Temperature dependence of the electron impact ionization in InGaP-GaAs-InGaP DHBTs

Temperature dependence of electron impact ionization in InGaP-GaAs-InGaP double heterojunction bipolar transistors (DHBTs) were comprehensively studied in the temperature range of 300 to 450 K. It has been found that, as the temperature increases, the electron multiplication in the InGaP collector is found to be weakly reduced, which results in a relatively small negative temperature dependence of junction breakdown. The temperature dependence of electron impact ionization at elevated temperatures for InGaP material is investigated based on the electron multiplications measured from the InGaP collector region. An empirical expression is obtained to predict the electron ionization coefficients at elevated temperature up to 450 K in the electric field range of 380 to 650 kV/cm. As compared to InP and GaP binaries, the ternary InGaP shows a lower electron ionization coefficient and much weaker temperature dependence. We found that, introducing additional scattering mechanism such as alloy scattering would provide a better interpretation on the low electron impact ionization and its weak temperature dependence observed in InGaP.     

Hot electron transport in wurtzite-GaN: effects of temperature and doping concentration

The hot electron transport in wurtzite phase gallium nitride (Wz-GaN) has been studied in this paper.An analytical expression of electron drift velocity under the condition of impact ionization has been developed by considering all major scattering mechanisms such as deformation potential acoustic phonon scattering,piezoelectric acoustic phonon scattering,optical phonon scattering,electron-electron scattering and ionizing scattering.Numerical calculations show that electron drift velocity in Wz-GaN saturates at 1.44 x 105 m/s at room temperature for the electron concentration of 1022 m-3.The effects of temperature and doping concentration on the hot electron drift velocity in Wz-GaN have also been studied.Results show that the saturation electron drift velocity varies from 1.91 × 105-0.77 × 105 m/s for the change in temperature within the range of 10--1000 K,for the electron concentration of 1022 m-3;whereas the same varies from 1.44 x 105-0.91 × 105 m/s at 300 K for the variation in the electron concentration within the range of 1022-1025 m-3.The numerically calculated results have been compared with the Monte Carlo simulated results and experimental data reported earlier,and those are found to be in good agreement.     

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     

Extremely Low Excess Noise in InAs Electron Avalanche Photodiodes

Measurements of the avalanche multiplication noise in InAs p-i-n and n-i-p diodes at room temperature demonstrate unambiguously that the avalanche multiplication process is dominated by impact ionization of electrons. This results in the excess noise factor for electron initiated multiplication asymptotically approaching a maximum value just less than two and becoming virtually gain-independent for higher gains. Measurements for predominantly hole initiated multiplication show corresponding high excess noise factors suggesting the electron to hole ionization coefficient ratios are comparable to those reported for $hbox{Hg}_{1-{x}}hbox{Cd}_{x}hbox{Te}$ electron avalanche photodiodes.      

Monte Carlo simulation of impact ionization in SiGe HBTs

Measurements and Monte Carlo simulations of impact ionization in the base-collector region of SiGe HBTs are presented. A device with low germanium concentration (graded from 0 to 12%) is considered and no differences are found between the experimental multiplication factor in that device and the corresponding silicon control. Because impact ionization (II) occurs inside the bulk-Si collector, phonon and II scattering rates for bulk silicon can be used in the Monte Carlo simulation, avoiding the need to model the strained SiGe layers. Full-Band Monte Carlo simulations are shown to reproduce the multiplication factors measured in SiGe devices featuring different collector profiles     

Particle conservation in the hot‐carrier solar cell

In conventional p–n junction solar cells, carrier multiplication by impact ionisation, is negligible, owing to the low temperature of the electron–hole pairs. This leads to particle conservation between the net number of absorbed photons and the number of electron–hole pairs withdrawn from the cell. In hot‐carrier solar cells, in which electrons are at a high temperature by assuming suppression of electron–phonon scattering, such particle conservation leads to peculiar results. Numerical calculations show that entire current–voltage characteristics with meaningful values of temperature and chemical potential do not exist. If the energy at which electron–hole pairs are extracted is smaller than the average energy of absorbed photons, the temperature of the electrons and holes becomes much larger than the tem perature of the sun. When the extraction energy is larger than the average energy of the absorbed photons, an entire current–voltage curve cannot always be obtained. It follows that impact ionisation and Auger recombination cannot be neglected when the thermal energy of the electron–hole pairs is comparable to the bandgap of the absorber. Accounting for these processes results in current–voltage characteristics that are well behaved. Copyright © 2005 John Wiley & Sons, Ltd.     

Normalized theory of impact ionization and velocity saturation in nonpolar semiconductors via a Markov chain approach

This paper presents an investigation of the velocity, energy, and impact ionization distributions in nonpolar semiconductors at very high fields. The treatment uses a finite Markov chain formulation. When optical phonon collisions and impact ionization are the major scattering mechanisms in the semiconductor, a transition matrix which characterizes the transition probabilities between virtual states defined by small discrete energy intervals can be easily computed. The resulting matrix provides the means not only to study the impact ionization phenomenon but also the steady state transport velocity and energy distribution of the charge carriers at high electrical fields and a given lattice temperature. In addition, the effects on the transport properties due to either an abrupt infinite (AI) or a finite energy dependent (FED) ionization cross-section above the ionization threshold energy are examined. The calculated avalanche transport velocity shows excellent agreement with the experimental data in Si obtained by Duh and Moll. The resulting calculations when extrapolated to a lower field also agree favorably with existing saturation drift velocity data in n and p type Si and p type Ge. The energy distribution is shown to be strongly affected by the choice of the model for the energy dependence of the ionization cross-section. One of the main applications of the results is to assist investigation of the non-localized nature of electron and hole avalanche ionization coefficients previously noted by Okuto and Crowell (O-C). The present results for this spatial distribution can replace O-C's intuitively chosen exponential approximation. The spatial ionization distribution generated by the present calculation is essentially exponential with a threshold energy dark space. This result provides a useful kernel for a more precise formulation in studies that relate impact ionization coefficients to charge multiplication data. The normalized ionization coefficients obtained from the AI model are very similar to Baraff's calculation as are the FED model results after appropriate normalization. Simple analytical expressions with meaningful asymptotic results for the average ionization energy and the ionization coefficient are also derived from the present data. These results are applicable for a range of different energy dependence of the ionization cross section provided that the average energy for pair production is used as the effective threshold parameter.     

Nonlinear analysis of the solid-state gyrotron oscillator by the Monte Carlo method

A nonlinear analysis of the solid-state gyrotron oscillator is described to calculate the efficiency (η) and output power (Pw) of the device. Electron trajectories are calculated numerically. The motion of the electrons inside the cavity consists alternately of drift along helical trajectories followed by scattering. A Monte Carlo method has been used to treat scattering. Scattering processes included in the calculation are polar optic phonon, acoustic phonon, impurity, and impact ionization. Nonparabolicity and wave vector dependence of the periodic part of block functions are also used since phase bunching of electrons occurs due to the variation of effective mass with energy in the conduction band. η and Pware calculated as functions of frequency, temperature, impurity concentration, applied magnetic field, and other physical parameters ot the electron beam and the cavity made from InSb. At 500-GHz frequency and 4 K, output power of about 100 µW (assuming that Q of the cavity is 10) can be obtained with an efficiency of 5 percent.     

A Monte Carlo investigation of multiplication noise in thin p+-i-n+ GaAs avalanche photodiodes

A Monte Carlo (MC) model has been used to estimate the excess noise factor in thin p⁺-i-n⁺ GaAs avalanche photodiodes (APD's). Multiplication initiated both by pure electron and hole injection is studied for different lengths of multiplication region and for a range of electric fields. In each ease a reduction in excess noise factor is observed as the multiplication length decreases, in good agreement with recent experimental measurements. This low noise behavior results from the higher operating electric field needed in short devices, which causes the probability distribution function for both electron and hole ionization path lengths to change from the conventionally assumed exponential shape and to exhibit a strong dead space effect. In turn this reduces the probability of higher order ionization events and narrows the probability distribution for multiplication. In addition, our simulations suggest that fur a given overall multiplication, electron initiated multiplication in short devices has inherently reduced noise, despite the higher feedback from hole ionization, compared to long devices     

Measurements of InGaP electron ionization coefficient using InGaP-GaAs-InGaP double HBTs

Electron impact ionization coefficients (/spl alpha/) in In/sub 0.52/Ga/sub 0.48/P have been extracted based on the measurements of electron multiplication factor in npn InGaP-GaAs-InGaP double heterojunction bipolar transistors (HBTs). The electron ionization coefficient of InGaP determined in this brief extends the previously reported data in low electric field by two orders of magnitude down to 1 cm/sup -1/ with the electric field as low as 330 kV/cm.     

Full-Band Monte Carlo Simulation of HgCdTe APDs

A full-band Monte Carlo model has been developed for understanding the carrier multiplication process in HgCdTe infrared avalanche photodiodes. The proposed model is based on a realistic electronic structure obtained by pseudopotential calculations and a phonon dispersion relation determined by ab initio techniques. The calculated carrier–phonon scattering rates are consistent with the electronic structure and the phonon dispersion relation, thus removing adjustable parameters such as deformation potential coefficients. The computation of the impact ionization transition rate is based on the calculated electronic structure and the corresponding wavevector-dependent dielectric function. The Monte Carlo model is applied to investigate key performance figures of long-wavelength infrared (LWIR) and mid-wavelength infrared (MWIR) HgCdTe avalanche photodetectors such as carrier multiplication and noise properties. Good agreement is achieved between simulations and experimental results. The multiplication process in LWIR (λ _c = 9.0 μm at 80 K) and MWIR (λ _c = 5.1 μm at 80 K) devices is found to be initiated only by electrons, as expected from excess noise measurements. This single-carrier multiplication behavior can be traced back to the details of the computed valence-band structure and phonon scattering rates.     

Intraband relaxation time in quantum-well lasers

Intraband relaxation time, which causes spectral broadening of optical gain and spontaneous emission spectra, is estimated theoretically for quantum-well lasers. Carrier-carrier and carrier-longitudinal-optical (LO) phonon scattering mechanisms are considered, and it is shown that hole-hole, electron-hole, and hole-LO phonon scattering are dominant in spectral broadening. Intraband relaxation time determined by all of these mechanisms increases slightly with the decrease of well width. The dependence of intraband relaxation time on temperature, carrier density, and energy of electron and hole is also shown. Spectral line shape is discussed as an extension of the above calculation, and an approximated formula is given     

Monte Carlo simulations of high-speed InSb-InAlSb FETs

Self consistent Monte Carlo simulations which include impact ionization are used to study the high-speed potential of InSb field-effect transistors. It is found that the impact ionization has a strong influence on the performance of InSb for high speed. The ionization leads to a high electron drift velocity and substrate bias can be used to extract the holes which are generated in the channel. Residual hole density within the channel, however, limits the maximum speed. The substrate bias and buffer doping are critical for extracting holes from the channel without inducing excess ionization. Simulations yield a peak cutoff frequency of 820 GHz with a 0.03125-/spl mu/m gate, a source to drain voltage of 0.58, and a sheet doping density of 1.7/spl times/10/sup 12/ cm/sup -2/.     

Measurement of collector-base junction avalanche multiplicationeffects in advanced UHV/CVD SiGe HBT's

This paper presents measurements of the avalanche multiplication factor (M-1) in SiGe HBTs using a new technique capable of separating the avalanche multiplication and Early effect contributions to the increase of collector current with collector-base bias, as well as allowing safe measurements at practical current densities. The impact of collector doping, current density, Ge profile, and operation temperature are reported for the first time using measured and simulated results from a production quality UHV/CVD SiGe HBT technology. Limitations of the technique in the presence of significant self-heating are discussed. By turning on the secondary hole impact ionization, we revealed the difference in impact ionization between strained SiGe and Si in the presence of the “dead space” effect. Despite its smaller bandgap, the compressively strained SiGe layer shows an apparent decrease in the secondary hole impact ionization rate compared to Si     

Carrier transport in HfO/sub 2//metal gate MOSFETs: physical insight into critical parameters

Electron and hole mobility in HfO/sub 2//metal gate MOSFETs is deeply studied through low-temperature measurements down to 4.2 K. Original technological splits allow the decorrelation of the different scattering mechanisms. It is found that even when charge trapping is negligible, strong remote coulomb scattering (RCS) due to fixed charges or dipoles causes most of the mobility degradation. The effective charges are found to be located in the HfO/sub 2/ near the SiO/sub 2/ interface within 2 nm. Experimental results are well reproduced by RCS calculation using 7/spl times/10/sup 13/ cm/sup -2/ fixed charges at the HfO/sub 2//SiO/sub 2/ interface. We also discuss the role of remote phonon scattering in such gate stacks. Interactions with surface soft-optical phonon of HfO/sub 2/ are clearly evidenced for a metal gate but remain of second order. All these remote interactions are significant for an interfacial oxide thickness up to 2 nm, over which, these are negligible. Finally, the metal gate (TiN) itself induces a modified surface-roughness term that impacts the low to high effective field mobility even for the SiO/sub 2/ gate dielectric references.     

Temperature dependent studies of InP/InGaAs avalanche photodiodesbased on time domain modeling

Using a simplified time domain modeling approach, the temperature dependent performance characteristics, such as multiplication gain, breakdown voltage, -3 dB bandwidth, gain bandwidth product and excess noise factor, have been systematically investigated for InP/InGaAs separate absorption, grading, charge and multiplication avalanche photodiodes as a function of temperature from -50°C to 110°C. In order to model the -3 dB bandwidth versus gain dependence based on the simplified approach, empirical expressions have been proposed to consider the effects of hole diffusion, hole trapping, RC (resistance-capacitance) and gain-bandwidth product limit together with the fast Fourier transform component of the impulse response from the time domain modeling. The modeling results generally agree with or can explain the corresponding experimental results. The effects of changing material parameters on the modeling results are also discussed. In addition, we have found that E_rO, the average energy loss per collision due to optical phonon scattering at 0 K, plays a dominant role in determining the -3 dB bandwidth near breakdown and the slope of the temperature dependence of the breakdown voltage. Further, the improved performance characteristics at decreased temperatures indicate the potential application prospects of the InP/lnGaAs APDs in low temperature environments     

Electron transport and ionization in silicon at high fields

The saturated drift velocity measured for electrons at high fields is inconsistent with Shockley's model for impact ionization in silicon. It is explained in terms of a field-dependent mean free path for high energy phonon creation in the electric field direction, electrons creating a high energy phonon as soon as they have acquired sufficient energy from the field. Assuming that the electron wavepacket travels at the saturated drift velocity without dispersion, it can be shown that the increased scattering rate at high fields must result in a large spread in the carrier energy. If a drifted Maxwellian distribution is assumed, a unique expression can be obtained for the carrier temperature T^* which is in good agreement with the measured field dependence of the ionization coefficient. In this model, a cylindrical hot carrier distribution must be assumed with the hot carrier energy in a plane perpendicular to the applied field. Exact calculations of the magneto-resistance of such a distribution can be made verifying that the drift velocity is indeed saturated.     

Avalanche multiplication in InP/InGaAs double heterojunctionbipolar transistors with composite collectors

The experimental and theoretical studies of electron multiplication in InP/InGaAs double heterojunction bipolar transistors (DHBT's) with an InGaAs/InP composite collector are carried out. Both local electric field model and energy model are used to investigate the electron impact ionization in the composite collector. The analysis reveals that the nonlocal effect of the electron impact ionization in the composite collector is responsible for the suppression of the contribution of electron multiplication in the InGaAs layer. Experimental results for the fabricated devices were compared with the theoretical calculations, indicating that the conventional impact ionization models based on the local electric field significantly overestimate the electron multiplication for the composite collector. The energy model which takes into account the nonlocal effect is found to provide a more accurate prediction of electron multiplication for the DHBT's