Impact Ionization Coefficients Research Articles

The hot electron distribution function under impurity breakdown conditions

AbstractThe Boltzmann transport equation is solved by sparse‐matrix method under conditions that are typical for experiments of neutral impurity breakdown at low lattice temperatures. A strong cooling effect due to impact‐ionizing collisions is found on the hot carrier distribution function in moderately doped semiconductors. Implications of the cooling effect on the impact ionization coefficient are discussed. The results of simulation are presented for parameter values that are typical for n‐type GaAs doped with shallow donors and compensating acceptors, and compared with experimental data.

Laser induced impact ionization in semiconductors: A Monte Carlo study for silicon

Monte Carlo computer simulations are carried out to study impact ionization due to a sinusoidal field present in high-power laser pulses. As an application we study the impact ionization coefficient, α, for electrons in silicon as a function of the field frequency, pulse width, and the rms value of the field. In all cases we stay below the frequency values where band-to-band absorption would create electron-hole pairs. As is the case for constant (dc) fields, log α is found to be linear with field strength. For fields oscillating at frequencies much below the inverse of the carrier scattering rate, the impact ionization coefficient is found to have the same value as in the constant field case with the rms field replacing the dc value. At higher frequencies the impact ionization rate decreases. The dependence of α on field frequency and pulse width is studied.

Impact ionization model for full band Monte Carlo simulation in GaAs

The impact ionization rate in GaAs is derived from a first principle’s calculation which includes realistic band structure and a wave-vector- and frequency-dependent dielectric function. The impact ionization rate is highly anisotropic at low electron energy, while it becomes isotropic at higher energy range in which impact ionization events frequently occur. The calculated impact ionization rate is well fitted to a modified Keldysh formula with two sets of power exponents of 7.8 and 5.6, indicating very soft threshold characteristics. Using a full band Monte Carlo simulation which includes the empirical phonon scattering rate based on first principles theory, we derived the impact ionization coefficient. The calculated impact ionization coefficients agree well with available experimental data. Our isotropic model shows better agreement with reported experimental data than a previous anisotropic model, especially in low electric field. The mean energy of secondary generated electrons is found to be expressed as two sets of linear functions of the primary electron energy.

Resonant-cavity enhanced (RCE) separate absorption and multiplication (SAM) avalanche photodetector (APD)

We report a highly-efficient and wavelength-selective separate absorption and multiplication (SAM) avalanche photodiode (APD) with a thin (500 /spl Aring/) absorbing layer. The improved characteristics of the photodetector were obtained by placing the absorption and multiplication layers in a Fabry-Perot cavity. An external quantum efficiency of 77% was achieved with a spectral linewidth of less than 4 nm and an avalanche gain of more than 50. Noise measurements indicate that the impact ionization coefficient for electrons is larger than that for holes.

Deterministic modeling of impact ionization with a random-k approximation and the multiband Boltzmann equation

We present here an approach for determining impact ionization coefficients for the spherical multiband model in silicon. Using random-k approximation, the impact ionization rate is determined to reflect the multiband density of states in silicon. To account for the actual density of states, we have solved four coupled Boltzmann transport equations by combining a generalized Legendre polynomial expansion method with numerical techniques using finite differences and sparse matrices. Calculated values for the impact ionization coefficients agree with experiments for electrons in silicon, while being obtained in significantly less CPU time than required by analogous Monte Carlo calculations. Different multiband transport parameter sets are also compared.

Impact ionization in balance equation theory

We present a theoretical investigation of electron impact ionization processes under a high electric field within the framework of the Lei-Ting balance equation approach in the case where the hole gas is approximately in thermal equilibrium. An expression for the impact ionization coefficient for an arbitrary conduction band is obtained. As an example, the impact ionization coefficient of bulk InSb is calculated in the approximation of a parabolic conduction band and the result is compared with existing experimental data.

An isotropic two band model for hot electron transport in silicon: Including electron emission probability into SiO2

An isotropic two band model is proposed for electrons in silicon, that has the same density of states and magnitude of group velocity as those of the full band structure based on empirical pseudopotential method calculations. The band model and transport parameters are calibrated through extensive comparisons with Monte Carlo simulation results and various experiments related to electron transport in silicon. Specifically, the drift velocity, impact ionization coefficient, quantum yield, 2p core level line intensity and broadening from x-ray photoemission spectroscopy have all been used in calibration. Through the study of electron emission at the Si/SiO2 interface in metal-oxide-semiconductor structures using the Monte Carlo method, it is demonstrated that the model has good accuracy in modeling high field transport phenomena in silicon.

Impact ionization coefficients in (100) GaInP

Electron and hole impact ionization coefficients in (100)Ga0.5In0.5P have been measured by photomultiplication measurements. The ratio of hole to electron ionization coefficients, β/α, is shown to decrease from 2 to 1 when the electric field is increased from 3.5×105 to 6.5×105 V/cm. As confirmation, breakdown voltages were measured for several p+−n−−n+ diodes with various concentrations in the n− region. The values observed showed good agreement with those calculated from the ionization coefficients. Typical breakdown voltages are on the order of 1.6 times higher than those expected for GaAs.

Impact ionization in GaAs metal–semiconductor field-effect transistors with a lightly doped drain structure and an Al0.2Ga0.8As/GaAs heterobuffer layer

Kink effects (abrupt increases in drain current) were observed with an abrupt increase of gate current (IG), substrate current (Isub), substrate potential (Vsub), and photoemission intensity (Iphoto) in GaAs metal–semiconductor field-effect transistors (MESFETs) with a lightly doped drain (LDD) structure and an Al0.2Ga0.8As/GaAs heterobuffer layer. The kink drain voltage (VKD) increases as substrate temperature increases. Since impact ionization has a negative coefficient for increase of temperature, the increase of VKD indicates that impact ionization occurs at VKD. VKD also increases as VG becomes more negative and as the ratio of the dose of the silicon ions is reduced in the LDD region. Thus it is confirmed that impact ionization occurs at the drain side along the channel current path because those changes of VG and dose ratio reduce the electric field at the drain-side channel. In addition, impact ionization coefficients were calculated from IG and Isub based on the method proposed by Hui et al. Both the coefficients were exponentially proportional to the negative inverse of the electric field, although the magnitude of Isub was approximately 250× greater than that of IG. On the other hand, it was found that Iphoto was linearly proportional to Vsub. It suggests that Iphoto depends on the number of holes which overflow the n-GaAs channel/i-GaAs buffer interface potential barrier into the channel layer. These behaviors of IG, Isub, Iphoto, and Vsub are attributed to this FET structure which has a thin channel layer with a high donor density and a heterobuffer layer.

Measurement of the electron ionization coefficient at low electric fields in InGaAs-based heterojunction bipolar transistors

The behavior of the electron impact-ionization coefficient αn in In0.53Ga0.47As is measured with unprecedented sensitivity down to very low electric fields. The data are derived from measurements of the multiplication coefficient M−1 in suitably designed heterojunction bipolar transistors. Previously available data are extended by two orders of magnitude in the low field domain, down to αn≊1 cm−1. The experimental behavior of αn at fields below 200 kV/cm is in agreement with the theoretical prediction of a weak field dependence of αn at low electric fields.

Temperature dependence of the electron impact ionization coefficient in silicon

We have used a Monte Carlo simulation to study the temperature dependence of the electron impact ionization coefficient in silicon. On the basis of the results of the Monte Carlo calculations, we propose an empirical model for the impact ionization coefficient as a function of electric field or average electron energy, which is applicable over a wide range of lattice temperatures.

Spatio-temporal impact ionisation transients: A Lucky drift model study in GaAs

The impact ionisation occurring under a high field in a semiconductor can be described in terms of the ionisation coefficient, the number of ionisation events directly produced by a carrier per unit length it travels. The position dependence of this impact ionisation coefficient is at present poorly understood, and is usually assumed to be constant, possibly with the inclusion of a deadspace length (where the coefficient is zero). It is more complicated in reality however as spatial oscillations can occur. In this paper we employ a Lucky drift model to give an explanation of the origin of spatial oscillations in the coefficients, and the way their features vary with a range of model parameters is investigated. In addition to constant fields, a piecewise linear/constant field is modelled, as is a quantum barrier placed in a region of constant fields. The results are specifically for GaAs, but have qualitative validity for the other wide bandgap III–V's. A realistic value for effective electron deadspace in GaAs is obtained, which is approx. 1.3 times the minimum deadspace.

Impact ionization coefficients in Si1−xGex

We have measured the electron and hole impact ionization coefficients in Si1−xGex alloys. Carrier multiplication measurements were made on relaxed Si1−xGex/Si diodes grown by gas source molecular beam epitaxy. The hole to electron impact ionization coefficient ratio, β/α, varies from 0.3 to 4 in the composition range of x=0.08–1.0.

Measurement of Electron Impact Ionisation and Attachment Coefficients in NO2/He Gas Mixtures and Estimated Electron Collision Cross Sections for NO2

The electron impact ionisation a/po and attachment coefficients r]/po in N02/He gas mixtures, where po is the gas pressure at O�C, are measured by a steady-state Townsend method over a wide range of compositions and E/po values. Based on the experimental values of a/po and r]/ po, a preliminary set of the cross sections for N02 is estimated by a Boltzmann equation analysis and values of the cross sections are discussed.

Reaction rates for dense nonideal alkali plasmas

The quantum statistical theory of collisional rate coefficients of nonideal plasmas, developed in some recent papers for hydrogen, is applied to calculate the impact ionization and three-body recombination coefficients for the valence electron of the atoms in Li-, Na-, K-, Rb- and Cs-plasmas. The many-body effects are included by static screening in the quasiparticle energy shifts and in the effective potentials. Because the ionization of alkali atoms represents a multielectron problem, an effective two-body electron-ion potential is derived using the method of close coupling equations of quantum scattering theory. The latter is replaced by a suited two-parametric pseudopotential taking into account the shielding effects of the inner shell atomic electrons. Finally, numerical results are given for the ionization cross sections and the rate coefficients.

Nonequilibrium Phase Transition and Current Filaments in Extrinsic Semiconductors

Abstract A phenomenological model for charge transport in extrinsic semiconductors is presented. For shallow impurities, large saturated impact-ionization coefficient and sufficiently low lattice temper­ature, the current-field characteristic is S-shaped (SNDC) due to the interplay between impact ionization and scattering of carriers from acoustic phonons, ionized and neutral impurities. The present model provides and explanation of the experimentally observed disappearance of SNDC above a critical lattice temperature. In the region of negative differential conductivity where a current-controlled uniform state is unstable, current filaments are calculated numerically.

Procedure for fitting Monte Carlo calculated impact ionization coefficient to experiment

A procedure for fitting of Monte Carlo calculated impact ionization coefficient to experimental data has been proposed. This procedure has been applied for optimization and sensitivity analysis of fitting parameters of impact ionization model for electrons in Si. Strong correlation between threshold energy and preexponential factor of the impact ionization model and redundancy of power exponent have been found. A wide range of data on impact ionization coefficient can be fitted by adjusting the parameters of the microscopic impact ionization model.

Modeling of the hot electron subpopulation and its application to impact ionization in submicron silicon devices-Part I: transport equations

Impact ionization (II) in three different n/sup +/-n/sup -/-n/sup +/ device structures is investigated using self-consistent Monte Carlo simulations. A subset of electrons participating in II-referred to as the hot electron subpopulation (HES)-is identified. The data obtained from the Monte Carlo (MC) simulations indicate that the average energy of the HES (/spl omega//spl tilde/) is an appropriate variable for the macroscopic quantification of II in all the devices under consideration. In order to calculate /spl omega//spl tilde/, a set of macroscopic transport equations for the HES is derived from the Boltzmann transport equation and calibrated using data from the MC simulations. Numerical solutions to the proposed II model applied to the three devices considered here will be presented in Part II. Therein, values of the II coefficient (IIC) predicted by our model will be compared to those obtained from our MC simulations and also to IIC values predicted by models proposed earlier by other authors. >

Effect of impact ionization coefficient ratio on gain and frequency response of an avalanche photodiode

The frequency response of an avalanche photodiode is computed by solving the carrier transport equation in both the multiplication and the absorption regions numerically for different values of the ionization rate. The ionization coefficient rate and the velocity of the carriers are electric field dependent and vary with distance. An expression for the ionization rate and the carrier velocity as function of distance is assumed. The calculated bandwidth has a minimum value when the ionization rate ratio α( x = 0) / β( x = 0) approaches unity, and enhances as the ionization rate α( x = 0) and β( x = 0) has different value. The avalanche photodiode gain is also determined for different values of the ionization rate.

Laser-induced breakdown by impact ionization in SiO2 with pulse widths from 7 ns to 150 fs

Results of laser-induced breakdown experiments in fused silica (SiO2) employing 150 fs–7 ns, 780 nm laser pulses are reported. The avalanche ionization mechanism is found to dominate over the entire pulse-width range. Fluence breakdown threshold does not follow the scaling of Fth∼ √τp, when pulses are shorter than 10 ps. The impact ionization coefficient of SiO2 is measured up to ∼3×108 V/cm. The relative role of photoionization in breakdown for ultrashort pulses is discussed.