A unified mobility model for device simulation—I. Model equations and concentration dependence
TL;DR: In this article, the authors presented a physics-based analytical model that unifies the descriptions of majority and minority carrier mobility and that includes screening of the impurities by charge carriers, electron-hole scattering, clustering of impurities and the full temperature dependence of both minority and majority carrier mobility.
Abstract: The first physics-based analytical model is presented that unifies the descriptions of majority and minority carrier mobility and that includes screening of the impurities by charge carriers, electron-hole scattering, clustering of impurities and the full temperature dependence of both majority and minority carrier mobility Using this model, excellent agreement is obtained with published experimental data on Si The model is especially suited for device simulation purposes, because the carrier mobility is given as an analytical function of the donor, acceptor, electron and hole concentrations and of the temperature
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TL;DR: The synthesis of core–multishell structures, including a high-performance coaxially gated field-effect transistor, indicates the general potential of radial heterostructure growth for the development of nanowire-based devices.
Abstract: Semiconductor heterostructures with modulated composition and/or doping enable passivation of interfaces and the generation of devices with diverse functions. In this regard, the control of interfaces in nanoscale building blocks with high surface area will be increasingly important in the assembly of electronic and photonic devices. Core-shell heterostructures formed by the growth of crystalline overlayers on nanocrystals offer enhanced emission efficiency, important for various applications. Axial heterostructures have also been formed by a one-dimensional modulation of nanowire composition and doping. However, modulation of the radial composition and doping in nanowire structures has received much less attention than planar and nanocrystal systems. Here we synthesize silicon and germanium core-shell and multishell nanowire heterostructures using a chemical vapour deposition method applicable to a variety of nanoscale materials. Our investigations of the growth of boron-doped silicon shells on intrinsic silicon and silicon-silicon oxide core-shell nanowires indicate that homoepitaxy can be achieved at relatively low temperatures on clean silicon. We also demonstrate the possibility of heteroepitaxial growth of crystalline germanium-silicon and silicon-germanium core-shell structures, in which band-offsets drive hole injection into either germanium core or shell regions. Our synthesis of core-multishell structures, including a high-performance coaxially gated field-effect transistor, indicates the general potential of radial heterostructure growth for the development of nanowire-based devices.
2,022 citations
TL;DR: In this article, the authors compared carbon nanotube, metal nanowire networks, and regular metal grids with the usual transparent conductive oxides for optically transparent electrode applications.
Abstract: Increasing demand for raw materials means that alternatives to indium-tin oxide are desired for optically transparent electrode applications. Carbon nanotube, metal nanowire networks and regular metal grids have been investigated as possible options. In this review, these materials and recently rediscovered graphene are compared with the usual transparent conductive oxides.
1,697 citations
TL;DR: In this article, the influence of the improved state-of-the-art parameters on the limiting efficiency for crystalline silicon solar cells under 1-sun illumination at 25°C, by following the narrow-base approximation to model ideal solar cells was analyzed.
Abstract: Recently, several parameters relevant for modeling crystalline silicon solar cells were improved or revised, e.g., the international standard solar spectrum or properties of silicon such as the intrinsic recombination rate and the intrinsic carrier concentration. In this study, we analyzed the influence of these improved state-of-the-art parameters on the limiting efficiency for crystalline silicon solar cells under 1-sun illumination at 25°C, by following the narrow-base approximation to model ideal solar cells. We also considered bandgap narrowing, which was not addressed so far with respect to efficiency limitation. The new calculations that are presented in this study result in a maximum theoretical efficiency of 29.43% for a 110-μm-thick solar cell made of undoped silicon. A systematic calculation of the I-V parameters as a function of the doping concentration and the cell thickness together with an analysis of the loss current at maximum power point provides further insight into the intrinsic limitations of silicon solar cells.
755 citations
TL;DR: In this article, the structural and electronic properties of lattice-mismatched Si/SiGe heterostructures are discussed in terms of scattering mechanisms and experimental results, and an assessment of the possible role of such heterodevices in future microelectronic circuits is given.
Abstract: Silicon-based heterostructures have come a long way from the discovery of strain as a new and essential parameter for band structure engineering to the present state of electron and hole mobilities, which surpass those achieved in the traditional material combination by more than an order of magnitude and are rapidly approaching the best III - V heteromaterials. It is the purpose of this article to report on the most recent developments, and the performance level achieved to date in this material system, in a concise and critical manner. The first part of this review is concerned with the structural and electronic properties of the lattice-mismatched Si/SiGe heterostructure. Emphases are put on the effects of strain both on the band structure and on the band offsets, as well as on means to actually control the strain in a stack of heteroepitaxial layers. The second part is dedicated to the transport properties of low-dimensional carrier systems in Si/SiGe and Ge/SiGe heterostructures. The prospects and limitations of the different layer concepts are discussed in terms of scattering mechanisms and experimental results. This part also reviews the most recent magneto-transport experiments on quantum wires and quantum point contacts, which became possible by the enhanced mean free paths in these materials. The third part covers the device aspects of these high-mobility materials, which is of special interest, because silicon-based heterostructures can significantly enhance the performance level of contemporary Si devices without sacrificing the essential compatibility with standard Si technologies. The recent achievements in this application-driven research field, but also the foreseeable problems and limitations, are discussed, and an assessment of the possible role of such heterodevices in future microelectronic circuits is given.
752 citations
TL;DR: In this article, the authors present a review of the charge carrier transport in zinc oxide and show that a physical limit due to ionized impurity scattering is reached for homogeneously doped layers, which can be attributed to the clustering of charge carriers connected with increased scattering due to the Z-2 dependence of the scattering cross section on the charge Z.
Abstract: Heavily doped zinc oxide films are used as transparent and conductive electrodes, especially in thin film solar cells. Despite decades of research on zinc oxide it is not yet clear what the lower limit of the resistivity of such films is. Therefore, the electrical parameters of zinc oxide films deposited by magnetron sputtering, metal organic chemical vapour deposition and pulsed laser ablation are reviewed and related to the deposition parameters. It is found that the lowest resistivities are in the range of 1.4 to 2×10-4 Ω cm, independently of the deposition method. The highest reported Hall mobilities are about 60 cm2 V-1 s-1. The thin film electrical data are compared with the corresponding values of single crystalline zinc oxide and with that of boron and phosphorous doped crystalline silicon. From this comparison it can be seen that the dependence of the Hall mobilities on the carrier concentration n are quite similar for silicon and zinc oxide. In the region n>5×1020 cm-3, which is most important for the application of zinc oxide as a transparent and conductive electrode, phosphorous doped silicon has a mobility only slightly higher than zinc oxide. The experimental data on the electron and hole mobilities in silicon as a function of the impurity concentration have been described by a fit function (Masetti et al 1983), which can also be applied with different fitting parameters to the available zinc oxide mobility data. A comparison of the experimental data with the well known ionized impurity scattering theories of Conwell-Weisskopf (1946) and Brooks-Herring-Dingle (1955) shows that these theories are not able to describe the data very well, even if the non-parabolic band structure is taken into account. As in the case of silicon, an additional reduction of the mobility also occurs for zinc oxide for concentrations n>5×1020 cm-3, which can be ascribed qualitatively to the clustering of charge carriers connected with increased scattering due to the Z-2 dependence of the scattering cross section on the charge Z of the scattering centre. The presented review of the charge carrier transport in zinc oxide indicates that a physical limit due to ionized impurity scattering is reached for homogeneously doped layers. Due to the universal nature of this limitation it is suggested that it also applies to the other important materials indium-tin (ITO) and tin oxide. Experiments are proposed to overcome this limit.
735 citations
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TL;DR: In this paper, the resistivity and impurity concentration in heavily doped silicon are reported and incorporated in a graph showing the resistivities (at T = 300°K) of n-and p-type silicon as a function of donor or acceptor concentration.
Abstract: Measurements of resistivity and impurity concentration in heavily doped silicon are reported. These and previously published data are incorporated in a graph showing the resistivity (at T = 300°K) of n- and p-type silicon as a function of donor or acceptor concentration. The relationship between surface concentration and average conductivity of diffused layers in silicon has been calculated for Gaussian and complementary error function distributions. The results are shown graphically. Similar calculations for subsurface layers, such as a transistor base region, are also given.
580 citations
TL;DR: In this paper, the authors presented a physics-based analytical model that unifies the descriptions of majority and minority carrier mobility and that includes screening of the impurities by charge carriers, electron-hole scattering and clustering of impurities.
Abstract: In Part I we presented the first physics-based analytical model that unifies the descriptions of majority and minority carrier mobility and that includes screening of the impurities by charge carriers, electron-hole scattering and clustering of impurities. Here the model is extended to include the full temperature dependence of both majority and minority carrier mobility. Based on our model and experimental data on the minority carrier diffusion length as a function of temperature, the temperature dependence of the carrier lifetime is determined. The model is especially suited for device simulation purposes, because the carrier mobility is given as an analytical function of the donor, acceptor, electron and hole concentrations and of the temperature.
442 citations
TL;DR: In this paper, the apparent bandgap narrowing in n - and p -type Si was recalculated using a recently published model, which describes both the majority and the minority carrier mobility.
Abstract: In the literature, separate models exist for the apparent bandgap narrowing in n - and p -type Si, yielding a smaller bandgap narrowing in n -type than in p -type Si. Using a recently-published model, which describes both the majority and the minority carrier mobility, we have recalculated the apparent bandgap narrowing from the measurements upon which the bandgap narrowing models mentioned above are based. The results of this new interpretation show no difference in apparent bandgap narrowing in n - and p -type Si. A function describing the unified bandgap narrowing is presented.
322 citations
TL;DR: In this article, an improved theoretical model for computing electron mobility and resistivity as functions of dopant density and temperature has been developed for n-type silicon, and the model has been applied to phosphorus-doped silicon for dopant densities from 10 13 to 10 19 cm −3, and temperatures between 100 and 500 K.
Abstract: Traditional analysis of electron mobility in n -type silicon neglects the effect of electron-electron scattering in the mobility calculations. As a result, theory fails to conform with experiment when dopant density exceeds 2 × 10 16 cm −3 . In this work, an improved theoretical model for computing mobility and resistivity as functions of dopant density and temperature has been developed for n -type silicon. The model has been applied to phosphorus-doped silicon for dopant densities from 10 13 to 10 19 cm −3 , and temperatures between 100 and 500 K. The mobility was calculated analytically by appropriately combining lattice, ionized impurity and neutral impurity scattering contributions. The effect of electron-electron scattering was incorporated empirically for dopant densities greater than 2 × 10 16 cm −3 . Additionally, the anisotropic scattering effect was included in the mobility formulations. Resistivity measurements on seven phosphorus-doped silicon wafers with dopant densities from 1.2 × 10 14 to 2.5 × 10 18 cm −3 were carried out for temperatures from 100 to 500 K. Electron mobility at 300 K was deduced from resistivity and junction C-V measurements for dopant densities from 10 14 to 10 18 cm −3 . Agreement between theoretical calculations and experimental data for both electron mobility and resistivity of phosphorus-doped silicon was within ±7% in the range of dopant densities and temperatures studied.
241 citations
TL;DR: In this paper, the relationship between resistivity and phosphorus concentration in doped silicon was determined by accurate electrical and analytical measurements, and the differences due to the various doping agents were discussed.
Abstract: Accurate electrical and analytical measurements allowed us to determine a relationship between resistivity and phosphorus concentration in doped silicon. This relationship is compared with that obtained by other authors in the case of n‐type silicon, and the differences due to the various doping agents are discussed. Differences between concentrations determined by analytical techniques and by Hall effect measurements are reported.
131 citations