- Email: [email protected]
1f Noise in silicon diodes
NOTES T e m p e r a t u r e effects can be explained by considering the b o u n d a r y states distribution and the F e r m i level position at the grain boundaries [9]. At low temperatures the F e r m i level at the boundaries rises, and the grain b o u n d a r y b e c o m e s less p-type, increasing b r e a k d o w n voltages. At 77°K a currentsaturated region appears under forward voltage, meaning holes are drifted with a scattering-limited velocity, and is followed by a double-injection negative resistance. W e may conclude that the b e h a v i o u r of P - I - N diodes in polycrystalline-silicon is dominated by the acceptor-like b o u n d a r y states at low currents, both forward and reverse. At high current densities double injection and impact ionization cause filamentary-like characteristics, with negative resistaflce and nearly constant voltage regions clearly present. Present devices, properly tailored, could be used as low-price varistors.
Acknowledgement--We wish to thank Prof. F. Rueda for his assistance and encouragement during the course of the present work. J. P. MONICO-GARCfA E. MUlqOZ-MERINO Laboratorio de Ffsica Aplicada, Departamento de Ffsica, Universidad Aut6noma de Madrid, Canto Blanco, Madrid, Spain. REFERENCES 1. K. E. Bean, P. Mentzchel and C. Colman, Semiconductor Silicon, Electrochem. Soc., New York (1969). 2. C. C. Mai, T. S. Whitehouse, R. C. Thomas and D. R. Goldstein, J. Electrochem. Soc. 18, 331 (1971). 3. T. I. Kamins, Solid-St. Electron. 15, 789 (1972). 4. J. D. Joseph and T. I. Kamins, Solid-St. Electron. 15, 355 (1972). 5. J. Manoliu and T. I. Kamins, Solid-St. Electron. 15, 1103 (1972). 6. E. Mufioz-Merino, Phys. Status. Solidi. (a) 15, K167 (1973). 7. I. Melngailis and A. G. Milnes, J. appl. Phys. 33, 995 (1962). 8. Williardson and Beer, (Eds.) Semiconductors and Semimetals, Vol. 6, pp. 141-200, Academic Press, New York (1970). 9. E. Mufioz, J. M. Boix, J. Llabr6s, J. P. M6nico and J. Piqueras, Solid-St. Electron. In press.
1517
Solid-State Electronics, 1973, Vol. 16, pp. 1517-1520. Pergamon Press. Printed in Great Britain
1/f Noise in silicon diodes* (Received 30 May 1973) THE g e n e r a t i o n - r e c o m b i n a t i o n noise is a well k n o w n p h e n o m e n o n [ I , 2 ] . The intensity of this noise is proportional to the square of the direct current AIo~ ~ • I02. The generation-recombination noise is a white noise up to a f r e q u e n c y of
f0 = 21% w h e r e To is the characteristic time constant of the centers. The shot noise occurs w h e n the electrons do not recombine, but migrate to the electrodes [2]. This is the case w h e n e v e r e l e c t r o n - h o l e pairs are generated in a space charge region of a reverse biased pn-junction. The shot noise is simply proportional to the direct current
l[f noise can be obtained by a distribution of time constants b e t w e e n two limits, which are related to f r e q u e n c i e s [1, 3]. T h e r e are several models. But up to n o w all theories concerning the 1/f noise show certain weaknesses. The tunneling model [5-7] and the modulation model [8-10] are discussed in a previous paper [4]. The tunneling model cannot be valid in general, because 1/f noise exists in devices and materials without an oxide layer. 1/f noise is m e a s u r e d in carbon resistors [11], ZnO-crystals [12], e v a p o r a t e d gold layers[13,14], platinum wires[15], and on atomically clean silicon[16] and germanium[17]
*Formerly presented at the Symposium on Noise in Electronic Materials and Devices, Galnesville, Florida, USA, Dec. 10-11, 1972. This work was supported by the technological program of the Federal Department of Education and Science of the FRG.
1518
NOTES
surfaces, l/f noise is a surface phenomena[18, 19], but it has also been observed in a boundary in the bulk of a GaAs-transistor [20], and furthermore it is shown that there is a discrepancy b e t w e e n the upper f r e q u e n c y limit of 1/f noise and the measured time constants of the surface states [4]. Schottky [21], van Vliet and van der Ziel [22] h a v e already p r o p o s e d that diffusing particles are responsible for 1If noise. H o w e v e r , the temperature independence of the upper f r e q u e n c y limit of 1/f noise [4] is an unsuitable result for the modulation model if there is assumed an activated diffusion of water molecules or ions on the surface. On the other hand, the modulation model may be applicable if there is supposed a quantummechanical transport of particles which also means a tunneling process. But, in this case, the transport has to be along the surface, in the interface or in a boundary in the bulk and not perpendicular to it. Lucas et a/.[23], E v a n s et al.[24] and Sak[25] have shown that electrons interact with surface phonons to f o r m surface polarons. The presence of surface phonons has been experimentally p r o v e n by Ibach [26]. Popp and Murray [27] have experimentally
shown that small v o l u m e polarons have mobilities down to lO ~°cmE/Vsec. H o w e v e r there is no reason w h y surface polarons may not also have such low mobilities, since all surfaces and interfaces are polarised e v e n for non-polar materials. If the modulation model should be correct, a mobility of the order of /.t -~ 10 9 cm 2 Vsec is necessary [4]. A low temperature d e p e n d e n c e occurs w h e n the polarons show a band conduction and no hopping process [28]. Figure 1 shows the noise current as a function of the reverse current measured in alloyed silicon diodes [29]. The f r e q u e n c y of 250 H z is in the region of the 1If noise. As expected, the noise intensity is proportional to the square of the reverse current, or the noise current is proportional to the reverse current itself [30]. A b o v e the l/f law at a f r e q u e n c y of 100kHz, h o w e v e r , a direct proportionality of the noise intensity to the reverse current is obtained. Yet, this direct proportionality is the d e p e n d e n c e of the shot noise.
2 5 0 Hz
×~~: Lo Z
03
I 0.4
I 0.5
I 06
I 0'7
Reverse current,
I 08
I 09
I I
2
p.A
Fig. 1. Noise current as a function of the reverse current of an alloyed silicon diode in the region of 1/f noise at 250 Hz and in the shot noise region at 100 kHz.
NOTES
1519
I ~-,
I0 ~
~,
10 2
Shot noise
_g .E ~
I0 ~ Generation recombination
noise
7r I I01
I rO z
I 10 3 I I
1 10 4
t 10 5
10 6 i I
f~o~ ~ lOS Hz
fo ~ IOSHz
Frequency,
Hz
Fig. 2. Schematic diagram spectral noise intensity of the alloyed silicon diodes. The generation-recombination noise corresponds to the measured time constant Zo. The 1If noise and the shot noise are observed experimentally. T h e situation is s h o w n in t h e s c h e m a t i c d i a g r a m (Fig. 2). T h e s u r f a c e s t a t e s g e n e r a t e t h e r e v e r s e c u r r e n t a n d t h e y h a v e a m e a s u r e d t i m e c o n s t a n t [4] in t h e m a g n i t u d e of 10 7sec. T h e g e n e r a t i o n r e c o m b i n a t i o n noise d r a w n w i t h a c h a r a c t e r i s t i c f r e q u e n c y of 106 H z w o u l d fit this t i m e c o n s t a n t of the s u r f a c e states. B u t t h e m e a s u r e m e n t s a c c o r d i n g to Fig. 1 give a shot noise, since a l t e r n a t e l y elect r o n s a n d h o l e s are e m i t t e d at r a n d o m . T h e r e is n o g e n e r a t i o n - r e c o m b i n a t i o n noise. T h i s n o i s e m a y b e s o m e w h a t s u p p r e s s e d , if t h e c a r r i e r s d o n o t t r a v e l t h e full d i s t a n c e of t h e s p a c e c h a r g e r e g i o n at low v o l t a g e s [31]. S i n c e n o t only t h e s h o t n o i s e b u t also t h e I / f noise comes from the reverse current, and hence f r o m t h e s u r f a c e states, it is m o s t r e a s o n a b l e to a s s u m e a slow m o d u l a t i o n of t h e g e n e r a t i o n rate of t h e c e n t e r s b y o n e of t h e m e c h a n i s m alluded to in this paper.
Acknowledgement--The authors wish to thank Professor E. Mollwo, Dr. Deuling and Dr. Birkholz for valuable discussions. Research Laboratories, Siemens AG, Erlangen, West Germany.
O. JA,NTSCH I. FEIGT
REFERENCES 1. A. van der Ziel, Fluctuation Phenomena in Semiconductors, Butterworths, London (1959). 2. H. Bittel and L. Storm, Rauschen, Springer, Berlin (1971). 3. M. Surdin, J. Physique Radium 12, 777 (1951). 4. I. Feigt and O. J~intsch, Solid-St. Electron. 14, 391 (1971). 5. A. L. McWhorter, Semiconductor Surface Physics pp. 169-196, Philadelphia (1957). 6. S. Christensson, I. LundstrSm and C. Svenson, SolidSt. Electron. 11, 797 (1968). 7. H. S. Fu and C. T. Sah, I E E E Trans. Electron. Devices ED-19, 273 (1972). 8. L. Bess, Phys. Rev. 103, 72 (1956). 9. O. Jfintsch, Solid-St. Electron. 11, 267 (1968). 10. K. M. van Vliet and R. R. Johnson, J. appL Phys. 35, 2039 (1964). 11. K. M. van Vliet, C. J. van Leeuwen, J. Blok and C. Ris, Physica 20, 481 (1954). 12. B. R. Russel, cited in K. M. van Vliet, Prec. IRE 46, 1004 (1958). 13. F. N. Hooge and A. M. H. Hoppenbrouwers, Physica 45, 386 (1969). 14. J. L. Williams and R. K. Burdett, 3". Phys. C 2, 298 (1969). 15. J. Bernamont, C.R. Acad. Sci., Paris 198, 1755 (1934). 16. A. U. Mac Rae, J. appl. Phys. 33, 2570 (1962). 17. R. L/iken, OberflficheneinfluB auf das l/f-Rauschen yon Germanium, Thesis, Braunschweig (1969). 18. C. T. Sah and F. H. Hielscher, Phys. Rev. Letts 17, 986 (1966). 19. S. T. Hsu, D. J. Fitzgerald and A. S. Grove, Appl. Phys. Letts 12, 287 (1968).
1520
NOTES
20. M. B. Colligan, Low Frequency Noise Characteristics of GaAs JFETs for Cryogenic Operation, Government Microelectronic Application Conference, San Diego (1972). 21. W. Schottky, Phys. Rev. 28, 74 (1926). 22. K. M. van Vliet and A. van der Ziel, Physica 24, 415 (1958). 23. A. A. Lucas, E. Kartheuser and R. G. Badro, Phys. Rev. B2, 2488 (1970). 24. E. Evans and D. I. Mills, Solid State Commun. 11, 1093 (1972). 25. J. Sak, Phys. Rev. B6, 3981 (1972). 26. H. Ibach, Phys. Rev. Letts. 27, 253 (1971).
27. R. D. Popp and R. B. Murray, J. Phys. chem. Solids 33, 607 (1972). 28. R. V. Baltz and U. Birkholz, Festk6rperprobleme, (edited by O. Madelung) Vol. XII, p. 233, Pergamon, Braunschweig (1972). 29. I. Feigt, Untersuchungen am l//-Rauschen yon legierten, sperrgepolten Siliziumdioden, Thesis, Erlangen (1972). 30. O. J~intsch and I. Feigt, Phys. Rev. Letts 23, 912 (1969). 31. P. O. Lauritzen, IEEE Trans. Electron. Devices ED-15, 770 (1968).
Acknowledgement--We wish to thank Prof. F. Rueda for his assistance and encouragement during the course of the present work. J. P. MONICO-GARCfA E. MUlqOZ-MERINO Laboratorio de Ffsica Aplicada, Departamento de Ffsica, Universidad Aut6noma de Madrid, Canto Blanco, Madrid, Spain. REFERENCES 1. K. E. Bean, P. Mentzchel and C. Colman, Semiconductor Silicon, Electrochem. Soc., New York (1969). 2. C. C. Mai, T. S. Whitehouse, R. C. Thomas and D. R. Goldstein, J. Electrochem. Soc. 18, 331 (1971). 3. T. I. Kamins, Solid-St. Electron. 15, 789 (1972). 4. J. D. Joseph and T. I. Kamins, Solid-St. Electron. 15, 355 (1972). 5. J. Manoliu and T. I. Kamins, Solid-St. Electron. 15, 1103 (1972). 6. E. Mufioz-Merino, Phys. Status. Solidi. (a) 15, K167 (1973). 7. I. Melngailis and A. G. Milnes, J. appl. Phys. 33, 995 (1962). 8. Williardson and Beer, (Eds.) Semiconductors and Semimetals, Vol. 6, pp. 141-200, Academic Press, New York (1970). 9. E. Mufioz, J. M. Boix, J. Llabr6s, J. P. M6nico and J. Piqueras, Solid-St. Electron. In press.
1517
Solid-State Electronics, 1973, Vol. 16, pp. 1517-1520. Pergamon Press. Printed in Great Britain
1/f Noise in silicon diodes* (Received 30 May 1973) THE g e n e r a t i o n - r e c o m b i n a t i o n noise is a well k n o w n p h e n o m e n o n [ I , 2 ] . The intensity of this noise is proportional to the square of the direct current AIo~ ~ • I02. The generation-recombination noise is a white noise up to a f r e q u e n c y of
f0 = 21% w h e r e To is the characteristic time constant of the centers. The shot noise occurs w h e n the electrons do not recombine, but migrate to the electrodes [2]. This is the case w h e n e v e r e l e c t r o n - h o l e pairs are generated in a space charge region of a reverse biased pn-junction. The shot noise is simply proportional to the direct current
l[f noise can be obtained by a distribution of time constants b e t w e e n two limits, which are related to f r e q u e n c i e s [1, 3]. T h e r e are several models. But up to n o w all theories concerning the 1/f noise show certain weaknesses. The tunneling model [5-7] and the modulation model [8-10] are discussed in a previous paper [4]. The tunneling model cannot be valid in general, because 1/f noise exists in devices and materials without an oxide layer. 1/f noise is m e a s u r e d in carbon resistors [11], ZnO-crystals [12], e v a p o r a t e d gold layers[13,14], platinum wires[15], and on atomically clean silicon[16] and germanium[17]
*Formerly presented at the Symposium on Noise in Electronic Materials and Devices, Galnesville, Florida, USA, Dec. 10-11, 1972. This work was supported by the technological program of the Federal Department of Education and Science of the FRG.
1518
NOTES
surfaces, l/f noise is a surface phenomena[18, 19], but it has also been observed in a boundary in the bulk of a GaAs-transistor [20], and furthermore it is shown that there is a discrepancy b e t w e e n the upper f r e q u e n c y limit of 1/f noise and the measured time constants of the surface states [4]. Schottky [21], van Vliet and van der Ziel [22] h a v e already p r o p o s e d that diffusing particles are responsible for 1If noise. H o w e v e r , the temperature independence of the upper f r e q u e n c y limit of 1/f noise [4] is an unsuitable result for the modulation model if there is assumed an activated diffusion of water molecules or ions on the surface. On the other hand, the modulation model may be applicable if there is supposed a quantummechanical transport of particles which also means a tunneling process. But, in this case, the transport has to be along the surface, in the interface or in a boundary in the bulk and not perpendicular to it. Lucas et a/.[23], E v a n s et al.[24] and Sak[25] have shown that electrons interact with surface phonons to f o r m surface polarons. The presence of surface phonons has been experimentally p r o v e n by Ibach [26]. Popp and Murray [27] have experimentally
shown that small v o l u m e polarons have mobilities down to lO ~°cmE/Vsec. H o w e v e r there is no reason w h y surface polarons may not also have such low mobilities, since all surfaces and interfaces are polarised e v e n for non-polar materials. If the modulation model should be correct, a mobility of the order of /.t -~ 10 9 cm 2 Vsec is necessary [4]. A low temperature d e p e n d e n c e occurs w h e n the polarons show a band conduction and no hopping process [28]. Figure 1 shows the noise current as a function of the reverse current measured in alloyed silicon diodes [29]. The f r e q u e n c y of 250 H z is in the region of the 1If noise. As expected, the noise intensity is proportional to the square of the reverse current, or the noise current is proportional to the reverse current itself [30]. A b o v e the l/f law at a f r e q u e n c y of 100kHz, h o w e v e r , a direct proportionality of the noise intensity to the reverse current is obtained. Yet, this direct proportionality is the d e p e n d e n c e of the shot noise.
2 5 0 Hz
×~~: Lo Z
03
I 0.4
I 0.5
I 06
I 0'7
Reverse current,
I 08
I 09
I I
2
p.A
Fig. 1. Noise current as a function of the reverse current of an alloyed silicon diode in the region of 1/f noise at 250 Hz and in the shot noise region at 100 kHz.
NOTES
1519
I ~-,
I0 ~
~,
10 2
Shot noise
_g .E ~
I0 ~ Generation recombination
noise
7r I I01
I rO z
I 10 3 I I
1 10 4
t 10 5
10 6 i I
f~o~ ~ lOS Hz
fo ~ IOSHz
Frequency,
Hz
Fig. 2. Schematic diagram spectral noise intensity of the alloyed silicon diodes. The generation-recombination noise corresponds to the measured time constant Zo. The 1If noise and the shot noise are observed experimentally. T h e situation is s h o w n in t h e s c h e m a t i c d i a g r a m (Fig. 2). T h e s u r f a c e s t a t e s g e n e r a t e t h e r e v e r s e c u r r e n t a n d t h e y h a v e a m e a s u r e d t i m e c o n s t a n t [4] in t h e m a g n i t u d e of 10 7sec. T h e g e n e r a t i o n r e c o m b i n a t i o n noise d r a w n w i t h a c h a r a c t e r i s t i c f r e q u e n c y of 106 H z w o u l d fit this t i m e c o n s t a n t of the s u r f a c e states. B u t t h e m e a s u r e m e n t s a c c o r d i n g to Fig. 1 give a shot noise, since a l t e r n a t e l y elect r o n s a n d h o l e s are e m i t t e d at r a n d o m . T h e r e is n o g e n e r a t i o n - r e c o m b i n a t i o n noise. T h i s n o i s e m a y b e s o m e w h a t s u p p r e s s e d , if t h e c a r r i e r s d o n o t t r a v e l t h e full d i s t a n c e of t h e s p a c e c h a r g e r e g i o n at low v o l t a g e s [31]. S i n c e n o t only t h e s h o t n o i s e b u t also t h e I / f noise comes from the reverse current, and hence f r o m t h e s u r f a c e states, it is m o s t r e a s o n a b l e to a s s u m e a slow m o d u l a t i o n of t h e g e n e r a t i o n rate of t h e c e n t e r s b y o n e of t h e m e c h a n i s m alluded to in this paper.
Acknowledgement--The authors wish to thank Professor E. Mollwo, Dr. Deuling and Dr. Birkholz for valuable discussions. Research Laboratories, Siemens AG, Erlangen, West Germany.
O. JA,NTSCH I. FEIGT
REFERENCES 1. A. van der Ziel, Fluctuation Phenomena in Semiconductors, Butterworths, London (1959). 2. H. Bittel and L. Storm, Rauschen, Springer, Berlin (1971). 3. M. Surdin, J. Physique Radium 12, 777 (1951). 4. I. Feigt and O. J~intsch, Solid-St. Electron. 14, 391 (1971). 5. A. L. McWhorter, Semiconductor Surface Physics pp. 169-196, Philadelphia (1957). 6. S. Christensson, I. LundstrSm and C. Svenson, SolidSt. Electron. 11, 797 (1968). 7. H. S. Fu and C. T. Sah, I E E E Trans. Electron. Devices ED-19, 273 (1972). 8. L. Bess, Phys. Rev. 103, 72 (1956). 9. O. Jfintsch, Solid-St. Electron. 11, 267 (1968). 10. K. M. van Vliet and R. R. Johnson, J. appL Phys. 35, 2039 (1964). 11. K. M. van Vliet, C. J. van Leeuwen, J. Blok and C. Ris, Physica 20, 481 (1954). 12. B. R. Russel, cited in K. M. van Vliet, Prec. IRE 46, 1004 (1958). 13. F. N. Hooge and A. M. H. Hoppenbrouwers, Physica 45, 386 (1969). 14. J. L. Williams and R. K. Burdett, 3". Phys. C 2, 298 (1969). 15. J. Bernamont, C.R. Acad. Sci., Paris 198, 1755 (1934). 16. A. U. Mac Rae, J. appl. Phys. 33, 2570 (1962). 17. R. L/iken, OberflficheneinfluB auf das l/f-Rauschen yon Germanium, Thesis, Braunschweig (1969). 18. C. T. Sah and F. H. Hielscher, Phys. Rev. Letts 17, 986 (1966). 19. S. T. Hsu, D. J. Fitzgerald and A. S. Grove, Appl. Phys. Letts 12, 287 (1968).
1520
NOTES
20. M. B. Colligan, Low Frequency Noise Characteristics of GaAs JFETs for Cryogenic Operation, Government Microelectronic Application Conference, San Diego (1972). 21. W. Schottky, Phys. Rev. 28, 74 (1926). 22. K. M. van Vliet and A. van der Ziel, Physica 24, 415 (1958). 23. A. A. Lucas, E. Kartheuser and R. G. Badro, Phys. Rev. B2, 2488 (1970). 24. E. Evans and D. I. Mills, Solid State Commun. 11, 1093 (1972). 25. J. Sak, Phys. Rev. B6, 3981 (1972). 26. H. Ibach, Phys. Rev. Letts. 27, 253 (1971).
27. R. D. Popp and R. B. Murray, J. Phys. chem. Solids 33, 607 (1972). 28. R. V. Baltz and U. Birkholz, Festk6rperprobleme, (edited by O. Madelung) Vol. XII, p. 233, Pergamon, Braunschweig (1972). 29. I. Feigt, Untersuchungen am l//-Rauschen yon legierten, sperrgepolten Siliziumdioden, Thesis, Erlangen (1972). 30. O. J~intsch and I. Feigt, Phys. Rev. Letts 23, 912 (1969). 31. P. O. Lauritzen, IEEE Trans. Electron. Devices ED-15, 770 (1968).