High Field Conduction Research Articles

Electrokinetics-Driven Anodic Oxide Pore Formation: Linear and Weakly Nonlinear Analysis

Anodization of aluminum in an acidic medium facilitates the formation of well-ordered nanoporous anodic oxide films. The mechanism of pore formation is investigated as a morphological instability using a simplified model. The model accounts for the high field conduction law and field-assisted reactions (oxide formation/dissolution) only at the oxide-solution interface. The role of Butler-Volmer electrokinetics, electrolyte pH, anodic efficiency, and interface curvature on reaction kinetics are taken into account. Linear stability analysis suggests that the oxide film is unstable to well-defined wavelengths in specific ranges of parameters such as anodizing efficiency, applied voltage and electrolyte pH. Subsequently, a weakly nonlinear analysis is carried out to determine the nature of bifurcation beyond the stability threshold. Our findings indicate that the instability exhibits a subcritical nature, well in agreement with experimental observations.

Epitaxial Growth and Doping of N-Polar AlN by Plasma-Assisted Molecular Beam Epitaxy

In recent years, AlN has garnered significant attention in the research community due to its excellent electronic properties. AlN, which is an ultra-wide bandgap material with a direct band gap of 6.2 eV, has a high breakdown electric field (12 MV/cm) and high thermal conductivity. In addition, band engineering can be achieved by alloying AlN with Gallium (Ga), Indium (In), and Scandium (Sc), and two-dimensional electron gas (2DEG) is formed at the AlGaN/AlN interface due to strong piezoelectric and spontaneous polarization. Furthermore, AlN has high-temperature stability, which is suitable for application in harsh environments. Due to these unique properties, AlN has gained attention as a promising candidate for the next generation of high power electronic and optoelectronic applications.In this talk, we present the demonstration of controllable Si doping in N-polar AlN films grown on single crystal AlN substrates by plasma assisted molecular beam epitaxy (PAMBE). Through optimization of growth conditions, we obtained high quality N-polar AlN films at high temperatures. However, our studies revealed that Si incorporation dramatically decreases at such high growth temperature. To enable higher Si incorporation, a hybrid growth scheme was developed, using a combination of low-temperature and high-temperature growth condition and by using Ga as a surfactant at low growth temperature. By lowering the growth temperature of AlN to 750°C, we were able to incorporate Si with concentrations as high as 2x1020 cm-3 and demonstrated an electron concentration as high as 1.25x1019 cm-3 at room temperature.

Bio-based epoxy resin demonstrating high breakdown strength and low dielectric loss via intrinsic molecular charge traps construction

In the ultra-high voltage, ultra-high capacity and high frequency energy systems, epoxy-based dielectric materials demonstrating high breakdown strength and low dielectric loss are urgently needed. This work reports a strategy to modulate the charge trap depth in bio-based epoxy dielectric materials by tailoring the local molecular chain structures, ultimately leading to the significant suppression of high-field conductivity and dielectric loss. With the introduction of octa (dimethylsiloxy)octasilsiloxane (POSS) as the intrinsic molecular charge traps, our synthesized epoxy dielectric material exhibits a high breakdown strength of Eb-DC = 81.5 kV/mm, 37 % higher than the traditional bisphenol A epoxy resin (DGEBA), and low dielectric loss of tan δ = 0.0022, 45 % lower than that DGEBA. Furthermore, simulation results give the structure-property relationships, guiding the molecular design. Specifically, the dielectric properties are positively correlated with the LUMO energy difference and charge separation index of the polymer molecular chains. This work provides a promising pathway to enhance the dielectric properties of polymers by building intrinsic molecular charge traps, which is prospective for practical electronics and electrical power systems.

Study of conduction mechanisms of InSeSb nano-chalcogenide alloys

The electrical conduction mechanisms for bulk samples of In0.1Se0.9−x Sb x (x = 0, 0.04, 0.08 and 0.12) nano-chalcogenide system, synthesized by the melt-quenching technique are investigated through current–voltage (I–V) characteristics. For the detailed study of conduction mechanism pellets of bulk samples are prepared. A thorough examination of electrical conductivity is done in the temperature range of 295–318 K and 0–50 V voltage range. From I–V measurements it is observed that samples are showing ohmic nature at lower field and non-ohmic nature at relatively higher field values. The temperature dependence of DC conductivity is analyzed using the Arrhenius relationship which is found to increase with Sb content. The value of activation energy and pre-exponential factor are calculated, which revealed that the conduction is due to the hopping of charge carriers among the localized states. Different parameters of Mott’s variable range hopping such as degree of disorder T 0, density of localized states N(E F), hopping distance (R hop), and hopping energy (W) are calculated. For the high field conduction process Poole–Frenkel, and Schottky processes are studied.

Phenomenology of M–N rule and high-field conduction in Ge–Te–Se–Sc rare-earth doped glasses

Phenomenology of M–N rule and high-field conduction in Ge–Te–Se–Sc rare-earth doped glasses

Improved Insulating Properties of Polymer Dielectric by Constructing Interfacial Composite Coatings.

Polymeric dielectrics exhibit remarkable dielectric characteristics and wide applicability, rendering them extensively employed within the domain of electrical insulation. Nevertheless, the electrical strength has always been a bottleneck, preventing its further utilization. Nanocomposite materials can effectively improve insulation strength, but uniform doping of nanofillers in engineering applications is a challenge. Consequently, a nanocomposite interfacial coating was meticulously designed to interpose between the electrode and the polymer, which can significantly improve DC breakdown performance. Subsequently, the effects of filler concentration and coating duration on DC breakdown performance, high field conductivity, and trap distribution characteristics were analyzed. The results indicate that the composite coating introduces deep traps between the electrode-polymer interface, which enhances the carrier confinement, resulting in reduced conductivity and enhanced DC breakdown strength. The incorporation of a composite coating at the interface between the electrode and polymer presents novel avenues for enhancing the dielectric insulation of polymers.

(Invited) Application of 3D in-Situ X-Ray Visualization to Track the Formation of Dislocation Clusters during PVT Growth of SiC

SiC has become the key player among wide bandgap semiconductors for power electronic applications. Since the first description of the physical vapour transport (PVT) growth process of SiC by Tairov and Tsvetkov (J. Crystal Growth, 43, 209(1978)), there has been steady progress in SiC-based crystal growth, epitaxy and device processing. The success of SiC compared to Si is related to its superior material properties such as extremely high electrical breakdown field and high thermal conductivity compared to the standard silicon counterpart. In addition, SiC device processing utilises much of the standard Si processing equipment. A major reason for the success of SiC in power electronic applications compared to other wide bandgap counterparts such as GaN, Ga2O3 and diamond is related to the availability of large diameter SiC wafer materials (150mm = standard, 200mm = developped). Bulk SiC growth is now a very well developed process with comparatively high yields. The extraordinary physical properties also include obstacles related to the strong chemical bonding and complex phase diagram of the material, which pose challenges to the growth process. Therefore, there are still a number of open questions related to the nucleation, progression and termination of the bulk growth process that require fundamental research in materials science and technology.The aim of this presentation is (i) to give an overview of the state-of-the-art PVT growth process and (ii) to discuss a current research topic dealing with the early stage of the growth process and the defect formation that can occur during the initial nucleation of SiC. We have applied 3D in-situ visualisation of the growth process using X-ray computed tomography to visualise island formation on the large seeding area. These data are related to growth process instabilities such as temperature variations during the seeding process and axial doping level changes from the seed to the newly grown crystal. Both process instabilities induce mechanical stress on the SiC lattice and act as sources for dislocation generation and multiplication. We will show a series of growth processes with varying growth parameters that shed light on the initial growth stage of SiC.As the crystal diameter of SiC increases from 150 mm to 200 mm, the results of this study become increasingly important.

Ultraviolet-Irradiated All-Organic Nanocomposites with Polymer Dots for High-Temperature Capacitive Energy Storage

HighlightsAll-organic polymer composites for high-temperature capacitive energy storage.Zero-dimensional polymer dots with high electron affinity are used as fillers.Deep charge traps from UV-irradiated films reduce the high-field conduction loss.

Effect of Fluorine in Redesigning Energy-Storage Properties of High-Temperature Dielectric Polymers.

Exploration of novel polymer dielectrics exhibiting high electric-field stability and high energy density with high efficiency at elevated temperatures is urgently needed for ever-demanding energy-storage technologies. Conventional high-temperature polymers with conjugated backbone structures cannot fulfill this demand due to their deteriorated performance at elevated electric fields. Here, in search of new polymer structures, we have explored the effect of fluorine groups on the energy-storage properties of polyoxanorbornene imide polymers with simultaneous wide band gap and high glass transition temperature (Tg). The systematic synthesis of polymers with varying amounts of fluorine is carried out and characterized for the energy-storage properties. The incorporation of fluorine imparts flexibility to the polymer structure, and free-standing films can be obtained. An oxanorbornene copolymer with 25% fluorination exhibits a high breakdown strength of 700 MV/m and a discharged energy density of 6.3 J/cm3 with 90% efficiency. The incorporation of fluorine helps to increase the polymer band gap, as observed using UV-vis spectroscopy, but lowers the polymer Tg, as shown by differential scanning calorimetry. Both the displacement-electric field (D-E) hysteresis loop and high-field conduction measurements show increased conduction loss for polymers with higher fluorine content, despite their larger band gap. The presence of excess free volume may play a key role in increasing the conduction current and lowering the efficiency of polymers with high fluorine content. Such an improved understanding of the effect of fluorination on the polymer energy-storage properties, as revealed in this systematic molecular engineering study, broadens the basis of material-informatic proxies to enable a more targeted codesign of scalable and efficient polymer dielectrics.

Thermal Analysis and In-Field Critical Current Estimation of Conduction-Cooled REBCO Magnet Considering Nonuniform Temperature Distribution

Due to the high upper critical field and transition temperature, REBCO coated conductor show great promise for conduction-cooled magnet applications. The normal zone of high temperature conductor (HTS) spreads slowly, and the conversion of a weak spot into a hot spot is localized and quite fast. Hence, in-field critical current weak spot evaluation under the nonuniform temperature gradient is important for conduction-cooled magnet stability estimation. Cooling path design needs to take the weak spot into account. In this study, a temperature-field-angle dependent critical current estimation neural network was first trained based on a public database of HTS critical current. The equivalent thermal conductivity was applied for the interface contact between the turns. Thermal contact conditions were given to the interface between the coil and bobbin considering actual production situations, such as thermal grease. Combing the non-uniform magnetic field and thermal distribution, the critical current distribution was evaluated to track the weak part. The results of this study will be employed in the design analysis of high magnetic field conduction cooling magnets in the future.

Tailoring Poly(Styrene-co-maleic anhydride) Networks for All-Polymer Dielectrics Exhibiting Ultrahigh Energy Density and Charge-Discharge Efficiency at Elevated Temperatures.

Polymer film capacitors have been widely used in electronics and electrical power systems due to their advantages of high power densities, fast charge-discharge speed, and great stability. However, the exponential increase of electrical conduction with temperature and applied electric field substantially degrades the capacitive performance of dielectric polymers at elevated temperatures. Here, the first example of controlling the energy level of charge traps in all-organic crosslinked polymers by tailoring molecular structures that significantly inhibit high-field high-temperature conduction loss, which largely differs from current approaches based on the introduction of inorganic fillers, is reported. The polymer network with optimized crosslinking structures exhibits an ultrahigh discharged energy density of 7.02 J cm-3 with charge/discharge efficiencies of >90% at 150°C, far outperforming current dielectric polymers and composites. The charge-trapping effects in different crosslinked structures, as the origins of the marked improvements in the high-temperature capacitive performance, are comprehensively investigated experimentally and confirmed computationally. Moreover, excellent cyclability and self-healing features are demonstrated in the polymer film capacitors. This work offers a promising pathway of molecular structure design to scalable high-energy-density polymer dielectrics capable of operating under harsh environments.

Interfacial polarization suppression of P(VDF-HFP) film through 2D montmorillonite nanosheets coating

Polymer based dielectrics with excellent high electric field withstanding capability are of great significance for enhancing the power density and payload efficiency for both electrical and electronic systems. However, polymer-metal interface is prone to defect formation, leading to the dielectric aging and the initialization of electrical breakdown failure. A facile Montmorillonite (MMT) coating is self-co-assembled on the surface of P(VDF-HFP) high-k film to form hundreds of 2D nanosheets layers to impede the charge injection over the metal-polymer interface. The MMT coating increases the breakdown strength of the P(VDF-HFP) co-polymer film from 405 to 452 MV/m. The high field conduction study reveals a highly enhanced Schottky injection barrier that blocks the charge injection from electrodes to polymer bulk, leading to significantly suppressed charge injection and conduction loss in polymer. In addition, the introduction of MMT layered coating leads to prominent suppression of interfacial polarization loss, a phenomenon known as the blocking capacitance, which would otherwise stem from the accumulated charges of polymer-metal interface, by one order of magnitude, as demonstrated by the dielectric response analysis by using the Dissado-Hill model over a broad range of temperature and frequency. The superior charge injection and interfacial polarization suppression via the application of MMT coating impart the P(VDF-HFP) co-polymer film with higher breakdown strength, and provides an effective approach to develop high performance polymer dielectrics by interfacial engineering. This work provides insights into the understanding of the enhancement mechanism of 2D coating.

Fermi energy, electrical conductivity, and the energy gap of NaNbO3

The energy of the valence band maximum of ${\mathrm{NaNbO}}_{3}$ is determined from the Schottky barrier heights at the contacts with low work function Sn-doped ${\mathrm{In}}_{2}{\mathrm{O}}_{3}$ and high work function ${\mathrm{RuO}}_{2}$ by means of x-ray photoelectron spectroscopy with in situ interface preparation. The measurements reveal a valence-band edge energy, which is comparable to that of ${\mathrm{SrTiO}}_{3}$ and ${\mathrm{BaTiO}}_{3}$. The energy gap of ${\mathrm{SrTiO}}_{3}$ and ${\mathrm{BaTiO}}_{3}$ is $3.2\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$ and comparable to the values of $3.4\phantom{\rule{0.16em}{0ex}}\mathrm{eV}\phantom{\rule{0.16em}{0ex}}\mathrm{to}\phantom{\rule{0.16em}{0ex}}3.5\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$, which are determined by means of optical and electron energy loss spectroscopy for ${\mathrm{NaNbO}}_{3}$. It is therefore expected that the conduction band minimum of ${\mathrm{NaNbO}}_{3}$ is also located at a similar energy as the conduction band minimum of ${\mathrm{SrTiO}}_{3}$ and ${\mathrm{BaTiO}}_{3}$. If this is the case, it can be expected that donor doping of ${\mathrm{NaNbO}}_{3}$ leads to an electrical conductivity, which is comparable to those of donor-doped ${\mathrm{SrTiO}}_{3}$ and ${\mathrm{BaTiO}}_{3}$ (up to $\ensuremath{\sim}$ $1\phantom{\rule{0.16em}{0ex}}\mathrm{S}/\mathrm{c}{\mathrm{m}}^{\ensuremath{-}1}$). In contrast, Sr- and Ca-doped ${\mathrm{NaNbO}}_{3}$ bulk ceramics exhibit a room temperature conductivity up to $10\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}\phantom{\rule{0.16em}{0ex}}\mathrm{S}/\mathrm{c}{\mathrm{m}}^{\ensuremath{-}1}$, only slightly higher than that of ${\mathrm{NaNbO}}_{3}$. High-field conductivity measurements and impedance spectroscopy give no indication that the low conductivity is caused by insulating grain boundaries separating electrically conductive grains. It is therefore suggested that the energy gap of ${\mathrm{NaNbO}}_{3}$ is substantially higher than the gap of $3.4\phantom{\rule{0.16em}{0ex}}\mathrm{eV}\phantom{\rule{0.16em}{0ex}}\mathrm{to}\phantom{\rule{0.16em}{0ex}}3.5\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$ determined from optical spectroscopy reported in literature and from electron energy loss spectroscopy within this paper, as also suggested from electronic structure calculations of ${\mathrm{LiNbO}}_{3}$ [Phys. Rev. B 77, 035106 (2008)].

Optimization Design of Packaging Insulation for Half-Bridge SiC MOSFET Power Module Based on Multi-Physics Simulation

With the development of power modules for high voltage, high temperature, and high power density, their size is becoming smaller, and the packaging insulation experiences higher electrical, thermal, and mechanical stress. Packaging insulation needs to meet the requirement that internal electric field, temperature, and mechanical stress should be as low as possible. Focusing on the coupling principles and optimization design among electrical, thermal, and mechanical stresses in the power module packaging insulation, a multi-objective optimization design method based on Spice circuit, finite element field numerical calculation, and multi-objective gray wolf optimizer (MOGWO) is proposed. The packaging insulation optimal design of a 1.2 kV SiC MOSFET half-bridge power module is presented. First, the high field conductivity characteristics of the substrate ceramic and encapsulation silicone of the packaging insulation material were tested at different temperatures and external field strengths, which provided the key insulation parameters for the calculation of electric field distribution. Secondly, according to the mutual coupling principles among electric–thermal–mechanical stress, the influence of packaging structure parameters on the electric field, temperature, and mechanical stress distribution of packaging insulation was studied by finite element calculation and combined with Spice circuit analysis. Finally, the MOGWO algorithm was used to optimize the electric field, temperature, and mechanical stress in the packaging insulation. The optimal structural parameters of the power module were used to fabricate the corresponding SiC MOSFET module. The fabricated module is compared with a commercial module by the double-pulse experiment and partial discharge experiment to verify the feasibility of the proposed design method.

Study of High field conduction in Se based Chalcogenide glasses

The present work reports the study of high field conduction in thin films of Se90Ge10-x Inx (x=2,6) because high field conduction in chalcogenide glasses is affected by the presence of localised states at the band edges as well as the defect states present in the mobility gap.To measure the density of states in these thin films , space charge limited conduction technique is used. I-V characteristics have been measured at various fixed temperatures. An ohmic behaviour is observed at low electric fields upto 102V/cm. Superohmic behaviour is observed at high electric fields (103 -104 V/cm).High field conduction theory of space charge limited conduction for uniform distribution of localised states in the mobility gap fits well with the experimental data.Using this theory, the density of defect states near Fermi level is calculated for all glassy alloys.

High-field conduction in fresh and aged samples of Se and As2Se3 glasses

High-field conduction in fresh and aged samples of Se and As2Se3 glasses

Dielectric permittivity, conductivity and breakdown field of hexagonal boron nitride

In view of the extensive use of hexagonal boron nitride (hBN) in 2D material electronics, it becomes important to refine its dielectric characterization in terms of low-field permittivity and high-field strength and conductivity up to the breakdown voltage. The present study aims at filling this gap using DC and RF transport in two Au-hBN-Au capacitor series of variable thickness in the 10–100 nm range, made of large high-pressure, high-temperature (HPHT) crystals and a polymer derivative ceramics (PDC) crystals. We deduce an out-of-plane low field dielectric constant ϵ ∥ = 3.4 ± 0.2 consistent with the theoretical prediction of Ohba et al, that narrows down the generally accepted window ϵ ∥ = 3–4. The DC-current leakage at high-field is found to obey the Frenkel-Pool law for thermally-activated trap-assisted electron transport with a dynamic dielectric constant ϵ ∥ ≃ 3.1 and a trap energy Φ B ≃ 1.3 eV, that is comparable with standard technologically relevant dielectrics.

Significantly enhancing the discharge efficiency of sandwich-structured polymer dielectrics at elevated temperature by building carrier blocking interface

Dielectric materials with high power densities have irreplaceable advantages in electrical energy storage. However, conventional polymer dielectrics are unable to meet the ever-increasing power demands in harsh environments. Here we report a high-temperature dielectric based on judiciously designed all-polymer sandwiched films consisting of polyimide (PI) and polyetherimides (PEIs). Due to the swelling effect of PEIs solution on the PI surface, it built a clear and complete interface with a gradient change molecular stacking structure between the PEIs and PI layers in the sandwiched film, resulting in an increase in the density of deep traps and the accumulation of space charges in the interface. It is found via direct experimental evidence that the high-field electrical conduction at high temperatures can be effectively suppressed. The sandwiched film exhibits excellent comprehensive capacitive performance even at 200 °C, e.g. a discharged energy density of 2.0 J cm−3 and a charge-discharge efficiency of 92% at 300 MV m−1. Along with facile technology compatible with roll-to-roll processing, this work also opens a new avenue to high-energy-density all-polymer dielectric for high-temperature applications by building interface carrier barrier.

On the Study of “Further Meyer–Neldel Rule” in Thermally Activated High Field Conduction of Se-Te-Pb Glassy Alloys

On the Study of “Further Meyer–Neldel Rule” in Thermally Activated High Field Conduction of Se-Te-Pb Glassy Alloys

Interface States Passivation for p-Channel 4H-SiC MOS Devices

Impressive material properties such as wide band gap, high breakdown electric field and thermal conductivity makes silicon carbide (4H-SiC) an attractive semiconductor for high power and high temperature electronics. Applications include, but are not limited to, power and control systems in hybrid and electric vehicles, space crafts and renewable energy sources [1-2]. In addition to discrete power components, an advanced 4H-SiC complementary metal-oxide-semiconductor (CMOS) integrated circuit technology has the potential to revolutionize high temperature electronics, for operational temperatures greater than 200 ºC [3-4], where Si is not efficient or usable. CMOS requires both n-channel (electron) and p-channel (hole) metal-oxide-semiconductor field effect transistors (MOSFETs) and it is critical for both polarities to have adequate performance. In n-channel 4H-SiC devices, nitrogen incorporation at the SiO2/4H-SiC interface reduces interface state density (Dit) energetically located in the upper half of the 4H-SiC band gap and near the conduction band-edge [5]. Research on p-channel is less extensive, but prior research motivates hydrogen [6] and more recent studies suggest nitrogen [7] as effective passivation agents for donor like traps in the lower half of the 4H-SiC band gap. In this work, we investigated several post-oxidation annealing (POA) processes involving nitrogen and hydrogen for Dit reduction in p-type MOS capacitors. For a comparative study, n-type capacitors were also fabricated and characterized. All samples were oxidized at 1150 °C to grow a ~60 nm oxide film and some samples were subjected to POA as summarized in Table 1. The results show that NO and H2 both reduce Dit in the lower half of the 4H-SiC band gap, with NO having a much larger effect. The reduction of positive trapped charge lowers the flat band voltage for p-type 4H-SiC MOS capacitors with different degrees of passivation as shown in Figure 1. The Dit profile near the band-edges, extracted from simultaneous high (100 kHz) - low frequency CV at room temperature, highlights the large reduction associated with NO, as shown in Figure 2. The effect of hydrogen is primarily in the reduction of energetically deep interface traps. To measure the density of the deep traps (Nit, deep), photon assisted CV measurements [8] were carried out, from which Nit, deep was calculated as shown in Figure 3 and summarized in Table 1. Overall, the results confirmed that 2 hour NO annealing at 1175 °C results in the lowest Dit in the lower half of the band gap. Longer NO annealing times or combination of NO with hydrogen resulted in higher Nit, deep as listed in Table 1. Therefore, long channel 4H-SiC p-MOSFETs were fabricated using the 2 hour NO POA process to investigate hole transport and gate control in devices operating at high temperature. The results from the transfer characteristics in Figure 4 indicate that with the increase of temperature, threshold voltage reduces which can be attributed to the reduction of occupied Dit at higher temperatures. A weak temperature dependence of the hole field effect mobility with temperature is present most likely due to surface roughness scattering limitations at higher channel hole concentrations. In this presentation, the field-effect mobility will be compared to Hall measurements for additional insights into surface hole transport. In addition, details of the CV analyses, FET fabrication procedure and high temperature bias instability will be discussed. Acknowledgements: The authors gratefully acknowledge the funding support from US Army Research Laboratory grant ARMY-W911NF-18-2-0160 and National Renewable Energy Laboratory/ US Department of Energy grant NREL-AHL-9-92362-01. References : [1] S. Srdic et al., IEEE Appl. Power Elec. Conf. and Expo.(APEC), 2714 (2016)[2] M. Abbasi et al., in IEEE Trans. Emerg. Sel. Topics Power Electron., 7, 798 (2019)[3]A. M. Francis et al., Proc. IMAPS High Temperature Electron. Conf., 2016, 242, (2016)[4] A. S. Kashyap et al., IEEE (WiPDA), 60 (2013)[5] G. Liu et al. Appl. Phys. Rev. 2, 021307 (2015)[6] M. Okamoto et al. Appl. Phys. Lett., 89, 023502 (2006)[7] K. Tachiki and T. Kimoto IEEE Trans. Elec. Dev., 68, 638 (2021)[8] J. A. Cooper, Jr., phys. stat. sol. 162, 305 (1997) Figure 1