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# Diffusion current

About: Diffusion current is a research topic. Over the lifetime, 1502 publications have been published within this topic receiving 26337 citations.

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01 Sep 1957

TL;DR: In this article, the authors show that the current due to generation and recombination of carriers from generation-recombination centers in the space charge region of a p-n junction accounts for the observed characteristics.

Abstract: For certain p-n junctions, it has been observed that the measured current-voltage characteristics deviate from the ideal case of the diffusion model. It is the purpose of this paper to show that the current due to generation and recombination of carriers from generation-recombination centers in the space charge region of a p-n junction accounts for the observed characteristics. This phenomenon dominates in semiconductors with large energy gap, low lifetimes, and low resistivity. This model not only accounts for the nonsaturable reverse current, but also predicts an apparent exp (qV/nkT) dependence of the forward current in a p-n junction. The relative importance of the diffusion current outside the space charge layer and the recombination current inside the space charge layer also explains the increase of the emitter efficiency of silicon transistors with emitter current. A correlation of the theory with experiment indicates that the energy level of the centers is a few kT from the intrinsic Fermi level.

1,852 citations

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TL;DR: In this article, the effects of the diffusion current on the three more important low-frequency dynamic characteristics (the short-circuit gate capacitance, the transconductance, and the drain conductance) are discussed.

Abstract: A qualitative discussion of the device operation is first given using three-dimensional energy band diagrams to show the significance of the diffusion current. The theoretical static I–V characteristics are the computed including both the diffusion and the drift currents, based on the one-dimensional and gradual channel model. Drain current saturation phenomena are evident in these exact solutions which are in good agreement with the calculations based on the bulk charge approximation and with the experimental data for the entire non-saturating and saturated ranges. The relative importance of the two current components along the length of the channel is illustrated. The effects of the diffusion current on the three more important low-frequency dynamic characteristics (the short-circuit gate capacitance, the transconductance, and the drain conductance) are discussed. The surface potential, the quasi-Fermi potential, the surface electric field and the surface carrier concentration along the channel are examined. The complete one-dimensional gradual channel model is inadequate to account for the large drain conductance observed in the saturation range, and it is shown that the electric field longitudinal to the channel current flow must be taken into account near the drain junction where it is larger than the transverse field due to the voltage applied to the gate electrode.

564 citations

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TL;DR: The electron current in a semiconductor at uniform lattice temperature, with a nonuniform electric field distribution (e.g., a barrier layer), consists of terms arising from conduction, diffusion, and thermal diffusion as discussed by the authors.

Abstract: The electron current in a semiconductor at uniform lattice temperature ${T}_{0}$, with a nonuniform electric field distribution (e.g., a barrier layer), consists of terms arising from conduction, diffusion, and thermal diffusion. The first two terms involve the mobility and diffusion coefficient which are functions of the electron temperature $T$ or, more generally, depend on certain averages over the nonequilibrium, field-dependent electron energy distribution function. The third term is due to the electron temperature gradient and is analogous to conventional thermal diffusion of a gas in a temperature gradient. In conventional theory, which neglects electron heating or cooling, the mobility and diffusion coefficient are material constants and thermal diffusion is absent. Contrary to the case of uniform fields, $T$ is not a unique function of the local field; it also depends on the current and can only be determined by a simultaneous solution of the equations for current flow and conservation of energy with boundary conditions for a particular structure. As an example, a one carrier metal-semiconductor contact rectifer has been analyzed in detail including a discussion of the Peltier effect. In the barrier region $T$ is greater than ${T}_{0}$ (i.e., hot electrons) for a reverse bias but less than ${T}_{0}$ (i.e., cold electrons) for a forward bias. Computer solutions have been obtained for a Schottky barrier and electron scattering due to acoustic phonons only.

463 citations

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27 Oct 2005

TL;DR: In this article, the Atoms-Bond model is used to evaluate the performance of current carriers in semiconductors, including three types of crystal structures: Graphene, carbon nanotubes and three-dimensional (3D) crystals.

Abstract: PART I INTRODUCTION TO SEMICONDUCTORS 1 lNTRODUCTION TO CRYSTALS AND CURRENT CARRIERS IN SEMICONDUCTORS, THE ATOMIC-BOND MODEL 1.1 INTRODUCTION TO CRYSTALS 1.1.1 Atomic Bonds 1.1.2 Three-Dimensional Crystals 1.1.3 Two-Dimensional Crystals: Graphene and Carbon Nanotubes 1.2 CURRENT CARRIERS 1.2.1 Two Types of Current Carriers in Semiconductors 1.2.2 N*Type and P-Type Doping 1.2.3 Electroneutrality Equation 1.2.4 Electron and Hole Generation and Recombination in Thermal Equilibrium 1.3 BASICS OF CRYSTAL GROWTH AND DOPING TECHNIQUES 1.3.1 Crystal-Growth Techniques 1.3.2 Doping Techniques Summary Problems Review Questions 2 THE ENERGY-BAND MODEL 12.1 ELECTRONS AS WAVES 2.1.1 De Broglie Relationship Between Particle and Wave Properties 2.1.2 Wave Function and Wave Packet 2.1.3 Schrodinger Equation 2.2 ENERGY LEVELS IN ATOMS AND ENERGY BANDS IN CRYSTALS 2.2.1 Atomic Structure 2.2.2 Energy Bands in Metals 2.2.3 Energy Gap and Energy Bands in Semiconductors and Insulators 12.3 ELECTRONS AND HOLES AS PARTICLES 2.3.1 Effective Mass and Real E-k Diagrams 2.3.2 The Question of Electron Size: The Uncertainty Principle 2.3.3 Density of Electron States 2.4 POPULATION OF ELECTRON STATES, CONCENTRATIONS OF ELECTRONS A:"D HOLES 2.4.1 Fermi-Dirac Distribution 2.4.2 Maxwell-Boltzmann Approximation and Effective Density of States 2.4.3 Fermi Potential and Doping 2.4.4 Nonequilibrium Carrier Concentrations and Quasi-Fermi Levels Summary Problems Review Questions 3 DRIFT 3.1 ENERGY BANDS WITH APPLIED ELECTRIC FIELD 3.1.1 Energy-Band Presentation of Drift Current 3.1.2 Resistance and Power Dissipation due to Carrier Scattering 3.2 OHM'S LAW, SHEET RESISTANCE, AND CONDUCTIVITY 3.2.1 Designing Integrated-Circuit Resistors 3.2.2 Differential Form of Ohm's Law 3.2.3 Conductivity Ingredients 3.3 CARRIER MOBILITY 3.3.1 Thermal and Drift Velocities 3.3.2 Mobility Definition 3.3.3 Scattering Time and Scattering Cross Section 3.3.4 Mathieson's Rule 3.3.5 Hall Effect Summary Problems Review Questions 4 DlFFUSION 4.1 DIFFUSION-CURRENT EQUATION 4.2 DIFFUSION COEFFICIENT 4.2.1 Einstein Relationship L4.2.2 Haynes-Shockley Experiment 4.2.3 Arrhenius Equation 4.3 BASIC CONTINUITY EQUATION Summary Problems Review Questions 5 GENERATION AND RECOMBINATION 5.1 GENERATION AND RECOMBINATION MECHANISMS 5.2 GENERAL FORM OF THE CONTINUITY EQUATION 5.2.1 Recombination and Generation Rates 5.2.2 Minority-Carrier Lifetime 5.2.3 Diffusion Length 5.3 GENERATION AND RECOMBINATION PHYSICS AND SHOCKLEYREAD- HALL (SRH) THEORY 5.3.1 Capture and Emission Rates in Thermal Equilibrium 5.3.2 Steady-State Equation for the Effective Thermal Generation/Recombination Rate 5.3.3 Special Cases 5.3.4 Surface Generation and Recombination Summary Problems Review Questions PART II FUNDAMENTAL DEVICE STRUCTURES 6 JUNCTIONS 6.1 P-N JUNCTION PRINCIPLES 6.1.1 p-~ Junction in Thermal Equilibrium 6.1.2 Reverse-Biased P-N Junction 6.1.3 Forward-Biased P-K Junction 6.1.4 Breakdown Phenomena 6.2 DC MODEL 6.2.1 Basic Current-Voltage (I-V) Equation 6.2.2 Important Second-Order Effects 6.2.3 Temperature Effects 6.3 CAPACITA CE OF REVERSE-BIASED P-:-I JUNCTION 6.3.1 C-V Dependence 6.3.2 Depletion-Layer Width: Solving the Poisson Equation 6.3.3 SPICE Model for the Depletion-Layer Capacitance 6.4 STORED-CHARGE EFFECTS 6.4.1 Stored Charge and Transit Time 6.4.2 Relationship Between the Transit Time and the Minority-Carrier Lifetime 6.4.3 Switching Characteristics: Reverse-Recovery Time 6.5 METAL-SEMICONDUCTOR CONTACT 6.5.1 Schottky Diode: Rectifying Metal-Semiconductor Contact 6.5.2 Ohmic Metal-Semiconductor Contacts Summary Problems Review Questions 7 MOSFET 7.1 MOS CAPACITOR 7.1.1 Properties of the Gate Oxide and the Oxide-Semiconductor Interface 7.1.2 C-V Curve and the Surface-Potential Dependence on Gate Voltage 7.1.3 Energy-Band Diagrams 7.1.4 Flat4Band Capacitance and Debye Length 7.2 MOSFET PRINCIPLES B.1.1 MOSFET Structure 7.2.2 MOSFET as a Voltage-Controlled Switch B.1.3 The Threshold Voltage and the Body Effect B.1.4 MOSFET as a Voltage-Controlled Current Source: Mechanisms of Current Saturation 7.3 PRINCIPAL CURRENT-VOLTAGE CHARACTERISTICS AND EQUATIONS 7.3.1 SPICE LEVEL 1 Model 7.3.2 SPICE LEVEL 2 Model 7.3.3 SPICE LEVEL 3 Model: Principal Effects 7.4 SECO:\D-OROER EFFECTS 7.4.1 Mobility Reduction with Gate Voltage 7.4.2 Velocity Saturation (Mobility Reduction with Drain Voltage) 7.4.3 Finite Output Resistance 7.4.4 Threshold-Voltage-Related Short-Channel Effects 7.4.5 Threshold Voltage Related Narrow-Channel Effects 7.4.6 Subthreshold Current 7.5 Nanoscale MOSFETs 7.5.1 Down-Scaling Benefits and Rules 7.5.2 Leakage Currents 7.5.3 Advanced MOSFETs 7.6 MOS-BASED MEMORY DEVICES 7.6.1 1C1T DRAM Cell 7.6.2 Flash-Memory Cell Summary Problems Review Questions 8 BJT 8.1 B.JT PRINCIPLES 8.1.1 BJT as a Voltage-Controlled Current Source 8.1.2 BJT Currents and Gain Definitions 8.1.3 Dependence of ? and ? Current Gains on Technological Parameters 8.1.4 The Four Modes of Operation: BJT as a Switch 8.1.5 Complementary BJT 8.1.6 BJT Versus MOSFET 8.2 PRINCIPAL CURRENT-VOLTAGE CHARACTERISTICS, EBERE-MOLL MODEL IN SPICE 8.2.1 Injection Version 8.2.2 Transport Version 8.2.3 SPICE Version 8.3 SECOND*ORDER EFFECTS 8.3.1 Early Effect: Finite Dynamic Output Resistance 8.3.2 Parasitic Resistances 8.3.3 Dependence of Common-Emitter Current Gain on Transistor Current: Low-Current Effects 8.3.4 Dependence of Common-Emitter Current Gain on Transistor Current: Gummel-Poon Model for High-Current Effects 8.4 HETEROJUNCTION BIPOLAR TRANSISTOR Summary Problems Review Questions PART III SUPPLEMENTARY TOPICS 9 PHYSICS OF NANOSCALE DEVICES 9.1 SINGLE-CARRIER EVENTS 9.1.1 Beyond the Classical Principle of Continuity 9.1.2 Current-Time Form of Uncertainty Principle 9.1.3 Carrier-Supply Limit to Diffusion Current 9.1.4 Spatial Uncertainty 9.1.5 Direct Nonequilibrium Modeling of Single-Carrier Events 9.2 TWO-DIMENSIONAL TRANSPORT IN MOSFETs AND HEMTs 9.2.1 Quantum Confinement 9.2.2 HEMT Structure and Characteristics 9.2.3 Application of Classical MOSFET Equations to Two-Dimensional Transport in MOSFETs and HEMTs 9.3 ONE-DIMENSUIONAL TRANSPORT IN NANOWIRES AND CARBON NANOTUBES 9.3.1 Ohmic Transport in Nanowire and Carbon-Nanotube FETs 9.3.2 One-Dimensional Ballistic Transport and the Quantum Conductance Limit Summary Problems Review Questions 10 DEVICE ELECTRONICS, EQUIVALENT CIRCUITS A D SPICE PARAMETERS 10.l DIODES 10.1.1 Static Model and Parameters in SPICE 10.1.2 Large-Signal Equivalent Circuit in SPICE 10.1.3 Parameter Measurement 10.1.4 Small-Signal Equivalent Circuit 10.2 MOSFET 10.2.1 Static Model and Parameters LEVEL 3 in SPICE 10.2.2 Parameter Measurement 10.2.3 Large-Signal Equivalent Circuit and Dynamic Parameters in SPICE 10.2.4 Simple Digital ~1od.el 10.2.5 Small-Signal Equivalent Circuit 10.3 BJT 10.3.1 Static Model and Parameters: Ebers-Moll and Gummel-Poon Levels in SPICE 10.3.2 Parameter Measurement 10.3.3 Large-Signal Equivalent Circuit and Dynamic Parameters in SPICE 10.3.4 Small-Signal Equivalent Circuit Summary Problems Review Questions 11 PHOTONIC DEVICES 11.1 LIGHT EMITTING DIODES (LED) 11.2 PHOTODETECTORS AND SOLAR CELLS 11.2.1 Biasing for Photodetector and Solar-Cell Applications 11.2.2 Carrier Generation in Photodetectors and Solar Cells 11.2.3 Photocurrent Equation 11.3 LASERS 11.3.1 Stimulated Emission, Inversion Population, and Other Fundamental Concepts 11.3.2 A Typical Heterojunction Laser Summary Problems Review Questions 12 JFET AND MESFET 12.1 JFET 12.1.1 JFET Structure 12.1.2 JFET Characteristics 12.1.3 SPICE Model and Parameters 12.2 MESFET 12.2.1 MESFET Structure 12.2.2 MESFET Characteristics 12.2.3 SPICE Model and Parameters Summary Problems Review Questions 13 POWER DEVICES 13.1 POWER DIODES 13.1.1 Drift Region in Power Devices 13.1.2 Switching Characteristics 13.1.3 Schottky Diode 13.2 POWER MOSFET 13.3 IGBT 13.4 THYRISTOR Summary Problems Review Questions

436 citations

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TL;DR: Theoretically, the oxygen diffusion current on the platinum electrode was studied theoretically in both circular and band type electrodes as mentioned in this paper, where the current of the band electrode was independent of the thickness of the bands.

Abstract: The oxygen diffusion current on the platinum electrode was studied theoretically in both circular and band type electrodes. For the oxygen current of the circular electrode the following equation was obtained; I=4naFDC0, where a is the radius of the electrode, D the diffusion coefficient and C0 the oxygen concentration in the bulk solution. The current of the band electrode was independent of the thickness of the band, as shown by the following; I=nΠlFDC2/Ψ, where l is the length of the band and Ψ is the parameter showing the extension of the boundary of the diffusion region; outside the boundary the concentration is maintained at a constant C0. The theoretical equation of the oxygen current of the circular electrode agreed well qualitatively with the experimental result. In the case of the band electrode, the oxygen diffusion current was found to be independent of the thickness; this was approximately ascertained by the experimental data.

409 citations