Threshold energy effect on avalanche breakdown voltage in semiconductor junctions

The band bending for avalanche breakdown in semiconductor junctions and its temperature dependence are predicted taking account of threshold energy effects on the ionization process in semiconductors. Where experimental results exist, the theoretical predictions and experimental results are in excellent agreement. In the high electric field region inclusion of both bulk and boundary threshold energy effects is essential. The predictions were based on exact solutions in the nonlocalized ionization coefficient formulation developed by Okuto and Crowell who showed that ionization coefficients as usually understood are functions of both electric field and position in a device. Predictions for abrupt and p-i-n junctions in Ge, Si, GaAs and GaP are presented.     

Sloped-junction LDD (SJLDD) MOSFET structures for improvedhot-carrier reliability

Sloped-junction lightly doped drain (SJLDD) structures, for 0.5- μm channel length MOSFETs, which exhibit exponential improvement in lifetime under high-field stress with source-drain implant energy are discussed. The improved lifetime correlates with reduced drain electric fields and increased depth of peak avalanche below the silicon-silicon dioxide as determined by simulation. The results present an interesting instance where the substrate current fails as a hot-carrier monitor and provide indirect evidence of a energy-dependent electron mean-free path decreasing from the known 5.7 nm at the impact ionization threshold to less than 3.2 nm at kinetic energy of about 4.6 eV     

Ga1-xAlxSb avalanche photodiodes: Resonant impact ionization with very high ratio of ionization coefficients

The liquid-phase epitaxy and device fabrication of p-n and p-i-n Ga1-xAlxSb avalanche photodiodes is described. Breakdown voltages up to 95 V and dark currents of 10^-4A/cm²have been obtained. With p-i-n diodes we have measured the impact ionization coefficients α (electrons) and β (holes) with different composition and temperature. A resonant enhancement of the hole ionization coefficient is found forx = 0.065(300 K) where the ratiobeta/alphaexceeds values of 20. This effect is attributed to impact ionization initiated by holes from the split-off valence band: if the spin orbit splitting Δ is equal to the bandgap energy Eg, the threshold energy for hole initiated impact ionization reaches the smallest possible value (E_{i} = E_{g}) and the ionization process occurs with zero momentum. This leads to a strong increase of β atDelta/E_{g} = 1. The experimentally determined dependence of ionization coefficients on threshold energy is compared with theoretical expectations.     

An avalanche photodiode with metal-insulator-semiconductor properties

A new design of the avalanche photodetector combining the avalanche photodiode and MIS structure properties was tested. The noise and high-frequency properties of the device were studied. The device exhibited a noise factor of less than 10 at a high multiplication factor (M>1000) even with hole injection. This is indicative of a drastic change in the effective ratio of the coefficients of impact ionization by electrons and holes in favor of the latter. Measurements of the photosensitivity distribution over a photodetector area for M=8000 showed a high uniformity.     

Influence of base thickness on collector breakdown in abruptAlInAs/InGaAs heterostructure bipolar transistors

The avalanche process in the collector of abrupt Al_0.48In_0.52As-In_0.53Ga_0.47 As heterostructure bipolar transistors (HBTs) is reported. It is reported that the collector multiplication constant decreases monotonically with increasing base thickness. When the base thickness is less than the mean-free path for energy relaxation in the base, the avalanche process in the collector is enhanced by high-energy injection from the emitter. On the other hand, no such dependence is observed for long-base transistors with equilibrium base transport. These effects are expected as the emitter injection energy of 0.48 eV is appreciable compared to the impact ionization threshold of 0.83 eV in the InGaAs collector     

Effect of dead space on gain and noise in Si and GaAs avalanchephotodiodes

The effect of dead space on the mean gain, the excess noise factor, and the avalanche breakdown voltage for Si and GaAs avalanche photodiodes (APDs) with nonuniform carrier ionization coefficients are examined. The dead space, which is a function of the electric field and position within the multiplication region of the APD, is the minimum distance that a newly generated carrier must travel in order to acquire sufficient energy to become capable of causing impact ionization. Recurrence relations in the form of coupled linear integral equations are derived to characterize the underlying avalanche multiplication process. Numerical solutions to the integral equations are obtained and the mean gain and the excess noise factor are computed     

Effect of dead space on avalanche speed [APDs]

The effects of dead space (the minimum distance travelled by a carrier before acquiring enough energy to impact ionize) on the current impulse response and bandwidth of an avalanche multiplication process are obtained from a numerical model that maintains a constant carrier velocity but allows for a random distribution of impact ionization path lengths. The results show that the main mechanism responsible for the increase in response time with dead space is the increase in the number of carrier groups, which qualitatively describes the length of multiplication chains. When the dead space is negligible, the bandwidth follows the behavior predicted by Emmons but decreases as dead space increases     

History-Dependent Impact Ionization Theory Applied to HgCdTe e-APDs

The variation of the gain and the excess noise factor in HgCdTe avalanche photodiodes (APDs) with different junction geometries are compared with published theoretical and numerical work. It is shown that, although some features of the gain curves are reproduced, such as the constant exponential increase in the gain, the theoretical work fails to predict the observed variation of the gain as a function of multiplication layer width. In contrast, a new analytical gain model based on local impact ionization coefficients and a first direct comparison of the prediction of history-dependent impact ionization theory are shown to give a good general fit to the experimental gain data. A generic model of the gain in HgCdTe APDs has been obtained by fitting the analytical local model to gain curves of APDs with various geometries and cut-off wavelengths. The study of different hypotheses on the electric field dependence of the dead-space length and the saturation value of the impact ionization coefficient has shown that a variable dead-space effect has a direct impact on the excess noise of APDs, which is why exact excess noise measurements are necessary to achieve a pertinent estimation of the nonlocal impact ionization function.     

Theory of steady-state plane tunneling-assisted impact ionization waves

The effect of band-to-band and trap-assisted tunneling on the properties of steady-state plane ionization waves in p ⁺-n-n ⁺ structures is theoretically analyzed. It is shown that such tunneling-assisted impact ionization waves do not differ in a qualitative sense from ordinary impact ionization waves propagating due to the avalanche multiplication of uniformly distributed seed electrons and holes. The quantitative differences of tunneling-assisted impact ionization waves from impact ionization waves are reduced to a slightly different relation between the wave velocity u and the maximum field strength E _M at the front. It is shown that disregarding impact ionization does not exclude the possibility of the existence of tunneling-assisted ionization waves; however, their structure radically changes, and their velocity strongly decreases for the same E _M . A comparison of the dependences u(E _M ) for various ionization-wave types makes it possible to determine the conditions under which one of them is dominant. In conclusion, unresolved problems concerning the theory of tunneling-assisted impact ionization waves are discussed and the directions of further studies are outlined.     

Avalanche multiplication properties of GaAs calculated from spatially transient ionisation coefficients

In this paper the high field phenomenon of avalanche multiplication in a GaAs p-i-n infrared detector is studied using a Monte-Carlo simulation. The Lucky-Drift model of impact ionization is used to give the characteristic lengths for transport through the device. The transport is then modelled by generating motion consistent with the probability functions derived from the mean free paths. This produces a spatially transient ionization coefficient for each carrier and allows the realistic statistical simulation of avalanche multiplication. Properties such as mean gain, multiplication noise and the transient response to a photonic pulse have been calculated and explained for a length of i-GaAs, with an emphasis on short active region phenomena. The effect on the ionization coefficients of a periodic field change has been investigated. It has been found that the effective carrier deadspace is approx. 1.35 times the absolute deadspace. The transient current calculations indicate the narrow bandwidth of this type of device. The presence of a periodic field change, caused by periodic δ-doping, was found to increase both electron and hole ionization coefficients by different proportions.     

Simplified particle simulation of millimeter-wave IMPATT devices

A simplified microscopic model for investigating energy relaxation effects in millimeter-wave IMPATT devices is presented. A statistical process is used to describe electron-hole multiplication by impact ionization from knowledge of the ionization coefficients. These coefficients are assumed to be functions of the individual energy of carriers (holes and electrons). A relaxation time formulation is used to calculate the energy of each carrier. Drift in the electric field and diffusion are modeled using the diffusive model proposed by Hockney. Simulations are carried out for silicon diodes. It is found that inclusion of the energy relaxation mechanisms modifies mainly the avalanche process for such material. The implications of these mechanisms on device performances are then discussed by calculating the large signal level dependence of the conversion efficiency and admittance for a typical double-drift structure at 100 GHz. The resulting calculations show good agreement with existing experimental data on these structures.     

Small-signal analysis of the Read avalanche diode

A small-signal analysis is made on the Read-type avalanche transit time diode in which both holes and electrons and differing ionization rates for holes and electrons are considered in a silicon diode. The avalanche region is assumed to be an unsymmetric abrupt junction in which the ionization coefficients vary with the distance through their exponential dependence on the field in the avalanche region. Solutions for the ionization integral are given in the dc case. The time-varying terms are introduced as small-signal perturbations on the dc case and solutions for the ionization integral are again obtained and expressed as a Fourier series. The coefficients of the series appear in the expressions for the admittance. This approach provides simple analytical solutions for the Read diode admittance. Also, direct evaluation of the Fourier coefficients is given in terms of the diode's breakdown voltage and other known parameters. An equivalent circuit for the Read diode is developed. Over a substantial frequency but for small transit angles of the drift region, it consists of a frequency independent negative conductance, inductance, and capacitance. The diode's spreading resistance is in series with these parallel elements. The circuit agrees with the measurements of Josenhans and Misawa. On the basis of the small-signal avalanche analysis the ultimate oscillator efficiency is estimated to be about 26 percent.     

Hg0.56 Cd0.44 Te 1.6- to 2.5-μm avalanchephotodiode and noise study far from resonant impact ionization

An investigation was made on the avalanche multiplication and impact ionization processes in p-n^--n⁺ junctions formed in Hg_0.56Cd_0.44Te solid solutions. Photocurrent multiplication was determined at 300 K in planar p-n^- -n⁺ structures characterized by a breakdown voltage of 30 V. The experimental results were used to calculate the electron, α, and hole, β, ionization coefficients. It was found that α is greater than β because Δ, the spin-orbit splitting energy, is higher than the bandgap energy. These experimental results were in satisfactory agreement with multiplication noise measurements using separate electron and hole injection     

"Soft" energy thresholds in impact ionization: A classical model

A new simplified approach to the problem of "soft" threshold energy in impact ionization in semiconductors is presented. The model used is entirely classical and leads to a simple exact formula for the ionization rate as a function of energy. This result is used as the basis for modifying the "lucky drift" model of impact ionization, as has been done previously for other models of the "soft" threshold. The final analytic relations show excellent agreement with the available experimental data for the ionization coefficients in GaAs but indicate that the impact ionization process may involve three (or more) incident particles rather than two as previously thought.     

Temperature dependence of carrier ionization rates and saturated velocities in silicon

The temperature dependencies of the carrier ionization rates and saturated drift velocities in silicon have been extracted from microwave admittance and breakdown voltage data of avalanche diodes. The avalanche voltage and broadband (2–8 GHz) microwave small-signal admittance were measured for junction temperatures in the range 280 to 590 K. An accurate model of the diode was used to calculate the admittance characteristic and voltage for each junction temperature. Subsequently, the values of ionization coefficients and saturated velocities were determined at each temperature by a numerical minimization routine to obtain the best fit between the calculated values and measured data. The resulting ionization rates are well fitted by the temperature dependent model developed by Crowell and Sze from the Baraff ionization-rate theory. The carrier scattering mean free path lengths, average energy loss per collision, and relative ionization cross section are obtained from the best fit agreement between the scattering model and experimental data. The parameter values determined here relevent for use with the above theory are the following:Parameter Holes Electrons ε_r(eV) 0.063 0.063 ε_i(eV) 1.6 1.6 λ_oo(Å) 81.2 77.4 σ 0.391 0.593 The values and temperature dependence of the saturated carrier velocities determined are in good agreement with other published results. At 300 K the low field (E?10⁴ V/cm) saturated velocity for electrons and holes is 10.4 and 7.4×10₆ cm/sec, respectively. The results obtained in this study are of general use for the modeling of effects related to avalanche breakdown and high-field carrier transport in silicon.     

超短脉冲激光对透明材料的破坏

基于固体的能带理论和能量守恒原理建立了一个描述激光与非金属材料作用时载流子随时间空间变化的理论模型。讨论了材料的破坏阈值、烧蚀深度与激光脉宽、波长和强度之间的关系,同时也讨论了破坏阈值、烧蚀深度与材料禁带宽度等特性之间的关系。讨论了多光子电离、隧道电离和雪崩电离在激光对材料破坏过程中的不同地位,理论结果表明,光电离在超短脉冲激光对非金属材料破坏过程中对破坏阈值的影响最大。     

Design considerations for high performance avalanche photodiodemultiplication layers

We have studied the effect of the thickness of the multiplication region on the noise performance characteristics of avalanche photodiodes (APD's). Our simulation results are based on a full band Monte Carlo model with anisotropic threshold energies for impact ionization. Simulation results suggest that the well known McIntyre expression for the excess noise factor is not directly applicable for devices with a very thin multiplication region. Since the number of ionization events is drastically reduced when the multiplication layer is very thin, the “ionization coefficient” is not a good physical parameter to characterize the process. Instead “effective quantum yield,” which is a measure of the total electron-hole pair generation in the device, is a more appropriate parameter to consider. We also show that for the device structure considered here, modeling the excess noise factor using a “discrete Bernoulli trial” model as opposed to the conventional “continuum theory” produces closer agreement to experimental measurements. Our results reinforce the understanding that impact ionization is a strong function of carrier energy and the use of simplified field-dependent models to characterize this high energy process fails to accurately model this phenomenon     

Impact ionization characteristics of III-V semiconductors for awide range of multiplication region thicknesses

Recently, an impact ionization model, which takes the nonlocal nature of the impact ionization process into account, has been described. This model incorporates history-dependent ionization coefficients. Excellent fits to experimental gain and noise measurements for GaAs were achieved using an effective field approach and simple analytical expressions for the ionization probabilities. In the paper, we briefly review the history-dependent model and apply it to Al_0.2 Ga_0.8As, In_0.52Al_0.48As and InP avalanche photodiodes. For the study, the gain and noise characteristics of a series of homojunction avalanche photodiodes with different multiplication thicknesses were measured and fit with the history-dependent model. A “size-effect” in thin (<0.5 μm) multiplication regions, which is not adequately characterized by the local-field avalanche theory, was observed for each of these materials. The history-dependent model, on the other hand, achieved close agreement with the experimental results     

Evaluation of the effective threshold energy of the Interband impact ionization in a deep-submicron silicon n-channel MOS transistor

Using the ensemble Monte Carlo method allowing for the main features of charge-carrier transport in conditions of strong electric fields, a deep-submicron silicon n-channel MOS transistor with a channel length of 50 nm is simulated. In the Keldysh impact ionization model with a soft threshold in a channel of the simulated transistor, the effective threshold energy of this process is calculated.