Showing papers in "Solid-state Electronics in 1978"

A charge-sheet model of the MOSFET

Abstract: Intuition, device evolution, and even efficient computation require simple MOSFET (metal-oxide-semiconductor field-effect transistor) models. Among these simple models are charge-sheet models which compress the inversion layer into a conducting plane of zero thickness. It is the purpose of this paper to test one such charge sheet model to see whether this approximation is too severe. This particular model includes diffusion which is expected to be important in the subthreshold and saturation regions. As a test the charge sheet model is applied to long-channel devices. Long-channel MOSFET behavior has been thoroughly studied, and is very well explained by the Pao-Sah double-integral formula for the current. Hence, a clear-cut test is a comparison of the charge sheet model with the Pao-Sah model. We find the charge sheet model has two advantages over the Pao-Sah model. (1) It leads to a very simple algebraic formula for the current of long-channel devices. The same formula applies in all regimes from subthreshold to saturation. Neither splicing nor parameter changes are needed. No discontinuities occur in either the current or the small-signal parameters, or in the derivatives of the small-signal parameters. (2) It is simpler to extend the charge sheet model to two or three dimensions than the Pao-Sah model. This simplification is a result of dropping the details of the inversion layer charge distribution. An important aspect of the gradual channel approximation is brought out by the analysis. Suppose the boundary condition relating the quasi-fermi level at the drain, φfL, to that at the source, φfo, namely φ ƒL =φ ƒ0 +V D where VD is the drain voltage, is applied in all bias regimes. Then it is shown that this means the potential at the drain end of the channel, φsL is not related to the potential at the source end of the channel, φso, by φ sL =φ s0 +V D Instead, φsL is computed, not imposed as a boundary condition. It is suggested that this failure of the potential to satisfy the boundary condition at the drain is justifiable. That is, φsL should be reinterpreted as the potential at the point in the channel where the gradual channel approximation fails. Hence, (2) may be relaxed. However, the “channel length” in the gradual-channel approximation now becomes a fitting parameter and is not the metallurgical source-to-drain separation. In addition several aspects of the long-channel MOSFET are brought out: (1) Pinch-off is achieved only asymptotically as the drain voltage tends to infinity. This is in marked contrast to the often-stated, textbook view that pinch-off is achieved for some finite drain voltage, the saturation voltage. (2) The channel or drain conductance approaches zero only asymptotically. (3) The transconductance saturates only asymptotically. Figures comparing the simple charge-sheet model formulas with the usual textbook formulas are included for direct-current vs drain voltage, channel conductance vs drain voltage, and transconductance vs drain voltage. The charge-sheet model agrees with the original Pao-Sah double-integral formula for the current at all gate and drain voltages, and possesses the correct subthreshold behavior. The textbook formulas do not.

Recombination enhanced defect reactions

Abstract: The energy liberated during an electronic transition may take the form of photons (luminescence), secondary electronic excitations (Auger), or phonons. In the case of phonon production, the vibrational excitation is localized at the recombination center (defect) before it dissipates to raise the temperature of the host lattice. A defect in an excited vibrational state may undergo simple solid state reactions such as diffusion, dissociation and annihilation which would not proceed under the Boltzmann distribution of energies determined by the temperature of the quiescent host lattice. The phenomenology of electronic enhancement is reviewed with emphasis on the roles of defect charge state, recombination and electric fields. The application of unimolecular reaction rate theory to the characterization of recombination enhanced reaction kinetics is discussed conceptually. Implications concerning the structural and chemical nature of host materials, recombination centers and reactant products is outlined. The role of recombination enhanced phenomena in device degradation is discussed and some useful applications of REDR in the selective programming of logic arrays and high definition electron beam data storage are presented.

Reaction of thin metal films with SiO2 substrates

Abstract: Thin films of Co, Cr, Cu, Fe, Hf, Mn, Nb, Ni, Pd, Pt, Ti, V and Zr vacuum-deposited on SiO 2 substrates of thermally oxidized Si wafers and/or fused quartz were annealed under vacuum at about 800°C for 3 hr and then analyzed by backscattering spectrometry and scanning electron microscopy. It is found that Hf, Nb, Ti, V and Zr react with SiO 2 . The result is a thin layer of metal silicide sandwiched between the substrate and a top layer of metal oxide. The other investigated metals apparently do not react. A table of the standard heats of formation for metal silicides has been compiled. These values were used to calculate the free energy change during reaction. The thermodynamic predictions are consistent with experimental observation. The results can also be correlated with the mean electronegativity of the metal, which offers a convenient empirical method to predict whether a metal will react with SiO 2 . It is found that metals with an average electronegativity (average of Allred-Rochow, relative compactness and Pauling electronegativities) of less than 1.5 on the Pauling scale react with the SiO 2 substrate.

Hot electrons and phonons under high intensity photoexcitation of semiconductors

Abstract: It has become well established during the last few years that intense photoexcitation of a semiconductor leads to the heating of the carriers and the generation of nonequilibrium phonons. These phenomena which result from the relaxation of photoexcited carriers to the band extrema by interaction with other carriers and by emission of phonons, are reviewed in this paper. At relatively low intensities ( 5 W/cm 2 for GaAs) the photoexcited carrier distribution is Maxwellian with a carrier temperature T e different from the lattice temperature. T e as high as 150K and effective phonon temperatures as high as 3700K have been observed in GaAs. The observed variation of T e with excitation intensity leads to the conclusion that in semiconductors like GaAs the polar optical mode scattering is the dominant energy loss mechanism from the electron gas to the lattice. Similar results are obtained in CdSe and CdS. At higher intensities (>10 5 W/cm 2 for GaAs), the carrier dist0ribution becomes non-Maxwellian for reasons not well understood at present. We will also discuss some recent measurements of variation of T e with excitation wavelength and of the transmission spectra of photoexcited GaAs.

Alloy scattering and high field transport in ternary and quaternary III–V semiconductors

Abstract: A technique is described for the estimation of the influence of random potential alloy scattering on the high field transport properties of quaternary III–V semiconductors obtained by Monte Carlo simulation. The approach is based on an extension of a theoretical model for scattering in the ternary alloys. The magnitude of the scattering potential is an important parameter in alloy scattering, and three proposed models for calculating this potential are discussed. These are the energy bandgap difference, the electron affinity difference, and the heteropolar energy difference for the appropriate binary compounds. The technique is used in the Monte Carlo method to study the influence of alloy scattering on the transport properties of III–V quaternary alloys. The results of this study are used in a device model to estimate device parameters for FETs.

Electrical current in solids with position-dependent band structure

Abstract: Conduction in materials with a position-dependent band structure, such as graded band gap semiconductors and graded heterojunctions, is considered. A brief discussion of the meaning of spatially varying band structure, based on an extension of Wannier's theorem, is given. Using this extended theorem, it is shown that the conventional Boltzmann transport equation is inadequate for the situation under discussion; a generalized form of the Boltzmann transport equation is derived. From this the complete electron and hole currents are obtained. Besides drift, chemical, and thermal diffusion, they contain two extra terms. One of these involves the gradient of the electron affinity and of the band gap, while the other one depends on the gradient of the density of states. The results thus extend previous results by van Ruyven and Williams and by van Overstraeten et al. It is further shown that the results can be transformed to a form which resembles the conventional current equations, providing a modified position-dependent mobility and diffusivity are introduced. A discussion of the realm of applicability of these results is also presented.

Hot-electron emission from silicon into silicon dioxide

Abstract: Recent progress in the study of hot-electron emission from silicon into silicon dioxide is discussed. Experimental techniques include avalanche injection using gated diodes and MOS capacitors, nonavalanche injection using IGFET structures with an underlying supply p - n junction, and optically induced injection using silicon-gate IGFET structures. IGFET structures allow the fields in the SiO2 layer and in the silicon depletion region to be varied independently. In addition, IGFET structures of reentrant geometry allow absolute emission probabilities of the hot electrons to be determined. Such absolute emission characteristics are useful not only for designing silicon devices but also for quantitative testing of theoretical models of the emission process. Several mechanisms of importance in the emission process have been identified. These are the Schottky lowering of the emission barrier, the scattering of hot electrons in the image-force potential well in the SiO2 layer, the tunneling of hot electrons, and the effect of lattice temperature on electron heating. There is also experimental evidence of the dependence of the hot-electron distribution on electric field gradient. At present, only phenomenological models based on the lucky-electron concept have been developed to the point where quantitative comparison with experimental results is possible. The essential features of these models are discussed.

The band structure dependence of impact ionization by hot carriers in semiconductors: GaAs

Abstract: We present the first systematic study of the dependence of impact ionization by electrons and holes upon the details of the electronic band structure. Our measurements, made in GaAs, establish the crucial role of the ionization threshold energy, and its location in the Brillouin zone, in determining the ionization rates. This relationship is apparent in the dependence of impact ionization rates on the temperature of the lattice, compositional changes for the alloy GaAs 1- x Sb x , and the orientation and strength of the electric field. The strong dependence of impact ionization upon specific features of the electronic band structure is a new principle which can be used to study the nature of electronic states in a wide variety of semiconductors through hot-carrier behavior.

Picosecond spectroscopy of semiconductors

Abstract: The time-resolved reflectivity of picosecond pulses from optically excited carrier distributions can provide important information about the energy relaxation rates of hot electrons and holes in semiconductors The basic optical properties of non-equilibrium carrier distributions are discussed, and in the specific case of GaAs, a semi-empirical analysis of the reflectivity spectrum is described which estimates the contributions from the principal critical points of the band structure Using Boltzmann factors to approximate the hot carrier distributions, it is found that the non-equilibrium reflectivity spectrum is a sensitive function of carrier temperature and that it can reverse its sign as the distribution relaxes These results are in good qualitative agreement with recent experiments employing a mode-locked cw dye laser

The dopant density and temperature dependence of hole mobility and resistivity in boron doped silicon

Abstract: Theoretical expressions for computing resistivity and conductivity mobility of holes as functions of dopant density and temperature have been derived for boron-doped silicon. The model is applicable for dopant densities from 1013 to 3 × 1018 cm−3 and temperatures between 100 and 400 K. Using a 3-band [i.e. heavy-hole, light-hole and the spin-orbit splitting (SO) band] model, the hole mobility was calculated by properly combining the contributions from scattering by lattice phonons, ionized impurities and neutral impurities. In addition, the effects of hole-hole (h-h) scattering and nonparabolicity of valence bands were taken into account in the mobility formulation. To verify our theoretical calculations, resistivity measurements on nine boron-doped silicon slices with dopant densities from 4.5 × 1014 to 3.2 × 1018 cm−3 were performed for 100 ≤ T ≤ 400 K, using planar square-array test structure. Agreement between our calculated and measured resistivity values was within 6 percent over the entire range of dopant density and temperature studied here. Excellent agreement (within ±5%) between our calculated hole mobility values and those of Wagner [9] was obtained for NA ≤ 1017 cm−3 for boron-doped silicon, while discrepancies were found for boron densities greater than 1017 cm−3. This discrepancy is attributed to neglecting the effect of deionization of boron impurities at higher dopant densities by Wagner (i.e. assuming hole density is equal to the total boron density).

C-V characteristics of metal-titanium dioxide-silicon capacitors

Abstract: Titanium dioxide capacitors were fabricated on silicon wafers using electron-beam evaporation. The TiO2 films varied in thickness from 500 to 2000 A. Post-deposition oxidation at 1000°C in dry O2 was used to promote stoichiometric conversion of the films to the rutile phase. Capacitive densities of greater than 2 pf/sq. mil were obtained (dielectric constants ranged from 4 to 40). For long oxidation times, significant silicon dioxide grows under the TiO2 as a result of oxygen diffusing through the TiO2 film. Titanium was also shown to diffuse into the silicon during the oxidation cycle resulting in an n-type diffusion. Surface state densities ranging from 1011 to 5 × 1011 cm−2 eV−1 at midgap were obtained for good devices. Longer oxidation times result in lower capacitance, leakage current and surface state density.

Thermodynamical analysis of optimal recombination centers in thyristors

Abstract: The main criterion for an optimal recombination center in thyristors has been reformulated, starting from a basic thermodynamical level. From an extended grand canonical ensemble, statistical expressions for the thermal emission rates of an impurity atom are obtained in terms of changes in enthalpy, electronic and vibrational entropy. The ratio between lifetimes at high and low injection levels is evaluated for single and double level recombination centers and calculated for different enthalpy positions and entropy changes of the center and for different resistivities of the thyristor middle region. It is shown that the expected changes in entropy, when a charge carrier is emitted or captured by the center influences the optimal enthalpy position in silicon by as much as 0.1 eV. Also, a complete change in the influence of injection level on lifetime at standard resistivities and temperature for high power devices is noted. The optimization criterion is compared with experimental data pertinent to thyristor optimization. The paper demonstrates the necessity of making a profound thermodynamical analysis of the charge carrier traffic at a recombination center when using experimental data for deep impurities in the optimization of thyristor lifetime ratings.

Carrier density dependence of Auger recombination

Abstract: Auger recombination (AR) is usually assumed to depend on the electron density n and the hole density p like n2p (or np2) But, there are deviations from these rules, mainly in degenerate semiconductors Studying this case the following results were obtained: 1 Normal AR which is only possible in narrow-gap semiconductors goes approximately as np 2 Phonon-assisted AR which predominates in “normal” gap semiconductors (Eg ≈ 1 eV) has the “usual” density dependence n2p 3 Second order AR with two Auger electrons goes with n 7 3 p (instead of an expected dependence n3p) Moreover, the density dependence may be influenced by the screening of the Coulomb interaction and by the strength of the excitation

Recombination at dislocations

Abstract: A dislocation in semiconductors behaves as a recombination flaw having a large number of charge states. The effective cross section of the dislocation is therefore a variable parameter depending by the electrostatic interaction on the occupation factor. This property manifests itself through peculiarities of photoconductivity of dislocated crystals e.g. logarithmic type decay of excess current carriers at low temperature. The elementary centres of recombination are most probably dangling bonds as indicated by spin-dependent effects. The magnitude of the spin-dependent cross section can be explained only if one takes into account the exchange interaction between neighbouring dangling electrons on a dislocation.

High field electronic properties of SiO2

Abstract: The effects of very high electric fields on the transport of electrons and holes in SiO2 are discussed. At fields above 5 × 105 V/cm, electrons emit optical phonons, which is a very efficient energy loss mechanism. Holes on the other hand form small polarons in about 10−12 s, and their mobility becomes very low, but is unaffected by field up to 5 × 106 V/cm. The field dependent generation of electron-hole pairs is fit by application of the geminate recombination theory with a distribution of thermalization distances and excitation by X-rays and bandgap radiation is discussed. The first dependent bulk recombination coefficient is discussed in terms of high field mobility of the electrons. The impact ionization of electrons in SiO2 is discussed by comparing recent results for laser-induced breakdown in SiO2 with experiments on thin films involving photocurrents, space charge buildup and prebreakdown currents, and also theoretical predictions. Below 107 V/cm the laser experiments indicate higher impact ionization rates than the thin film experiments or theory.

Conduction properties of lightly doped, polycrystalline silicon

Abstract: A hyperbolic-sine relationship describing the current-voltage characteristics of lightly-doped, n -type polycrystalline silicon films is derived. The derivation is based on a previous model which assumes that electron-trapping states exist at the grain boundaries of the polycrystalline film. The trapped electrons cause a surface-depletion zone and a potential barrier at each grain boundary. Electrons are transported over the barriers by thermionic emission. Conduction measurements carried out on commercially prepared samples are in good agreement with the theory developed both in voltage and temperature dependence. The model parameters obtained from conduction measurements correspond reasonably well with values inferred from scanning electron micrographs.

Low density photoexcitation phenomena in semiconductors: Aspects of theory and experiment

Abstract: The basic mechanisms related to the photoexcitation of electron-hole pairs in semiconductors under conditions of low excitation density, low temperature and high crystal purity are reviewed. The use of high-resolution emission spectroscopy of band-to-impurity optical transitions in GaAs to measure the energy distribution functions ƒ(E) of electrons and holes in optically excited carrier plasmas of well defined densities (1010 cm−3≤n≤ 1013 cm−3) is described. With this experimental method (i) the energy relaxation of initially hot carrier distributions after pulsed photoexcitation ( h ω ⪢ E g ), (ii) stationary non-equilibrium distributions of electrons in the conduction band under cw photoexcitation ( h ω ≳ E g ) and (iii) the transport properties of resonantly excited carrier plasmas in low electric fields ( 0≤| F |≤20 V/cm ) are investigated. The observed distribution functions are compared with theoretical results on the basis of the known band structure data of GaAs, taking into account polar optic and acoustic phonon scattering, the interaction among the carriers, ionized impurity scattering, and using approximate solutions of the appropriate transport equation.

Metal-N-type semiconductor ohmic contact with a shallow N+ surface layer

Abstract: Most papers covering metal-semiconductor ohmic contact theory which have been published up to date consider systems with homogeneous impurity concentration in the semiconductor. However, there are techniques of ohmic contact formation on nondegenerate semiconductor where only a very shallow surface layer is impurity enriched. In this paper a model of such contacts is proposed and a simple approximate analytical expression for the specific resistivity is derived. If the impurity concentration in the surface layer is very high, the contact specific resistivity is essentially proportional to NB−1, NB being the semiconductor substrate impurity concentration. To make a good ohmic contact, it is sufficient that the width of the heavily doped surface layer be equal to the equilibrium contact depletion region width. Any further enlargement of the enriched layer practically does not influence the total sample resistance due to the dominant share of the semiconductor body resistance. Experimental results confirm these conclusions qualitatively.

High field collision rates in polar semiconductors

Abstract: Quantum transport calculations for hot electrons in polar semiconductors reveal a strong distortion of the high momentum transfer scattering processes by intra-collisional field effects. The electric field induced distortion is analysed in terms of the non-Markonian nature of the conduction process and is dependent upon a finite collision duration. Implications for high field polaron transport in InSb at low temperatures are discussed.

On the multiphonon capture rate in semiconductors

Abstract: In the single-frequency approximation the multiphonon capture-rate into a localized state is characterized by the Huang-Rhys factor S . How S depends upon the energy depth of the trap and the charge on the centre is illustrated in the context of quantum-defect wavefunctions, and two types of electron-phonon coupling: deformation and polar with lattice modes. Simple expressions are obtained for the transition matrix elements using model free-electron wavefunctions.

High-field electronic conduction in insulators

Abstract: The quantum theory of electronic transport phenomena in large electric fields in highly dissipative media is critically examined. Serious conceptual problems and computational difficulties arise because neither the field nor the dissipation can be treated as a perturbation. We review a decade-old calculation of the velocity acquired by an electron in a finite electric field in a polar crystal and subsequent work which expanded our understanding of our method and results. A key feature of the earlier work was that in a single curve of electric field vs velocity, all the expected phenomena appeared, including a threshold field for producing hot electrons, in quantitative agreement with experiment, and a decreasing rate of energy loss with velocity for very fast electrons. A more recently studied problem, that of electron acceleration below the threshold field will be discussed. This problem is very important since such acceleration is the necessary precursor of ionization and breakdown. The physical significance of dissipation processes far from thermal equilibrium will also be mentioned.

Recombination in cadmium mercury telluride photodetectors

Abstract: Cadmium mercury telluride is of considerable importance as a material for the detection of IR radiation. Carrier lifetime has been studied intensively as it is the principal factor controlling detector performance. Bulk lifetime is dominated by Auger processes in the narrow bandgap material sensitive between 8 and 14 μm, while it is dominated by radiative recombination in the wider bandgap material sensitive below 5 μm. Auger processes have been studied by observing the photoconductive decay as a function of temperature. This has led to an experimental determination of the overlap integral as 0.3. A fresh calculation of radiative lifetime by the van Roosbroek-Shockley method has led to an analytic expression that agrees well with observed lifetime. Recombination at discontinuities (contacts, surfaces and flaws introduced in processing) are of importance in the photoconductive detectors. Surface recombination velocity can be reduced to low values (less than 200 cm s−1) in n-type material by obtaining an accumulated surface. The rate limiting processes are then transitions between filled surface states and holes. No such accumulation appears to occur at the contacts or lines of damage introduced in processing. As a result there is considerable recombination at these features. When lifetime is controlled by transit time effects it is called sweepout. In sweepout the dependence of ambipolar mobility on majority carrier concentration leads to novel effects. Auger lifetime is reduced in low carrier concentration samples by optical injection of carriers by the background. This effect has often been ascribed to Shockley-Read recombination. These results are being used in modelling of detector performance that reproduces most of the features seen in practical detectors.

Hot-electron relaxation effects in devices☆

Abstract: Whenever the electric field in a device varies sufficiently rapidly with distance and/or time, significant deviations of the electron drift velocity from the static velocity-field characteristic occur. These relaxation effects manifest themselves not only in the high-frequency properties, but also in the static device properties of devices such as transferred-electron devices and field-effect transistors. Important quasi-static effects are drift velocity overshoot in FET's and relaxation effects in the bistable switching in TE devices. The ultimate speed limitations of TE devices are governed by relaxation effects. Transit-time modes are superior to the LSA mode, barrier-type contacts to n + -on- n contacts, and InP to GaAs.

Temperature coefficient of resistance for p- and n-type silicon

Abstract: The temperature coefficient of resistance for n- and p-type silicon has been calculated between −50 and 125°C for a wide range of concentrations and levels of compensation. These results provide a useful guide for the design of silicon integrated resistors.

The first 70 semiconductor Auger processes

Abstract: Ten basic Auger recombination processes are considered: two phononless and two phonon-assisted band-band processes, four processes involving one type of trap and two donor-acceptor processes. Expressions are obtained for the recombination coefficient by making a constant matrix element approximation, working out the impact ionization rate, and using detailed balance, noting that impact ionization is the inverse process of the Auger effect. Assuming all bands involved (excepting the band which contains the impact ionizing carrier) to be parabolic, described by a diagonalized effective mass tensor, new results for eight of the ten cases are found. Different band structure types lead to a multiplicity of each of the ten processes, yielding seventy different types. They are classified by utilising recent work on impact ionization thresholds as van Hove singularities. Processes involving excitons, pairs of particles bound to the same centre, etc. are not included here and add further Auger-type processes.

Calculation of hot electron phenomena

Abstract: Analytical formulas are generally able to give a better account of a physical phenomenon than can be provided by a numerical description. The latter may be necessary for hot electrons, however, because of the inability of simple physical principles to truly encompass the dynamics of the distribution function, and because of complexity in the band and scattering scheme of the solid, of the particular phenomenon studied, or geometry of the situation. The traditional phenomenon of interest is the steady state with spatial homogeneity, and independent nondegenerate electrons. In suitable conditions the Boltzmann equation then reduces to one in a single variable (energy) which can be solved by relatively simple means. More generally, for this case, we need a numerical computation of the distribution function. Either the latter is represented by its values on a grid of points in the space of the electron variables, and the operators of the Boltzmann equation by operations on this array, or the “history” of a single electron is simulated by a Monte Carlo scheme. The former method has advantages within its range of applicability. Monte Carlo has been extensively applied, because of its greater ability to deal with band and scattering details. It is also applicable, by elaboration of the computational procedures, to a range of phenomena including time dependence; diffusion; impact ionization; effects of carrier-carrier interaction; field-effect surface scattering; thermalization of drifting carriers; semiconductor junctions; effect of degeneracy.

Steady-state characteristics of two terminal inversion-controlled switches

Abstract: The direct current-voltage (I–V) characteristics of three terminal inversion controlled switches are described. These devices are layered sequences of metal/conducting “insulator”/semiconductor junction with electrical terminals at the metal and both sides of the junction. If a bias is applied between the metal and the far side of the junction, in the sense which tends to deplete the surface and forward bias the junction, the device shows bistable impedance states similar to the current-voltage characteristics of a silicon-controlled rectifier. The intermediate terminal which contacts the semiconductor region between the insulator and the junction, can be used, in proper circuit and biasing arrangements, to switch the device both into and out of its low impedance state without varying the voltage supplied to the outer terminals of the device and a series-connected resistor. The I–V characteristics of these three terminal devices support the inversion-controlled conduction model of device behavior which permits high conductivity of the device only when inversion of the semi-conductor surface occurs. The high and low impedance states and the pulses required to induce transistions between states are contained entirely within the “active” bias configuration for these devices, which is defined by analogy with the active bias region of conventional bipolar transistors.

Carrier densities and emitter efficiency in degenerate materials with position-dependent band structure.

Abstract: We consider the electron and hole densities in degenerate and nondegenerate materials with a band structure that is position-dependent and/or having a nonparabolic density of states function. For nondegenerate materials it is shown that the pn -product deviates from its classical value n i 2 for two reasons which generally occur conjunctively. First a modifying factor exp ( ΔE g / kT ) occurs due to the real change in bandgap. Secondly, a factor exp [( Γ n + Γ p )/ kT ] is found stemming from the modified density of states or apparent change in band gap. These effects can be separated by studing the temperature dependence. Next we calculate the minority carrier current and the emitter efficiency and current gain. It is shown that β ψ will be degraded by the increased pn -product and will be further affected by the degeneracy of the emitter material, the direction of the change depending on the doping profiles.

Interband scattering effects on secondary ionization coefficients in GaAs

Abstract: The ionization rates of holes and electrons in GaAs were measured experimentally over a wide doping range covering field values from 2.2×10 5 V/cm to 4.7×10 5 V/cm. As opposed to most experimemental measurements in GaAs, no assumption of equal ionization rates of the two carriers has been made. By using the conventional theoretical relationship between carrier ionization coefficients and multiplication data, the effective α is observed to be larger than β in lightly doped diodes while β is larger than α in heavily doped diodes. Previous theories of ionization rates utilizing just the normal conduction and valence bands do not show any possibility of such a crossover. It is suggested that electron transitions to higher conduction bands, which effectively increase the equilibration time of the electron distribution function, offer a resolution of this difficulty. The dependence of the effective electron ionization rate on doping can be explained by the requirement that electrons must make an interband transition before reaching the ionization threshold energy. This interband transition time estimated by this experiment is of the order of 10 −13 sec and is comparable to the transit time of electrons in the avalanching region. The breakdown voltages extrapolated from the measured α and β are consistent with those observed experimentally.