Impact Ionization Model Research Articles

Modeling of the hot electron subpopulation and its application to impact ionization in submicron silicon devices-Part II: numerical solutions

A macroscopic transport model for the hot electron subpopulation (HES) and a nonlocal impact ionization (II) model were proposed in Part I of this article: see ibid. p. 1200, 1994. The transport equations have been derived from the Boltzmann transport equation (BTE) and closure has been provided by an empirically determined equation. The transport equations and the II model have been calibrated using data obtained from self-consistent Monte Carlo (SCMC) simulations. In this article we present the numerical solutions obtained by applying the proposed model to n/sup +/- n/sup -/-n/sup +/ structures with various doping profiles. The results are compared to the data obtained from SCMC simulations and also to those obtained from models proposed earlier by other authors.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Charge generation in metal-oxide-semiconductor capacitors during Fowler-Nordheim stress

Experimental ob~ervation~ are reported cnncerning the influence of ~ome technologi- cal processes on the generation rate of positive oxide charge and interface states during high electric field stress. Our results on positive oxide charge generation are consistent with a model of impact ionization in silicon dioxide and we think that acoustic-phonon runaway is the controlling process for impact ionization in SiO~ in films thicker than 20.0 nm at fields higher than 7 MV/cm. We have found that the positive charge is mainly due to trapped holes when the electrons are injected at the gate/SiO~ interface. ~~~~~~ ~'~~ (l)

Impact ionization model for full band Monte Carlo simulation

The impact ionization rate in silicon is numerically derived from wave functions and energy band structure based on an empirical pseudopotential method. The calculated impact ionization rate is well fitted to an analytical formula with a power exponent of 4.6, indicating soft threshold of impact ionization rate, which originates from the complexity of the Si band structure. The calculated impact ionization rate shows strong anisotropy at low electron energy (ε&amp;lt;3 eV), while it becomes isotropic at higher energy. Numerical calculation also reveals that the average energy of secondary generated carriers depends linearly on the primary electron energy at the moment of their generation. A full band Monte Carlo simulation using the newly derived impact ionization rate demonstrates that calculated quantum yield and ionization coefficient agree well with reported experimental data.

A Monte Carlo simulation of anisotropic electron transport in silicon including full band structure and anisotropic impact-ionization model

The physics of electron transport in bulk silicon is investigated by using a newly developed Monte Carlo simulator which improves the state-of-the-art treatment of hot carrier transport. (1) The full band structure of the semiconductor was computed by using an empirical-pseudopotential method. (2) A phonon dispersion curve was obtained from an adiabatic bond-charge model. (3) Electron-phonon scattering was computed by using a rigid pseudo-ion model. The calculated scattering rate is consistent with the full band structure and the phonon dispersion curve of silicon, thus leaving no adjustable parameters such as deformation potential coefficients. (4) The impact-ionization rate was calculated by using Fermi’s golden rule directly from the full band structure. We took into account the dielectric function depending on both wave vector and transition energy in the numerical calculation of the rate. The impact-ionization rate obtained in the present study strongly depends on both wave vector and band index of the conduction electron, which is ignored by the traditional Keldysh formula. (5) In the simulator, the final state of a scattering electron is determined in such a way as to conserve both energy and momentum in scattering processes. The simulated results, under the steady-state conditions as well as under the nonequilibrium conditions, are presented and compared with experimental results. Special attention is focused on anisotropic transport during velocity overshoot. Quantitative agreement between calculated and experimental results confirms the validity of the newly developed Monte Carlo simulator and the physical models that were used.

Breakdown voltage in ultra-thin pin diodes

The semianalytic trajectory method for hot carrier transport is combined with a new model for impact ionization to study breakdown in ultra-thin pin diodes where the dead space and spatial transient can dominate the ionization physics. Good agreement with the published data of Gaul et al (1991) is achieved.

Transient hot-electron effect and its impact on circuit reliability

Transient hot-electron effect and its impact on circuit reliability are investigated. The rate of device decay is monitored as a function of the gate pulse transient period. Simulation results reveal that excess charges during a fast turn off time may cause an increase in the maximum substrate current. This, along with our experimental data, identifies that transient excess carrier may cause the enhancement of device degradation under certain stress conditions. The enhancement factor of the degradation is a function of the gate pulse transient time. Correlation between the analysis based upon AC/DC measurement and calculations based upon transient simulation are shown in the paper. Better agreement with experimental data is obtained by using the transient analysis and on chip test/stress structures. The correlation between AC and DC stress data is also shown based on the impact ionization model. A hot-electron design guideline is proposed based on the circuit reliability analysis. This guideline can help improve the circuit reliability without adversely effecting the circuit performance.

INVESTIGATIONS OF A NEW IMPACT IONIZATION MODEL FOR SUBMICRON DEVICES

We discuss the device applications of a new impact ionization model. This model is based on a new formulation of the impact ionization rate for bulk semiconductors, derived from solvable high‐field Boltzmann transport equations. The model inputs are relaxation times which simulate the dominant electron‐phonon scatterings and are calibrated by realistic Monte Carlo simulations. Our impact ionization model is shown to be physically motivated and is easily implemented in the standard hydrodynamic device simulators HFIELDS and FIELDAY. An efficient numerical scheme is used to simulate three thin‐base silicon bipolar transistors. Results based on this impact ionization model are found to agree well with the experimental multiplication factors over a large range of applied voltages. These results are contrasted with the more phenomenological treatment of Scholl and Quade which is shown to be a low‐field limit of our model.

Design considerations of silicon avalanche cathodes

Silicon avalanche cathodes using ultrashallow p–n junction have been used as a current source in vacuum microelectronics and have shown promising potential for device applications. In this article, device simulation results with a two-dimensional, two-carrier device modeling program which simultaneously solves Poisson’s and both the electron and hole continuity equations are presented. The simulation includes impurity concentration and electric field dependent mobility models, impurity concentration dependent Shockley–Read–Hall and Auger recombination, band gap narrowing, and impact ionization model. Due to the small vertical dimension of the n-type shallow channel, the nonplanar surface structure resulting from subsequent processing steps influences the device performance. The simulation results indicate locations of current crowding in our prototype devices. In order to achieve maximum emission current density, it is very important to obtain a uniform emission across the entire emitter areas. The design considerations are discussed for the improved performance of the silicon avalanche cathodes.

Numerical analysis of kink effect in HJFET with a heterobuffer layer

The kink effect in an AlGaAs/GaAs HJFET with a heterobuffer layer is investigated using a two-dimensional device simulator with impact ionization and deep-trap models. It is confirmed that the accumulation of holes generated by impact ionization causes the kink effect. The influence of deep levels on the kink characteristics is also investigated. The kink effect is suppressed by electron traps in the channel region through the recombination of the generated holes. On the other hand, the kink effect is enhanced by hole traps, which are positively ionized by increases in hole concentration. However, excessive hole trap concentration suppresses the accumulation of holes, due to enhanced recombination with electrons. Under such conditions the kink effect vanishes. >

Monte Carlo analysis of band structure influence on impact ionization in InP

The influence of electronic band structure on the impact ionization phenomena in InP was studied using the Monte Carlo method. Realistic band structures evaluated using the nonlocal pseudopotential method were employed. Threshold energies for impact ionization were calculated throughout the first Brillouin zone. A new impact ionization model which explicitly takes into account the wave-vector dependence of impact ionization threshold energies was used to calculate the ionization rate. The simulation results of drift velocity and ionization coefficient agree very well with experimental data. In spite of significant anisotropy in the threshold energies and complex band structures, no significant orientational dependence was found in the ionization coefficients. An important result of the work presented here is the demonstration that the biaxial elastic strain in InP produced by the lattice mismatch between adjacent layers in a heterostructure can significantly alter the impact ionization thresholds.

A physics-based fitting and extrapolation method for measured impact ionization coefficients in III-V semiconductors

A general approach based on a physical model of impact ionization to fit and extrapolate measured ionization coefficients of electrons α and holes β in III-V semiconductors is described. Materials being considered include GaAs, AlxGa1−xAs (x=0.1–0.4), InP, In0.53Ga0.47As, and In0.52Al0.48As. Expressions giving the correct dependencies are obtained at very large or small electric fields outside the range of most measurements while at the same time a reasonable fit is achieved for experimental data. The results of the proposed approach yielded a set of physical parameters, which can be coupled with the temperature-dependence relationships in the model to predict impact ionization coefficients over a wide range of electric fields at different temperatures, and can be useful in calculations of temperature-dependent avalanche breakdown voltages of electronic and optical devices.

Direct simulation of re-entry flows with ionization

The Direct Simulation Monte Carlo (DSMC) method is applied in this paper to the study of rarefied, hypersonic, re-entry flows. The assumptions and simplifications involved with the treatment of ionization, free electrons, and the electric field are investigated. A new method is presented for the calculation of the electric field and handling of charged particles with DSMC. In addition, a two-step model for electron impact ionization is implemented. The flowfield representing a 10-km/s shock at an altitude of 65 km is calculated. The effects of the new modeling techniques on the calculation results are presented and discussed.

Two-dimensional analysis of the breakdown mechanism in the etched-groove silicon permeable base transistor

A two-dimensional, two-carrier simulation of a uniformly doped etched-groove permeable-base transistor which includes models for impact ionization and for Auger and Shockley-Read-Hall recombination is reported. It was found that for high current densities the breakdown voltage was reduced by channel avalanche. This mechanism was associated with a strong accumulation of electrons and holes in the source access region. In this region, the gate current remained low but the injection of electrons in the channel was enhanced, resulting in a degradation of the drain conductance and frequency performance.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Hydrodynamic simulation of electron heating in conventional and lightly‐doped‐drain MOSFETs with application to substrate current calculation

AbstractThis paper reviews the state of the art in hydrodynamic simulation of hot‐carrier transport in semiconductor devices with application to MOSFET substrate current calculation. Hydrodynamic equations for semiconductors and derived and discretized expressions of these equations for device simulation are presented. Special attention has been given to the discretization of the input power term that appears in the energy conservation equation. A new discretization method for the input power term, based on power generation consideration, is proposed. Energy‐based physical models for mobility and impact ionization are described for use in hydrodynamic simulation. Simulation results for both conventional and lightly‐doped‐drain MOSFETs are presented.

Experimental study of transport in a trap-dominated relaxation semiconductor.

The term ``relaxation semiconductor'' has been used to define a category of high-resistivity semiconductors in which the dielectric relaxation time exceeds the recombination lifetime (${\mathrm{\ensuremath{\tau}}}_{\mathit{D}}$\ensuremath{\gg}${\mathrm{\ensuremath{\tau}}}_{0}$). The transport behavior of semi-insulating GaAs, a trap-dominated relaxation semiconductor, in response to minority-carrier injection has been experimentally investigated. Using a ${\mathit{p}}^{+}$-\ensuremath{\nu}-${\mathit{n}}^{+}$ structure, the I-V characteristics have been probed over seven orders of magnitude in current and various regimes have been identified. The experimental results have been compared with previous numerical modeling. A sublinear regime at high bias has been shown to be associated with enhanced trapping by the midgap defects. Impact-ionization processes involving the traps have been demonstrated to be the cause of a sudden rise of current at threshold fields of approximately 1400 V/cm, and the data have been compared to a simple impact-ionization model.

Monte Carlo Analysis of Hot Electron Transport and Impact Ionization in Silicon

A novel impact ionization model which is consistent with a realistic band structure of Si has been developed. The present model contains only one parameter directly corresponding to the average matrix element for the ionization transition. The ionization probability is calculated at every k-point in the first Brillouin zone and the intrinsic anisotropy of the ionization probability is explicitly taken into account. Employing the Monte Carlo procedure including the present ionization model, the ionization coefficients are calculated and a best-fitting to the experimental ionization coefficients is obtained when the value of the parameter in the ionization model is equal to that extracted from the first-principles calculations.

SMART-II: a three-dimensional CAD model for submicrometer MOSFET's

The authors describe a three-dimensional CAD model for submicrometer MOSFETs. The model has been implemented in a three-dimensional process/device integrated simulator, SMART-II, using a supercomputer. The MOS device model for hot electron transport is based on a modified current relation including an electron temperature effect in an inhomogeneous field. The need for an improved mobility model in an inversion layer and an impact ionization model using the recent experimental data for the mean free path is discussed with emphasis on the numerical simulation for I/V characteristics of small-geometry MOSFETs from the threshold regime to the avalanche regime. It is found that this approach is effective in realizing a three-dimensional CAD model for 0.5- mu m MOSFETs. An application of the model reveals a three-dimensional effect of avalanche breakdown behavior in small-geometry MOSFETs.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

An improved impact-ionization model for high-energy electron transport in Si with Monte Carlo simulation

A new model for impact ionization in Si is presented, which goes beyond the limitations of the Keldysh formula and is based on a more realistic scheme developed starting from a first-order perturbation theory. This scattering mechanism is modeled by an extended band structure which includes many bands for electrons and one band for holes in a finite Brillouin zone. Some processes have been identified to bring the dominant contribution to the scattering probability, in the present approach, for electron energies ranging up to 3 eV. Expressions for the differential and integrated scattering probabilities have been obtained which are consistent with the band model and can be included in a Monte Carlo simulation of the electron gas. Results for transport quantities are shown for a bulk material in presence of homogeneous and static electric fields under physical conditions where impact ionization influences the carrier dynamics. A comparison with theoretical and experimental data from the literature is also given.

Monte Carlo simulations of high energy electrons and holes in Si-n-MOSFET's

Monte Carlo simulations of high-energy electrons and holes in Si n-MOSFETs are presented. Key features of this work include the use of a suitable silicon model for carrier transport at high electric fields, an original impact ionization model, and sophisticated numerical techniques to speed up the calculation. The case of submicrometer Si n-MOSFETs is considered as a relevant application.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Effect of electron temperature and impact ionization on Martian return AOTV flowfields

Various electron impact ionization models in conjunction with a quasi-equilibrium electron temperature model have been investigated and applied to the stagnation region of a hypothetical 2.3 m nose radius Martian return AOTV. For the conditions considered, U = 12 km/sec at 80 km, both multi-temperature inviscid and viscous results indicate that a two-step ionization impact model predicts ionization distances in agreement with experimental data, that nonequilibrium chemistry and radiation effects are important throughout the stagnation zone, and that the quasi-equilibrium electron temperature model is reasonable. Also, using a non-grey emission-absorption radiation step model, it is shown that nonequilibrium causes a reduction in radiative heating from that predicted for equilibrium conditions and that compared to an adiabatic wall a cool wall (1650 deg K) results in a 28 to 45 percent reduction in radiative heating due to absorption near the wall.