Impact Ionization Coefficients Research Articles

Role of hole trapping by deep acceptors in electron-beam-induced current measurements in β-Ga2O3 vertical rectifiers

Current increases in vertical-geometry Ga2O3 rectifiers during electron-beam-induced current measurements are dominated by the impact ionization of deep acceptors in the depletion region. At room temperature, mobile hole diffusion in the quasi-neutral region of Schottky diodes contributes significantly to the charge collection efficiency. Even when electron–hole pairs are created well inside the space charge region, there are significant losses of charge collection efficiency due to the trapping of holes by deep acceptors in the lower half of the bandgap. Capacitance–voltage profiling under illumination points to deep acceptors with optical ionization close to 2.3 eV as the most important agents of capture. Collection efficiency can be improved by increasing the electric field in the space charge region. The jump in collection efficiency at electric fields close to (5–6) × 105 V cm−1 is attributed to the impact ionization of these deep acceptors. These processes can manifest themselves in measurements of the impact ionization coefficients and breakdown voltages of β-Ga2O3 rectifiers and in analyses of the response times of β-Ga2O3 photodetectors.

Mean multiplication gain and excess noise factor of GaN and Al0.45Ga0.55N avalanche photodiodes

In this work, Monte Carlo model is developed to investigate the avalanche characteristics of GaN and Al0.45Ga0.55N avalanche photodiodes (APDs) using random ionization path lengths incorporating dead space effect. The simulation includes the impact ionization coefficients, multiplication gain and excess noise factor for electron- and hole-initiated multiplication with a range of thin multiplication widths. The impact ionization coefficient for GaN is higher than that of Al0.45Ga0.55N. For GaN, electron dominates the impact ionization at high electric field while hole dominate at low electric field whereas Al0.45Ga0.55N has hole dominate the impact ionization at higher field while electron dominate the lower field. In GaN APDs, electron-initiated multiplication is leading the multiplication gain at thinner multiplication widths while hole-initiated multiplication leads for longer widths. However for Al0.45Ga0.55N APDs, hole-initiated multiplication leads the multiplication gain for all multiplication widths simulated. The excess noise of electron-initiated multiplication in GaN APDs increases as multiplication widths increases while the excess noise decreases as the multiplication widths increases for hole-initiated multiplication. As for Al0.45Ga0.55N APDs, the excess noise for hole-initiated multiplication increases when multiplication width increases while the electron-initiated multiplication increases with the same gradient at all multiplication widths.

Monte Carlo simulation for development of electron avalanches in nitrogen at moderate and high reduced electric field

This paper addresses the simulation of electron avalanches in nitrogen by means of the Monte Carlo method. The data have been obtained for the conditions of classical measurements of the impact ionization coefficient in a wide range of reduced electric fields E/p. It is shown that at moderate E/p values, the results are in a good agreement with the generally accepted approaches in the description of the avalanches based on the drift motion of the electrons and on the diffusion. The high E/p is achieved in the vicinity of the minimum of Paschen's curve due to decreasing the gas pressure. Then the process of development of the single electron avalanche changes radically. The reason is that the runaway electrons appear, which leads to essential longitudinal expansion of the electron cloud. It is revealed that the average electron energy at the front of the cloud turns out to be larger than that at the backside of the cloud.

Experimental Determination of Impact Ionization Coefficients Along 〈1120〉 in 4H-SiC

The impact ionization coefficients along the $\langle 11 \bar{2}0\rangle $ direction in 4H-SiC were extracted by analyzing photocurrent of mesa epitaxial p-n diodes with punchthrough (PT) structures fabricated on 4H-SiC ( $11\bar{2}0$ ). Compared with the impact ionization coefficients along 4H-SiC $\langle {0001}\rangle $ , the coefficient for electrons is much higher, whereas the coefficient for holes is similar. As a result, the calculated critical electric field strength along 4H-SiC $\langle 11\bar{2}0\rangle $ is approximately 21% lower than that along 4H-SiC $\langle {0001}\rangle $ . This strong anisotropy of the electron impact ionization coefficient is discussed by taking account of the unique conduction band structure. The extracted impact ionization coefficients were validated by comparing the simulated and experimentally measured breakdown voltages of various 4H-SiC ( $11\bar{2}0$ ) p-n diodes with non-PT structures.

Investigation of Wide- and Ultrawide-Bandgap Semiconductors From Impact-Ionization Coefficients

We survey impact-ionization coefficients for silicon, wide bandgap semiconductors (gallium nitride and 4H-silicon carbide), and ultrawide-bandgap semiconductors (aluminum gallium nitride, beta-gallium oxide, and diamond). We employ a custom genetic algorithm to fit those existing coefficients into a modified Thornber model. This fitting process leads to an estimation of material properties, such as ionization energy, optical-phonon energy, and mean free path. After evaluating electric-field profiles by solving the Poisson equation, we use the impact-ionization integral to fundamentally calculate the breakdown voltage and the critical field of various p-i-n structures. This work captures how the doping concentration and the thickness of the drift layer shape the breakdown voltage as well as the critical field achievable with a given material. It is observed that a wider bandgap is not the sole requirement for the achievement of a higher breakdown voltage. Impact-ionization coefficients and dielectric constants are additional material properties that influence the calculation of the breakdown voltage. The performance limits of diamond are found to be surprisingly poor for its large bandgap. Al x Ga1– x N and $\beta $ -Ga2O3 have almost the same performance limits, but it is observed that aluminum gallium nitride can outperform gallium oxide at high voltage if its background doping (doping floor) can be reduced.

Characterization of Impact Ionization Coefficient of ZnO Based on a p-Si/i-ZnO/n-AZO Avalanche Photodiode.

The avalanche photodiode is a highly sensitive photon detector with wide applications in optical communication and single photon detection. ZnO is a promising wide band gap material to realize a UV avalanche photodiode (APD). However, the lack of p-type doping, the strong self-compensation effect, and the scarcity of data on the ionization coefficients restrain the development and application of ZnO APD. Furthermore, ZnO APD has been seldom reported before. In this work, we employed a p-Si/i-ZnO/n-AZO structure to successfully realize electron avalanche multiplication. Based on this structure, we investigated the band structure, field profile, Current–Voltage (I-V) characteristics, and avalanche gain. To examine the influence of the width of the i-ZnO layer on the performance, we changed the i-ZnO layer thickness to 250, 500, and 750 nm. The measured breakdown voltages agree well with the corresponding threshold electric field strengths that we calculated. The agreement between the experimental data and calculated results supports our analysis. Finally, we provide data on the impact ionization coefficients of electrons for ZnO along the (001) direction, which is of great significance in designing high-performance low excess noise ZnO APD. Our work lays a foundation to realize a high-performance ZnO-based avalanche device.

(Invited) Electron Transport in Bulk and 2DEGs in beta-Ga2O3 and kV Class Laterals Device in beta-Ga2O3

Monoclinic beta-Ga2O3 and (AlxGa1-x)2O3 alloys are an emerging ultra-widebandgap semiconductor system for next generation power, GHz power switching and RF applications. In this talk, we will present the low field and high field transport simulations in Ga2O3 using first-principles calculations. Density functional theory calculations is used to get the band structure. The density functional perturbation theory is used to understand the lattice dynamics and identify the infrared (IR) active and Raman active phonon modes. Electron-phonon scattering rates are calculated Boltzmann transport equation is solved to calculate the low field mobility, velocity-field profiles and the impact ionization coefficients. The effect of dynamic screening on the electron mobility is evaluated in a two-dimensional electron gas (2-DEG) system in (AlxGa1-x)2O3/Ga2O3 heterostructures.We will also report the Ga2O3 based power and RF devices. MOSFETs with spin-doping source/drain and n+ ohmic capped layers will be presented. kV breakdown voltages are seen with the devices limited by extrinsic breakdown. Temperature dependent characteristics show potential for high temperature applications.

Theoretical analysis of band structure effects on impact ionization coefficients in wide-bandgap semiconductors

This study theoretically investigates the effects of band structure parameters, such as the bandgap, effective mass, and Brillouin zone (BZ) width, on impact ionization coefficients. A Monte-Carlo simulation considering analytical and tunable band structures reveals that the smaller BZ width significantly reduces impact ionization coefficients, and its impacts can outperform those of the bandgap. The smaller BZ width also leads to positive temperature dependence of impact ionization coefficients, which is discussed focusing on the occurrence of the Bloch oscillation. Our results show the importance of the BZ width in discussing the behavior of impact ionization coefficients.

A unified model for vertical doped and polarized superjunction GaN devices

A unified model is proposed to characterize the breakdown voltage (BV) and specific on-resistance (Ron,sp) for vertical doped superjunction (d-SJ) and polarized superjunction (p-SJ) GaN power devices. This study is based on the recently published compensated-pillar superjunction (cp-SJ) structure. A two-dimensional model for the electric field is analytically formulated using the Green's function method. Numerical calculations and TCAD simulations demonstrate that, for a given pillar depth, the p-SJ device has a lower BV than the d-SJ device with a wide pillar width. However, when the pillar width is less than 200 nm, both devices demonstrate a maximum BV that is close to the intrinsic structure. The Ron,sp unified model for the cp-SJ device, taking into account the junction field-effect transistor (JFET) effect in the drift region, also demonstrates that the p-SJ device has a superior Ron,sp over the d-SJ device. Considering the recently published impact ionization coefficients, the BV of the p-SJ device is analytically modeled as a function of the pillar depth. Finally, by applying the Lambert W-function, an exact closed-form relationship between Ron,sp and BV is presented.

Observation of ID-VD Kink in N-Polar GaN MIS-HEMTs at Cryogenic Temperatures

This paper reports on the hot-carrier effects and semi-on-state behavior of nitrogen-polar GaN MIS-HEMTs at cryogenic temperatures (from 300 K down to 100 K). In the semi-on-state $(\text {V}_{\text {G}} \approx -{2}\,\,\text {V})$ , holes are generated by impact ionization in the high field region at the drain-side of the gate-edge. At room temperature, holes overcome the SiN/AlGaN stack and are collected at the gate-terminal, resulting in measurable hole gate-current (~11 nA/mm). Conversely, at cryogenic temperatures, the top SiN/AlGaN stack confines the holes within the GaN channel, thus inducing a negative threshold voltage shift (−0.4 V) and a sharp increase in drain current (0.18 A/mm). This behavior, referred to as “ kink ,” is readily observable on the $\text {I}_{\text {D}} - \text {V}_{\text {D}}$ characteristics. We demonstrated that the kink is related to impact ionization and follows a non-monotonic behavior maximized in the semi-on-state. Our interpretation is supported by a quantitative analysis based on the latest experimental impact-ionization coefficients available in the literature.

Back-illuminated AlGaN heterostructure solar-blind avalanche photodiodes with one-dimensional photonic crystal filter.

AlGaN heterostructure solar-blind avalanche photodiodes (APDs) were fabricated on a double-polished AlN/sapphire template based on a separate absorption and multiplication (SAM) back-illuminated configuration. By employing AlGaN heterostructures with different Al compositions across the entire device, the SAM APD achieved an avalanche gain of over 1×105 at an operated reverse bias of 92 V and a low dark current of 0.5 nA at the onset point of breakdown. These excellent performances were attributed to the acceleration of holes by the polarization electric field with the same direction as the reverse bias and higher impact ionization coefficient of the low-Al-content Al0.2Ga0.8N in the multiplication region. However, the Al0.2Ga0.8N layer produced a photocurrent response in the out of the solar-blind band. To retain the solar-blind detecting characteristic, a periodic Si3N4/SiO2 photonic crystal was deposited on the back of the AlN/sapphire template as an optical filter. This significantly improved the solar-blind characteristic of the device.

A Low-Voltage Si-Ge Avalanche Photodiode for High-Speed and Energy Efficient Silicon Photonic Links

Silicon-germanium (Si-Ge) avalanche photodiodes (APDs) have large gain bandwidth product (GBP) and low excess noise due to the low impact ionization coefficient ratio of silicon. Optical receivers using APDs are able to achieve high-speed and energy efficient optical transceiver systems. We demonstrate a waveguide Si-Ge APD with low breakdown voltage of −10 V, achieving 60 Gb/s PAM4 successfully. A compact APD circuit model was constructed to allow photonic devices and transceiver circuitry co-design. The APD receiver has achieved −16 dBm sensitivity at 50 Gb/s PAM4 with a bit error rate (BER) of 2.4 $\times \,10^{-4}$ . The sensitivity of APD receivers changes with the multiplication gain. In our analysis, compared to a PIN PD receiver the APD receiver operating at optimum gain can obtain $\sim$ 8 dB more sensitivity for NRZ signaling at $ 50 Gb/s and 3–4 dB more sensitivity for PAM4 signaling at 50–100 Gb/s. Also, the APD receiver operating at optimum gain can reduce power consumption by $\sim\!\text{10}\%$ at PAM4 data rates of 50 Gb/s and $\sim\!\text{15}\%$ at 100 Gb/s in a silicon carrier-depletion microring modulator based WDM photonic link.

High Gain, Low Dark Current Al0.8In0.2As0.23Sb0.77 Avalanche Photodiodes

We report Al0.8In0.2As0.23Sb0.77 avalanche photodiodes with high gain ( $M>1300$ ) and low dark current at room temperature. Impact ionization coefficients for this material system are also extracted, indicating electron-dominant impact ionization. Low avalanche breakdown temperature dependence is demonstrated.

Sensivity analysis of impact ionization coefficients in an electronic device

Terminal current in a device increases when energetic carriers create additional carriers by impact ionization. Okuto and Crowell suggested an empirical model for describe this phenomenon. In this paper, Monte Carlo techniques were used to observe the effect of variability in the impact ionization coefficients on the results obtained from a computational model for electrons and holes transport. The model was implemented in FEM simulation tool, in order to study avalanche current in a MOSFET including uncertainty of the impact ionization coefficients of material.

Monte-Carlo simulation of the ionization processes for discharges in the left branch of the Paschen curve

The paper deals with the development of the simulation methods applied to the low-pressure discharges in which the reduced electric field E/p is extremely high and there exists a problem for the correct description of the ionization processes in the classical electron avalanches. Here we use the PIC/MC code xoopic for calculation of the impact ionization coefficient α, the electron drift velocity and the electron diffusion coefficient D in the electron avalanches in nitrogen. The range of calculations covers the ratio E/p ≤ 1000 V·(cm·Torr)−1. The simulation method was tested on a simple analytical model of an electron avalanche and showed good agreement in low and moderate E/p. It is shown that in conditions of high E/p the spatial distribution of electrons in the avalanche head based on the concepts of electron mobility during their drift motion and diffusion coefficient is not quite correct. The work confirmed that at the very low pressures pre-breakdown phenomena and the transition to the next stage of high-current breakdown cannot be based on ideas about classical electron avalanches.

Avalanche Multiplication Noise in GaN p–n Junctions Grown on Native GaN Substrates

GaN p–n junction diodes grown on native GaN substrates have been fabricated and characterized. The devices exhibit a positive temperature coefficient of breakdown obtained from variable temperature current–voltage measurements, confirming the impact ionization avalanche. The low‐frequency noise characteristics of these devices have been measured under forward and reverse bias conditions. The forward bias noise spectra are dominated by the 1/f noise, and the current spectral density is proportional to I1.6. Under reverse bias, the noise spectra show 1/f noise at reverse biases below the avalanche threshold. However, at reverse biases in the avalanche regime, the multiplication noise overwhelms the 1/f noise, resulting in a white noise spectrum. To further characterize the avalanche process, the excess noise factor, F, is obtained from the measured noise spectra of diodes biased in reverse avalanche. For the case of pure hole injection (achieved by incorporating a thin pseudomorphic In0.07Ga0.93N layer at the cathode of the device and illuminating with 390 nm UV light), a low excess noise factor is achieved. The impact ionization ratio α/β extracted from the multiplication noise ranges from 0.07 to 0.38 over the electric field ranging from 2.8 to 3.7 MV cm−1, consistent with the impact ionization coefficients reported previously using the photomultiplication method.

Carrier Transport Properties of GAN in High Electric Field

The Monte Carlo (MC) simulation of the carrier transport mechanisms including impact ionization at high electric field in GaN is presented. Two non-parabolic conduction and valence bands were considered for the simulation of transport properties of electron and hole respectively. The carriers’ drift velocity and energy are simulated as a function of applied electric field at room temperature. The maximum velocity of electron is 2.85 × 107 cm/s at 140 kV/cm. The velocity of electron is saturated at 2 × 107 cm/s at electric field greater than 300 kV/cm. In our work, the velocity of hole is 5 × 106 cm/s at 500 kV/cm. Electron energy increases as the electric field increase and fluctuated at electric field greater than 600 kV/cm when impact ionization occurred. The impact ionization rates are obtained by using modified Keldysh equation. The hole impact ionization rate is higher than that of electron. This work also shows higher electron impact ionization coefficient than that of hole at electric field greater than 4.04 MV/cm

Modeling Temperature-Dependent Avalanche Characteristics of InP

Avalanche photodiodes (APDs), and single photon avalanche diodes (SPADs), with InP avalanche regions and InGaAs absorption regions, are used for detecting weak infrared light at ∼1.55 μm wavelength. These devices are often cooled to below room temperature during operation yet both validated simulation models and impact ionization coefficients that accurately describe the avalanche characteristics of InP are lacking in the temperature range of interest (200 K to room temperature). In this article we present an accessible, validated temperature dependent simulation model for InP APDs/SPADs. The model is capable of simulating avalanche gain, excess noise, breakdown voltage, and impulse current at 150–300 K. Temperature dependent ionization coefficients in InP, which may be used with other APD/SPAD simulation models, are also presented. The data reported in this article is available from the ORDA digital repository (DOI: 10.15131/shef.data.c.4373006).

Experimental determination of impact ionization coefficients of electrons and holes in gallium nitride using homojunction structures

In this study, we experimentally determined the impact ionization coefficients of GaN using homoepitaxially grown p-n diodes with avalanche capability. The extracted hole impact ionization coefficient is obtained as β(E) = 4.39 × 106 exp (−1.8 × 107/E) cm−1, and the electron impact ionization coefficient is obtained as α(E) = 2.11 × 109 exp (−3.689 × 107/E) cm−1. This study also presents the temperature dependence of impact ionization coefficients in GaN. The results presented in this experimental study are an important contribution to the database on the material properties of GaN, which will enable more accurate prediction of the avalanche in GaN devices.

Avalanche characteristics in thin GaN avalanche photodiodes

A Monte Carlo model using random ionization path lengths describing the carriers quantum transport in thin gallium nitride (GaN) avalanche photodiodes (APDs) for ultraviolet detection in industry is developed. This work simulated avalanche characteristics such as impact ionization coefficients, mean multiplication gain and excess noise factor of GaN APDs at 0.05 μm, 0.1 μm, 0.2 μm and 0.3 μm multiplication widths in an electric field. The model simulates higher electron impact ionization coefficients than that of the hole for an electric field greater than 4.04 MV cm−1. Mean multiplication gain and excess noise factor are simulated based on the electric field dependent impact ionization coefficients. Our results show that electron-initiated multiplication gives higher multiplication gain and lower excess noise than hole-initiated multiplication for a multiplication width below 0.3 μm. Devices with dead space in general give a lower excess noise.