Bulk hot-electron properties of cubic semiconductors

Abstract This paper contains a review of charge transport properties at high electric fields in bulk cubic semiconductors. The microscopic theoretical interpretation follows a semi-classical approach and is based on the knowledge of the band structure and scattering mechanism of the material under investigation. For the solution of the Boltzmann equation, the Monte-Carlo simulation technique is considered, which provides an ‘exact’ numerical solution limited only by the simplifying assumptions inherent in the physical model assumed. Experimental techniques for the measurements of the most important transport quantities are briefly surveyed. Comparison between theory and experiment is reported for both electron and hole transport properties in Si, Ge and GaAs. These substances, besides being the best known materials, can in fact be considered as models for any other cubic semiconductor.

[1]  K. Seeger,et al.  The anisotropy of conductivity of n-type germanium in strong d.c. fields , 1965 .

[2]  I. Yokota.  On the Deviation from the Einstein Relation Observed for Diffusion of Ag+ Ions in α-Ag2S and Others , 1966 .

[3]  A. Dargys,et al.  Dependence of the Phenomenological Energy Relaxation Time on Electric Field in n‐Si and n‐Ge at 77 °K , 1972 .

[4]  Peter A. Houston,et al.  Electron drift velocity in n-GaAs at high electric fields , 1977 .

[5]  C. Hamaguchi,et al.  Microwave measurement of differential negative conductivity due to intervalley transfer of hot electrons in n-type GaAs , 1967 .

[6]  C. Jacoboni,et al.  Electron-electron in Monte Carlo transport calculations , 1972 .

[7]  J. Groot,et al.  Measurements of the current-field strength characteristic of n-type gallium arsenide using various high-power microwave techniques , 1967 .

[8]  C. Pickering,et al.  The effect of pressure on the high electric field instabilities in n-type GaAs , 1975 .

[9]  C. Canali,et al.  Hole drift velocity in silicon , 1975 .

[10]  K. Seeger.  Microwave Field Dependence of Drift Mobility in Germanium , 1959 .

[11]  Michael A. Littlejohn,et al.  Velocity‐field characteristics of GaAs with Γc6‐Lc6‐Xc6 conduction‐band ordering , 1977 .

[12]  C. Jacoboni,et al.  Velocity autocorrelation function and low-temperature mobility of electrons in silicon , 1975 .

[13]  N. Sclar.  Neutral Impurity Scattering in Semiconductors , 1956 .

[14]  William Shockley,et al.  The Mobility and Life of Injected Holes and Electrons in Germanium , 1951 .

[15]  Ralph Bray,et al.  DETERMINATION OF HOT CARRIER DISTRIBUTION FUNCTIONS FROM ANISOTROPIC FREECARRIER ABSORPTION IN P-TYPE GERMANIUM. , 1963 .

[16]  T. Maloney,et al.  Transient and steady‐state electron transport properties of GaAs and InP , 1977 .

[17]  J. Nougier.  Symmetry relations between the mobility and differential mobility-tensor components of cubic semiconductors in the hot carrier range , 1972 .

[18]  A. M. Mazzone,et al.  Current transport in narrow-base transistors , 1977 .

[19]  C. Jacoboni,et al.  A review of some charge transport properties of silicon , 1977 .

[20]  W. Harrison.  Scattering of Electrons by Lattice Vibrations in Nonpolar Crystals , 1956 .

[21]  The electrical conductivity of germanium , 1964 .

[22]  H. Levinstein,et al.  Determination of Compensation Density by Hall and Mobility Analysis in Copper-Doped Germanium , 1972 .

[23]  D. E. Aspnes,et al.  GaAs lower conduction-band minima: Ordering and properties , 1976 .

[24]  V. Dalal.  HOLE VELOCITY IN p‐GaAs , 1970 .

[25]  J. W. Granville,et al.  XXV. The Measurement of Drift Mobility in Germanium at High Electric Fields , 1956 .

[26]  C. Canali,et al.  Diffusion coefficient of holes in Ge , 1978 .

[27]  P. Landsberg,et al.  Two formulations of semiconductor transport equations , 1977 .

[28]  J. Nash,et al.  Experimental determination of highly concentration‐sensitive effects of intervalley electron‐electron scattering on electric‐field‐dependent repopulation in n‐Si at 77 K , 1974 .

[29]  C. Erginsoy.  Neutral Impurity Scattering in Semiconductors , 1950 .

[30]  D. Bartelink,et al.  High‐Field Diffusivity of Electrons in Silicon , 1971 .

[31]  P. N. Butcher,et al.  Calculation of the velocity-field characteristic for gallium arsenide , 1966 .

[32]  H. D. Rees,et al.  Calculation of steady state distribution functions by exploiting stability , 1968 .

[33]  K. Lischka,et al.  Hot electron faraday-effect and non-equivalent inter-valley transfer in n-type Ge , 1973 .

[34]  C. Jacoboni,et al.  Electron drift velocity in silicon , 1975 .

[35]  B. Ridley,et al.  Reconciliation of the Conwell-Weisskopf and Brooks-Herring formulae for charged-impurity scattering in semiconductors: Third-body interference , 1977 .

[36]  M. Lampert,et al.  Current injection in solids , 1970 .

[37]  G. Kino,et al.  A NEW MEASUREMENT OF THE VELOCITY‐FIELD CHARACTERISTIC OF GaAs , 1969 .

[38]  J. Simmons,et al.  Frequency response of bulk traps in the metal-oxide-silicon structure under strong-inversion conditions , 1977 .

[39]  T. C. Mcgill,et al.  Neutral impurity scattering in semiconductors , 1975 .

[40]  Lino Reggiani,et al.  Hole drift velocity in germanium , 1977 .

[41]  W. Fawcett,et al.  Monte Carlo determination of electron transport properties in gallium arsenide , 1970 .

[42]  Dietrich Meyerhofer,et al.  Physics of III-V compounds , 1964 .

[43]  T. M. Sanders,et al.  Acoustoelectric Effect in n-Type Germanium , 1959 .

[44]  W. Fawcett,et al.  Negative differential mobility of electrons in germanium: A Monte Carlo calculation of the distribution function, drift velocity and carrier population in the (111) and (100) minima , 1971 .

[45]  Victor F. Weisskopf,et al.  Theory of Impurity Scattering in Semiconductors , 1950 .

[46]  T. B. Watkins,et al.  The Possibility of Negative Resistance Effects in Semiconductors , 1961 .

[47]  V. Riginos.  Nonsaturating velocity-field characteristic of gallium arsenide experimentally determined from domain measurements , 1974 .

[48]  H. Fröhlich,et al.  On the theory of dielectric breakdown in solids , 1947, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[49]  O. Wada,et al.  Monte Carlo calculations of diffusion coefficient of hot electrons in n‐type GaAs , 1974 .

[50]  D. J. Bartelink,et al.  DIFFUSION OF ELECTRONS IN SILICON TRANSVERSE TO A HIGH ELECTRIC FIELD , 1970 .

[51]  L. Reggiani,et al.  On the saturated drift velocity of electrons in Si from 77 °K to 500 °K , 1970 .

[52]  W. Shockley,et al.  Hot electrons in germanium and Ohm's law , 1951 .

[53]  K. Seeger,et al.  HARMONIC MIXING OF MICROWAVES BY WARM ELECTRONS IN GERMANIUM , 1966 .

[54]  N. I. Meyer,et al.  Method for Measuring Small Nonlinearities of Electric Characteristics , 1965 .

[55]  E. Bonek.  Millimeter‐wave investigation of electronic conduction in semiconducting III‐V compounds , 1972 .

[56]  W. Sasaki,et al.  Anisotropy of hot electrons in germanium , 1959 .

[57]  M. H. Jørgensen.  Warm-Electron Effects in n-Type Silicon and Germanium , 1967 .

[58]  C. Canali,et al.  High‐field diffusion of electrons in silicon , 1975 .

[59]  C. Jacoboni.  Generalization of Fick's Law for Non‐Local Complex Diffusion in Semiconductors , 1974 .

[60]  M. Asche,et al.  Influence of electron‐electron scattering on the anisotropic conductivity at high electric fields in Si , 1971 .

[61]  R. N. Euwema,et al.  Energy-Band Structure of Aluminum Arsenide , 1969 .

[62]  J. D. Wiley.  Polar Mobility of Holes in III-V Compounds , 1971 .

[63]  R. Robson,et al.  Diffusivity of Charge Carriers in Semiconductors in Strong Electric Fields , 1973 .

[64]  M. Shur,et al.  Transferred electron effects in n-GaAs and n-InP under hydrostatic pressure , 1978 .

[65]  M. Nicolet,et al.  Drift Velocity of Electrons in Silicon at High Electric Fields from 4.2° to 300°K , 1969 .

[66]  G. S. Kino,et al.  Transport Properties of GaAs , 1968 .

[67]  S Bosi,et al.  Acoustic scattering in a two-band system and its application to hole transport properties in cubic semiconductors , 1979 .

[68]  OBSERVATION OF MICROWAVE REPOPULATION MODULATION IN n‐Si AT 77 °K , 1970 .

[69]  J. W. Granville,et al.  A study of energy-loss processes in germanium at high electric fields using microwave techniques , 1961 .

[70]  W. Fawcett,et al.  Calculation of the hot electron diffusion rate for GaAs , 1969 .

[71]  John J. Hall,et al.  Electronic Effects in the Elastic Constants of n -Type Silicon , 1967 .

[72]  J. A. Van Vechten,et al.  Quantum Dielectric Theory of Electronegativity in Covalent Systems. II. Ionization Potentials and Interband Transition Energies , 1969 .

[73]  A. L. McWhorter,et al.  The Gunn effect in polar semiconductors , 1966 .

[74]  B. Nag.  Theory of electrical transport in semiconductors , 1972 .

[75]  Ž. Kancleris,et al.  Influence of E–E scattering on the phenomenological energy relaxation time in nonpolar semiconductors , 1975 .

[76]  H. Levinstein,et al.  Impurity and Lattice Scattering Parameters as Determined from Hall and Mobility Analysis in n-Type Silicon , 1973 .

[77]  E. J. Ryder,et al.  Mobility of Holes and Electrons in High Electric Fields , 1953 .

[78]  R. Bray,et al.  Experimental Determination of the Energy Distribution Functions and Analysis of the Energy-Loss Mechanisms of Hot Carriers in p-Type Germanium , 1964 .

[79]  H. Ehrenreich.  Transport of electrons in intrinsic InSb , 1959 .

[80]  L. Reggiani,et al.  Scattering probabilities for holes. II. Polar optical scattering mechanism , 1973 .

[81]  R. Stratton.  The influence of interelectronic collisions on conduction and breakdown in polar crystals , 1958, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[82]  G. Glover.  EFFECTS OF DOPING PROFILE ON THE MEASURED VELOCITY‐ELECTRIC FIELD CHARACTERISTIC OF n‐TYPE GaAs , 1970 .

[83]  K. Hess,et al.  Energie-Relaxation warmer Ladungsträger in Germanium und Silizium , 1969 .

[84]  J. Nougier,et al.  Mobility, Noise Temperature, and Diffusivity of Hot Holes in Germanium , 1973 .

[85]  A. R. Hutson,et al.  Mechanism of the gunn effect from a pressure experiment , 1965 .

[86]  C. Jacoboni,et al.  Noise and diffusion of hot holes in Si , 1978 .

[87]  M.A.C.S. Brown.  Deviations from Ohm's law in germanium and silicon , 1961 .

[88]  A. Reklaitis,et al.  DIFFUSION COEFFICIENT OF HOT ELECTRONS IN GaAs , 1978 .

[89]  J. Barker,et al.  Quantum transport theory of high-field conduction in semiconductors , 1973 .

[90]  L. Reggiani,et al.  Bloch states mixing in Si conduction band , 1973 .

[91]  C. Canali,et al.  On the diffusivity of holes in silicon , 1979 .

[92]  B. N. Brockhouse,et al.  Lattice Vibrations in Silicon and Germanium , 1959 .

[93]  E. Constant,et al.  Monte Carlo calculation of microwave and far‐infrared hot‐carrier mobility in N‐Si: Efficiency of millimeter transit‐time oscillators , 1978 .

[94]  V. I. Startsev,et al.  Effect of the Superconducting Transition on the Creep in Lead , 1970 .

[95]  R. Crandall.  Low-Temperature Non-Ohmic Electron Transport in GaAs , 1970 .

[96]  Infrared Faraday effect and electron transfer in many valley semiconductors : n GaSb☆ , 1970 .

[97]  A. Reklaitis,et al.  Monte Carlo treatment of electron-electron collisions , 1975 .

[98]  C. Jacoboni,et al.  Intervalley diffusion of hot electrons in germanium , 1978 .

[99]  A. Mircea,et al.  Determination of saturated electron velocity in GaAs , 1975 .

[100]  George Weiss,et al.  Fluctuation Phenomena in Solids , 1965 .

[101]  C. Herring,et al.  Transport and Deformation-Potential Theory for Many-Valley Semiconductors with Anisotropic Scattering , 1956 .

[102]  Jr John E. Smith.  Longitudinal Anisotropy of the High-Field Conductivity of n -Type Germanium at Room Temperature , 1969 .

[103]  M. Asche,et al.  Electric Conductivity of Hot Carriers in Si and Ge , 1969 .

[104]  D. K. Schroder,et al.  The doping concentrations of indium‐doped silicon measured by Hall, C‐V, and junction‐breakdown techniques , 1978 .

[105]  P. S. Hauge,et al.  Microwave measurement of the velocity-field characteristic of GaAs , 1970 .

[106]  C. Jacoboni,et al.  Monte Carlo Calculations on Electron Transport in CdTe , 1972 .

[107]  L. Reggiani,et al.  Nonparabolicity and intrinsic carrier concentration in Si and Ge , 1975 .

[108]  P. Lebwohl,et al.  Direct Microscopic Simulation of Gunn‐Domain Phenomena , 1971 .

[109]  C. Jacoboni,et al.  Negative differential mobility in III–V and II–VI semiconducting compounds , 1971 .

[110]  Dietrich Wolf,et al.  Noise in physical systems , 1978 .

[111]  E. Kane,et al.  Energy band structure in p-type germanium and silicon , 1956 .

[112]  Marvin L. Cohen,et al.  Band Structures and Pseudopotential Form Factors for Fourteen Semiconductors of the Diamond and Zinc-blende Structures , 1966 .

[113]  G. Majni,et al.  Warped band and anisotropy of the hot-hole drift velocity in Si between 300 and 430 K , 1975 .

[114]  H. Ruegg,et al.  Measurement of the drift velocity of holes in silicon at high-field strengths , 1967 .

[115]  W. Thirring,et al.  The Boltzmann Equation , 1973 .

[116]  J. Gunn,et al.  Measurement of the negative differential mobility of electron in GaAs , 1966 .

[117]  L. Reggiani,et al.  Electron energy relaxation time in Si and Ge , 1973 .

[118]  W. Dumke.  High-Field Conductivity of the〈111〉Valleys of Ge , 1970 .

[119]  D. Lynch,et al.  Ordering and Absolute Energies of the L6c and X6c Conduction Band Minima in GaAs , 1976 .

[120]  K. S. Champlin,et al.  Warm-Carrier dc Transport in n Si , 1972 .

[121]  V. Svelto,et al.  ERRATUM: Indirect Electron Drift Velocity versus Electric Field Measurement in GaAs , 1971 .

[122]  W Fawcett,et al.  Effect of field-dependent diffusion on stable domain propagation in the Gunn effect , 1967 .

[123]  L. W. James,et al.  Location of the L 1 and X 3 Minima in GaAs as Determined by Photoemission Studies , 1968 .

[124]  F. Blatt,et al.  Physics of Electronic conduction in Solids , 1968 .

[125]  M. O. Vassell,et al.  High-Field Transport inn- Type GaAs , 1968 .

[126]  C. Hilsum,et al.  Transferred electron amplifiers and oscillators , 1962, IRE Transactions on Electron Devices.

[127]  L. Reggiani.  The anisotropy of the hot-hole drift velocity in Ge☆ , 1976 .

[128]  C. Jacoboni,et al.  Effects of band non-parabolicity on electron drift velocity in silicon above room temperature , 1975 .

[129]  T. Sigmon,et al.  DIFFUSIVITY OF ELECTRONS AND HOLES IN SILICON , 1969 .

[130]  M. Asche,et al.  Conductivity of Hot Holes in Silicon at 77 °K , 1970 .

[131]  J. L. Moll,et al.  Electron drift velocity in avalanching silicon diodes , 1967 .

[132]  D. Ferry.  First-order optical and intervalley scattering in semiconductors , 1976 .