Electron Impact Ionization Coefficients Research Articles

Semi-empirical cross-section formulas for electron-impact ionization and rate coefficient calculations

We propose a semi-empirical formula for the cross section of ionization by electron impact. The formula involves adjustable parameters which are determined by comparison with measured or numerically calculated cross sections. In the latter case, the ions are perturbed by their environment which is a high-density plasma. As a consequence, the cross section is significantly modified. We investigate Be-like carbon, nitrogen and oxygen as well as aluminum ions. We also show that the formula is well-suited for interpolation and extrapolation. Knowing the cross section, we calculate the rate coefficient within the Boltzmann and Fermi–Dirac statistics. In the first case, the rate can be calculated analytically. In the second one, it can be expressed in terms of special functions, but the numerical evaluation is more convenient while providing accurate results. Our results are compared to experiment and to other calculations.

Very low excess noise Al0.75Ga0.25As0.56Sb0.44 avalanche photodiode.

AlxGa1-xAsySb1-y grown lattice-matched to InP has attracted significant research interest as a material for low noise, high sensitivity avalanche photodiodes (APDs) due to its very dissimilar electron and hole ionization coefficients, especially at low electric fields. All work reported to date has been on Al concentrations of x = 0.85 or higher. This work demonstrates that much lower excess noise (F = 2.4) at a very high multiplication of 90 can be obtained in thick Al0.75Ga0.25As0.56Sb0.44 grown on InP substrates. This is the lowest excess noise that has been reported in any III-V APD operating at room temperature. The impact ionization coefficients for both electrons and holes are determined over a wide electric field range (up to 650 kV/cm) from avalanche multiplication measurements undertaken on complementary p-i-n and n-i-p diode structures. While these ionization coefficients can fit the experimental multiplication over three orders of magnitude, the measured excess noise is significantly lower than that expected from the β/α ratio and the conventional local McIntyre noise theory. These results are of importance not just for the design of APDs but other high field devices, such as transistors using this material.

Study of Impact Ionization Coefficients in Silicon With Low Gain Avalanche Diodes

Impact ionization in silicon devices has been extensively studied and several models for a quantitative description of the impact ionization coefficients have been proposed. We evaluate those models against gain measurements on Low Gain Avalanche diodes (LGADs) and derive new parameterizations for the impact ionization coefficients optimized to describe a large set of experimental data. We present pulsed IR-laser based gain measurements on 5 different types of $50\mu m$-thick LGADs from two different producers (CNM and HPK) performed in a temperature range from $-15^oC$ to $40^oC$. Detailed TCAD device models are conceived based on SIMS doping profiles measurements and tuning of the device models to measured C-V characteristics. Electric field profiles are extracted from the TCAD simulations and used as input to an optimization procedure (least squares fit) of the impact ionization model parameters to the experimental data. It is demonstrated that the new parameterizations give a good agreement between all measured data and TCAD simulations which is not achieved with the existing models. Finally, we provide an error analysis and compare the obtained values for the electron and hole impact ionization coefficients against existing models.

Impact ionization coefficients and critical electric field in GaN

Avalanche multiplication characteristics in a reverse-biased homoepitaxial GaN p–n junction diode are experimentally investigated at 223–373 K by novel photomultiplication measurements utilizing above- and below-bandgap illumination. The device has a non-punch-through one-side abrupt p–-n+ junction structure, in which the depletion layer mainly extends to the p-type region. For above-bandgap illumination, the light is absorbed at the surface p+-layer, and the generated electrons diffuse and reach the depletion layer, resulting in an electron-injected photocurrent. On the other hand, for below-bandgap illumination, the light penetrates a GaN layer and is absorbed owing to the Franz–Keldysh effect in the high electric field region (near the p–n junction interface), resulting in a hole-induced photocurrent. The theoretical (non-multiplicated) photocurrents are calculated elaborately, and the electron- and hole-initiated multiplication factors are extracted as ratios of the experimental data to the calculated values. Through the mathematical analyses of the multiplication factors, the temperature dependences of the impact ionization coefficients of electrons and holes in GaN are extracted and formulated by the Okuto–Crowell model. The ideal breakdown voltage and the critical electric field for GaN p–n junctions of varying doping concentration are simulated using the obtained impact ionization coefficients, and their temperature dependence and conduction-type dependence were discussed. The simulated breakdown characteristics show good agreement with data reported previously, suggesting the high accuracy of the impact ionization coefficients obtained in this study.

Low Noise Short Wavelength Infrared Avalanche Photodetector Using SB-Based Strained Layer Superlattice

We demonstrate low noise short wavelength infrared (SWIR) Sb-based type II superlattice (T2SL) avalanche photodiodes (APDs). The SWIR GaSb/(AlAsSb/GaSb) APD structure was designed based on impact ionization engineering and grown by molecular beam epitaxy on a GaSb substrate. At room temperature, the device exhibits a 50% cut-off wavelength of 1.74 µm. The device was revealed to have an electron-dominated avalanching mechanism with a gain value of 48 at room temperature. The electron and hole impact ionization coefficients were calculated and compared to give a better prospect of the performance of the device. Low excess noise, as characterized by a carrier ionization ratio of ~0.07, has been achieved.

Mid-wavelength infrared avalanche photodetector with AlAsSb/GaSb superlattice

In this work, a mid-wavelength infrared separate absorption and multiplication avalanche photodiode (SAM-APD) with 100% cut-off wavelength of ~ 5.0 µm at 200 K grown by molecular beam epitaxy was demonstrated. The InAsSb-based SAM-APD device was designed to have electron dominated avalanche mechanism via the band structure engineered multi-quantum well structure based on AlAsSb/GaSb H-structure superlattice and InAsSb material in the multiplication region. The device exhibits a maximum multiplication gain of 29 at 200 K under -14.7 bias voltage. The maximum multiplication gain value for the MWIR SAM-APD increases from 29 at 200 K to 121 at 150 K. The electron and hole impact ionization coefficients were derived and the large difference between their value was observed. The carrier ionization ratio for the MWIR SAM-APD device was calculated to be ~ 0.097 at 200 K.

Low noise Al0.85Ga0.15As0.56Sb0.44 avalanche photodiodes on InP substrates

We report on the demonstration of Al0.85Ga0.15As0.56Sb0.44 (hereafter, AlGaAsSb) avalanche photodiodes (APDs) with a 1000 nm-thick multiplication layer. Such a thick AlGaAsSb device was grown by a digital alloy technique to avoid phase separation. The current-voltage measurements under dark and illumination conditions were performed to determine gain for the AlGaAsSb APDs. The highest gain was ∼ 42, and the avalanche initiation occurred at 21.6 V. The breakdown voltage was found to be around −53 V. The measured dark current densities of bulk and surface components were 6.0 μA/cm2 and 0.23 μA/cm, respectively. These values are about two orders of magnitude lower than those for previously reported 1550 nm-thick AlAs0.56Sb0.44 APDs [Yi et al., Nat. Photonics 13, 683 (2019)]. Excess noise measurements showed that the AlGaAsSb APD has a low k of 0.01 (the ratio of electron and hole impact ionization coefficients) compared to Si APDs. The k of the 1000-nm AlGaAsSb APD is similar to that of the thick AlAsSb APDs (k ∼ 0.005) and 5–8 times lower than that of 170 nm-thick AlGaAsSb APDs (k ∼ 0.5–0.8). Increasing the thickness of the multiplication layer over 1000 nm can also reduce k further since the difference between electron and hole impact ionization coefficients becomes significant in this material system as the thickness of the multiplication layer increases. Therefore, this thick AlGaAsSb-based APD on an InP substrate shows the potential to be a high-performance multiplier that can be used with available short-wavelength infrared (SWIR) absorption layers for a SWIR APD.

Temperature Dependence of Electron and Hole Impact Ionization Coefficients in GaN

The temperature dependence of the electron and hole impact ionization coefficients in GaN has been investigated experimentally. Two types of p-i-n diodes grown on bulk GaN substrates have been fabricated and characterized, and the impact ionization coefficients for both electrons and holes have been extracted using the photomultiplication method. Both the electron and hole impact ionization coefficients decrease as the temperature increases. The Okuto–Crowell model was used to describe the temperature dependence of the electron and hole impact ionization coefficients. Based on the measured impact ionization coefficients, the temperature dependence of the breakdown voltage of GaN non-punch through p-n diodes can be predicted; good agreement with experimentally reported results is obtained.

Avalanche Photodetector Based on InAs/InSb Superlattice

This work demonstrates a mid-wavelength infrared InAs/InSb superlattice avalanche photodiode (APD). The superlattice APD structure was grown by molecular beam epitaxy on GaSb substrate. The device exhibits a 100 % cut-off wavelength of 4.6 µm at 150 K and 4.30 µm at 77 K. At 150 and 77 K, the device responsivity reaches peak values of 2.49 and 2.32 A/W at 3.75 µm under −1.0 V applied bias, respectively. The device reveals an electron dominated avalanching mechanism with a gain value of 6 at 150 K and 7.4 at 77 K which was observed under −6.5 V bias voltage. The gain value was measured at different temperatures and different diode sizes. The electron and hole impact ionization coefficients were calculated and compared to give a better prospect of the performance of the device.

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.

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.

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

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.

Extremely low excess noise and high sensitivity AlAs0.56Sb0.44 avalanche photodiodes

Fast, sensitive avalanche photodiodes (APDs) are required for applications such as high-speed data communications and light detection and ranging (LIDAR) systems. Unfortunately, the InP and InAlAs used as the gain material in these APDs have similar electron and hole impact ionization coefficients (α and β, respectively) at high electric fields, giving rise to relatively high excess noise and limiting their sensitivity and gain bandwidth product1. Here, we report extremely low excess noise in an AlAs0.56Sb0.44 lattice matched to InP. A deduced β/α ratio as low as 0.005 with an avalanche region of 1,550 nm is close to the theoretical minimum and is significantly smaller than that of silicon, with modelling suggesting that vertically illuminated APDs with a sensitivity of −25.7 dBm at a bit error rate of 1 × 10−12 at 25 Gb s−1 and 1,550 nm can be realized. These findings could yield a new breed of high-performance receivers for applications in networking and sensing.

Impact ionization coefficients of 4H-SiC in a wide temperature range

The temperature dependence of impact ionization coefficients of electrons and holes along 4H-SiC 〈0001〉 was determined in a wide temperature range from 156 K to 561 K. Photomultiplication measurements were conducted using several types of 4H-SiC photodiodes (PDs) with different structures under high vacuum conditions. The hole ionization coefficient showed a negative temperature dependence, which can be attributed to enhanced phonon scattering at elevated temperatures. Temperature dependence of the electron ionization coefficient was small, and this result may be ascribed to the simultaneous effects of enhanced phonon scattering and shrinkage of minigaps in the conduction band. Accuracy of the obtained results was verified by comparing the calculated breakdown voltage with the experimental breakdown voltage of various diodes.

Experimental characterization of impact ionization coefficients for electrons and holes in GaN grown on bulk GaN substrates

Epitaxial p-i-n structures grown on native GaN substrates have been fabricated and used to extract the impact ionization coefficients in GaN. The photomultiplication method has been used to experimentally determine the impact ionization coefficients; avalanche dominated breakdown is confirmed by variable-temperature breakdown measurements. To facilitate photomultiplication measurements of both electrons and holes, the structures include a thin pseudomorphic In0.07Ga0.93N layer on the cathode side of the drift layer. Illumination with 193 nm and 390 nm UV light has been performed on diodes with different intrinsic layer thicknesses. From the measured multiplication characteristics, the impact ionization coefficients of electrons (α) and holes (β) were determined for GaN over the electric field range from 2 MV/cm to 3.7 MV/cm. The results show that for transport along the c-axis, holes dominate the impact ionization process at lower electric field strengths; the impact ionization coefficient of electrons becomes comparable to that of holes (β/α<5) for electric field strengths above 3.3 MV/cm.

Demonstration of large ionization coefficient ratio in AlAs0.56Sb0.44 lattice matched to InP

The electron and hole avalanche multiplication characteristics have been measured in bulk AlAs0.56Sb0.44 p-i-n and n-i-p homojunction diodes, lattice matched to InP, with nominal avalanche region thicknesses of ~0.6 μm, 1.0 μm and 1.5 μm. From these and data from two much thinner devices, the bulk electron and hole impact ionization coefficients (α and β respectively), have been determined over an electric-field range from 220–1250 kV/cm for α and from 360–1250 kV/cm for β for the first time. The α/β ratio is found to vary from 1000 to 2 over this field range, making it the first report of a wide band-gap III-V semiconductor with ionization coefficient ratios similar to or larger than that observed in silicon.

Characterization of breakdown behavior of diamond Schottky barrier diodes using impact ionization coefficients

Diamond has the advantage of having an exceptionally high critical electric field owing to its large band gap, which implies its high ability to withstand high voltages. At this maximum electric field, the operation of Schottky barrier diodes (SBDs), as well as FETs, may be limited by impact ionization, leading to avalanche multiplication, and hence the devices may breakdown. In this study, three of the reported impact ionization coefficients for electrons, αn, and holes, αp, in diamond at room temperature (300 K) are analyzed. Experimental data on reverse operation characteristics obtained from two different diamond SBDs are compared with those obtained from their corresponding simulated structures. Owing to the crucial role played by the impact ionization rate in determining the carrier transport, the three reported avalanche parameters implemented affect the behavior not only of the breakdown voltage but also of the leakage current for the same structure.

Intersection of Paschen's curves for argon

The intersection of Paschen's curves for argon with a same gap length but a different electrode radius was observed. While the breakdown voltage increases with the increase of the nonuniformity in the electric field of the gap at lower pressures, it decreases at higher pressures. The reason for the intersection of Paschen's curves was given based on the mean free path length of the electrons inversely proportional to the gas pressure and the electron impact ionization coefficient exponentially increasing with the electric field. The intersection of the Paschen's curves was qualitatively reproduced by a numerical simulation.