Impact Ionization Coefficients Research Articles

Impact ionization coefficients along 4H-SiC ⟨11-20⟩ in a wide temperature range

Abstract The impact ionization coefficients along 4H-SiC ⟨11-20⟩ were determined in a wide temperature range from 294 K to 473 K. 4H-SiC (11-20) p-n diodes were fabricated and photomultiplication measurements were conducted on two types of photodiodes to measure the multiplication factors of carriers. The extracted impact ionization coefficients of both electrons and holes along 4H-SiC ⟨11-20⟩ decreased at high temperatures, which can be ascribed to the enhanced phonon scattering. On the basis of the results above, the critical electric field along 4H-SiC ⟨11-20⟩ calculated from the obtained impact ionization coefficients increased with the temperature.

Low-energy and tunable LIF neuron using SiGe bandgap-engineered resistive switching transistor

We have proposed leaky integrate-and-fire (LIF) neuron having low-energy consumption and tunable functionality without external circuit components. Our LIF neuron has a simple configuration consisting of only three components: one bandgap-engineered resistive switching transistor (BE-RST), one capacitor, and one resistor. Here, the crucial point is that BE-RST with a silicon–germanium heterojunction possesses an amplified hysteric current switching with a low latch-up voltage due to improved hole storage capability and impact ionization coefficient. Therefore, the proposed neuron utilizing BE-RST requires an energy consumption of 0.36 pJ/spike, which is approximately six times lower than 2.08 pJ/spike of pure silicon-RST based neuron. In addition, the spiking properties can be tuned by modulating the leakage rate and threshold through gate bias, which contributes to energy-efficient sparse-activity and high learning accuracy. As a result, our proposed neuron can be a promising candidate for executing various spiking neural network applications.

Impact ionization coefficients and excess noise in Al0.55Ga0.45As0.56Sb0.44 lattice matched to InP

The avalanche multiplication and noise characteristics of Al0.55Ga0.45As0.56Sb0.44p–i–n and n–i–p structures grown lattice matched on InP have been investigated. From measurements undertaken using 530 nm illumination on several devices, the electron (α) and hole (β) impact ionization coefficients have been determined. While α only shows a relatively small increase compared to the higher Al composition alloys of AlxGa1−xAsSb, β is found to increase significantly. Although the β/α ratio is increased to ∼0.125–0.2, higher than the ∼0.003–0.02 seen in the higher-Al alloys, a relatively low excess noise factor of 2.2 was measured in the p-i-n with electron-initiated multiplication of 20. This noise performance is significantly lower than that predicted using a local-field model and comparable to some commercial silicon APDs. This avalanching material with a bandgap of ∼1.24 eV will have the advantages of a smaller band discontinuity with the absorber region and should also operate at a lower voltage.

Accurate determination of impact ionization coefficient ratio and temperature dependence of InGaAs/InP avalanche photodiodes

We propose a broadband noise test method (10 Hz–1 MHz) using a direct power method to measure the excess noise of InGaAs/InP avalanche photodiodes (APDs) with a separate absorption, grading, charge, and multiplication structure. By this means, the impact ionization coefficient ratio (the k value) can be accurately determined. Compared with previous studies, this method can distinguish between low-frequency noise and excess noise, so for an appropriate high frequency spectral range, the excess noise can be analyzed without mixing in other noise information. Three different APDs fabricated in-house with different diameters (12, 25, and 60 µm) were investigated using the above-mentioned method under temperatures varying from −10 to −40 °C. Our findings showed that the k value of the APDs decreased as the temperature decreased. When the temperature decreased to −40 °C, the k value of the 12, 25, and 60 µm diameter diodes was as low as 0.1, 0.3, and 0.2, respectively. The measurement results are consistent with our device design and not only provide useful information for the future selection of device materials and structures but also demonstrate the feasibility of the broadband noise measurement method in the accurate determination of the k value. It indicates that low excess noise can be achieved by utilizing the temperature dependence of k.

Direct observation of radio-frequency negative differential resistance in GaN-based single drift region IMPATT diodes

We report the direct observation of radio-frequency negative differential resistance, via on-wafer S-parameter measurements, in GaN-based impact ionization avalanche transit time (IMPATT) diodes. Clear signatures of reflection gain are observed from 18.7 to 30.6 GHz. These observations have been made possible by suppressing the reverse leakage current (and thereby parasitic shunt conductance) by optimization of the fabrication process, in conjunction with the use of pulsed measurements to suppress device self-heating. Consistent with avalanche-dominated behavior, the measured DC reverse bias current–voltage measurements show a positive temperature coefficient of breakdown. For the high-frequency on-wafer characterization, pulsed-bias S-parameter measurements with low (0.0067%) duty cycle were used to mitigate thermal effects. The measured avalanche frequency aligns closely with theoretical predictions based on Gilden and Hines' small signal model [Gilden and Hines, IEEE Trans. Electron Devices ED-13(1), 169–175 (1966)], measured impact ionization coefficients [Cao et al., Appl. Phys. Lett. 112(26), 262103 (2018)], and experimental saturation velocity measurements [Bajaj et al., Appl. Phys. Lett. 107(15), 153504 (2015)]; this excellent agreement confirms IMPATT operation and provides insights needed to further optimize device performance.

A comparative study of impact ionization and avalanche multiplication in InAs, HgCdTe, and InAlAs/InAsSb superlattice

We use an ensemble Monte Carlo transport approach to calculate and compare the impact ionization and avalanche photodiode excess noise characteristics in three materials—a band-engineered InAlAs/InAsSb type-II superlattice, bulk InAs, and HgCdTe—all with an identical bandgap of 370 meV at 250 K. The electronic band structures and energy–momentum conservation conditions are used to calculate the impact ionization rates, carrier histories, multiplication gains, and excess noise characteristics. The calculated impact ionization coefficients and excess noise factors indicate a single carrier species multiplication in all three materials under low applied electric fields. We find the ratio of impact ionization coefficients to be k=7×10−4 for InAs and 3×10−4 for HgCdTe under an applied field of 50 kV/cm, and the superlattice to be k<10−6 at fields up to 400 kV/cm. The bulk materials experience avalanche breakdown as the applied field increases, transitioning to Geiger mode behavior at gains above 103 for InAs and 104 for HgCdTe. However, this breakdown is absent from the superlattice at the highest fields considered in this study due to hole confinement, indicating superior performance compared to the bulk materials. Our results demonstrate the role of superlattice band engineering in designing quality avalanche photodiode materials.

Doping Effects and Relationship between Energy Band Gaps, Impact of Ionization Coefficient and Light Absorption Coefficient in Semiconductors

The doping process is very important in semiconductor technology that is widely used in the production of electronic devices. The effects of doping on the resistivity, mobility and energy band gap of semiconductors are significant and can greatly impact the performance of electronic devices. This thesis aims to investigate the impact of doping on the resistivity, mobility, energy band gap, impact of ionization coefficient, and light absorption coefficient of semiconductors. The study involves an in-depth analysis of the electronic properties of doped semiconductors and their behavior in various conditions. This thesis will provide a comprehensive understanding of the impact of doping on the electronic properties of semiconductors. The energy band gap, impact of ionization coefficient, and Light absorption coefficient were observed in this thesis. In the experimental result, the relation between energy band gap and atomic density, light absorption coefficient and atomic density, impact ionization and atomic density, impact ionization coefficient and Light absorption coefficient, resistivity and mobility has been found.

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.

(Invited) A Closer Look at Impact Ionization Coefficients in Wide Band Gap Semiconductors: Theoretical Models and Measured Data

The direct measurement of ionization coefficients in wide band gap semiconductor materials is challenging due to the need to operate at high field strengths and the requirement of specific test structures that enable single carrier injection. More often than not, ionization coefficients are inferred from current multiplication data measured in p-n junctions or transistors structures. Unfortunately, sub-par material quality, processing issues and inappropriate measuring techniques have led to ionization coefficients values that are contradictory and with large variation among different datasets.As a result, theoretical models that attempt to predict the values of the carriers’ ionization coefficients are important since they provide an estimate of the expected values and a first order evaluation of the material performance. Developing theoretical models presents its own set of challenges. The established approach is based on a full electronics structure description of the semiconductor material and a suitable model to quantify the interaction of carriers with phonons, impurities and material imperfections. While this methodology has been successful with conventional elemental and compound semiconductors, and it has been applied to some wide band gap materials such as GaN, 4H-SiC [1,2] and diamond, a number of open issues still exists. The main difficulty is the determination of the carrier-phonon scattering strength at high electric field strengths that cannot be inferred from low-field mobility measurements.Among all wide band gap semiconductors, 4H-SiC [3] and GaN [4] are the material for which ionization coefficients have been measured by several groups. In the case of GaN, different measured ionization coefficients datasets are available and seems to provide a consistent indication of the expected values. Corresponding theoretical models based on full-band Monte Carlo simulations have been able to predict the correct trends, namely the fact that holes dominate the ionization process, but a quantitative agreement between predicted and measured values has only been achieved recently [5].This talk will provide an overview of the currently available experimentally measured ionization coefficients for wide band gap semiconductors and compare them to the ones obtained with theoretical models of different complexity. Specifically the development of the theoretical models for high-field transport for 4H-SiC, GaN will be discussed. Three different approaches, one based on empirical carrier-phonon scattering rates, one using the rigid pseudo ion model, and the direct evaluation of the interaction parameters based on a ab-initio DFT approach will be compared, and the outcome for each one of them benchmarked against the measured values. Additionally, the models will be applied to determine the ionization coefficients in AlGaN alloys, cubic BN and diamond.[1] E. Bellotti et al., J. Appl. Phys., 87, (8), p.3864, 15 April 2000.[2] F. Bertazzi et al., J. Appl. Phys., Vol.106, N6, p.063719, 15 September 2009.[3] A.O. Kostantinov, Appl. Phys. Lett. 71, 90, 1997, T. Hatakeyama, Appl. Phys. Lett. 85, 8, 2004[4] Cao et al., APL, N.112, 2018, Maeda et al., JAP, N.129, 2021, McClintock et al., APL, N.90, 2007, Ji et al., APL, N115, 2019[5] E. Bellotti and M. Matsubara, unpublished.

(Invited) Gallium Oxides Devices for Grid-Scale Power Electronics and High Power Switched Mode RF Amplifiers

Within a decade of the first demonstration of a MESFET device, monoclinic β-Ga2O3 (Ga2O3) devices have made incredible progress in breakdown voltages, power device figure of merit and high-speed performance. It has emerged as a promising ultra-widebandgap semiconductor for next generation power, GHz switching and RF applications. In this talk, we will present an overview of our studies on fundamental transport properties, kilovolt class power MOSFETs and aggressively scaled RF devices. The large bandgap of Ga2O3 leads to a high critical field strength. This high field strength in combination with demonstrated room temperature mobility and calculated electron velocity leads to a higher Baliga’s Figure of Merit (BFoM) and Johnston Figure of Merit (JFoM) than current commercially available widebandgap technologies. Additionally, the large bandgap also enables high temperature operation and radiation hardness making it attractive for space applications such as Mars and Venus missions.In the first part, we will discuss the deep insights gained from the first-principles based transport calculations in Ga2O3. We will discuss the limits to low field mobility, saturation velocities and impact ionization coefficients. The impact of the plasmon-phonon coupling on the phonon limited transport will be discussed. We will present the experimental signatures of plasmon-phonon coupling and anti-screening behavior in ionic gated accumulation layers.Next, I will describe our work on the lateral MOSFETs with improved field plate design and beyond-kV breakdown. Temperature dependent analysis and device simulation suggest an extrinsic breakdown mechanism outside the channel. A simple and yet effective SU-8 polymer passivation technology was developed that results in significant improvement in breakdown voltages. The higher field strength of the SU-8 polymer enables a significant increase in breakdown voltage to 8 kVs in lateral MOSFETs. However, these devices show a high Ron, which is due to the depletion caused by RIE of the channel. We will present the use of ultra-high vacuum annealing techniques to improve the on-resistance of the devices still maintaining the multi-kilo-volt rating of the devices.Due to its high JFoM, Ga2O3 is a potential candidate for high power density RF amplifiers. We will also present the performance advancement that can be obtained in RF power performance using Ga2O3 technology. We will present the challenges in the technology and potential solutions. We will present the experimental DC and pulsed measurements on laterally scaled MOSFETs with 100 nm gate length. Severe DC-RF dispersion was observed which is attributed to the RIE damage and surface states on the oxide. Passivation of the devices shows reduced current collapse. Using aggressive gate lengths and gate-source spacing scaling, (AlxGa1-x)2O3/Ga2O3 heterostructure FETs were fabricated that show record high RF performance. The device transconductance was limited by the regrowth interface resistance. Ex-situ silicon nitride passivation was shown to be effective to reduce DC-RF dispersion. Recently, thin channel MOSFETs with deep-sub-micron gate lengths and source/drain regrowth have demonstrated devices with simultaneously low on resistance, high frequency, high voltages.

Temperature dependence of avalanche breakdown in 4H-SiC devices

We report new data on the temperature coefficient of the avalanche breakdown voltage (BV) in 4H-SiC devices. We compare avalanche in different device types (MOSFETs/Schottky diodes), different measurement types [Id(Vd)-sweeps and unclamped inductive switching stress], and avalanche directions (vertical and lateral) for a wide range of avalanche voltages. We fit the measured BV(T)-curves to the one-sided abrupt junction model and extract values for the temperature coefficients of impact ionization coefficients in their Chynoweth and Thornber forms for both holes and electrons.

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.

Trichel pulse characteristics and mechanism of negative corona discharge in sub-millimeter gaps

A negative corona discharge system of a needle-plate electrode suitable for sub-millimeter gaps is established to investigate Trichel pulse characteristics of negative corona discharge, in which an optical acquisition system is especially applied to timely observe a discharging corona. Electrostatics–hydrodynamics coupling simulations of air discharging in 100 μm-gaped needle-plate electrodes are performed to elucidate the micro-physical process of negative corona discharge. The impact ionization coefficient used for simulations and the experimentally recorded images of discharge corona are combined to characterize the active region of secondary electron emission. Dynamical distribution and transport of the charged particles are analyzed from multiphysics simulations to explain the microscopic mechanism for various stages of Trichel pulses. Even though the corona front near the plate electrode maintains a high rate of collision ionization and secondary electron excitation, the needle tip corona has not reached the threshold electric field of electron avalanche required for glow discharge, as manifested by discharge sawtooth waves comprised of corona and glow components. The amplitude and frequency of Trichel pulses increase, respectively, with impact ionization and secondary electron emission, which is evidently dependent on attachment coefficient and anion mobility. A higher attachment coefficient will lead to a significant reduction in amplitude of Trichel pulses. The present study provides a theoretical basis and experimental verification for micrometer discharges, which is the key point of insulation protections in microelectromechanical systems.

General optimization of breakdown voltage and resistivity on power components in terms of doping level and thickness

The emergence of wide band-gap (WBG) materials promises improved performance in semiconductor devices, but also presents significant technical challenges. Developing this immature technology and adapting market-ready silicon-based technology to new materials requires a thorough understanding of the relationship between material properties and the final electrical performance of the component. In this work, we propose a model that relates generic material properties and device-specific parameters (such as doping level or thickness) to the final breakdown voltage and performance of unipolar vertical diodes. Our approach enables optimized device design and evaluation by connecting the electrical performance target with the optimal drift layer characteristics. This model can be applied universally to any material with known impact ionization coefficients, carrier mobility, and thermal activation energy. We focus on diamond as a paradigm for WBG materials, illustrating specific characteristics such as incomplete carrier ionization or elevated doping-dependent critical electric fields. Our model predicts that diamond-based vertical devices with 70 μm layers and doping levels of 1.1015 cm−3 can sustain 20 kV.

Impact Ionization Coefficient Prediction of a Lateral Power Device Using Deep Neural Network

Nowadays, the impact ionization coefficient in the avalanche breakdown theory is obtained using 1-D PN junctions or SBDs, and is considered to be a constant determined by the material itself only. In this paper, the impact ionization coefficient of silicon in a 2D lateral power device is found to be no longer a constant, but instead a function of the 2D coupling effects. The impact ionization coefficient of silicon that considers the 2D depletion effects in real-world devices is proposed and extracted in this paper. The extracted impact ionization coefficient indicates that the conventional empirical impact ionization in the Fulop equation is not suitable for the analysis of 2D lateral power devices. The veracity of the proposed impact ionization coefficient is validated by the simulations obtained from TCAD tools. Considering the complexity of direct modeling, a new prediction method using deep neural networks is proposed. The prediction method demonstrates 97.67% accuracy for breakdown location prediction and less than 6% average error for the impact ionization coefficient prediction compared with the TCAD simulation.

TCAD Modeling of High-Field Electron Transport in Bulk Wurtzite GaN: The Full-Band SHE-BTE

Gallium Nitride (GaN) High-Electron Mobility Transistors (HEMTs) actually represent one of the best candidates for medium-high power and radio frequency applications. As they operate at large bias and electric fields, a comprehensive analysis of the high-field transport properties is fundamentals, as hot electrons are expected to play a relevant role for the device reliability. In this perspective, Technology Computer-Aided Design (TCAD) simulations can be a very useful tool for the understanding of the phenomena dominating hot-electron degradation mechanisms. The most-accurate modeling approaches are based on the direct solution of the Boltzmann equation, which is not actually available for the GaN material. In this work, the deterministic solution of the Boltzmann transport equation via the spherical-harmonics expansion (SHE-BTE), as incorporated in a commercial TCAD tool, has been extended to the analysis of GaN electrons. To this purpose, the details of the full-band structure has been derived from DFT calculations as in state-of-art literature works, and the electron density of states, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$g(E)$ </tex-math></inline-formula> , and group velocity <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$u_{g}(E)$ </tex-math></inline-formula> , have been calculated for the SHE-BTE for the first time. In addition to this, an accurate calibration of the total scattering rate accounting for nonpolar acoustic and optical carrier-phonon interaction, Coulomb scattering and impact ionization has been carried out against available Monte Carlo data and experiments. The proposed model is also shown to correctly predict the temperature dependence of the electron impact-ionization coefficient and current density up to breakdown.

Hard- and soft-breakdown modeling in &amp;lt;001&amp;gt; oriented β-Ga2O3 Schottky barrier diode

Gallium oxide (Ga2O3) attracts considerable technological interest because of its high Baliga’s figure-of-merit and high breakdown voltages. As the models for the breakdown behavior of n-doped Ga2O3 that consider soft (barrier lowering) and hard (avalanche effect) breakdowns are still lacking, in this study, we model the breakdown operations in &amp;lt;001&amp;gt; oriented Schottky barrier diodes considering both the soft- and hard-breakdown phenomena. The completion of the impact ionization model of β-Ga2O3 in &amp;lt;001&amp;gt; orientation is proposed by determining the hole impact ionization coefficient, thereby reproducing hard breakdown operations. Moreover, a barrier lowering model is determined for reproducing soft breakdown operations. The outcomes of the proposed modeling investigation are expected to be crucial for predicting the reverse-biased operations of β-Ga2O3 in &amp;lt;001&amp;gt; orientation to facilitate further technological development and applications of Ga2O3.

A steep switching WSe2 impact ionization field-effect transistor

The Fermi-Dirac distribution of carriers and the drift-diffusion mode of transport represent two fundamental barriers towards the reduction of the subthreshold slope (SS) and the optimization of the energy consumption of field-effect transistors. In this study, we report the realization of steep-slope impact ionization field-effect transistors (I2FETs) based on a gate-controlled homogeneous WSe2 lateral junction. The devices showed average SS down to 2.73 mV/dec over three decades of source-drain current and an on/off ratio of ~106 at room temperature and low bias voltages (<1 V). We determined that the lucky-drift mechanism of carriers is valid in WSe2, allowing our I2FETs to have high impact ionization coefficients and low SS at room temperature. Moreover, we fabricated a logic inverter based on a WSe2 I2FET and a MoS2 FET, exhibiting an inverter gain of 73 and almost ideal noise margin for high- and low-logic states. Our results provide a promising approach for developing functional devices as front runners for energy-efficient electronic device technology.

Accurate Nonlocal Impact Ionization Models for Conventional and Staircase Avalanche Photodiodes Derived by Full Band Monte Carlo Transport Simulations

We present a procedure to extract the nonlocal impact ionization coefficients in Avalanche Photodiodes (APDs) operating in the linear regime from Full Band Monte Carlo simulations. The Monte Carlo calculations have been calibrated on existing experimental data for GaAs p-i-n APDs with different thickness of the intrinsic region. Inspection of impact ionization generation rate in p-i-n and staircase GaAs APDs led us to identify the limitations of existing nonlocal-history dependent impact ionization models. The introduction of an energy dependent relaxation length for the computation of the effective fields significantly improves the model accuracy in predicting the gain and noise associated to conduction and valence band steps in staircase APDs without additional computational burden. This improved nonlocal-history dependent model is thus a powerful tool to design and optimize APDs with different architectures.

Dark Current and Gain Modeling of Mid-Wave and Short-Wave Infrared Compositionally Graded HgCdTe Avalanche Photodiodes

We present a detailed methodology for drift-diffusion (DD) modeling of gain and dark currents in mid-wave infrared (MWIR) and short-wave infrared (SWIR) <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathrm {Hg}}_{{1}-{x}}$ </tex-math></inline-formula> Cd <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>x</i></sub> Te <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p-around-n</i> avalanche photodiodes (APDs) based on a comprehensive analysis of experimentally obtained data from three different sets of devices. These devices are fabricated on homogeneous and compositionally-graded films with cadmium composition ranging from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${x}\,\,=0.37$ </tex-math></inline-formula> to 0.45, each with differing geometrical dimensions, and tested at operating temperatures ranging from 140 to 240 K. The temperature, composition, and electric-field dependent impact ionization (ImI) coefficients are calibrated first according to the given experimental gain data. The gain-normalized dark current (GNDC) curve, along with the presumption of electron-only multiplication, is then used to thoroughly understand and model the behavior of diffusion and generation currents. At high biases, the GNDC curve reveals contributions from tunneling, which are classified as either trap-assisted or band-to-band based on their temperature dependence. The tunneling mechanisms are modeled accordingly: trap-assisted tunneling (TAT) is scaled inversely with Shockley–Read–Hall (SRH) lifetime, while band-to-band tunneling (BTBT) is scaled with bandgap, effective mass, and an additional empirical temperature term. Finally, the comprehensive model is applied to all three experimental devices across the operating temperature range with good agreement.