Thermally Stimulated Current Research Articles

Identification of shallow trap centers in InSe single crystals and investigation of their distribution: A thermally stimulated current spectroscopy

Identification of trap centers in semiconductors takes great importance for improving the performance of electronic and optoelectronic devices. In the present study, we employed the thermally stimulated current (TSC) method within a temperature range of 10–280 K to explore trap centers in InSe crystal—a material with promising applications in next-generation devices. Our findings revealed the existence of two distinct hole trap centers within the InSe crystal lattice located at 0.06 and 0.14 eV. Through the leveraging the Tstop method, we offered trap distribution parameters of revealed centers. The results obtained from the experimental methodology employed to investigate the distribution of trap centers indicated that one of the peaks extended between 0.06 and 0.13 eV, while the other spanned from 0.14 to 0.31 eV. Notably, our research uncovers a remarkable variation in trap density, spanning one order of magnitude, for every 10 and 88 meV of energy variation. The results of our research present the characteristics of shallow trap centers in InSe, providing important information for the design and optimization of InSe-based optoelectronic devices.

Investigating the role of palladium electrical contacts in interactions with carbyne nanomaterial solid matter

Introduction: Traps at the interface between carbyne and palladium nanocoatings, produced at different growth conditions, are explored by current-voltage characteristics, scanning electron microscopy and thermal stimulation of charges for evaluation of their nature. It was found that the Pd films can form an Ohmic contact with the carbyne at certain deposition conditions and such deviated from the Ohmic behavior according to the RF sputtering voltage. This growth parameter was found to affect the interfacial traps formation on the carbyne surface, which is important feature for the charge trapping and releasing properties for hydrogen isotopes in the context of the energy release applications.Methods, Results and Discussion: The sputtering voltages of 0.5 kV and 0.7 kV were found unsuitable for controlled trap formation. Based on the currentvoltage and thermally stimulated current (TSC) measurements, a sputtering voltage of 0.9 kV appeared to be more favorable compared to 0.5 kV and 0.7 kV. At 0.9 kV thermal activation of charge carriers are enabled at lower thermal energies, showing a distinct change in TSC behavior correlated to trap activation.

Revealing defect centers in PbWO4 single crystals using thermally stimulated current measurements

The trap centers have a significant impact on the electronic properties of lead tungstate (PbWO4), suggesting their crucial role in optoelectronic applications. In the present study, we investigated and revealed the presence of shallow trap centers in PbWO4 crystals through the utilization of the thermally stimulated current (TSC) method. TSC experiments were performed in the 10–280 K range by applying a constant heating rate. The TSC spectrum showed the presence of a total of four peaks, two of which were overlapped. As a result of analyzing the TSC spectrum using the curve fit method, the activation energies of revealed centers were found as 0.03, 0.11, 0.16, and 0.35 eV. The trapping centers were associated with hole centers according to the comparison of TSC peak intensities recorded by illuminating the opposite polarity contacts. Our findings not only contribute to the fundamental understanding of the charge transport mechanisms in PbWO4 crystals but also hold great promise for enhancing their optoelectronic device performance. The identification and characterization of these shallow trap centers provide valuable insights for optimizing the design and fabrication of future optoelectronic devices based on PbWO4.

Investigation of high resistivity [formula omitted]-type FZ silicon diodes after 60Co [formula omitted]-irradiation

In this work, the effects of 60Co γ-ray irradiation on high resistivity p-type diodes have been investigated. The diodes were exposed to dose values of 0.1, 0.2, 1, and 2MGy. Both macroscopic (I–V, C–V) and microscopic investigations, by means of Thermally Stimulated Current (TSC) and Deep Level Transient Spectroscopy (DLTS) techniques, were conducted to characterize the radiation-induced changes. The investigated diodes were manufactured on high resistivity p-type Float Zone (FZ) silicon and were further classified into two types based on the isolation technique between the pad and guard ring: p-stop and p-spray. After irradiation, the macroscopic results of current–voltage and capacitance–voltage measurements were obtained and compared with existing literature data. Additionally, the microscopic measurements focused on the development of the concentration of different radiation-induced defects, including the Boron interstitial-Oxygen interstitial (BiOi) complex, the Carbon interstitial-Oxygen interstitial (CiOi) defect, the H40K, and the so-called IP∗.To investigate the thermal stability of induced defects in the bulk, isochronal annealing studies were performed in the temperature range of 100°C to 300°C. These annealing processes were carried out on diodes irradiated with doses of 1 and 2MGy. Furthermore, in order to investigate the unexpected results observed in the C–V measurements after irradiation with high dose values, the surface conductance between the pad and guard ring was measured as a function of both dose and annealing temperature.

Defects of perovskite semiconductor CsPbBr3 investigated via photoluminescence and thermally stimulated current spectroscopies

Halide perovskites are essential materials for hard radiation detectors at ambient temperature. To improve detector performance, charge transport must be investigated and optimized. Using photoluminescence (PL) and thermally stimulated current (TSC) spectroscopies, we investigate photogenerated charge carriers in Bridgman-grown CsPbBr3 single crystals to understand the nature of charge transport. PL spectroscopy of these halide perovskites revealed the presence of strong emission bands at the band edge, which were attributed to free or bound excitons. It is shown that a wide broadening of the excitonic linewidth in these halide perovskites arises from strong exciton–phonon coupling, which is substantially dominated by longitudinal optical phonons via Fröhlich interaction. An additional contribution due to the presence of ionized impurities was also observed. Crystals with a detectable sensitivity to high-energy gamma radiation are characterized by a higher intensity and a narrower linewidth of the principal PL peak at 2.326 eV. Defect states beyond 2.214 eV have a negative impact on detector sensitivity to high-energy gamma radiation. TSC spectroscopy reveals an array of trap levels spanning 0.15–0.70 eV, attributed to intrinsic point defects and multiple extrinsic defects involving dopants or impurities. Defects identified included Cs and Br vacancies, as well as Pb interstitials with concentrations in the 1011–1016 cm−3 range. Understanding how the synthesis process impacts the types and concentrations of the defects present is currently under investigation. Elimination or suppression of the defect/trap states should result in halide perovskite materials with longer carrier diffusion lengths and improved detector characteristics.

Effect of crosslinking on EVA-based encapsulant properties during photovoltaic module fabrication process

The key objective of this work is to create a comprehensive comparison between experimental analysis methods for detecting crosslinking reaction in EVA encapsulant material during PV module fabrication process. Several analytical methods, spanning from classical gel content extraction measurements over different thermo-analytic and mechanical approaches to spectroscopic analysis as Thermally Stimulated Current (TSC), have been investigated as to their ability to reveal the crosslinking state of ethylene vinyl acetate (EVA). The basic results show that TSC complements perfectly other thermal analysis methods like as Differential Scanning Calorimetry (DSC), Dynamic Mechanical Thermal Analysis (DMTA) to determine fundamental properties of EVA such as molecular mobility characteristics and also to monitor the crosslinking reaction. Exothermic peak as revealed by DSC analysis can be used to estimate the crosslinking rate of EVA during PV module encapsulation process as fast quality control test.

Properties of Nanogenerator Materials for Energy-Harvesting Application

Advancements in nanotechnology and materials science have led to the development of a variety of nanogenerator materials with improved properties, making energy harvesting technologies increasingly viable for various applications, such as powering wearable devices, remote sensors, and even small electronic gadgets in the future. The evolution of hybrid materials consisting of polymers and nanoparticles as efficient energy harvesters and energy storage devices is in high demand nowadays. Most investigations on organic ferroelectric P(VDF-TrFE) as a polymer host of polymer nanocomposite devices were primally focused on the β phase due to its excellent electrical properties for various application purposes. Nanofiller is also introduced into the polymer host to produce a polymer nanocomposite with enhanced properties. A brief description of various physical quantities related to ferroelectric, dielectric, pyroelectric effects and Thermally Stimulated Current (TSC) for energy harvesting applications in nanogenerator materials is presented. This article explores the different materials and uses of various nanogenerators. It explains the basics of the pyroelectric effect and the structure of pyroelectric nanogenerators (PNGs), as well as recent advancements in micro/nanoscale devices. Additionally, it discusses how the performance of ferroelectric, dielectric, pyroelectric, and TSC are impacted by the annealing treatment of P(VDF-TrFE) polymer.

Investigation of temperature-dependent DC breakdown characteristics of nano-Al2O3/epoxy composites at low temperatures

Epoxy resin is extensively utilized as an insulating material in low-temperature superconducting devices. Nevertheless, its breakdown behavior and mechanism at low temperatures have rarely been studied. This study aims to investigate the breakdown characteristics of bisphenol F epoxy resin and its nano-alumina composites under different temperatures. Additionally, a thermally stimulated current (TSC) platform was established to examine the molecular relaxation and trap charge parameters of epoxy from 4.2 K to 300 K. The epoxy resin matrix was modified by incorporating a series of nano-alumina particles (1%, 2%, 3%, 4%, 5%). In this paper, a breakdown transition temperature (Tb) between 77 K and 150 K was observed for epoxy resin, with a significant decline in insulation performance above and below Tb. This phenomenon can be attributed to the interplay between collisional ionization and thermal breakdown mechanisms. The inclusion of nano-alumina particles in the epoxy resin matrix demonstrates an improvement in insulation performance at low temperatures, with an optimal filler ratio of approximately 2%. However, an excessive amount of alumina nanoparticles may reduce the insulating capabilities of the epoxy resin. The experiments conducted on thermally stimulated currents revealed that trap charges within the resin are more readily excited at low temperatures.

Investigation of the Boron removal effect induced by 5.5 MeV electrons on highly doped EPI- and Cz-silicon

This study focuses on the properties of the BiOi (interstitial Boron–interstitial Oxygen) and CiOi (interstitial Carbon–interstitial Oxygen) defect complexes by 5.5MeV electrons in low resistivity silicon. Two different types of diodes manufactured on p-type epitaxial and Czochralski silicon with a resistivity of about 10 Ω⋅cm were irradiated with fluence values between 1 × 1015cm-2 and 6 × 1015cm-2. Such diodes cannot be fully depleted and thus the accurate evaluation of defect concentrations and properties (activation energy, capture cross-section, concentration) from Thermally Stimulated Currents (TSC) experiments alone is not possible. In this study we demonstrate that by performing Thermally Stimulated Capacitance (TS-Cap) experiments in similar conditions to TSC measurements and developing theoretical models for simulating both types of BiOi signals generated in TSC and TS-Cap measurements, accurate evaluations can be performed. The changes of the position-dependent electric field, the effective space charge density Neff profile as well as the occupation of the BiOi defect during the electric field dependent electron emission, are simulated as a function of temperature. The macroscopic properties (leakage current and Neff) extracted from current–voltage and capacitance–voltage measurements at 20°C are also presented and discussed.

The slow molecular mobility in the amorphous solid and supercooled liquid phases of brucine, an anti-cancer drug. A study by differential scanning calorimetry (DSC), thermostimulated currents (TSC) and dielectric relaxation spectroscopy (DRS)

In this work, we explore in detail the molecular mobility in amorphous brucine, i.e. in the glassy state and in the supercooled liquid immediately above the glass transition, where viscosity is high and where a spatially heterogeneous dynamic is detected. Brucine is an alkaloid used in ancient times by Chinese medicine in the treatment of cancer, it can be obtained in the amorphous form by cooling from the melt and the high stability exhibited makes it a good candidate for being use in novel formulations.Combining thermostimulated depolarization currents (TSDC), and dielectric relaxation spectroscopy (DRS) different types of motions have been probed. In the glassy state, two secondary relaxations γ and β were characterized, the latter with features compatible with a Johari-Goldstein mobility. The cooperative α relaxation was clearly identified, and by combining also with results taken from differential scanning calorimetry (DSC), it was possible to determine parameters such as the glass transition temperature, and fragility index which indicate a moderately fragile glass former. In addition, the determination of the βJG relaxation times and activation energy, both above and below Tg, were a new result of the current investigation.Additionally, TSDC measurements, although with some uncertainty, reveal the existence of a mobility above Tg. On the other hand, in the supercooled liquid region, the analysis of the conductivity obtained by DRS, shows a breakdown of the Debye-Stokes-Einstein relation pointing to a heterogeneous dynamic that could be in the origin of the observed mobility by TSDC.

Mechanism for Long Photocurrent Time Constants in α-Ga2O3 UV Photodetectors

Deep centers and their influence on photocurrent spectra and transients were studied for interdigitated photoresistors on α-Ga2O3 undoped semi-insulating films grown by Halide Vapor Phase Epitaxy (HVPE) on sapphire. Characterization involving current-voltage measurements in the dark and with monochromatic illumination with photons with energies from 1.35 eV to 4.9 eV, Thermally Stimulated Current (TSC), Photoinduced Current Transients Spectroscopy (PICTS) showed the Fermi level in the dark was pinned at Ec−0.8 eV, with other prominent centers being deep acceptors with optical thresholds near 2.3 eV and 4.9 eV and deep traps with levels at Ec−0.5 eV, Ec−0.6 eV. Measurements of photocurrent transients produced by illumination with photon energies 2.3 eV and 4.9 eV and Electron Beam Induced Current (EBIC) imaging point to the high sensitivity and external quantum efficiency values being due to hole trapping enhancing the lifetime of electrons and inherently linked with the long photocurrent transients. The photocurrent transients are stretched exponents, indicating the strong contribution of the presence of centers with barriers for electron capture and/or of potential fluctuations.

Fluorination Treatment and Nano-Alumina Concentration on the Direct Current Breakdown Performance & Trap Levels of Epoxy/Alumina Nanocomposite for a Sustainable Power System

Epoxy resin is extensively used in gas insulated switches as a renewable energy coating due to its exceptional insulation, mechanical characteristics, and environmental friendliness. The higher resistivity of the epoxy resin causes numerous surface charges to accumulate on the surface of the epoxy resin as a result of carrier injection due to the high DC electric field, which may cause insulation failure of the power transmission system. In this study, various concentrations of epoxy resins blended with nano-alumina (nano-Al2O3) at 0 wt%, 1 wt%, 3 wt%, and 5 wt% were created. Afterwards, the epoxy resin and Al2O3 nanocomposites were fluorinated by utilizing a combination of F2 and N2 with a ratio of 20% F2 at 0.05 MPa while maintaining the temperature at 40 °C. In order to improve dispersion, nano- Al2O3 was treated with a silane coupling agent called γ-aminopropyltriethoxysilane (KH550). Additionally, infrared spectroscopy based on the Fourier transform was used to investigate the structure of chemical bonds. Furthermore, the changes in the molecular chains were verified by the FTIR spectra. The DC breakdown strength of epoxy resin\Al2O3 nano-composites showed that breakdown strength significantly improved after gas-phase fluorination. Moreover, 1 wt% nano- Al2O3 showed a higher breakdown strength. The fluorinated layer had a charge-suppressing effect, reducing the charge injected into the polymer matrix of the epoxy-resin matrix and increasing its DC breakdown capability. Thermally stimulated current (TSC) measurements indicate that epoxy resin’s trap energy and trap density are altered by nano- Al2O3 incorporation and fluorination treatment (gas-phase). It was also observed that introducing nano- Al2O3 at a lower concentration (e.g., 1 wt%) can hinder the growth of space charge in the polymer matrix of the epoxy resin, thus enhancing the deep traps’ energy. Furthermore, a fluorination layer containing a strong polarization of C-F bonding would seize the charge injection from electrodes, thus decreasing the conductivity and suppressing the charge injection.

Modification of insulating oils and oil-based titanium dioxide nanofluids for transformers: a review.

In the last decade, oil-based titanium dioxide nanofluids (TiO2 NFs) have gained immense interest due to their unique insulating properties and excellent thermal performance, which endow them with the potential for application in the field of modified insulating oils. A timely comparison, analysis and summary of recent advances in the preparation, characterization, and properties of different oil-based TiO2 NFs for oil-immersed power transformers will contribute to provide a useful reference for the subsequent development of such materials. Preparation methods are reviewed along with their merits and demerits. Characterization techniques including scanning electron microscopy (SEM), transmission electron microscopy (TEM), optical microscopy (OM), X-ray diffraction (XRD), energy-dispersive X-ray spectroscopy (EDX), dynamic light scattering (DLS), Fourier transform infrared (FTIR) spectroscopy, thermally stimulated current (TSC), pulse electroacoustic technique (PEA), finite element analysis (FEA), fluorescence spectroscopy, Raman spectroscopy and zeta potential analysis are all applied to determine the crystal structure, particle size, surface function, surface charge and stability. Stabilization mechanisms are also discussed in detail. Some critical properties of oil-based TiO2 NFs under the application of different influencing factors such as base oils, crystal structure, size of nanoparticles, surface modifiers, mixing percentage, and aging environment are highlighted. Finally, the existing challenges and perspectives are presented for future research.

Shallow trapping centers in Bi12GeO20 single crystals by thermally stimulated current measurements

Bi 12 GeO 20 single crystals were investigated by thermally stimulated current (TSC) experiments performed in the temperature range of 10-290 K. Recorded TSC glow curve exhibited six distinctive peaks with maxima at around 90, 105, 166, 209, 246, 275 K. The analyses of the obtained glow curve were accomplished by curve fitting and initial rise methods. The analysis results were in good agreement that the TSC peaks appeared in the glow curve due to existence of trapping levels with activation energies of 0.10, 0.18, 0.23, 0.53, 0.68 and 0.73 eV. These trapping levels were estimated to be hole traps above valence band. The heating rate dependent TSC glow curves were also obtained for various rates between 0.30 and 0.45 K/s. The changes of TSC intensity, peak maximum temperature and full-widths-half-maximum values with heating rates were studied in detail. TSC intensity decreased and peak maximum temperature increased with increasing heating rate. Determination of defects and trapping/stimulation mechanism of those are significant for technological applications since local states in these materials take critical role for device performance.

Improved DC Insulation Performance of XLPE With Graftable Voltage Stabilizer

Voltage stabilizers have the potential to improve the overall insulation properties of polymeric cables, but the poor compatibility with the polymer matrix limits their practical application. In this work, the reaction of 2,4-dihydroxybenzophenone (DHBP) with maleic anhydride (MAH) provides a novel and reactive aromatic ketone voltage stabilizer 4-(4-benzoyl-3-hydroxyphenoxy)-4-oxobut- 2-enoic acid denoted by MDVS, which can be grafted onto the backbone of polyethylene (PE) during the cross-linking process. The physicochemical and dc insulation properties of the cross-linked PE grafted with different addition of MDVS (XLPE-g-MDVS) are investigated, and the underlying mechanism is discussed. In comparison with the pristine XLPE, substantially suppressed space charge accumulation and decreased electrical conductivity are obtained in the XLPE-g-MDVS materials. As the content of MDVS is 1.2 wt%, XLPE-g-MDVS materials exhibit higher breakdown strength than that of the pristine XLPE. Furthermore, the graftable voltage stabilizer MDVS presents more efficient stabilizing effect than conventional voltage stabilizer DHBP before and after high-temperature degassing. Thermally stimulated current (TSC) tests and quantum chemical calculations are consistent with the experimental results of insulation properties, illustrating that capture and trap mechanisms cooperate in the improvement of XLPE dc insulation performance.

Rare-earth ferrobismuthites: ferromagnetic ceramic semiconductors with applicability in spintronic devices

We report here the synthesis process of the perovskite-like complex material Bi0.5R0.5FeO3 (R=Eu, Sm, Dy) using the ceramic method, as well as its structural, optical, magnetic, and electrical characterizations. Refined X-ray diffraction data revealed that this material crystallizes in an orthorhombic structure (space group Pnma number 62). The band gap value in the optical response shown in the diffuse reflectance spectroscopy curve was typical of semiconductor materials. The magnetization exhibited a very low coercive field hysteretic behavior, which is characteristic of weak ferromagnetism, for all temperatures examined below 300 K and the various magnetic fields applied. The real and complex electric permittivity curves showed the occurrence of dielectric relaxation processes at 113 K in agreement with reports of pyroelectric and thermo-stimulated currents as a function of temperature revealing the appearance of ferroelectric polarization below 113 K with possible magnetoelectric coupling. On the other hand, we made a theoretical study of the electronic structure with and without the inclusion of a Berry distortional phase and ab-initio calculations following the density functional theory formalism and the pseudopotential plane wave method. In this formalism, the exchange and correlation mechanisms are described by the generalized gradient approach (GGA + U) considering spin polarization. The Berry phase analysis suggested the occurrence of ferroelectricity at temperatures below 113 K consistent with the experimental analysis evidencing a biferroic behavior at low temperatures given that the distortional phase introduces hybridizations between the 3d-Fe and 2p-O states favoring the appearance of Dzyaloshinskii-Moriya interactions, which, in turn, facilitate the appearance of ferroelectricity coexisting with a weak ferromagnetism. The thermodynamic properties in the presence or absence of the Berry phase by means of the Debye quasiharmonic model revealed the appearance of a ferroelectric transition at 113 K, which corroborates their magnetoelectric nature at low temperatures. The ferromagnetic semiconducting character found at room temperature enhances this material for applications in spintronics technology.

Role of Fermi-level depinning in quenching of V4+ related photoluminescence in semi-insulating 4H-SiC

Vanadium atoms in 4H-silicon carbide (SiC) single crystals have prospective applications as solid-state quantum emitters, making it crucial to understand the modifications of vanadium-related optical properties due to defects in the host lattice. We introduce controlled defects using 100 MeV Ag ion irradiation and report on quenching of luminescence from neutral vanadium V4+ atoms in vanadium-doped semi-insulating (SI) 4H-SiC. A reduction in intensity from V4+ related α and β emissions, and a correlated increase in thermally stimulated current (TSC), attributed to the increase in irradiation-induced defects, are observed with increasing ion fluence (Ag cm−2). Activation energies of the defect levels involved in compensation loss are estimated from TSC. We also demonstrate a partial recovery of SI behavior after thermal annealing.

Defect levels in CsPbCl3 single crystals determined by thermally stimulated current spectroscopy

Thermally stimulated current (TSC) spectroscopy was used to characterize electronic trap states in the perovskite CsPbCl3 bulk single crystals which are promising for gamma ray detection. The TSC spectra indicate the presence of multiple traps over the temperature range from 80 K to above room temperature. The possible analytical defects identified were VCs and VCl vacancies and Pbi interstitials that have concentrations of the order of 1011−1016 cm−3 and capture cross sections of ∼10−18 cm2. A comparison of crystals grown from different ingots reveals that the concentration of defects in the crystal with an improved growth procedure is about one to four orders of magnitude less than those of a crystal from an earlier growth process. A further reduction and elimination of trap states within the perovskite ingot should lead to crystals with improved mobilities, carrier lifetimes, and detector response characteristics.

Point defect creation by proton and carbon irradiation of α-Ga2O3

Films of α-Ga2O3 grown by Halide Vapor Phase Epitaxy (HVPE) were irradiated with protons at energies of 330, 400, and 460 keV with fluences 6 × 1015 cm−2 and with 7 MeV C4+ ions with a fluence of 1.3 × 1013 cm−2 and characterized by a suite of measurements, including Photoinduced Transient Current Spectroscopy (PICTS), Thermally Stimulated Current (TSC), Microcathodoluminescence (MCL), Capacitance–frequency (C–f), photocapacitance and Admittance Spectroscopy (AS), as well as by Positron Annihilation Spectroscopy (PAS). Proton irradiation creates a conducting layer near the peak of the ion distribution and vacancy defects distribution and introduces deep traps at Ec-0.25, 0.8, and 1.4 eV associated with Ga interstitials, gallium–oxygen divacancies VGa–VO, and oxygen vacancies VO. Similar defects were observed in C implanted samples. The PAS results can also be interpreted by assuming that the observed changes are due to the introduction of VGa and VGa–VO.

Scrutinizing thermally stimulated current transients originating from trapped charges in organic semiconductors: A drift-diffusion study

Thermally stimulated current (TSC) is a widely used technique to assess trap states and extract their density, energy, and capture rate using analytical expressions. In many cases, the latter are derived from physical models pertaining to inorganic semiconductors stipulating the absence of space charge or constant lifetime of free charge carriers. Especially for organic semiconductors, the validity of these equations can, therefore, be argued. Here, we investigate the validity range of this approach by fitting the classical equations to synthetic TSC data obtained from drift-diffusion simulation using representative input parameters for organic semiconductors. We find that the equation derived for slow recapture rate as well as the initial rise method provide excellent trap parameter predictions. On the other hand, the equation using the temperature of the peak current as well as the one derived for fast retrapping have a limited range of validity. An important merit of drift-diffusion modeling is the possibility to access local variables such as charge carrier density, electric field, and recombinaton. We unravel that a small fraction of traps nearby the electrode cannot be emptied even at high temperature due to the diffusion of charge carriers from the electrode into the semiconductor. Additionally, we find that an important electrostatic factor relates the extracted charge carriers measured by the external circuit and the input trap density. For the homogeneously distributed trap states used here, this factor is precisely two. Finally, extensions of the model are analyzed by implementing temperature and field dependent mobility into the drift-diffusion model.