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Recombination and ionization processes at impurity centres in hot-electron semiconductor transport

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La Rivista del Nuovo Cimento (1978-1999) Aims and scope

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Abbreviations

a :

Decay length of the neutral-cell potential

a :

i Decay length of an extra electron wave function

a :

B Bohr radius

a :

0 Effective Bohr radius for a hydrogenic impurity in a semiconductor

b :

Equilibrium normalized probability of generation

d :

Dipole length of the donor-acceptor pair

e :

Electron charge with its sign

f :

Frequency

f (k,r,t) :

One-electron energy distribution function

f dr:

Driven frequency

h :

Equilibrium normalized probability of recombination

h α:

Equilibrium normalized probability of recombination due toα-process

ħ :

Reduced Planck constant

j :

Current density

jext :

External current density

j0:

d.c. current density

Δj :

Amplitude of a time-dependent current density

k :

Electron wavevector

k 0 :

Degree of compensation

l :

Azhimutal quantum number

l (E 0):

Auxiliary function to define S(E 0)

l c :

Equilibrium mean-free path

l m,a :

Momentum mean-free path for acoustic scattering

l ε,a :

Energy mean free-path for acoustic scattering

m :

Carrier effective mass in units of the free electron mass

m h :

Heavy hole effective mass in units of the free-electron mass

m 1 :

Light hole effective mass in units of the free-electron mass

m 0 :

Free electron mass

n :

Principal quantum number

n :

Free-carrier concentration

n i :

Population of thei-th level

n α :

Concentration of carriers in valleyα

p :

Free-hole concentration

r :

Vector space

r 0 :

Distance measured from the impurity centre

s :

Sound velocity (longitudinal or appropriate average)

t :

Time

t ff :

Time spent by a carrier in the conducting band

t sl :

Time spent by a carrier in the impurity states

t tot :

Total time of simulation

u :

Fraction of active impurities which is ionized

u eq :

Equilibrium value ofu

v :

Group velocity associated to the carrier kinetic energy

v d :

Free-carrier drift velocity

v rd :

Reduced drift velocity accounting for trapping-detrapping mechanisms

v 0 :

Velocity of the carrier in the positive-energy region

w :

Dimensionless squared ratio of optical-to-acoustic matrix element

z(x):

Boundary contour function

A :

Value of the ratio λr,op/We,ac

A I :

Integrated volume ionization rate due to impact ionization from neutral impurities

A T :

Integrated thermal generation rate from neutral centres

A I,i :

Integrated volume impact ionization rate from thei-th impurity excited level

A T,i :

Integrated thermal generation rate from thei-th impurity excited level

A I,α :

Integrated ionization rate due to impact ionization from valleyα

A 0T :

Integrated thermal generation rate from negatively charged donors

A 1T :

Integrated thermal generation rate from dipoles

A *I :

Integrated effective volume ionization rate due to impact ionization for a many-valley model

A T,ac :

Integrated thermal ionizatiom rate from neutral centres due to acoustic phonons

B :

Magnetic field

B :

Frequency coefficient related to carrier diffusion in the negative-energy region

B I :

Average square volume recombination rate due to an Auger process to positively charged donors

B T :

Average volume recombination rate of free charge to charged donors

B I,αβ :

Average volume recombination rate of an electron from valleyα due to collision with an electron from valleyβ

B T,i :

Average volume recombination rate to thei-th impurity excited level

B T,α :

Volume thermal recombination rate from valleyα

B *I :

Average effective square Auger recombination rate for a many-valley semiconductor

B eqT :

Average volume recombination rate at equilibrium

B 1T :

Average volume recombination rate of free charge to dipoles

B *T :

Integrated volume thermal recombination effective rate for a many-valley model

D :

Diffusion coefficient

D(λ):

Auxiliary function for calculating -σop

D cross :

Diffusion coefficient associated to fluctuations in number and velocity

D gr :

Diffusion coefficient associated to number fluctuations

D tot :

Total diffusion coefficient

D vf :

Diffusion coefficient associated to velocity fluctuations

E c :

Acoustic deformation potential

E F :

Energy related to the Poole-Frenkel effect

E 0 :

Given value of the electron (total) energy

E Ni :

Energy level for a neutral impurity

E f0 :

Energy fluctuation due to the impurity potential

E fc0 :

Energy fluctuation due to the impurity potential for compensated materials

E p0 :

Energy of the percolation level

E (0)I :

Ground-state energy in the hydrogenic model

E (n)I :

n- th excited energy level of the impurity in the hydrogenic model

E NI :

Binding energy of a neutral-cell potential

E *I :

Experimental value of the impurity ground-state energy

F :

Electric-field strength

F α :

Effective electric field in valleyα

F ac :

Value of the characteristic electric field limited by acoustic phonons

F b :

Value of the breakdown electric field

F m :

Value of the electric field corresponding to a minimum population in the cold valleys of Si

F ph :

Value of the electric field correspondent to a decrease of AI (or an increase of BT)

F s :

Value of the sustained electric field

F H :

Hall electric field

G :

Average generation rate per unit volume

G i :

Average generation rate per unit volume from thei-th ionized impurity level

G ph,α :

Equilibrium average value of γph,α

I :

Electrical current

I k :

Total collision operator

I collk :

Collision operator for scattering with thermal bath and imperfections

I eek :

Collision operator for e-e scattering

I 0k :

Total collision operator in positive energy space

I 0,grk :

Collision operator for generation and recombination processes assisted by phonons in positive energy space

I 0,eek :

Collision operator for e-e interaction in positive energy space

K :

Boltzmann constant

N :

Number of free carriers

dN(E0):

Number of carriers in the energy interval between Eo and E0 + dE0

dN r(E0):

Number of carriers in the energy interval between E0 and E0 + dE0 which recombines to charged donors per unit time

N I :

Number of single charged impurities

N I :

Number of excited impurity levels

N A :

Acceptor concentration

N -A :

Charged acceptor concentration

N c :

Capture centre concentration

N C :

Coulomb centre concentration in the presence of dipoles and two-donor complexes

N D :

Donor concentration

N 0D :

Neutral donor concentration

N +D :

Charged donor concentration

N 1 :

Dipole concentration

N α :

Concentration of recombination centres ofα type

P :

Sticking function

P ac :

Sticking function for acoustic phonons

P dip :

Sticking function for dipoles

P i :

Discrete sticking function of thei-th ionized impurity level

P op :

Sticking function for optical phonons

P N :

Sticking function for neutral impurities

Q :

Modified sticking function

Q′ :

Modified sticking function independent of carrier concentration and electric field

R :

Average total recombination rate per unit volume

R i :

Average total recombination rate per unit volume to thei- th ionized impurity level

R 0 :

Resistance

S(f):

Electric field power spectrum for driven chaos

S(E0):

Dimensionless function modeling the energy dependence of thermal recombination rate

S I :

Current spectral density

S Icross :

Current spectral density due to fluctuations in number and velocity

S Igr :

Current spectral density due to number fluctuations

S Ivf :

Current spectral density due to velocity fluctuations

T :

Absolute temperature

T e :

Electron temperature

U 0 :

Binding energy of the trap

U(r):

Impurity potential energy

U C(r):

Coulomb potential energy

U d(r):

Electric dipole potential energy

U F(r):

Coulomb potential energy in the presence of an electric field

V :

Voltage

V 0 :

Volume of the crystal

W :

Total transition rate for scattering processes

W ee :

Transition rate for e-e interaction

W i :

Transition rate for thei-th scattering process

W ac,em :

Acoustic phonon emission rate including transitions to impurity levels

W e,ac :

Scattering rate for elastic acoustic scattering

W op,em :

Optical phonon emission rate including transitions to impurity levels

W I,ij :

Ionization rate between excited levelsi, j due to Auger processes

W T,ij :

Transition rate between excited levelsi, j assisted by acoustic phonons

Z :

Number of unit charge of the recombination centre

β :

Numerical parameter describing Poole-Frenkel effect

β :

Dimensionless binding energy of a neutral-cell potential

γ :

Dimensionless thermal energy

γ(E0):

Total generation rate

γ F,ac :

Ionization rate due to acoustic phonons in the presence of an electric field

γ ph :

Thermal generation rate

γ 0ph :

Thermal generation rate from a neutral donor (acceptor)

γ ph,α :

Thermal generation rate for the process of typeα

γ T,ac :

Thermal ionization rate due to acoustic phonons

γ 0 :

Ionization rate per unit energy

ε :

Electron kinetic energy

ε> :

Mean electron kinetic energy

ε c :

Energy to detach an empty donor state from an acceptor

η :

Dimensionless binding energy

x :

Relative static-dielectrie constant of the material

x 0 :

Vacuum permittivity

λ:

Number of equivalent valleys

λ(k):

Total scattering rate

λr(E 0):

Total recombination rate in positive energy space

λr + :

Recombination rate to a positively charged donor

λr,i :

Recombination rate for thei-th process

λr,op :

Recombination rate assisted by optical phonons

λr,N :

Recombination rate to neutral impurities assisted by acoustic phonons

μ :

Mobility

μac :

Mobility limited by acoustic phonons

ξ:

Dimensionless electron energy

ρ:

Density of states of free electrons

ρI :

Density of states of electrons including the impurity potential

ρ0 :

Density of the material

σ:

Generic energy dependent cross-section for capture of an electron

σac :

Cross-section for capture assisted by acoustic phonons

σdip :

Cross-section for capture due to a dipole centre

σop :

Cross-section for capture due to optical phonons

σI :

Cross-section for impact ionization

σg :

Value for σI(E0) for E0 = E (0)I

σ1 :

Effective cross-section for acoustic modes

σα :

Cross-section for the α-th process of recombination assisted by optical and/or intervalley phonons

σ(A) :

Cross-section for capture to neutral impurities assisted by acoustic phonons

σ0 :

Generic differential cross-section per unit energy

σ0,ac :

Differential cross-section per unit energy due to acoustic phonons

σ0,ee :

Differential cross-section per unit energy for capture assisted by e-e interaction

gs:

Generic (velocity average) cross-section

gsac :

Average cross-section for capture assisted by acoustic phonons

gsee :

Average cross-section for capture assisted by e-e interaction

gsop :

Average cross-section for capture assisted by optical and/or intervalley phonons

gsI :

Average cross-section for impact ionization

σc :

Conductivity

τ:

Transport mean free time

τcoll :

Duration of a collision

τl :

Lifetime

τα,β :

Intervalley scattering time between valleys α, β

τ ε :

Energy relaxation time

τα * :

Effective intervalley scattering time from valleyα to another valley β

τr,ac :

Average recombination time assisted by acoustic phonons

ω :

Angular frequency

ω0 :

Optical-phonon angular frequency

ω q :

Generic-phonon angular frequency

References

Section 1

  1. K. Seeger:Semiconductor Physics (Springer-Verlag, Berlin, Heidelberg, 1985).

    Google Scholar 

  2. S. M. Sze:Physics of Semiconductor Devices (Wiley, New York, N.Y., 1981).

    Google Scholar 

  3. W. Kohn:Solid State Phys.,5, 257 (1957).

    Google Scholar 

  4. F. Bassani, G. Iadonisi andB. Preziosi:Rep. Prog. Phys.,37, 1099 (1974).

    ADS  Google Scholar 

  5. J. M. Baramowski, M. Grynberg andS. Porowski: inHandbook of Semiconductors, Vol.1, edited byW. Paul (North-Holland, Amsterdam, 1982), p. 323.

    Google Scholar 

  6. V. L. Bonch-Bruevich andE. G. Landsberg:Phys. Status Solidi,29, 9 (1968) and references therein.

    Google Scholar 

  7. V. V. Mitin:Sov. Phys. Semicond.,21, 142 (1987).

    Google Scholar 

  8. V. V. Mitin andN. A. Zakhlenik:Proceedings of the XVIII ICPS, edited byO. Engstroem (World Scientific, Singapore, 1987).

    Google Scholar 

  9. V. V. Mitin:Appl. Phys. A,39, 123 (1986).

    ADS  Google Scholar 

  10. Z. S. Gribnikov andV. A. Kochelap:Sov. Phys. JETP,31, 562 (1970).

    ADS  Google Scholar 

  11. E. J. Ryder, I. N. Moss andD. A. Kleinmann:Phys. Rev.,95, 1342 (1954).

    ADS  Google Scholar 

  12. W. Schokley:Bell Syst. Techn. J.,30, 990 (1951).

    Google Scholar 

  13. E. Erlbach andJ. B. Gunn:Phys. Rev. Lett.,8, 280 (1962).

    ADS  Google Scholar 

  14. E. A. Davies:J. Phys. Chem. Solids,25, 201 (1964).

    ADS  Google Scholar 

  15. P. J. Price: inFluctuation Phenomena in Solids, edited byR. E. Burgess (Academic Press, New York, N.Y., 1965), p. 355.

    Google Scholar 

  16. E. M. Conwell:High field transport in semiconductors, inSolid State Phys., Suppl.9 (Academic Press, New York, N.Y., 1967).

    Google Scholar 

  17. L. Reggiani:Hot Electron Transport in Semiconductors, inTopics in Applied Physics, Vol.58 (Springer-Verlag, Berlin, Heidelberg, 1985).

    Google Scholar 

  18. R. S. Levitt andA. Honig:J. Phys. Chem. Solids,22, 269 (1961).

    ADS  Google Scholar 

  19. S. M. Koenig, R. D. Brown andW. Schillinger:Phys. Rev.,128, 1668 (1962).

    ADS  Google Scholar 

  20. P. Norton, T. Braggins andH. Levinstein:Phys. Rev. Lett,30, 488 (1973).

    ADS  Google Scholar 

  21. M. Asche, H. Kostial andO. G. Sarbey:Phys. Status Solidi B,91, 521 (1979).

    ADS  Google Scholar 

  22. M. Lax:Phys. Rev.,119, 1502 (1960).

    ADS  Google Scholar 

  23. R. A. Brown andS. Rodriguez:Phys. Rev.,153, 890 (1967).

    ADS  Google Scholar 

  24. V. N. Abakumov, V. I. Perel andI. N. YassieviCH:Sov. Phys. Semicond.,12, 1 (1978).

    Google Scholar 

  25. P. T. Ladsberg andA. W. Willoughby (Editors):Proceedings of the International Conference on Recombination in Semiconductors, inSolid State Electron.,21, 1275 (1978).

  26. W. Pickin:Solid State Electron.,21, 1299 (1978).

    ADS  Google Scholar 

  27. W. Pickin:Phys. Rev. B,20, 2451 (1979).

    ADS  Google Scholar 

  28. W. Pickin:Phys. Status Solidi B,96, 617 (1979).

    ADS  Google Scholar 

  29. W. Pickin:Phys. Status Solidi B,97, 431 (1980).

    ADS  Google Scholar 

  30. C. Jacoboni andL. Reggiani:Rev. Mod. Phys.,55, 645 (1983) and references therein.

    ADS  Google Scholar 

  31. L. Reggiani, P. Lugli andV. Mitin:Appl. Phys. Lett.,51, 925 (1987).

    ADS  Google Scholar 

  32. L. Reggiani, P. Lugli andV. Mitin:Proceedings of the IX International Conference on Noise in Physical Systems, edited byC. M. Van Vliet (World Scientific, Singapore, 1987), p. 105.

    Google Scholar 

  33. L. Reggiani, P. Lugli andV. Mitin:Solid State Electron,31, 543 (1988).

    ADS  Google Scholar 

  34. L. Reggiani, P. Lugli andV. Mitin:Phys. Rev. Lett.,60, 736 (1988).

    ADS  Google Scholar 

  35. L. Reggiani, P. Lugli andV. Mitin:Proceedings of the XIX ICPS, edited byW. Zawadzki, Wrodawska Drukarnia Naukowa (Wroclaw, 1988) p. 1723.

  36. L. Reggiani, P. Lugli andV. Mitin:Proceedings of the III International Conference on Shallow Impurities in Semiconductors, edited byB. Monemar,The Institute of Physics Conf. Ser. No. 95 (Bristol, 1989) p. 545.

  37. L. Reggiani, L. Varani, J. C. Vaissiere, J. P. Nougier andV. Mitin: to be published inJ. Appl. Phys. (1989).

Section 2

  1. V. N. Abakumov andI. N. Yassievich:Sov. Phys. JETP,44, 345 (1976).

    ADS  Google Scholar 

  2. V. N. Abakumov, L. N. Kreshchuk andI. N. Yassievich:Sov. Phys. Semicond.,12, 152 (1977).

    Google Scholar 

  3. V. N. Abamukov, V. I. Perel andI. N. Yassievich:Sov. Phys. JETP,45, 354 (1977).

    ADS  Google Scholar 

  4. V. N. Abakumov andZ. N. Sokolova:Sov. Phys. Semicond.,12, 962 (1979).

    Google Scholar 

  5. V. N. Abakumov:Sov. Phys. Semicond.,13, 566 (1979).

    Google Scholar 

  6. V. N. Abakumov:Sov. Phys. Semicond.,14, 510 (1980).

    Google Scholar 

  7. V. V. Akulinichev andI. N. Yassievich:Sov. Phys. Semicond.,14, 1058 (1980).

    Google Scholar 

  8. V. V. Akulinichev andI. N. Yassievich:Sov. Phys. Semicond.,16, 159 (1982).

    Google Scholar 

  9. L. P. Pitaevskii:Sov. Phys. JETP,15, 919 (1962).

    Google Scholar 

  10. D. Bimberg, H. Münzel, A. Steckenborn andJ. Christen:Phys. Rev. B,12, 7788 (1985).

    ADS  Google Scholar 

  11. A. L. Efros, B. I. Shklovskii andI. Y. Yanchev:Phys. Status Solidi B,50, 45 (1972).

    ADS  Google Scholar 

  12. Sh. M. Kogan andT. M. Lifshits:Phys. Status Solidi A,39, 11 (1977).

    ADS  Google Scholar 

  13. L. Reggiani:J. Phys. Chem. Solids,37, 293 (1976).

    ADS  Google Scholar 

  14. O. Sarbei andM. Asche:Sov. Phys. Lett. JETP,28, 625 (1978).

    Google Scholar 

  15. A. V. Gurevich andL. P. Pitaevskii:Sov. Phys. JETP,19, 870 (1964).

    Google Scholar 

  16. M. Asche, H. Kostial andO. G. Sarbei:Phys. Status Solidi B,91, 521 (1979).

    ADS  Google Scholar 

  17. G. N. Goltsman, N. G. Ptitsina andE. R. Riger:Sov. Phys. Semicond.,18, 1053 (1984).

    Google Scholar 

  18. E. M. Gershenzon, G. M. Goltsman, G. N. Ptitsina andN. G. Riger:Sov. Phys. JETP,64, 889 (1986).

    Google Scholar 

  19. D. J. Robbins andP. T. Landsberg:J. Phys. C,13, 2425 (1980).

    ADS  Google Scholar 

  20. C. Jacoboni:Proceedings of the XIII ICPS, edited byF. Fumi (Marves, Roma, 1976), p. 1195.

    Google Scholar 

  21. F. Williams:Phys. Status Solidi B,25, 493 (1962).

    ADS  Google Scholar 

  22. B. I. Shklovskii, A. L. Efros andI. Yu. Yanchev:JETP Lett.,14, 233 (1971).

    ADS  Google Scholar 

  23. S. Chandrasekhar:Rev. Mod. Phys.,15, 1 (1943).

    MathSciNet  ADS  MATH  Google Scholar 

  24. E. M. Gershenzon, A. P. Melnikov, R. I. Rabinovich andN. A. SerebzyaKAVA:Sov. Phys. Usp.,23, 684 (1980).

    ADS  Google Scholar 

  25. E. B. Goldgur andR. I. Rabinovich:Sov. Phys. JETP,57, 643 (1983).

    Google Scholar 

  26. Yu. N. Demkov andV. N. Ovstrovskii: inMethods of Zero-Radius Potentials in Atomic Physics (Leningrad University Press, Leningrad, 1975).

    Google Scholar 

  27. A. I. Baz, Ya. B. Zeldovich andA. M. Peremolov:Scattering, Reactions, and Decay in Nonrelativistic Quantum Mechanics (Wiley, New York, N.Y., 1969).

    Google Scholar 

  28. E. M. Gershenzon, A. P. Melnikov, R. I. Rabinovich andV. B. Smirnova:Sov. Phys. Semicond.,17, 311 (1983).

    Google Scholar 

Section 3

  1. J. S. Blakemore:Semiconductor Statistics (Pergamon Press, Oxford, London, 1962);F. Reif:Fundamentals of Statistical and Thermal Physics (McGraw-Hill, New York, N.Y., 1965).

    MATH  Google Scholar 

  2. J. Frenkel:Phys. Rev.,54, 685 (1938).

    Google Scholar 

  3. G. Ottaviani, C. Canali, C. Jacoboni, A. Alberigi Quaranta andK. Zanio:J. Appl. Phys.,44, 360 (1973).

    ADS  Google Scholar 

  4. J. L. Hartke:J. Appl. Phys.,39, 4871 (1968).

    ADS  Google Scholar 

  5. V. Dalla Casa andC. Paracchini:Phys. Rev. B,34, 8967 (1986).

    ADS  Google Scholar 

  6. E. Rosencher, V. Mosser andG. Vincent:Phys. Rev. B,29, 1135 (1984).

    ADS  Google Scholar 

  7. I. Masayuki, S. Goro andK. Sousuke:J. Appl. Phys.,42, 3737 (1971).

    Google Scholar 

  8. E. Rosencher, V. Mosser andG. Vincent:Phys. Rev. B,29, 1135 (1984).

    ADS  Google Scholar 

  9. L. V. Keldysh:Sov. Phys. JETP,10, 509 (1960).

    Google Scholar 

  10. H. W. Dravin:Z. Phys.,164, 513 (1961).

    ADS  Google Scholar 

  11. A. Zylberstejn:Phys. Rev.,127, 744 (1962).

    ADS  Google Scholar 

  12. Z. S. Kachlishvili:Phys. Status Solidi B,48, 65 (1971).

    ADS  Google Scholar 

  13. V. A. Chuenkov:Sov. Phys. Semicond.,2, 292 (1968).

    Google Scholar 

  14. V. F. Bannaya, L. I. Veselova, E. M. Gershenzon andV. A. Chuenkov:Sov. Phys. Semicond.,7, 1315 (1976);10, 202 (1976).

    Google Scholar 

  15. V. A. Chuenkov:Sov. Phys. Semicond.,11, 624 (1977).

    Google Scholar 

  16. A. A. Kastalskii:Phys. Status Solidi A,15, 599 (1973).

    ADS  Google Scholar 

  17. F. A. Khan andD. P. Bhattacharya:J. Phys. C,17, 3463 (1984).

    ADS  Google Scholar 

  18. J. F. Palmier:Phys. Rev. B,12, 4557 (1972).

    ADS  Google Scholar 

  19. T. K. Pramanik andD. P. Bhattacharya:Solid State Commun.,59, 737 (1986).

    ADS  Google Scholar 

  20. A. Baldereschi:Proceedings of the XII ICPS, edited byM. H. Pilkhum (Teubner, Stuttgart, 1974), p. 345.

    Google Scholar 

  21. M. Jaros:Deep Levels in Semiconductors (Adam Hilger Ltd., Bristol, 1982).

    Google Scholar 

  22. V. V. Mitin, M. Asche andH. Kostial:Phys. Rev. B,33, 4100 (1986).

    ADS  Google Scholar 

Section 4

  1. S. V. Gantsevich, V. L. Gurevich andR. Katilius:Riv. Nuovo Cimento,2, 1 (1979).

    MathSciNet  Google Scholar 

  2. J. J. Duderstadt andW. R. Martin:Transport Theory (Wiley, New York, N.Y., 1979).

    MATH  Google Scholar 

  3. F. A. Khan andD. P. Bhattacharya:J. Phys. C,17, 3463 (1984).

    ADS  Google Scholar 

  4. E. Schoell:Nonequilibrium Phase Transition in Semiconductors, inSpringer Series in Synergetics, Vol.35 (Springer-Verlag, Berlin, 1987).

    Google Scholar 

  5. E. Schoell:Festkoerperprobleme, inAdvances in Solid State Physics, Vol.26, edited byP. Grosse (Vieweg, Braunschweig, 1986), p. 309.

    Google Scholar 

  6. J. R. Barker andC. J. Hearn:J. Phys. C,6, 3097 (1973).

    ADS  Google Scholar 

  7. J. R. Barker andC. J. Hearn:Proceedings of the I Conference on Computational Physics, Culham Rept. CLM-CD, Vol.2 (HMSO, London, 1969), p. 34.

    Google Scholar 

  8. P. J. Price: inSemiconductors and Semimetals (Academic Press, New York, N.Y., 1979), p. 249.

    Google Scholar 

  9. L. Reggiani: inProceedings of the XV ICPS, J. Phys. Soc. Jpn. Suppl.,49, 317 (1980).

    Google Scholar 

  10. E. M. Conwell andV. F. Weisskopf:Phys. Rev.,77, 388 (1950).

    ADS  MATH  Google Scholar 

  11. A. Van der Ziel:Noise Source Characterization (Englewood Cliffs, Prentice Hall, N.J., 1970).

    Google Scholar 

  12. J. C. Vaissiere: Ph.D. Dissertation, University of Montpellier (1986), unpublished.

  13. L. Reggiani, L. Varani, V. Mitin andC. M. Van Vliet,Phys. Rev. Lett. 63, 1094 (1989).

    ADS  Google Scholar 

  14. V. N. Abakumov:Sov. Phys. Semicond.,13, 34 (1979).

    Google Scholar 

Section 5

  1. J. Parisi, U. Rau, J. Peinke andK. M. Mayer:Z. Phys B, in print (1988).

  2. Sheng S. Li:Solid State Electron.,21, 1109 (1978).

    ADS  Google Scholar 

  3. E. E. Godik andYa. E. Pokrovskii:Sov. Phys. Semicond.,1, 333 (1967).

    Google Scholar 

  4. C. Canali, C. Jacoboni, F. Nava, G. Ottaviani andA. Alberigi Quaranta:Phys. Rev. B,12, 2265 (1975).

    ADS  Google Scholar 

  5. V. V. Mitin:Solid State Commun.,55, 997 (1985).

    ADS  Google Scholar 

  6. H. B. Callen andT. A. Welton:Phys. Rev.,83, 34 (1951).

    MathSciNet  ADS  MATH  Google Scholar 

  7. R. Kubo:Response, Relaxation and Fluctuations, inLectures Notes in Physics, Vol. 31, edited byJ. Ehlers, K. Hepp andH. A. Weiden Muller (Springer, Berlin, Heidelberg, 1974), p. 74.

    Google Scholar 

  8. V. Bareikis, J. Pozhela andI. Matulionis:Proceedings of the IX ICPS, edited byS. M. Ryvkin (Nauka, Leningrad, 1968), p. 760.

    Google Scholar 

  9. J. P. Nougier andM. Rolland:Phys. Rev. B,8, 5728 (1973).

    ADS  Google Scholar 

  10. J. Zimmermann, S. Bonfis, Y. Leroy andE. Constant.:Appl. Phys. Lett,30, 245 (1977).

    ADS  Google Scholar 

  11. G. Bosman andR. J. J. Zijlstra:Phys. Lett. A,71, 464 (1979).

    ADS  Google Scholar 

  12. B. Pellegrini:Phys. Rev. B,34, 5921 (1986).

    ADS  Google Scholar 

  13. P. J. Price:J. Appl. Phys.,6, 949 (1960).

    ADS  Google Scholar 

  14. W. Shockley, J. A. Copeland andR. P. James: inQuantum Theory of Atoms, Molecules and the Solid State (Academic Press, New York, N. Y., 1966), p. 537.

    Google Scholar 

  15. R. Brunetti, C. Jacoboni andL. Reggiani:J. Phys. (Paris),42, 118 (1981).

    Google Scholar 

  16. D. Gasquet, B. Azais, J. C. Vaissiere andJ. P. Nougier: inNoise in Physical Systems and 1/f Noise, edited byA. D’Amico andP. Mazzetti (North-Holland, Amsterdam, 1985), p. 231.

    Google Scholar 

  17. J. Bernamont:Ann. Phys. (Leipzig),7, 71 (1937);M. B. Weissman:Rev. Mod. Phys.,60, 537 (1988).

    Google Scholar 

  18. H. Haken:Synergetics (Springer Verlag, Berlin, Heidelberg, 1983).

    Google Scholar 

  19. K. Aoki, K. Miyame, T. Kobayashi andK. Yamamoto:Physica B,117-118, 570 (1983).

    Google Scholar 

  20. S. W. Teitsworth, R. M. Westervelt andE. E. Haller:Phys. Rev. Lett,51, 825 (1983).

    ADS  Google Scholar 

  21. S. W. Teitsworth andR. M. Westervelt:Phys. Rev. Lett.,53, 2587 (1984);56, 516 (1986).

    ADS  Google Scholar 

  22. J. Peinke, A. Muhlbach, R. P. Huebener andJ. Parisi:Phys. Lett. A,108, 407 (1985).

    ADS  Google Scholar 

  23. J. Testa, J. Perez andC. Jeffries:Phys. Rev. Lett,48, 714 (1982).

    MathSciNet  ADS  Google Scholar 

  24. B. C. Eu:J. Chem. Phys.,80, 2123 (1984).

    ADS  Google Scholar 

  25. V. V. Mitin:Appl. Phys. A,39, 123 (1986).

    ADS  Google Scholar 

  26. E. M. Gershenzon, G. N. Goltsman, V. V. Multanovskii andN. G. Ptitsyna:Sov. Phys. JETP,50, 728 (1979).

    ADS  Google Scholar 

  27. E. Schoell:J. Phys. (Paris),42, 57 (1981).

    Google Scholar 

  28. E. Schoell:Z. Phys. B,46, 23 (1982).

    ADS  Google Scholar 

  29. E. Schoell:Physica B,134, 271 (1985).

    Google Scholar 

  30. E. Schoell:Phys. Rev. B,34, 1395 (1986).

    ADS  Google Scholar 

  31. E. Schoell:Proceedings of the XVIII ICPS, edited byO. Engstroem (World Scientific, Singapore, 1987), p. 1555.

    Google Scholar 

  32. A. L. Dubitskii, B. S. Kerner andV. V. Osipov:Sov. Phys. Solid State,28, 725 (1986).

    Google Scholar 

  33. B. S. Kerner andV. V. Osipov:Sov. Phys. Semicond.,13, 523 (1979).

    Google Scholar 

  34. V. V. Gafilchuk, B. S. Kerner andV. V. Osipov:Sov. Phys. Semicond.,15, 1261 (1981).

    Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Fisica e Centro Interuniversitario di Struttura della Materia dell’Università di Modena, Via Campi 213/A, 41100, Modena, Italy

    L. Reggiani

  2. Institute of Semiconductors, Academy of Sciences of the Ukrainian SSR, Kiev, USSR

    V. Mitin

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Reggiani, L., Mitin, V. Recombination and ionization processes at impurity centres in hot-electron semiconductor transport. Riv. Nuovo Cim. 12, 1–90 (1989). https://doi.org/10.1007/BF02740011

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