Hole Impact Research Articles

A New Expression for the Gain-Noise Relation of Single-Carrier Avalanche Photodiodes With Arbitrary Staircase Multiplication Regions

We propose a simple expression to relate the total excess noise factor of a single-carrier multiplication staircase avalanche photodiode (APD) to the excess noise factor and gain given by the individual conduction band discontinuities. The formula is valid when electron impact ionization dominates hole impact ionization; hence, it is especially suited for staircase APDs with In-rich multiplication regions, as opposed, for example, to GaAs/AlGaAs systems where hole ionization plays an important role. The formula has been verified by accurate means of numerical simulations based on a newly developed nonlocal history dependent impact ionization model.

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.

An Improved Nonlocal History-Dependent Model for Gain and Noise in Avalanche Photodiodes Based on Energy Balance Equation

We present a nonlocal history-dependent model for impact ionization gain and noise in avalanche photodiodes (APDs) especially suited for staircase APDs. The model uses a simple energy balance equation to define effective electric fields valid also in the presence of band discontinuities which are then used to express the ionization coefficients. The model parameters have been calibrated against literature data for gain and noise in GaAs and Al x Ga1− x As $({x} = {0.2}, {0.6}, {0.8})$ p-i-n diodes. Application to the experimental data for gain and noise in heterojunction and staircase separate absorption and multiplication APDs is reported to demonstrate the ability of the model in describing complex APD structures. It is found that, in spite of conduction band discontinuities being much larger than valence band ones, hole impact ionization contributes a significant degradation of the noise metrics in GaAs/AlGaAs staircase APDs. These nontrivial insights demonstrate the usefulness of the model to steer device design and optimization.

Impact Ionization Coefficients in 4H-SiC Toward Ultrahigh-Voltage Power Devices

A temperature dependence of impact ionization coefficients in 4H-SiC was studied in a wide range of electric field toward the accurate designing of ultrahigh-voltage devices. The photomultiplication measurement was conducted for various photodiodes with different multiplication layer structures to obtain multiplication factors and ionization coefficients in a wide range of electric field strength. Especially, using multiplication layer structure with low doping concentration, the hole impact ionization coefficient was extracted at low electric field of 1 MV/cm. In high-temperature measurement, the hole ionization coefficient decreased with the increase of temperature, as observed in other semiconductor materials. For the electron ionization coefficient, however, its temperature dependence was very small and values obtained at room temperature could be used, at least up to 150 °C.

Temperature and field dependent effective hole mobility and impact ionization at extremely high fields in amorphous selenium

An analytical model for the electric field and temperature dependent effective drift mobility of holes in amorphous selenium (a-Se) has been developed by considering density of states distribution near the valence band, field enhancement release rate from the shallow traps, and carrier heating. The models for the field-dependent microscopic mobility and momentum relaxation mean free path considering carrier heating are also proposed. The models are fitted with the published experimental results on effective hole mobility and impact ionization with wide variations of applied electric fields and temperatures. The fittings of the model with the published experimental data on the effective hole mobility reveal that, while the effective hole drift mobility increases with increasing temperature and field, the microscopic mobility and momentum relaxation mean free path in a-Se decreases with increasing electric field. A better fitting considering thermally activated tunneling for the field-enhancement release rate indicates that the shallow hole traps in a-Se are neutral defects.

Non-Local Model for the Spatial Distribution of Impact Ionization Events in Avalanche Photodiodes

We report an extension of the analytical dead space multiplication theory that provides the means to theoretically determine the spatial distribution of electron and hole impact-ionization events in an arbitrarily specified heterojunction multiplication region. The model can be used to understand the role of the dead space in regularizing the locations of impact ionization. It can also be utilized to analyze, design, and optimize new generations of ultra-low noise, multistaged gain avalanche photodiodes based upon judiciously energizing and relaxing carriers to enhance electron impact ionization and suppress hole impact ionization.

Temperature dependence of gain and excess noise in InAs electron avalanche photodiodes

Measurement and analysis of the temperature dependence of avalanche gain and excess noise in InAs electron avalanche photodiodes (eAPDs) at 77 to 250 K are reported. The avalanche gain, initiated by pure electron injection, was found to reduce with decreasing temperature. However no significant change in the excess noise was measured as the temperature was varied. For avalanche gain > 3, the InAs APDs with 3.5 µm i-region show consistently low excess noise factors between 1.45 and 1.6 at temperatures of 77 to 250 K, confirming that the eAPD characteristics are exhibited in the measured range of electric field. As the dark current drops much more rapidly than the avalanche gain and the excess noise remains very low, our results confirmed that improved signal to noise ratio can be obtained in InAs eAPDs by reducing the operating temperature. The lack of hole impact ionization, as confirmed by the very low excess noise and the exponentially rising avalanche gain, suggests that hole impact ionization enhancement due to band "resonance" does not occur in InAs APDs at the reported temperatures.

Impact ionization coefficients of 4H- and 6H-SiC

The Monte Carlo (MC) simulation of electron and hole impact ionization rates for 4H- and 6H-SiC in high electric field is presented. This work focuses on the study of impact ionization rates and impact ionization coefficients since these parameters play a very important role in determining the device performance. In our simulation, the impact ionization rates are obtained by using modified Keldysh equation with a softness factor fitted to the experimental data described by other researchers. The electron and hole impact ionization coefficients in 4H- and 6H-SiC are parameterized at high electric field. The electron and hole impact ionization coefficients for a wide range of electric fields have been successfully derived in our model.

Hard breakdown mechanisms of compensated p-type and n-type single-crystalline silicon solar cells

The hard breakdown behaviors of boron–phosphorus compensated p-type and n-type Czochralski silicon solar cells were studied as functions of the type of conductivity, the net doping concentration and the temperature. We showed as expected from previous studies that the hard breakdown was governed by avalanche mechanisms (impact ionization) and that for a given net doping concentration the hard breakdown voltage was almost the same for both p-type and n-type solar cells, despite the different reported values for the electron and hole impact ionization coefficients. The studied compensated materials offered the opportunity to determine the hard breakdown voltages for samples with the same net doping concentration but different total amount of doping species. However no major effects of the dopant compensation were observed, the experimental data being described by the empirical expressions used for uncompensated silicon samples.

Interaction of hot carriers with optical phonons in Selenium

An interaction of hot charge carriers with optical phonons in Selenium is studied theoretically from first principles. The results suggest that the electron–phonon matrix element for energetic electrons is significantly greater than that for holes. This effect is attributed to the weak coupling of lone-pair states to lattice perturbations associated with optical vibrational modes. Hence, the energy relaxation time due to the emission of optical phonons for holes is expected to be longer than that for electrons. The longer relaxation time favors the impact ionization of holes.

Impact Ionization Coefficients in $\hbox{Al}_{0.52} \hbox{In}_{0.48}\hbox{P}$

Electron and hole multiplication characteristics have been measured on a series of Al0.52In0.48P p+-i-n+ and n+-i-p+ homojunction diodes with nominal avalanche region thicknesses ranging from 0.22 to 1.03 μm. From these, the electron and hole impact ionization coefficients are deduced over an electric-field range from 530 to 990 kV/cm. The results suggest that the electron ionization coefficient is larger than the hole ionization coefficient, particularly at lower electric fields. Extremely low dark currents were obtained, and there was no evidence of any tunneling dark current even at electric fields of approximately 1.0 MV/cm. From these ionization coefficients, we deduce that the breakdown voltage in Al0.52In0.48P is almost 2.5× greater than that of GaAs and 4.5× lower than that of GaN.

Avalanche Multiplication and Excess Noise in InAs Electron Avalanche Photodiodes at 77 K

The findings of a study of impact ionization, avalanche multiplication and excess noise in InAs avalanche photodiodes at 77 K are reported. It is shown that hole impact ionization is negligible in practical devices which continue to operate as electron avalanche photodiodes, as they do at room temperature. A new electron ionization coefficient capable of modeling multiplication at 77 K is presented and it is shown that significant multiplication can be achieved in practical devices without excessive tunneling currents. The characteristic changes observed between room temperature and 77 K are discussed. This paper helps to demonstrate the potential for practical InAs electron avalanche photodiodes, operating cooled.

Nonlocal analysis to study of the impact ionization and avalanche characteristics of deep submicron Si devices

In this paper, we have presented electric field dependence of the electron and hole impact ionization coefficients and threshold energies in submicron Si diodes with intrinsic region thicknesses down to 31 nm. To do so, we have used a nonlocal analysis, in order to take the effects of arbitrary distribution of ionization events in both space and time domains and the effects of enhancement in the average speed of those carriers which ionize early in their trajectories as well as nonuniform electric fields in the multiplication region and its surrounding ambient, carrier’s dead space history and its spatial ionization rate, into consideration all in one comprehensive analytic model.

Lone-pair states as a key to understanding impact ionization in chalcogenidesemiconductors

Impact ionization of holes and domination of p-conductivity in chalcogenide semiconductorsare attributed to a weak electron–phonon interaction inherent to lone-pair states. Thisargument is supported by first-principles calculations of an acoustical deformation potentialin trigonal selenium. Results of the calculations reveal a strong dependence of thedeformation potential on the excess energy of charge carriers. The latter is interpretedusing a simple tight-binding model.

10.1007/s11453-008-1002-4

A complete analytical solution of the problem of the linear stage of evolution of electron-hole avalanches in the uniform time-independent electric field E ext is derived. The theory accounts for the drift, diffusion, and impact ionization of electrons and holes, thus providing a means for calculating the space-time distributions of fields and charges as well as all the basic parameters of the avalanches up to the onset of nonlinear effects at the time t a . Formulas for the group velocity of the avalanches and for the velocity of its leading fronts are derived. It is shown that the time t a must be determined from the condition that the impact ionization coefficient α in the center of the avalanche be reduced by a specified small quantity η. A transcendent equation is derived, which allows the calculation of the time t a as a function of the quantity η, the unperturbed coefficient α(E ext), and other parameters of the semiconductor. It is found that, when α(E ext) is increased by two orders of magnitude, the total number of electron-hole pairs generated up to the point t a decreases by nearly three orders of magnitude.

Monte Carlo Investigation of Size-Dependent Impact Ionization Properties in InP Under Submicron Scale

The impact ionization properties in InP have been studied by using an ensemble Monte Carlo (EMC) method. In our EMC model, analytical model which contains three conduction bands and three valance bands is adopted to describe the band structure. The electron and hole impact ionization rate is fitted to the available measurement in the wide range of electric field by using Keldysh formula. The steady properties of InP are presented and analyzed. Particularly, the impact ionization behaviors in InP under submicron scale are discussed in detail. It is found that the impact ionization coefficient is not only a function of the applied electric filed but also behaves a size-dependent property when the size is down to submicron scale. We also find that, the size-dependent impact ionization effect which results from the dead space effect and the confined size, can help to prevent the carriers from impact ionization. Finally, the ratio of the electron impact ionization coefficient and the hole impact ionization coefficient is further studied. By taking the size-dependent impact ionization effect into consideration, this ratio is no longer holding as a constant but changing with the size of the devices under the specific electric field. As the size scaling down, the ratio will tend to deviate from one unit, which may contribute to a new look at the noise theory of APD devices.

Comparison of 4H-SiC impact ionization models using experiments and self-consistent simulations

We report comparisons of measured photocurrent versus voltage curves of avalanche photodiodes (APDs) with those calculated using different 4H-SiC hole and electron impact ionization coefficients. As the published impact ionization coefficients result in ionization rates that differ greatly in magnitude, the predicted breakdown voltages using these models vary by many volts. To this end, we investigate the breakdown voltage prediction capability of three prevailing impact ionization models in conjunction with several experiments. To obtain APD performance numerically, we developed a device simulator, which shows that the inclusion of proper electric field-dependent impact ionization rates can accurately predict a variety of measured current-voltage curves, breakdown voltages, and current multiplication rates.

High-field properties of carrier transport in bulk wurtzite GaN: A Monte Carlo perspective

The transport properties of both electron and hole in bulk wurtzite phase GaN in the high electric field domain are presented by using an ensemble Monte Carlo (EMC) method. In our EMC simulation, the impact ionization process, which is seldom studied due to the lack of experimental data, is included. The impact ionization is treated as an additional scattering mechanism, and the impact ionization rate is described by the Keldysh formula, with the parameters in the formula determined by fitting the simulation results to the numerical calculation results. Such a treatment makes it convenient to simulate the impact ionization initiated by either an electron or hole with the EMC method compared to the previous study of carrier transport properties in GaN up to the high field. Steady-state properties of carriers under an applied electric field up to 1 MV/cm are presented and analyzed. Particularly, the impact ionization process here is further studied and detailed discussions are also given. It is found that the impact ionization coefficients of both the electron and hole upon applied electric field can be described by two simple experiential equations. Moreover, for the first time, to the best of our knowledge, we obtain the ratio of the electron impact ionization coefficient to the hole impact ionization coefficient in wurtzite GaN and find out that it can be smaller than that in InP, which means wurtzite GaN may have good gain noise behaviors according to the present noise theories.

The linear stage of evolution of electron-hole avalanches in semiconductors

A complete analytical solution of the problem of the linear stage of evolution of electron-hole ava- lanches in the uniform time-independent electric field E ext is derived. The theory accounts for the drift, diffu- sion, and impact ionization of electrons and holes, thus providing a means for calculating the space-time dis- tributions of fields and charges as well as all the basic parameters of the avalanches up to the onset of nonlinear effects at the time t a . Formulas for the group velocity of the avalanches and for the velocity of its leading fronts are derived. It is shown that the time t a must be determined from the condition that the impact ionization coef- ficient α in the center of the avalanche be reduced by a specified small quantity η . A transcendent equation is derived, which allows the calculation of the time t a as a function of the quantity η , the unperturbed coefficient α ( E ext ), and other parameters of the semiconductor. It is found that, when α ( E ext ) is increased by two orders of magnitude, the total number of electron-hole pairs generated up to the point t a decreases by nearly three orders of magnitude.

Single p-Type/Intrinsic/n-Type Silicon Nanowires as Nanoscale Avalanche Photodetectors

We report the controlled synthesis of axial modulation-doped p-type/intrinsic/n-type (p-i-n) silicon nanowires with uniform diameters and single-crystal structures. The p-i-n nanowires were grown in three sequential steps: in the presence of diborane for the p-type region, in the absence of chemical dopant sources for the middle segment, and in the presence of phosphine for the n-type region. The p-i-n nanowires were structurally characterized by transmission electron microscopy, and the spatially resolved electrical properties of individual nanowires were determined by electrostatic force and scanning gate microscopies. Temperature-dependent current-voltage measurements recorded from individual p-i-n devices show an increase in the breakdown voltage with temperature, characteristic of band-to-band impact ionization, or avalanche breakdown. Spatially resolved photocurrent measurements show that the largest photocurrent is generated at the intrinsic region located between the electrode contacts, with multiplication factors in excess of ca. 30, and demonstrate that single p-i-n nanowires function as avalanche photodiodes. Electron- and hole-initiated avalanche gain measurements performed by localized photoexcitation of the p-type and n-type regions yield multiplication factors of ca. 100 and 20, respectively. These results demonstrate the significant potential of single p-i-n nanowires as nanoscale avalanche photodetectors and open possible opportunities for studying impact ionization of electrons and holes within quasi-one-dimensional semiconductor systems.