Shockley Read Hall Model Research Articles

Harnessing Persistent Photocurrent in a 2D Semiconductor-Polymer Hybrid Structure: Electron Trapping and Fermi Level Modulation for Optoelectronic Memory.

Recently, 2D semiconductor-based optoelectronic memory has been explored to overcome the limitations of conventional von Neumann architectures by integrating optical sensing and data storage into one device. Persistent photocurrent (PPC), essential for optoelectronic memory, originates from charge carrier trapping according to the Shockley-Read-Hall (SRH) model in 2D semiconductors. The quasi-Fermi level position influences the activation of charge-trapping sites. However, the correlation between quasi-Fermi level modulations and PPC in 2D semiconductors has not been extensively studied. In this study, we demonstrate optoelectronic memory based on a 2D semiconductor-polymer hybrid structure and confirm that the underlying mechanism is charge trapping, as the SRH model explains. Under light illumination, electrons transfer from polyvinylpyrrolidone to p-type tungsten diselenide, resulting in high-level injection and majority carrier-type transitions. The quasi-Fermi level shifts upward with increasing temperature, improving PPC and enabling optoelectronic memory at 433 K. Our findings offer valuable insights into optimizing 2D semiconductor-based optoelectronic memory.

In‐gap States and Carrier Recombination in Quasi‐2D Perovskite Films

In‐gap states and their effect on recombination rates in quasi‐2D lead–iodide‐based perovskites, intercalated with various spacer molecules, are studied using a combination of scanning tunneling spectroscopy and temperature‐dependent photoconductivity measurements. The results are further analyzed by a Shockley–Read–Hall model. Indications for shallow in‐gap states, positioned at about 0.15–0.2 eV below the bottom of the conduction band, are found. These states are identified as dominating the recombination route of photogenerated carriers in these systems, with a relatively large capture coefficient of about 10−5–10−6 cm3 s−1 at room temperature. First‐principles calculations based on density functional theory imply that these states are not an intrinsic effect of the inclusion of the spacer molecules, but rather one that arises from chemical defect formation or structural deformation of the perovskite layers. The results suggest that further improvement of the performance of solar cells that are based on quasi‐2D perovskites requires, along with enhancing carrier mobility, efforts to suppress the concentration of these detrimental defect states.

Light-induced trap emptying revealed by intensity-dependent quantum efficiency of organic solar cells

Revisiting the intensity-dependent quantum efficiency (IDQE) technique in the context of non-fullerene acceptors, we find that at forward-bias conditions, the response exhibits what seems to be anomalous behavior that is not consistent with light excitation induced trap filling. Analysis based on the Shockley–Read–Hall model leads to the conclusion that the contacts cause the traps to be completely full in the dark. The role of the light excitation is to half-empty the traps, and thus, the “anomalous” behavior is created. By fitting the IDQE at several bias levels, we find that the trapping is consistent with multiphonon capture by a state close to the middle of the gap. As trap-assisted recombination is a significant loss mechanism, it is essential to fully monitor it for indoor applications as well as to cross the single junction 20% power conversion efficiency limit.

Modeling diffusion length damage coefficient in GaAs and InGaP solar cells under electron irradiation

A method is proposed for calculating the diffusion length damage coefficient for minority carriers (KL) in GaAs and InGaP solar cells under electron irradiation using the Shockley–Read–Hall (SRH) model for defect-assisted recombination. In the SRH model, the damage coefficient KL is proportional to the product kσc, where k is the defect introduction rate under particle radiation and σc is the minority carrier capture cross section of the said defects. The introduction rate k is evaluated using the atomic theory for displacement under electron radiation, and the calculation for σc is adapted from Henry and Lang’s high-temperature multiphonon emission formulation. A linear scaling relationship is observed between k,KL and nonionizing energy loss—validated by bibliographic data in the radiation energy range E≈0.7–12 MeV. Our model reproduces the increasing trend in KL with doping, as observed in the literature, while also capturing the anisotropy between the p-type and n-type materials, with the p-type exhibiting greater radiation resistance than its n-type counterpart. The calculated KL is fed into the physical model for solar cell operation to obtain the post-irradiated Isc,Voc,Pmax at a given fluence Φ. The degradation of the electrical quantities is consistent with the measurements recorded in the literature. The findings show that InGaP is more radiation resistant than GaAs. It is demonstrated that calculating k not only aids in determining the degradation of solar cell parameters from first principles, but also in obtaining the empirical function for degradation: a−blog(1+ckΦ), used in fitting the experimental measurements. The limitations and potential scope of improvements in the model are also discussed.

Characterization of Plasma Process-Induced Low-Density Defect Creation by Lateral Junction Leakage

In the design of ultralow leakage devices such as image sensors, it is necessary to understand the influence of low-density defects during plasma processing-plasma-induced physical damage (PPD)-on device performance. Defects created by plasma exposure act as carrier conduction sites and induce an increase in leakage (e.g., dark) current. This study proposes a PPD evaluation scheme for low-density defect assessments, specifically defects created in the lateral direction due to lateral stochastic straggling (lateral PPD). Two test structures were designed: a single device with a leakage current (Ileak) and a complementary metal-oxide-semiconductor image sensor (CIS) circuit with a dark current (Idark). The energy level and density of defects distributed in the lateral direction were estimated using the Shockley-Read-Hall (SRH) model. The energy level (Et) was derived using the SRH model from the temperature dependence of Ileak and Idark defined as the activation energy Ea. The trap density (Nt) was also determined. A comprehensive comparison of these parameters was conducted. Both Ileak and Idark are dependent on the contact opening diameter after plasma exposure, which implies the presence of defects in the lateral direction via lateral PPD. From the analysis of the temperature dependence of Ileak and Idark, the lateral PPD influenced the mean value of Ea. Moreover, we confirmed that an increase in Idark indicates an increase in the number of trap sites, and more specifically, an increase in defects at shallow levels. The derived trap site density in the CIS circuit was consistent with that of a single device. The proposed evaluation scheme is useful for PPD evaluation in the presence of low-density defects, and is critical for the design of future low-leakage devices.

Are Shockley-Read-Hall and ABC models valid for lead halide perovskites?

Metal halide perovskites are an important class of emerging semiconductors. Their charge carrier dynamics is poorly understood due to limited knowledge of defect physics and charge carrier recombination mechanisms. Nevertheless, classical ABC and Shockley-Read-Hall (SRH) models are ubiquitously applied to perovskites without considering their validity. Herein, an advanced technique mapping photoluminescence quantum yield (PLQY) as a function of both the excitation pulse energy and repetition frequency is developed and employed to examine the validity of these models. While ABC and SRH fail to explain the charge dynamics in a broad range of conditions, the addition of Auger recombination and trapping to the SRH model enables a quantitative fitting of PLQY maps and low-power PL decay kinetics, and extracting trap concentrations and efficacies. However, PL kinetics at high power are too fast and cannot be explained. The proposed PLQY mapping technique is ideal for a comprehensive testing of theories and applicable to any semiconductor.

Applicability of Shockley–Read–Hall Theory for Interface States

The Shockley-Read-Hall (SRH) model has been successfully used for decades to describe the dynamics of interface states. Interestingly, the SRH model neglects structural relaxation at the defect site, which has a dramatic effect on the dynamics of oxide defects. One may, therefore, wonder why this omission has not led to serious and obvious discrepancies with experimental data. Using ab initio approaches to investigate Si dangling bonds, known as P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> centers, within a realistic Si/a-SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> environment together with the more complete nonradiative multiphonon (NMP) theory, we explore why the SRH model provides an excellent approximation for interface traps but not for bulk oxide defects. We will also show that the commonly used Arrhenius correction of the capture cross section can be used to introduce a modified SRH model, which provides a reasonable approximation to the results obtained from a full NMP approach. However, it is shown that this Arrhenius correction may lead to incorrect relaxation energy estimations, especially for bulk oxide defects.

A Simple Method to Differentiate between Free‐Carrier Recombination and Trapping Centers in the Bandgap of the p‐Type Semiconductor

In this research, the ranges of the localized states in which the recombination and the trapping rates of free carriers dominate the entire transition rates of free carriers in the bandgap of the p‐type semiconductor are described. Applying the Shockley–Read–Hall model to a p‐type material under a low injection level, the expressions for the recombination rates, the trapping rates, and the excess carrier lifetimes (recombination and trapping) were described as functions of the localized state energies. Next, the very important quantities called the excess carriers’ trapping ratios were described as functions of the localized state energies. Variations of the magnitudes of the excess carriers’ trapping ratios with the localized state energies enable us to categorize the localized states in the bandgap as the recombination, the trapping, the acceptor, and the donor levels. Effects of the majority and the minority carriers’ trapping on the excess carrier lifetimes are also evaluated at different localized energy levels. The obtained results reveal that only excess minority trapping affects the excess carrier lifetimes, and excess majority carrier trapping has no effect.

Suppression of Electron-Hole Recombination by Intrinsic Defects in 2D Monoelemental Material.

The Shockley-Read-Hall (SRH) model, in which the deep trap defect states in the band gap are proposed as nonradiative electron-hole (e-h) recombination centers, has been widely used to describe the nonradiative e-h recombination through the defects in semiconductor. By using the ab initio nonadiabatic molecular dynamics method, we find that the SRH model fails to describe the e-h recombination behavior for defects in 2D monoelemental material such as monolayer black phosphorus (BP). Through the investigation of three intrinsic defects with shallow and deep defect states in monolayer BP, it is found that, surprisingly, none of these defects significantly accelerates the e-h recombination. Further analysis shows that because monolayer BP is a monoelemental material, the distinct impurity phonon, which often induces fast e-h recombination, is not formed. Moreover, because of the flexibility of 2D material, the defects scatter the phonons present in pristine BP, generating multiple modes with lower frequencies compared with the pristine BP, which further suppresses the e-h recombination. We propose that the conclusion can be extended to other monoelemental 2D materials, which is important guidance for the future design of functional semiconductors.

Impact of defects on the electrical properties of p–n diodes formed by implanting Mg and H ions into N-polar GaN

The relationship between the junction properties and point defects in p–n diodes, formed by implanting magnesium (Mg) and hydrogen (H) ions into a GaN layer, was investigated. Vertical diodes were fabricated by implanting Mg ions with and without H ions into nitrogen-polar n-type GaN substrates, followed by annealing at 1150 °C or 1230 °C without the use of protective layers. Samples annealed at 1150 °C showed Schottky-barrier-diode (SBD)-like properties with an insufficient build-in potential, indicating surface depletion due to poor activation of Mg acceptors. The Mg/H-ion-implanted diode annealed at 1230 °C exhibited an improved rectifying property with a build-in potential around 3 V, close to an ideal p–n junction of GaN, whereas the sample with only implanted Mg-ions exhibited mixed properties of a p–n junction and SBD due to imperfect activation. In addition, leakage currents in the forward bias below 3 V for the Mg/H-ion-implanted diodes can be explained by a recombination current based on the Shockley–Read–Hall model with an estimated recombination lifetime of 3 to 10 ps. To clarify the sources of the difference in the junction properties, positron annihilation spectroscopy was employed. The samples annealed at 1150 °C contained high-density vacancy clusters such as (VGaVN)3, whose concentrations were reduced by the higher temperature annealing. We found that introduced H atoms can enhance the activation of Mg acceptors and/or reduce the defect concentrations. The results indicate the combination of the H ion introduction and higher temperature annealing improves the junction properties.

Temperature-Dependent Effect of Near-Interface Traps on SiC MOS Capacitance**Supported by the Science Challenge Project under Grant No TZ2018003.

A two-dimensional electrical SiC MOS interface model including interface and near-interface traps is established based on the relevant tunneling and interface Shockley–Read–Hall model. The consistency between simulation results and measured data in the different temperatures shows that this interface model can accurately describe the capture and emission performance for near-interface oxide traps, and can well explain the hysteresis-voltage response with increasing temperature, which is intensified by the interaction between deep oxide traps and shallow oxide traps. This also indicates that the near-interface traps result in an increase of threshold-voltage shift in SiC MOSFET with increasing temperature.

Study on the mechanism of using IR illumination to improve the carrier transport performance of CdZnTe detector

Different wavelength IR light (770–1150 nm) was used to evaluate the effect of IR light on the carrier transport performance of CdZnTe detector. The effective mobility-lifetime product (μτ*) of CdZnTe achieved 10−2 cm2 V−1 when the IR wavelength was in the range of 820–920 nm, but decreased to 1 × 10−4 cm2 V−1 when the wavelength was longer than 920 nm. The mechanism about how IR light affecting the carrier transport property of CdZnTe detector was analyzed with Shockley–Read–Hall model. The defect of doubly ionized Cd vacancy ([VCd]2−) was found to be the main factor that assist IR light affecting the μτ of CdZnTe detector. The photoconductive experiment under 770–1150 nm IR illumination was carried out, and three kinds of photocurrent curve were detected and analyzed by solving the Hecht equation. The experiments demonstrated the effect of [VCd]2− defect on the carrier transport property of CdZnTe detector under IR illumination.

Investigation of breakdown performance in $$L_{g}$$ L g = 20 nm novel asymmetric InP HEMTs for future high-speed high-power applications

In this paper, we investigated the breakdown performance of novel nanoscale asymmetric InP high-electron-mobility transistors (HEMTs). The novel asymmetric InP HEMT features $$\Gamma $$ -gate, heavily doped multilayer cap, $$n^{+}$$ -type In $$_{0.52}$$ Ga $$_{0.48}$$ As source/drain (S/D) regions, InAs-rich composite channel, SiN passivation and double $$\delta $$ -doping planes. The impact of asymmetric gate recess width on DC, RF and breakdown performance of novel asymmetric InP HEMT has been investigated using hydrodynamic carrier transport model along with other physical models such as Shockley–Read–Hall model, recombination models, high-field mobility model and density gradient model. Sentaurus TCAD simulations were carried out at room temperature for gate lengths of 50 and 20 nm in order to analyse the scalability of the new device architecture. In order to consider the quantum effects at nanoscale regime, density gradient model of eQuantum potential was used for TCAD simulations. $$L_{g}$$ = 20 nm proposed HEMT achieved a peak $$g_{m}$$ and $$I_\mathrm{DS}$$ of 3470 mS/mm and 1300 mA/mm, respectively. The proposed HEMT has a $$f_{T}$$ and $$f_\mathrm{max}$$ of 749 and 1460 GHz, respectively. The $$L_{g}$$ = 20 nm proposed HEMT also showed an ON-state and OFF-state breakdown voltages of 2.2 and 4.5 V, respectively, at a gate recess width of 150 nm. To the best of authors’ knowledge, this is the record combination of DC, RF and breakdown performance reported for InP HEMTs which makes them the most suitable transistors for future high-speed high-power applications.

Fabrication, Characterization, and Analysis of Ge/GeSn Heterojunction p-Type Tunnel Transistors

We present a detailed study on fabrication and characterization of Ge/GeSn heterojunction p-type tunnel-field-effect-transistors (TFETs). Critical process modules as high-k stack and p-i-n diodes are addressed individually. As a result an ultrathin equivalent oxide thickness of 0.84 nm with an accumulation capacitance of $3~\mu \text{F}$ /cm2 was achieved on an extremely scaled tri-layer stack of GeSnOx/Al2O3/HfO2 deposited by atomic-layer deposition monitored in situ by spectroscopic ellipsometry. Combining these process modules, Ge/GeSn heterojunction pTFETs are fabricated and characterized to demonstrate the best in-class pTFET performance in the GeSn material system. The transfer characteristics of the TFETs show signatures of the trap-assisted thermal generation in the subthreshold regime which is explained by a modified Shockley–Read–Hall model. For the ON-state current, we used band-to-band tunneling models calculated using parameters from the density functional theory. We then use the calibrated model to project performance of GeSn pTFETs with increased Sn content (lower bandgap), reduced trap density and ultrathin body geometry. Both experimental and projected results are benchmarked against state-of-the art III–V (e.g., In0.65Ga0.35/GaAs0.4Sb0.6) pTFETs. We demonstrate the ability of GeSn to achieve superior performance with both high ON-current and sub-60mV/decade switching benefiting from the small and direct bandgap for higher Sn contents.

Carrier Lifetimes of Iodine-Doped CdMgTe/CdSeTe Double Heterostructures Grown by Molecular Beam Epitaxy

Iodine-doped CdMgTe/CdSeTe double heterostructures (DHs) have been grown by molecular beam epitaxy and studied using time-resolved photoluminescence (PL), focusing on absorber layer thickness of 2 μm. The n-type free carrier concentration was varied to ∼7 × 1015 cm−3, 8.4 × 1016 cm−3, and 8.4 × 1017 cm−3 using iodine as dopant in DHs. Optical injection at 1 × 1010 photons/pulse/cm2 to 3 × 1011 photons/pulse/cm2, corresponding to initial injection of photocarriers up to ∼8 × 1015 cm−3, was applied to examine the effects of excess carrier concentration on the PL lifetimes. Iodine-doped DHs exhibited an initial rapid decay followed by a slower decay at free carrier concentration of 7 × 1015 cm−3 and 8.4 × 1016 cm−3. The optical injection dependence of the carrier lifetimes for DHs was interpreted based on the Shockley–Read–Hall model. The observed decrease in lifetime with increasing n is consistent with growing importance of radiative recombination.

Numerical simulation of the impact of surface traps on the performance of InP‐based high electron mobility transistors

In this paper, the DC and RF characteristics of our own InP‐based HEMTs were investigated comprehensively with surface traps concentration varying among 0 cm−2, 1 × 1012 cm−2, 3 × 1012 cm−2. Reasonable physical models were used to describe the device performances, including hydrodynamic transport model, density gradient model, recombination models and so on. Moreover, surface Shockley–Read–Hall model and improved Possion's equation were introduced to implement for the impact of surface traps. The DC and RF characteristics have shown compatible trends between computation and experiment. With the increasing surface traps concentration over the gate‐recess region, the channel current, transconductance, current gain cut‐off frequency (fT) and maximum oscillation frequency (fmax) exhibit apparent decrease trends. The observed obvious changes of the DC and RF properties with surface traps could be accounted for carrier sheet density reduction, which resulted from the surface potential modulated by negatively charged surface traps. Additionally, the charged surface traps could deplete the electrons in channel region, which leads to an increase in channel sheet resistance, and thus, further decreasing the fmax.

Effect of free-carrier concentration and optical injection on carrier lifetimes in undoped and iodine doped CdMgTe/CdSeTe double heterostructures grown by molecular beam epitaxy

Time-resolved and time integrated photoluminescence (PL) studies are reported for undoped and doped CdMgTe/CdSeTe double heterostructures (DHs) grown by molecular beam epitaxy. Undoped DHs are studied with absorber layer thickness varying from 0.5 to 2.5 µm. The n-type free-carrier concentration is varied ~7 × 1015, 8.4 × 1016, and 8.4 × 1017 cm−3 using iodine as a dopant in different absorber layer thicknesses (0.25–2.0 µm). Optical injection is varied from 1 × 1010 to 3 × 1011 photons/pulse/cm2, corresponding to the initial injection of photo-carriers up to ~8 × 1015 cm−3, to examine the effects of excess carrier concentration on the PL lifetimes. Undoped DHs exhibit an initial rapid decay followed by a slower dependence with carrier lifetimes up to ~485 ns. The dependence of carrier lifetimes on the thickness of the absorber layers (0.5–2.5 µm) suggests interface recombination velocities () ~ 1288 and 238 cm s−1 in the initial and later decay times, respectively, corresponding to high and low photo-carrier concentrations. The Shockley–Read–Hall model is used to describe the results in which variations are observed in for undoped DHs. The lifetimes of doped DHs show a consistent trend with thickness. The ~ 80–200 cm s−1 is estimated for doping n ~ 7 × 1015 cm−3 and 240–410 cm s−1 for n ~ 8.4 × 1016 cm−3. The observed decrease in carrier lifetimes with increasing n is consistent with growing importance of the radiative recombination rate due to the excess carrier concentration. The effect of carrier concentration on the PL spectrum is also discussed.

Trap-assisted recombination in disordered organic semiconductors extended by considering density dependent mobility

Understanding recombination processes in organic semiconductors is fundamental in modeling solar cells and lighting diodes. However, recognition on recombination processes is still controversial. In this work, the trap-assisted Shockley–Read–Hall (SRH) recombination proposed by Kuik et al. (2011) is modified by considering three factors. The first one is the density of state (DOS) for recombination centers in SRH process, the second one is the trapped charges of recombination centers in Poisson equation, the third one is the density dependence of mobility. The modified model is applied to typical devices with experimental data about open circuit voltage (Voc) with light intensity (Pin) which having been used to distinguish recombination processes. These Voc−log(Pin) data previously were explained by using the Langevin recombination, or SRH recombination, or mixing of both recombinations. The results show that these experimental data can be uniformly well fitted and explained by using the modified SRH model. The DOS for recombination centers is not important, but the density dependence of mobility is very important in arriving good fittings. The influence of Langevin recombination is compared, and is shown not enough to explain the saturation effects in Voc−log(Pin) curves at high light strength, if neglecting the density dependence of mobility.

Temperature-dependent recombination velocity analysis on artificial small angle grain boundaries using electron beam induced current method

The details of the process of carrier recombination via the Shockley-Read-Hall (SRH) defect level, at the grain boundaries of multicrystalline silicon, were investigated. For this, the temperature-dependent recombination velocities, as determined by experiments, were analyzed by the application of an electron beam induced current method. For the model, the misorientation angles at the grain boundaries were defined using a multi-seed casting-growth method. The results of our experiments indicated different temperature behaviors at low and high temperatures. These can be explained by controlling the process anticipated by the SRH model, that is, the process whereby minority carriers (electrons) are captured at lower temperatures, followed by the reemission of the carriers before recombination with Arrhenius behavior at higher temperatures. The minority capture process appeared to conform to the power law T−α temperature behavior. Thus, there are two candidate electron capture mechanisms, namely, cascade phonon emission capture for shallow centers and excitonic-Auger capture for deep centers. The activation energy for the reemission of carriers was around 0.1 eV. These findings regarding the temperature dependence are essentially independent of the misorientation angles, suggesting a common defect level and recombination mechanism. The difference in the recombination velocities can be regarded as being derived from the difference in the density at the defect level.

An upgraded drift–diffusion model for evaluating the carrier lifetimes in radiation-damaged semiconductor detectors

The transport properties of a series of n- and p-type Si diodes have been studied by the ion beam induced charge (IBIC) technique using a 4MeV proton microbeam. The samples were irradiated with 17MeV protons at fluences ranging from 1×1012 to 1×1013p/cm2 in order to produce a uniform profile of defects with depth. The analysis of the charge collection efficiency (CCE) as a function of the reverse bias voltage has been carried out using an upgraded drift–diffusion (D–D) model which takes into account the possibility of carrier recombination not only in the neutral substrate, as the simple D–D model assumes, but also within the depletion region. This new approach for calculating the CCE is fundamental when the drift length of carriers cannot be considered as much greater that the thickness of the detector due to the ion induced damage. From our simulations, we have obtained the values of the carrier lifetimes for the pristine and irradiated diodes, which have allowed us to calculate the effective trapping cross sections using the one dimension Shockley–Read–Hall model. The results of our calculations have been compared to the data obtained using a recently developed Monte Carlo code for the simulation of IBIC analysis, based on the probabilistic interpretation of the excess carrier continuity equations.