by dots. The profile was also calculated from the known time and temperature of diffusion using the SUPREM 11[13]computer program. The profile thus calculated is shown by a continuous line which is not very different from the experimental profile. This validates the procedure used for profiling the diffused layer from the measured sheet resistance data. Acknowledgment-The authors express their gratitude to Prof. J. R. Ord of the Physics Department for his help in the measurement of oxide thickness using his computerised ellispometric ton leave from Solid State Physics Laboratory, Lucknow Road, Delhi, 110007,India.
Solid-Slole Electronics Vol. 25, No. 9, pp. %7-W, Printed in that Britain.
setup. The authors also thank Roger Grant for the fabrication of the samples. N. D. hort.At D. J. ROUSTON S. G. CHAMBERLAIN
Deparimenf of Elecfrical Engineering, Universityof Warerloo, Waterloo, Ontario, Canada N2L3GI REFERENCES
1. P. J. Severin, Phil. Res. Rep. 26,359 (1971). 2. C. Van Opdrop, So/id-St Electron. 11, 397 (1%8). 3. J. C. C. Tsai, Proc. IEEE 57, 1499(1%9). 4. H. D. Barber, H. B. Lo and J. E. Jones, J..Electrochem. Sot. 123, 1404(1976). 5. J. L. Ord. Surface Science 16. 155(1%9). 6. G. C. ia&, A.‘Prasad and B. c. Ch‘akraiarty, J. Electrochem Sot. 1X,89 (1979). 7. A. Manara, P. Ostidich, G. Pedroli and G. Restelli, Thin Solid Films 8,359 (1971). 8. R. A. Evans and R. P. Donovan, Solid-St. Electron. 10, 155 (1%7). 9. P. Craven and G. Wahda, Numer. Math 31,377 (1979). 10. J. Ahlberg, E. Nilsom and J. Walsh, Theory of Spline and Their Applications. Academic Press, New York (1%7). 11. N. D. Arora, J. R. Hauser and D. J. Roulston, Trans. IEEE Electron Lkv. ED-29, 292 (1982). 12. K. M. Brown, Siam .I. Num Analv. 6,560 (1%9). 13. D. A. Antoniadis and R. W. D&on, IEEE J.’ Solid Stare Circuits SC-13,412 (1979).
~384I01/82l09096742$0340l0 PergamonPressLtd.
1982
COMMENT ON HILL AND COLEMAN’S SINGLE HIGH FREQUENCY APPROXIMATION FOR INTERFACE STATE DENSITY DETERMINATION (Received 8 October 1981)
Hill and Coleman[l], hereafter referred as H.C., have developed a single hi frequency method for obtaining surface state density at the insulator-semiconductor interface. For this G-V and corresponding C-V characteristics at a single high frequency are measured. Usually the G-V curve goes through a maximum. The sharpness of the maximum increases with frequency. These authors have obtained condition for the maximum in G-V curve and have tried to correlate the parallel substrate conductance (G,) value of the system corresponding to the measured maximum conductance (G,,,,d value with the corresponding maximum value of G. obtained from G$o vs o curve-a parameter used for surface state density technique developed by Nicollian and Goetzberger[2]. H.C. in their approximate formulation employed single time constant (7). This has been taken to be dependent on the gate voltage via surface potential (k) as 7 = (C.n,)-’ exp (- q$JkT).
(1)
The present authors were interested to use the H.C. method for estimating the surface-state-density in their devices. While examining their method, rather critically, the present authors have detected some serious mistakes in the derivation of the condition for maximum G,,,. The purpose of the present com-
munication is to point out these mistakes so that the workers in this field may not be misled. H.C. using the equivalent diagram and total MOS impedance (2,) given by Nicollian and Goetzberger[2] obtained expressions for the measured admittance (I’,,,) and measured conductance (G,). Both expressions of Y, and G,,, of H.C. are in error. As a result the corresponding expressions of the partial derivatives i.e. (aG,,,/aG,) and (aG,,,/X,) also need corrections. The correct expression in the notations used by H.C. are as,
y = ~*G,Ck +joCoJG~ + o*C,(C, + Cd G: o'(C, C,,p 111
t
G,,, =
02G,C& G,‘+
8G -AL=
ac,
(3)
o*(C, t C,,J2
t G,A2ac,=02C&[02(C. 80,
(2)
t
G:]
b2(C,+ Cd + CT2
- 02G,C&[202(C, + C,)] [or’(C,t C,,)z + G:12
(4)
(5)
Notes
%8
The expressions for (dG,/dr) and (dCJdr) would remain unchanged. For G,,, to be maximum
which yields [o’(C, t C&*- G,z](l- w2r8)+4G,(C, + C,,)o*T= 0
(6)
G$o, at G,, mu _ 2(C0X+ C, + C,,)(C,, + C,) - (Cl, + CD)*+ (Crl, + Co + C,,P (Gjo),,
(8)
where o,,, is the angular frequency at which G,,, is measured and o is the frequency at which Gjo is maximum in Gjo vs o curve of Nicollian and Goetzberger technique. Although accidentally, the conclusions drawn by H.C. still remain valid since the ratio obtained from eqn (8) is nearly equal to unity if C,, is small. REFERENCES
leading to “7
=
1+ C”,(C, t C&.
(7)
1. W. A. Hill and C. C. Coleman, J. Solid St. EZectron.23, 987 (1980). 2. E. H. Nicollian and A. Goetzberaer. Bell. Svsf. Tech. J. 46. 1055(1%7). I
This condition for G,,,,., obtained by H.C. is different and needs correction. The ratio of [GJo,,, at G, ,881 and [(GAO),, = G/21 can be obtained as
Department of Physics Banaras Hindu University Vamnasi-221005, India
Solid-SIateElectronicsVol. 25. No. 9, pp. %8-!770,1982 Printedin Gnat Britain.
J. P. SINGH R. S. SRIVASTAVA
003~1101/82M968-O3803.00/0 Perpmoo Press Ltd.
MEASUREMENTS OF THE THICKNESS OF THIN OXIDE FILMS AND THIN NITRIDE FILMS ON SILICON BY INFRA-RED ABSORPTION (Received 23 January 1981; in revised form 25 September 1981) INTRODUCTION
It has been necessary for us to measure the thickness (in the range lOM,OMlA”) of thin tiims of silicon oxide grown on single crystal slices of silicon. In silicon dioxide there is a strong lattice absorption band in the i&a-red at a wave-number of approx. 1,064cm-’ (or wave-length 9.4 pm). We believed that it would be possible to estimate the thickness of the oxide fdms by measuring the transmission (and hence the absorption) in this region of wave-number, in which silicon itself is transparent. Dial, et al. [l] have discussed similar measurements on silicon dioxide and Pliskin and Lehman[2] have shown that infra-red measurements can be very useful in evaluating the quality of silicon dioxide films. In the present work measurements have been made on films of silicon dioxide in the thickness range 80-6,OOtJ A” which includes thinner films than those previously studied by Dial et al. We have also applied the Ma-red absorption method to silicon nitride (SisN,). -AL. DEML-S The Iilms were grown by oxidising both sides of thin, polished silicon discs [P-type, thickness 270 pm, with faces perpendicular to the (111) direction], in an atmosphere of oxygen and steam. The temperature of oxidation was usually 800°Cand the duration of the process varied from 5-105min; for the thickest Iihns a temperature of 1,loo”C was used. Two methods of measuring or comparing thicknesses of the oxide layers were used; briefly, the two methods are (a) by using an ellipsometer, as described by Archer [3] and (b) by measuring the transmission of the SiO,Si-SiO, disc at a wave-number of l,O64cm-’ (Fig. 1). If values of the absorption constant (a) are known, the thickness of the Si02 films can be estimated. For the measurement of transmission through the oxidised silicon slices we have used a double beam Infra-red Spectrophotometer, Perkin Elmer type SP 521, in the wave-number range 1,7OO&NJcm-‘.In this range there are absorption bands associated with Si-0 bonds and arising from the fundamental vibrations of SiO, tetrahedra (Izawa et al. [4]) at approx. 1,064,
460 and 796cm-’ in that order of strength. Some of the transmission spectra obtained are shown in Fig. 1. Multiple reflections within a parallelsided slice of silicon cause an interference effect and lead to the sinusoidal appearance of the trace in some regions of wave-number. The effect is not exhibited by every specimen and it is assumed that in such cases the sides of the specimen are not perfectly parallel. In the reference beam of the Spectrophotometer we used normally (a) a semi-transparent grid and occasionally (b) a polished silicon slice identical to the original silicon samples without oxidation treatment. By procedure (b) any effect due to oxygen within the silicon slice in the sample beam could be eliminated from the recorded signal. However since each silicon slice, not deliberately oxidised, wig be covered normally by a thin, stable layer ( - 30 A”) of “native” oxide grown in the normal room atmosphere, allowance must be made for this oxide layer on the reference sample when procedure (b) is adopted. RESULTS ANDDIsCUsSlON In the present investigation we have used mainly the band at 1$64cm-’ for making sign&ant measurement8 of “t”. In order to estimate “t” from the absorption due to SiO, we have to know the transmission fraction with and without absorption. We have used the simple formula for the intensity (I) of the transmitted beam Z = I,,.R.exp (- 2at)
(1)
where Z, is the incident intensity, R allows for reflection losses at the four interfaces and a is the absorption coefficient of Si02 at 1,064cm-‘; in this case the total thickness of the oxide iibns is “21” (one film on each side of the silicon). For SiO, we have taken Z,R as the value of the sianal at wave-number 1,700cm-‘, where ihere is no absorption. Irt Fig. 2(a) measured values of (Z/Z$) for samples of SiO,-Si-SiO, are shown as a function of “t”‘, where “t”’ is the thickness of each Si9 layer as measured by means of the ellipsometer; the samples to which Fig. 2(a) applies were all oxidised for dierent times. For comparison
Notes tive of the function and has the advantage that it requires less function evaluation per iterative step as compared to the Newton method. Thus, using eqns (2) and (3) one can easily calculate the concentration N as a function of distance x. The computer program used to determine the concentration profile from sheet resistance data, using eqns (2) and (3), is available from the authors on request. EXPERMENTALaRESUL.TS As discussed earlier, n+-diffused samples on p-substrates with (100)orientation were used to measure the profile of the diffused layer. For the profiling work, repeated anodization was carried out at a preset voltage of 60V corresponding to silicon oxide removed between successive runs of 280+ 5 A. About 40 layers of the silicon were stripped during the measurement process. The resulting surface resistivity data were then processed through the computer profiling program discussed earlier. The results are shown in Fig. 2 by dots. The profile was also calculated from the known time and temperature of diffusion using the SUPREM 11[13]computer program. The profile thus calculated is shown by a continuous line which is not very different from the experimental profile. This validates the procedure used for profiling the diffused layer from the measured sheet resistance data. Acknowledgment-The authors express their gratitude to Prof. J. R. Ord of the Physics Department for his help in the measurement of oxide thickness using his computerised ellispometric ton leave from Solid State Physics Laboratory, Lucknow Road, Delhi, 110007,India.
Solid-Slole Electronics Vol. 25, No. 9, pp. %7-W, Printed in that Britain.
setup. The authors also thank Roger Grant for the fabrication of the samples. N. D. hort.At D. J. ROUSTON S. G. CHAMBERLAIN
Deparimenf of Elecfrical Engineering, Universityof Warerloo, Waterloo, Ontario, Canada N2L3GI REFERENCES
1. P. J. Severin, Phil. Res. Rep. 26,359 (1971). 2. C. Van Opdrop, So/id-St Electron. 11, 397 (1%8). 3. J. C. C. Tsai, Proc. IEEE 57, 1499(1%9). 4. H. D. Barber, H. B. Lo and J. E. Jones, J..Electrochem. Sot. 123, 1404(1976). 5. J. L. Ord. Surface Science 16. 155(1%9). 6. G. C. ia&, A.‘Prasad and B. c. Ch‘akraiarty, J. Electrochem Sot. 1X,89 (1979). 7. A. Manara, P. Ostidich, G. Pedroli and G. Restelli, Thin Solid Films 8,359 (1971). 8. R. A. Evans and R. P. Donovan, Solid-St. Electron. 10, 155 (1%7). 9. P. Craven and G. Wahda, Numer. Math 31,377 (1979). 10. J. Ahlberg, E. Nilsom and J. Walsh, Theory of Spline and Their Applications. Academic Press, New York (1%7). 11. N. D. Arora, J. R. Hauser and D. J. Roulston, Trans. IEEE Electron Lkv. ED-29, 292 (1982). 12. K. M. Brown, Siam .I. Num Analv. 6,560 (1%9). 13. D. A. Antoniadis and R. W. D&on, IEEE J.’ Solid Stare Circuits SC-13,412 (1979).
~384I01/82l09096742$0340l0 PergamonPressLtd.
1982
COMMENT ON HILL AND COLEMAN’S SINGLE HIGH FREQUENCY APPROXIMATION FOR INTERFACE STATE DENSITY DETERMINATION (Received 8 October 1981)
Hill and Coleman[l], hereafter referred as H.C., have developed a single hi frequency method for obtaining surface state density at the insulator-semiconductor interface. For this G-V and corresponding C-V characteristics at a single high frequency are measured. Usually the G-V curve goes through a maximum. The sharpness of the maximum increases with frequency. These authors have obtained condition for the maximum in G-V curve and have tried to correlate the parallel substrate conductance (G,) value of the system corresponding to the measured maximum conductance (G,,,,d value with the corresponding maximum value of G. obtained from G$o vs o curve-a parameter used for surface state density technique developed by Nicollian and Goetzberger[2]. H.C. in their approximate formulation employed single time constant (7). This has been taken to be dependent on the gate voltage via surface potential (k) as 7 = (C.n,)-’ exp (- q$JkT).
(1)
The present authors were interested to use the H.C. method for estimating the surface-state-density in their devices. While examining their method, rather critically, the present authors have detected some serious mistakes in the derivation of the condition for maximum G,,,. The purpose of the present com-
munication is to point out these mistakes so that the workers in this field may not be misled. H.C. using the equivalent diagram and total MOS impedance (2,) given by Nicollian and Goetzberger[2] obtained expressions for the measured admittance (I’,,,) and measured conductance (G,). Both expressions of Y, and G,,, of H.C. are in error. As a result the corresponding expressions of the partial derivatives i.e. (aG,,,/aG,) and (aG,,,/X,) also need corrections. The correct expression in the notations used by H.C. are as,
y = ~*G,Ck +joCoJG~ + o*C,(C, + Cd G: o'(C, C,,p 111
t
G,,, =
02G,C& G,‘+
8G -AL=
ac,
(3)
o*(C, t C,,J2
t G,A2ac,=02C&[02(C. 80,
(2)
t
G:]
b2(C,+ Cd + CT2
- 02G,C&[202(C, + C,)] [or’(C,t C,,)z + G:12
(4)
(5)
Notes
%8
The expressions for (dG,/dr) and (dCJdr) would remain unchanged. For G,,, to be maximum
which yields [o’(C, t C&*- G,z](l- w2r8)+4G,(C, + C,,)o*T= 0
(6)
G$o, at G,, mu _ 2(C0X+ C, + C,,)(C,, + C,) - (Cl, + CD)*+ (Crl, + Co + C,,P (Gjo),,
(8)
where o,,, is the angular frequency at which G,,, is measured and o is the frequency at which Gjo is maximum in Gjo vs o curve of Nicollian and Goetzberger technique. Although accidentally, the conclusions drawn by H.C. still remain valid since the ratio obtained from eqn (8) is nearly equal to unity if C,, is small. REFERENCES
leading to “7
=
1+ C”,(C, t C&.
(7)
1. W. A. Hill and C. C. Coleman, J. Solid St. EZectron.23, 987 (1980). 2. E. H. Nicollian and A. Goetzberaer. Bell. Svsf. Tech. J. 46. 1055(1%7). I
This condition for G,,,,., obtained by H.C. is different and needs correction. The ratio of [GJo,,, at G, ,881 and [(GAO),, = G/21 can be obtained as
Department of Physics Banaras Hindu University Vamnasi-221005, India
Solid-SIateElectronicsVol. 25. No. 9, pp. %8-!770,1982 Printedin Gnat Britain.
J. P. SINGH R. S. SRIVASTAVA
003~1101/82M968-O3803.00/0 Perpmoo Press Ltd.
MEASUREMENTS OF THE THICKNESS OF THIN OXIDE FILMS AND THIN NITRIDE FILMS ON SILICON BY INFRA-RED ABSORPTION (Received 23 January 1981; in revised form 25 September 1981) INTRODUCTION
It has been necessary for us to measure the thickness (in the range lOM,OMlA”) of thin tiims of silicon oxide grown on single crystal slices of silicon. In silicon dioxide there is a strong lattice absorption band in the i&a-red at a wave-number of approx. 1,064cm-’ (or wave-length 9.4 pm). We believed that it would be possible to estimate the thickness of the oxide fdms by measuring the transmission (and hence the absorption) in this region of wave-number, in which silicon itself is transparent. Dial, et al. [l] have discussed similar measurements on silicon dioxide and Pliskin and Lehman[2] have shown that infra-red measurements can be very useful in evaluating the quality of silicon dioxide films. In the present work measurements have been made on films of silicon dioxide in the thickness range 80-6,OOtJ A” which includes thinner films than those previously studied by Dial et al. We have also applied the Ma-red absorption method to silicon nitride (SisN,). -AL. DEML-S The Iilms were grown by oxidising both sides of thin, polished silicon discs [P-type, thickness 270 pm, with faces perpendicular to the (111) direction], in an atmosphere of oxygen and steam. The temperature of oxidation was usually 800°Cand the duration of the process varied from 5-105min; for the thickest Iihns a temperature of 1,loo”C was used. Two methods of measuring or comparing thicknesses of the oxide layers were used; briefly, the two methods are (a) by using an ellipsometer, as described by Archer [3] and (b) by measuring the transmission of the SiO,Si-SiO, disc at a wave-number of l,O64cm-’ (Fig. 1). If values of the absorption constant (a) are known, the thickness of the Si02 films can be estimated. For the measurement of transmission through the oxidised silicon slices we have used a double beam Infra-red Spectrophotometer, Perkin Elmer type SP 521, in the wave-number range 1,7OO&NJcm-‘.In this range there are absorption bands associated with Si-0 bonds and arising from the fundamental vibrations of SiO, tetrahedra (Izawa et al. [4]) at approx. 1,064,
460 and 796cm-’ in that order of strength. Some of the transmission spectra obtained are shown in Fig. 1. Multiple reflections within a parallelsided slice of silicon cause an interference effect and lead to the sinusoidal appearance of the trace in some regions of wave-number. The effect is not exhibited by every specimen and it is assumed that in such cases the sides of the specimen are not perfectly parallel. In the reference beam of the Spectrophotometer we used normally (a) a semi-transparent grid and occasionally (b) a polished silicon slice identical to the original silicon samples without oxidation treatment. By procedure (b) any effect due to oxygen within the silicon slice in the sample beam could be eliminated from the recorded signal. However since each silicon slice, not deliberately oxidised, wig be covered normally by a thin, stable layer ( - 30 A”) of “native” oxide grown in the normal room atmosphere, allowance must be made for this oxide layer on the reference sample when procedure (b) is adopted. RESULTS ANDDIsCUsSlON In the present investigation we have used mainly the band at 1$64cm-’ for making sign&ant measurement8 of “t”. In order to estimate “t” from the absorption due to SiO, we have to know the transmission fraction with and without absorption. We have used the simple formula for the intensity (I) of the transmitted beam Z = I,,.R.exp (- 2at)
(1)
where Z, is the incident intensity, R allows for reflection losses at the four interfaces and a is the absorption coefficient of Si02 at 1,064cm-‘; in this case the total thickness of the oxide iibns is “21” (one film on each side of the silicon). For SiO, we have taken Z,R as the value of the sianal at wave-number 1,700cm-‘, where ihere is no absorption. Irt Fig. 2(a) measured values of (Z/Z$) for samples of SiO,-Si-SiO, are shown as a function of “t”‘, where “t”’ is the thickness of each Si9 layer as measured by means of the ellipsometer; the samples to which Fig. 2(a) applies were all oxidised for dierent times. For comparison