- Email: [email protected]
Recombination oscillations in Si P+PN+ structures at low temperature
NOTES Solid-SlnreEIecrronics
Pergamon Press 1971. Vol. 14, pp. 341-342. Printed in Great Britain
Recombination oscillations in Si P+PN+ structures temperature (Received
WE
at low
8 June 1970; in revisedform 14 September 1970)
HAVE observed relaxation oscillations well stabilized in amplitude and frequency in Si P+PN+ structures for high level double-injection in the low temperature range IO-25°K. These waves, investigated by use of microwave attenuation by carriers in the P region, show recombination phases which determine the frequency in agreement with a model previously proposed [ 11. In recent years, experiments have shown that semiconductors carrying space-charge limited current exhibit oscillations in a positive resistance region of the I.V. characteristic[2]. These oscillations occur in PIN, NIN, PIP structures which contain deep-level recombination centers. In Si PIN structures with double-carrier injection this effect has been reported with Au[3,4], Co[2,5], Zn[61 deep level compensating impurities: it appears that the charge condition of traps is fundamental for the oscillations and that the frequency is strongly dependent on the recombination kinetic of the i region[4,7]. The models proposed by Konstantinov et al.[8], BonchBruevich and Kalashnikov[9] and others involve recombination but do not require the existance of the space charge; they do not explain the oscillation mechanism. In a previous paper[l], referred as (I), we have proposed a model which takes into account the trapped part of the space charge on recombination centers and carrier recombination kinetic. With double-carrier injection in the i region of a long structure in which diffusion effects may be neglected and when thermal generation from deep recombination centers is very weak, this model excludes the usual travelling space-charge domain treatment [ lo] and supports some sort of a relaxation mechanism which assumes a center region instability at a critical injection level. The result is that if a perturbation rises near the center (more accurately at the “cross-over point” n, = pO, where the field is maximum[l 1, 121, some breakdown effect not identified in (I) is presumed to occur when the
341
applied voltage reaches a threshold) it will propagate toward the contacts with a decreasing velocitythe ambipolar drift velocity - and will decay due to recombination with a relaxation time equal to the carrier lifetime (l/C,N); when it vanishes the device can repeat the process. Actually we may extend this result as follows: if diffusion effects are taken into account, an exact compact solution of the dispersion equation obtained in (I) is also possible, and the only alteration is that the perturbation decay more generally is governed by recombination and diffusion so that its relaxation time is no longer given by (1 /C,N) but by (1 /C,N + k*D). The associated frequency of relaxation oscillation will be generally C,N + k*D. In these experiments of Moore et al.[4] analysed in (I), taking k = (27r/L) = 27r X lw cm-l (the wave vector for a fundamental mode), D = 20 cm*. cm-’ (the diffusion constant from the Moore et al. paper) and C, = 1.7 X 10mgcm-3. set-l for the gold acceptor capture rate [ 131 we obtain C,N + k2D = (1.7 x low9 NAu + 8 X 106)s-l which is in very good agreement with the Moore et al. experimental data fitted by (2.1 X 10PgNAu +S.l x 106) set-I. We have clearly verified the model in P+PN+ silicon structures at low temperature. The devices were parallelopiped samples [4 x 20 x (O-050 + 0.150 + O.O50)mm]. They were made with pulled melt materials, the P+ and N+ contacts being degenerate 0.050 mm depth diffused regions. The middle region was P type (due to boron) compensated silicon (0.150 mm-O.250 mm thickness and 20-5Oa. cm resistivities at room temperature). In such structures oscillations appear when the diodes are cooled typically between 10 and 25°K and when they are biased by a forward current above the cube-law region of the characteristic, i.e. in a space charge and recombination limited regime [14]. For a better way to observe these oscillations we have used the structures as microwave attenuators; our set-up for measuring the carrier lifetime into the middle region has been already described [ 151. We observe that voltage oscillations and oscillations in microwave power have opposite phases in agreement with conductivity oscillation in the middle region. The relaxation character is strongly evident on voltage and microwave transmitted power at once. The striking feature of the microwave modulation is the similarity between the slope of the asymmetric
NOTES
342
oscillation and the slope of the transient stage of recombination which occurs when the current is suppressed (arrows on the figure). This proves that the relaxation phases of the wave are effectively recombination phases whose duration-approximately equal to the carrier lifetime (l/C,N)-determines a frequency generally not far from the reciprocal of the carrier lifetime (C,N). Moreover, the breakdown effect which initiates the instability in the neighbourhood of the “crossover point” is possibly due to impact ionisation of the shallow centers in this case. The magnitude of the electric field at this point is typically (AV/L ^- lOO- 150 V/cm at threshold between 10 and 25”K(AI/ being the potential drop across the middle region [ 141). The double injection regime being accompanied by the filling of shallow centers (most of which are neutral) the conditions for impact ionisation are favourable, probably as good as those of Godik [ 161 who observes an analogous breakdown field in boron-doped silicon under illumination. According to the model (1) we propose the following process in two steps (at constant current): (i) when the applied voltage is sufficient (AV/L = breakdown field), a large carrier density arises at the center due to impact ionisation which is accompanied by a reduction of voltage (and an increase of microwave attenuation); (ii) consequently breakdown requirements are no longer maintained while the perturbation drifts toward each contact driven by the field with ambipolar drift velocity [@.(n,,--Pp,/nO+pO)] as shown in (I), and decay with a relaxation time equal to the carrier lifetime (l/C,N)(we have previously established that the structures are “long” so that diffusion effects may be neglected in such case). This step is associated with an increase of the applied voltage (and a decrease of the microwave attenuation) until the breakdown field is attained again at the “cross-over point”. Then the device repeats the process.
M. BROUSSEAU J. BARRAU J. C. BRABANT Laboratoire de Physique des Solides, FacultP des Sciences et I.N.S.A., I 18, route de Narbonne, 3 I, Toulouse France
(04)
REFERENCES I. M. Brousseau, J. Barrau, J. C. Brabant and Nguyen van Tuyen, Solid-St. Electron. 13,906 (1970). 2. N. Holonyak Jr. and S. F. Bevacqua, Appl. Phys. Lett. 2, 71 (1963). 3. J. S. Moore, C. M. Penchina, N. Holonyak, Jr., M. D. Sirkis and T. Yamada, J. uppl. Phys. 37,2009 ( 1966). 4. J. S. Moore, N. Holonyak Jr. and M. D. Sirkis, Solid-St. Electron. 10,823 (1967). 5. B. G. Streetman, M. M. Blouke and N. Holonyak, Jr., Avvl. Phvs. Lett. 11,200 (I 967). 6. Yu. I. iavadsku and B. V. Kornilov, Soviet Phys. Solid-St., 11. 12 13 (1969). N. Holonyak, Jr., I.B.M. J. Res. 7. B. G. Streetman, Dev. 13,529 (I 969). 8. 0. V. Konstantinov, V. I. Perel and G. V. Tsarenkov, Sooiet Phys. solid-St. 9, 1381 ( 1967). 9. V. L. Bench-Bruevich and S. G. Kalashnikov, Soviet Phys. solid-St. 7,599 (1965). IO. S. G. Kalashnikov and V. I. Bench-Bruevich. Phys. Status Solidi 16, I97 (I 966). 1 I. R. Baron,J. uppl. Phys. 39, 1435 ( 1968). 12. J. W. Mayer, 0. J. Marsh and R. Baron, J. uppl. Phys. 39, 1447 ( 1968). 13. J. M. Fairfield and B. V. Gokhale, Solid-St. Electron. 8,685 (I 965). 14. M. Brousseau, J. Barrau and J. C. Brabant. Appl. Phys. Lett. 17, 297 (1970). and R. Schuttler, Solid-St. Electron. 15. M. Brousseau 12,4 I 7 ( 1969). 16. E. E. Godik, Soviet Phys. solid-St. 8. I228 (I 966).
Solid-Srare
Electron~rs
Pergamon Press 1971. Vol. Printed in Great Britain
14. pp. 342-345.
Optical probing of resistivity profiles in CdS and their relation with acoustoelectric current oscillations” (Received
27 July 1970)
oscillations due to acoustoelectric domains have been observed in many piezoelectric semiconductors [ 11. Investigators have reported that these current oscillations are specimen dependent. In particular, Hobson and Paige[2] have shown that acoustoelectric domains can form in the high resistivity region of CdS, similar results were found for GaAs by Bray and Spear[3]. In this note, we present the correlation of current oscillations with resistivity profiles for samples of semiconducting CdS. Resistivity profiles are meaCURRENT
*This research was partly Research Office - Durham.
supported
by the U.S. Army
Pergamon Press 1971. Vol. 14, pp. 341-342. Printed in Great Britain
Recombination oscillations in Si P+PN+ structures temperature (Received
WE
at low
8 June 1970; in revisedform 14 September 1970)
HAVE observed relaxation oscillations well stabilized in amplitude and frequency in Si P+PN+ structures for high level double-injection in the low temperature range IO-25°K. These waves, investigated by use of microwave attenuation by carriers in the P region, show recombination phases which determine the frequency in agreement with a model previously proposed [ 11. In recent years, experiments have shown that semiconductors carrying space-charge limited current exhibit oscillations in a positive resistance region of the I.V. characteristic[2]. These oscillations occur in PIN, NIN, PIP structures which contain deep-level recombination centers. In Si PIN structures with double-carrier injection this effect has been reported with Au[3,4], Co[2,5], Zn[61 deep level compensating impurities: it appears that the charge condition of traps is fundamental for the oscillations and that the frequency is strongly dependent on the recombination kinetic of the i region[4,7]. The models proposed by Konstantinov et al.[8], BonchBruevich and Kalashnikov[9] and others involve recombination but do not require the existance of the space charge; they do not explain the oscillation mechanism. In a previous paper[l], referred as (I), we have proposed a model which takes into account the trapped part of the space charge on recombination centers and carrier recombination kinetic. With double-carrier injection in the i region of a long structure in which diffusion effects may be neglected and when thermal generation from deep recombination centers is very weak, this model excludes the usual travelling space-charge domain treatment [ lo] and supports some sort of a relaxation mechanism which assumes a center region instability at a critical injection level. The result is that if a perturbation rises near the center (more accurately at the “cross-over point” n, = pO, where the field is maximum[l 1, 121, some breakdown effect not identified in (I) is presumed to occur when the
341
applied voltage reaches a threshold) it will propagate toward the contacts with a decreasing velocitythe ambipolar drift velocity - and will decay due to recombination with a relaxation time equal to the carrier lifetime (l/C,N); when it vanishes the device can repeat the process. Actually we may extend this result as follows: if diffusion effects are taken into account, an exact compact solution of the dispersion equation obtained in (I) is also possible, and the only alteration is that the perturbation decay more generally is governed by recombination and diffusion so that its relaxation time is no longer given by (1 /C,N) but by (1 /C,N + k*D). The associated frequency of relaxation oscillation will be generally C,N + k*D. In these experiments of Moore et al.[4] analysed in (I), taking k = (27r/L) = 27r X lw cm-l (the wave vector for a fundamental mode), D = 20 cm*. cm-’ (the diffusion constant from the Moore et al. paper) and C, = 1.7 X 10mgcm-3. set-l for the gold acceptor capture rate [ 131 we obtain C,N + k2D = (1.7 x low9 NAu + 8 X 106)s-l which is in very good agreement with the Moore et al. experimental data fitted by (2.1 X 10PgNAu +S.l x 106) set-I. We have clearly verified the model in P+PN+ silicon structures at low temperature. The devices were parallelopiped samples [4 x 20 x (O-050 + 0.150 + O.O50)mm]. They were made with pulled melt materials, the P+ and N+ contacts being degenerate 0.050 mm depth diffused regions. The middle region was P type (due to boron) compensated silicon (0.150 mm-O.250 mm thickness and 20-5Oa. cm resistivities at room temperature). In such structures oscillations appear when the diodes are cooled typically between 10 and 25°K and when they are biased by a forward current above the cube-law region of the characteristic, i.e. in a space charge and recombination limited regime [14]. For a better way to observe these oscillations we have used the structures as microwave attenuators; our set-up for measuring the carrier lifetime into the middle region has been already described [ 151. We observe that voltage oscillations and oscillations in microwave power have opposite phases in agreement with conductivity oscillation in the middle region. The relaxation character is strongly evident on voltage and microwave transmitted power at once. The striking feature of the microwave modulation is the similarity between the slope of the asymmetric
NOTES
342
oscillation and the slope of the transient stage of recombination which occurs when the current is suppressed (arrows on the figure). This proves that the relaxation phases of the wave are effectively recombination phases whose duration-approximately equal to the carrier lifetime (l/C,N)-determines a frequency generally not far from the reciprocal of the carrier lifetime (C,N). Moreover, the breakdown effect which initiates the instability in the neighbourhood of the “crossover point” is possibly due to impact ionisation of the shallow centers in this case. The magnitude of the electric field at this point is typically (AV/L ^- lOO- 150 V/cm at threshold between 10 and 25”K(AI/ being the potential drop across the middle region [ 141). The double injection regime being accompanied by the filling of shallow centers (most of which are neutral) the conditions for impact ionisation are favourable, probably as good as those of Godik [ 161 who observes an analogous breakdown field in boron-doped silicon under illumination. According to the model (1) we propose the following process in two steps (at constant current): (i) when the applied voltage is sufficient (AV/L = breakdown field), a large carrier density arises at the center due to impact ionisation which is accompanied by a reduction of voltage (and an increase of microwave attenuation); (ii) consequently breakdown requirements are no longer maintained while the perturbation drifts toward each contact driven by the field with ambipolar drift velocity [@.(n,,--Pp,/nO+pO)] as shown in (I), and decay with a relaxation time equal to the carrier lifetime (l/C,N)(we have previously established that the structures are “long” so that diffusion effects may be neglected in such case). This step is associated with an increase of the applied voltage (and a decrease of the microwave attenuation) until the breakdown field is attained again at the “cross-over point”. Then the device repeats the process.
M. BROUSSEAU J. BARRAU J. C. BRABANT Laboratoire de Physique des Solides, FacultP des Sciences et I.N.S.A., I 18, route de Narbonne, 3 I, Toulouse France
(04)
REFERENCES I. M. Brousseau, J. Barrau, J. C. Brabant and Nguyen van Tuyen, Solid-St. Electron. 13,906 (1970). 2. N. Holonyak Jr. and S. F. Bevacqua, Appl. Phys. Lett. 2, 71 (1963). 3. J. S. Moore, C. M. Penchina, N. Holonyak, Jr., M. D. Sirkis and T. Yamada, J. uppl. Phys. 37,2009 ( 1966). 4. J. S. Moore, N. Holonyak Jr. and M. D. Sirkis, Solid-St. Electron. 10,823 (1967). 5. B. G. Streetman, M. M. Blouke and N. Holonyak, Jr., Avvl. Phvs. Lett. 11,200 (I 967). 6. Yu. I. iavadsku and B. V. Kornilov, Soviet Phys. Solid-St., 11. 12 13 (1969). N. Holonyak, Jr., I.B.M. J. Res. 7. B. G. Streetman, Dev. 13,529 (I 969). 8. 0. V. Konstantinov, V. I. Perel and G. V. Tsarenkov, Sooiet Phys. solid-St. 9, 1381 ( 1967). 9. V. L. Bench-Bruevich and S. G. Kalashnikov, Soviet Phys. solid-St. 7,599 (1965). IO. S. G. Kalashnikov and V. I. Bench-Bruevich. Phys. Status Solidi 16, I97 (I 966). 1 I. R. Baron,J. uppl. Phys. 39, 1435 ( 1968). 12. J. W. Mayer, 0. J. Marsh and R. Baron, J. uppl. Phys. 39, 1447 ( 1968). 13. J. M. Fairfield and B. V. Gokhale, Solid-St. Electron. 8,685 (I 965). 14. M. Brousseau, J. Barrau and J. C. Brabant. Appl. Phys. Lett. 17, 297 (1970). and R. Schuttler, Solid-St. Electron. 15. M. Brousseau 12,4 I 7 ( 1969). 16. E. E. Godik, Soviet Phys. solid-St. 8. I228 (I 966).
Solid-Srare
Electron~rs
Pergamon Press 1971. Vol. Printed in Great Britain
14. pp. 342-345.
Optical probing of resistivity profiles in CdS and their relation with acoustoelectric current oscillations” (Received
27 July 1970)
oscillations due to acoustoelectric domains have been observed in many piezoelectric semiconductors [ 11. Investigators have reported that these current oscillations are specimen dependent. In particular, Hobson and Paige[2] have shown that acoustoelectric domains can form in the high resistivity region of CdS, similar results were found for GaAs by Bray and Spear[3]. In this note, we present the correlation of current oscillations with resistivity profiles for samples of semiconducting CdS. Resistivity profiles are meaCURRENT
*This research was partly Research Office - Durham.
supported
by the U.S. Army