Author

# B. R. Nag

Other affiliations: Bangor University, Saha Institute of Nuclear Physics, University College of the North

Bio: B. R. Nag is an academic researcher from University of Calcutta. The author has contributed to research in topics: Electron mobility & Scattering. The author has an hindex of 22, co-authored 213 publications receiving 2769 citations. Previous affiliations of B. R. Nag include Bangor University & Saha Institute of Nuclear Physics.

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06 May 1980

TL;DR: In this paper, the Boltzmann Transport Equation is used to calculate the collision probability of the Sphalerite and the Chalcopyrite structures, and the Brillouin Zone is used for the Wurtzite structure.

Abstract: 1. Introduction.- 1.1 Historical Note.- 1.2 Applications.- 1.3 Transport Coefficients of Interest.- 1.4 Scope of the Book.- 2. Crystal Structure.- 2.1 Zinc-Blende Structure.- 2.2 Wurtzite Structure.- 2.3 Rock-Salt Structure.- 2.4 Chalcopyrite Structure.- 3. Energy Band Structure.- 3.1 Electron Wave Vector and Brillouin Zone.- 3.2 Brillouin Zone for the Sphalerite and Rock-Salt Crystal Structure.- 3.3 Brillouin Zone for the Wurtzite Structure.- 3.4 Brillouin Zone for the Chalcopyrite Structure.- 3.5 E-k Diagrams.- 3.5.1 Energy Bands for the Sphalerite Structure.- 3.5.2 Energy Bands for the Wurtzite Structure.- 3.5.3 Energy Bands for the Rock-Salt Structure.- 3.5.4 Band Structure of Mixed Compounds.- 3.6 Conclusion.- 4. Theory of Efiergy Band Structure.- 4.1 Models of Band Structure.- 4.2 Free-Electron Approximation Model.- 4.3 Tight-Binding Approximation Model.- 4.4 Energy Bands in Semiconductor Super!attices.- 4.5 The k-p Perturbation Method for Derivating E-k Relation.- 4.5.1 Single-Band Perturbation Theory.- 4.5.2 Two-Band Approximation.- 4.5.3 Effect of Spin-Orbit Interaction.- 4.5.4 Nonparabolic Relation for Extrema at Points Other than the r Point.- 4.6 External Effects on Energy Bands.- 4.6.1 Effects of Doping.- 4.6.2 Effects of Large Magnetic Fields.- 5. Electron Statistics.- 5.1 Fermi Energy for Parabolic Bands.- 5.2 Fermi Energy for Nonparabolic Bands.- 5.3 Fermi Energy in the Presence of a Quantising Magnetic Field.- 5.3.1 Density of States.- 5.3.2 Fermi Level.- 5.4 Fermi Energy and Impurity Density.- 5.4.1 General Considerations.- 5.4.2 General Formula.- 5.4.3 Discussion of Parabolic Band.- 5.4.4 Effect of Magnetic Field.- 5.5 Conclusions.- 6. Scattering Theory.- 6.1 Collision Processes.- 6.2 Transition Probability.- 6.3 Matrix Elements.- 6.4 Free-Carrier Screening.- 6.5 Overlap Integrals.- 6.6 Scattering Probability S(k).- 6.6.1 S(k) for Ionised Impurity Scattering.- 6.6.2 S(k) for Piezoelectric Scattering.- 6.6.3 S(k) for Deformation-Potential Acoustic Phonon Scattering.- 6.6.4 S(k) for Polar Optic Phonon Scattering.- 6.6.5 S(k) for Intervalley and Nonpolar Optic Phonon Scattering.- 6.7 Scattering Probabilities for Anisotropic Bands.- 6.7.1 Herring-Vogt Transformation.- 6.7.2 Scattering Integrals.- 6.8 S(k) for Neutral Impurity, Alloy, and Crystal-Defect Scattering.- 6.8.1 Neutral-Impurity Scattering.- 6.8.2 Alloy Scattering.- 6.8.3 Defect Scattering.- 6.9 Conclusions.- 7. The Boltzmann Transport Equation and Its Solution.- 7.1 The Liouville Equation and the Boltzmann Equation.- 7.2 The Boltzmann Transport Equation.- 7.3 The Collision Integral.- 7.4 Linearised Boltzmann Equation.- 7.5 Simplified Form of the Collision Terms.- 7.5.1 Collision Terms for Elastic Scattering.- 7.5.2 Collision Terms for Inelastic Scattering.- 7.6 Solution of the Boltzmann Equation.- 7.6.1 Relaxation-Time Approximation.- 7.6.2 Variational Method.- 7.6.3 Matrix Method.- 7.6.4 Iteration Method.- 7.6.5 Monte Carlo Method.- 7.7 Method of Solution for Anisotropic Coupling Constants and Anisotropic Electron Effective Mass.- 7.7.1 Solution for Elastic Collisions.- 7.7.2 Solution for Randomising Collisions.- 7.7.3 Solution for Nonrandomising Inelastic Collisions.- 7.8 Conclusions.- 8. Low-Field DC Transport Coefficients.- 8.1 Evaluation of Drift Mobility.- 8.1.1 Formulae for Relaxation-Time Approximation.- 8.1.2 Evaluation by the Variational Method.- 8.1.3 Evaluation by Matrix and Iteration Methods.- 8.1.4 Evaluation by the Monte Carlo Method.- 8.2 Drift Mobility for Anisotropic Bands.- 8.2.1 Ellipsoidal Band.- 8.2.2 Warped Band.- 8.3 Galvanomagnetic Transport Coefficients.- 8.3:1 Formulae for Hall Coefficient, Hall Mobility, and Magnetoresistance.- 8.3.2 Reduced Boltzmann Equation for the Galvanomagnetic Coefficients.- 8.3.3 Solution Using the Relaxation-Time Approximation Method.- 8.3.4 A Simple Formula for the Low-Field Hall Mobility.- 8.3.5 Numerical Methods for the Galvanomagnetic Coefficients for Arbitrary Magnetic Fields.- 8.3.6 Evaluation of the Galvanomagnetic Transport Coefficients for Anisotropic Effective Mass.- 8.4 Transport Coefficients for Nonuniform conditions.- 8.4.1 Diffusion.- 8.4.2 Thermal Transport Coefficients.- 8.4.3 Formula for Thermoelectric Power.- 8.4.4 Electronic Thermal Conductivity.- 8.5 Conclusions.- 9. Low-Field AC Transport Coefficients.- 9.1 Classical Theory of AC Transport Coefficients.- 9.1.1 Solution for the Relaxation-Time Approximation.- 9.1.2 Solution for Polar Optic Phonon and Mixed Scattering.- 9.1.3 Solution for Nonparabolic and Anisotropic Bands.- 9.2 AC Galvanomagnetic Coefficients.- 9.3 Cyclotron Resonance and Faraday Rotation.- 9.3.1 Propagation of Electromagnetic Waves in a Semiconductor in the Presence of a Magnetic Field.- 9.3.2 Cyclotron Resonance Effect.- 9.3.3 Faraday Rotation.- 9.4 Free-Carrier Absorption (FCA).- 9.4.1 Classical Theory of FCA.- 9.4.2 Quantum-Mechanical Theory of FCA.- 9.5 Concluding Remarks.- 10. Electron Transport in a Strong Magnetic Field.- 10.1 Scattering Probabilities.- 10.2 Mobility in Strong Magnetic Fields.- 10.3 Electron Mobility in the Extreme Quantum Limit (EQL).- 10.3.1 Electron Mobility for Polar Optic Phonon Scattering in the EQL.- 10.4 Oscillatory Effects in the Magnetoresistance.- 10.4.1 Shubnikov-de Haas Effect.- 10.4.2 Magnetophonon Oscillations.- 10.5 Experimental Results on Magnetophonon Resonance.- 10.6 Conclusions.- 11. Hot-Electron Transport.- 11.1 Phenomenon of Hot Electrons.- 11.2 Experimental Characteristics.- 11.3 Negative Differential Mobility and Electron Transfer Effect.- 11.4 Analytic Theories.- 11.4.1 Differential Equation Method.- 11.4.2 Maxwellian Distribution Function Method.- 11.4.3 Displaced Maxwellian Distribution Function Method.- 11.5 Numerical Methods.- 11.5.1 Iteration Method.- 11.5.2 Monte Carlo Method.- 11.6 Hot-Electron AC Conductivity.- 11.6.1 Phenomenological Theory for Single-Valley Materials.- 11.6.2 Phenomenological Theory for Two-Valley Materials.- 11.6.3 Large-Signal AC Conductivity.- 11.7 Hot-Electron Diffusion.- 11.7.1 Einstein Relation for Hot-Electron Diffusivity.- 11.7.2 Electron Diffusivity in Gallium Arsenide.- 11.7.3 Monte Carlo Calculation of the Diffusion Constant.- 11.8 Conclusion.- 12. Review of Experimental Results.- 12.1 Transport Coefficients of III-V Compounds.- 12.1.1 Indium Antimonide.- 12.1.2 Gallium Arsenide.- 12.1.3 Indium Phosphide.- 12.1.4 Indium Arsenide.- 12.1.5 Indirect-Band-Gap III-V Compounds.- 12.2 II-VI Compounds.- 12.2.1 Cubic Compounds of Zinc and Cadmium.- 12.2.2 Wurtzite Compounds of Zinc and Cadmium.- 12.2.3 Mercury Compounds.- 12.3 IV-VI Compounds.- 12.4 Mixed Compounds.- 12.5 Chalcopyrites.- 12.6 Conclusion.- 13. Conclusions.- 13.1 Problems of Current Interest.- 13.1.1 Heavily Doped Materials.- 13.1.2 Alloy Semiconductors.- 13.1.3 Transport Under Magnetically Quantised Conditions.- 13.1.4 Inversion Layers.- 13.1.5 Superlattices and Heterostructures.- 13.2 Scope of Further Studies.- Appendix A: Table of Fermi Integrals.- Appendix B: Computer Program for the Evaluation of Transport Coefficients by the Iteration Method.- Appendix C: Values of a. and b. for Gaussian Quadrature Integration. 417 Appendix D: Computer Program for the Monte Carlo Calculation of Hot-Electron Conductivity and Diffusivity.- List of Symbols.- References.

716 citations

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01 Jan 2000

TL;DR: In this article, the authors introduce the Quantum Well Detector, Modulator and Switch (QWDT) and Quantum Well Laser (QLL) as well as Resonant Tunneling Diode.

Abstract: Preface. Acknowledgments. 1. Introduction. 2. Heterostructure Growth. 3. Band Offset. 4. Electron States. 5. Optical Interaction Phenomena. 6. Transport Properties. 7. High Electron Mobility Transistor. 8. Resonant Tunneling Diode. 9. Quantum Well Laser. 10. Quantum Well Detector, Modulator and Switch. References. Index.

124 citations

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TL;DR: In this article, a theory of the band structure of semiconductor superlattices has been developed for both the direct-bandgap and indirect-band-gap barrier layers taking into account the multivalley and nonparabolic band structure.

Abstract: A theory of the band structure of semiconductor superlattices has been developed for both the direct-band-gap and indirect-band-gap barrier layers taking into account the multivalley and nonparabolic band structure of the materials forming the superlattice. For direct-band-gap barrier layers the nonparabolicity in the band structure may alter the electronic energy levels measured from the bottom of the potential wells by as much as 26%. On the other hand for indirect-band-gap barrier layers the alteration due to the nonparabolicity is about 14%. It is also found that even for indirect-band-gap barrier layers the band structure is mainly determined by the states corresponding to the direct-gap minimum. Energy levels calculated on the basis of the theory presented are also found to agree with those obtained in recent experiments with double-barrier heterostructures.

71 citations

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TL;DR: In this paper, large diameter (2-inch) n-type ZnO boules were grown by a new vapor-phase transport method using temperature-dependent Hall-effect technique.

Abstract: Large-diameter (2-inch), n-type ZnO boules grown by a new vapor-phase transport method were investigated by the temperature-dependent Hall-effect technique. The 300-K Hall carrier concentration and mobility were about 6 × 1016 cm−3 and 205 cm2 V−1 s−1, respectively, and the peak mobility (at 50 K) was about 2000 cm2 V−1 s−1, comparable to the highest values reported in the past for ZnO. The dominant donor had a concentration of about 1 × 1017 cm−3 and an energy of about 60 meV, close to the expected hydrogenic value, whereas the total acceptor concentration was much lower, about 2 × 1015 cm−3. Photoluminescence measurements confirm the high quality of the material.

806 citations

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TL;DR: In this paper, basic knowledge of thermoelectric materials and an overview of parameters that affect the figure of merit ZT are provided, as well as the prospects for the optimization and their applications are also discussed.

Abstract: Developing thermoelectric materials with superior performance means tailoring interrelated thermoelectric physical parameters – electrical conductivities, Seebeck coefficients, and thermal conductivities – for a crystalline system. High electrical conductivity, low thermal conductivity, and a high Seebeck coefficient are desirable for thermoelectric materials. Therefore, knowledge of the relation between electrical conductivity and thermal conductivity is essential to improve thermoelectric properties. In general, research in recent years has focused on developing thermoelectric structures and materials of high efficiency. The importance of this parameter is universally recognized; it is an established, ubiquitous, routinely used tool for material, device, equipment and process characterization both in the thermoelectric industry and in research. In this paper, basic knowledge of thermoelectric materials and an overview of parameters that affect the figure of merit ZT are provided. The prospects for the optimization of thermoelectric materials and their applications are also discussed.

663 citations

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TL;DR: The fabrication of graphene nanoribbon heterojunctions and heterostructures by combining pristine hydrocarbon precursors with their nitrogen-substituted equivalents are reported, and it is shown that these materials bear a high potential for applications in photovoltaics and electronics.

Abstract: p–n junctions are formed in heterostructures made of pristine and nitrogen-doped graphene nanoribbons. Despite graphene's remarkable electronic properties1,2, the lack of an electronic bandgap severely limits its potential for applications in digital electronics3,4. In contrast to extended films, narrow strips of graphene (called graphene nanoribbons) are semiconductors through quantum confinement5,6, with a bandgap that can be tuned as a function of the nanoribbon width and edge structure7,8,9,10. Atomically precise graphene nanoribbons can be obtained via a bottom-up approach based on the surface-assisted assembly of molecular precursors11. Here we report the fabrication of graphene nanoribbon heterojunctions and heterostructures by combining pristine hydrocarbon precursors with their nitrogen-substituted equivalents. Using scanning probe methods, we show that the resulting heterostructures consist of seamlessly assembled segments of pristine (undoped) graphene nanoribbons (p-GNRs) and deterministically nitrogen-doped graphene nanoribbons (N-GNRs), and behave similarly to traditional p–n junctions12. With a band shift of 0.5 eV and an electric field of 2 × 108 V m–1 at the heterojunction, these materials bear a high potential for applications in photovoltaics and electronics.

515 citations

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TL;DR: In this article, a new semiconductor superlattice where the interaction of the conduction band in one host material with the valence band of the other host material plays an important role is treated theoretically, through the use of Bloch functions.

Abstract: We treat theoretically, through the use of Bloch functions, a new semiconductor superlattice where the interaction of the conduction band in one host material with the valence band of the other host material plays an important role. The result indicates that this superlattice offers new intriguing features, realizable with the In1−xGaxAs‐GaSb1−y Asy system. In addition, the tunneling probability is calculated across a barrier involving this system.

492 citations

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TL;DR: A theoretical evaluation of the thermoelectric-related electrical transport properties of 36 half-Heusler (HH) compounds, selected from more than 100 HHs, is carried out in this paper.

Abstract: A theoretical evaluation of the thermoelectric-related electrical transport properties of 36 half-Heusler (HH) compounds, selected from more than 100 HHs, is carried out in this paper. The electronic structures and electrical transport properties are studied using ab initio calculations and the Boltzmann transport equation under the constant relaxation time approximation for charge carriers. The electronic structure results predict the band gaps of these HH compounds, and show that many HHs are narrow-band-gap semiconductors and, therefore, are potentially good thermoelectric materials. The dependence of Seebeck coefficient, electrical conductivity, and power factor on the Fermi level is investigated. Maximum power factors and the corresponding optimal p- or n-type doping levels, related to the thermoelectric performance of materials, are calculated for all HH compounds investigated, which certainly provide guidance to experimental work. The estimated optimal doping levels and Seebeck coefficients show reasonable agreement with the measured results for some HH systems. A few HHs are recommended to be potentially good thermoelectric materials based on our calculations.

446 citations