Principles of Electronic Devices

Principles of Electronic Devices

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Bart J. Van Zeghbroeck (303) 492-2809 [email protected] http://ece-www.colorado.edu/~bart/6355.htm Department of Electrical and Computer Engineering Campus Box 425 Boulder, Colorado 80309-0425

January 16, 1996

 Bart J. Van Zeghbroeck 1996


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© Bart J. Van Zeghbroeck 1996

Table of contents 0. Introduction:

1.1

1. General solution to semiconductor devices 1.1 Multilayer structures 1.1.1 Electrostatics 1.1.2 Simplifying multilayer structures 1.2 Parameters of bulk semiconductors 1.2.1 Temperature dependence of the energy bandgap 1.2.2 Doping dependence of the energy bandgap 1.2.3 Calculation of carrier densities at thermal equilibrium 1.3 Recombination and generation mechanisms 1.3.1 Light absorption 1.3.2 Band-to-Band recombination 1.3.3 Trap assisted recombination a) Bulk recombination b) Surface recombination 1.3.4 Auger recombination 1.3.5 Recombination in a quantum well a) Band-to-band recombination b) Schockley Hall Read recombination

1.3 1.3 1.3 1.3 1.5 1.5 1.7 1.9 1.14 1.14 1.16 1.17 1.17 1.18 1.19 1.20 1.20 1.21

2. Heterojunction material systems 2.1 The GaAs/AlGaAs material system 2.2 Strained GaInAs material

2.1 2.4 2.9

3. Unipolar devices 3.1 The Metal-Semiconductor (M-S) junction 3.1.1 Electrostatics of the M-S junction 3.1.2 Exact solution of the M-S junction 3.1.2 Numeric solution a) Depletion at the Metal-Semiconductor interface α) large potential approximation β) small potential approximation b) Accumulation at the Metal-Semiconductor interface 3.1.3 Schottky barrier with an interfacial layer 3.1.4 Current across a M-S junction a) Diffusion theory b) Thermionic emission theory c) Tunneling across a barrier. 3.2 The n-n+ junction 3.2.1 The n-n+ homojunction 3.2.2 The n-n+ heterojunction a) Analysis without quantization b) Analysis including quantization 3.2.3 Currents across a n+-n heterojunction a) Thermionic emission current across a n+-n heterojunction

3.1 3.1 3.1 3.3 3.5 3.7 3.8 3.8 3.9 3.11 3.13 3.14 3.15 3.17 3.19 3.19 3.23 3.23 3.24 3.27 3.27


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b) Calculation of the Current and quasi-Fermi level throughout a Depletion Region 3.29 c) Calculation of the current due to thermionic emission and drift/diffusion 3.32 3.3 Currents through insulators 3.33 3.3.1 Fowler-Nordheim tunneling 3.33 3.3.2 Poole-Frenkel emission 3.34 3.3.3 Space charge limited current 3.35 3.3.4 Ballistic Transport in insulators 3.37 4. The p-n junction 4.1 4.1 Electrostatic solution of the p-n homojunction 4.1 4.1.1. Approximate solution using the full depletion approximation 4.1 a) Abrupt p-n junction 4.1 b) Linearly graded junction 4.1 c) Abrupt p-i-n junction 4.2 d) Capacitance of a p-i-n junction diode 4.3 4.1.2 Exact solution for the p-n diode 4.3 4.2 Currents in a p-n homojunction 4.5 4.2.1 Ideal diode characteristics 4.5 a) "Long" diode case 4.6 b) "Short" diode case 4.6 c) General cases 4.7 4.2.2 Recombination in the depletion region 4.7 a) Band-to-band recombination 4.8 b) Trap-assisted recombination 4.8 c) Total diode current 4.9 4.2.3 High injection 4.9 4.2.4 Resistive drop 4.10 4.3 Quasi-Fermi levels in a p-n diode 4.10 4.4 The heterojunction p-n diode 4.12 4.4.1 Band diagram of a heterojunction p-n diode under Flatband conditions 4.12 4.4.2 Calculation of the contact potential (built-in voltage) 4.12 4.4.3 Electrostatics 4.13 a) Abrupt p-n junction 4.13 b) Abrupt P-i-N junction 4.14 c) A P-M-N junction with interface charges 4.16 d) Quantum well in a p-n junction 4.17 4.5 Currents across a p-n heterojunction 4.22 4.5.1 Ideal diode equation 4.22 4.5.2 Recombination/generation in the depletion region 4.23 a) Band-to-band recombination 4.23 b) Schockley-Hall-Read recombination 4.24 4.5.3 Recombination/generation in a quantum well 4.25 a) Band-to-band recombination 4.25 α) Low voltage approximation (non-degenerate carrier concentration) 4.26 β) High voltage approximation (strongly degenerate) 4.26 Principles of Electronic Devices

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b) SHR recombination 4.5.4 Recombination mechanisms in the quasi-neutral region 4.5.5 The total diode current 4.5.6 The graded p-n diode a) General discussion of a graded region b) Ideal diode current

4.27 4.28 4.28 4.29 4.29 4.32

5. Photodetectors 5.1. P-i-N photodiodes 5.1.1. Responsivity of a P-i-N photodiode a) generation of electron hole pairs b) Photocurrent due to absorption in the depletion region c) Photocurrent due to absorption in the quasi-neutral region d) Absorption in the p-contact region e) Total responsivity: f) Dark current of the Photodiode: 5.1.2 Noise in a photodiode a) shot noise sensitivity b) Equivalence of shot noise and Johnson noise c) Examples. d) Noise equivalent Power and ac noise analysis α) optical power limited NEP β) dark current limited NEP 5.1.3 Switching of a P-i-n photodiode b) Solution in the presence of drift,diffusion and recombination c) Harmonic solution d) Time response due to carriers generated in the Q.N. region e) dynamic range of a photodiode 5.2 Photoconductors 5.3 Solar cells 5.3.1 The solar spectrum: 5.3.2 Calculation of maximum power 5.3.3 Conversion efficiency for monochromatic illumination 5.3.4 Effect of diffusion and recombination in a solar cell a) photo current versus voltage 5.3.5 Spectral response 5.3.6 Influence of the series resistance 5.4 Metal-Semiconductor-Metal (MSM) Photodetector 5.4.1. Responsivity of an MSM detector 5.4.2 Pulse response of an MSM detector 5.4.3 Equivalent circuit of an MSM detector.

5.1 5.2 5.5 5.5 5.6 5.6 5.7 5.7 5.8 5.9 5.9 5.10 5.11 5.11 5.12 5.13 5.14 5.16 5.17 5.19 5.19 5.21 5.22 5.22 5.23 5.25 5.25 5.25 5.26 5.26 5.27 5.27 5.30 5.31

6. Light emitting devices 6.1 The light emitting diode 6.1.1 Introduction 6.1.2 Rate equations 6.1.3. DC solution to the rate equations 6.1.4 AC solution to the rate equations

6.1 6.1 6.1 6.1 6.2 6.3


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6.1.5 Equivalent circuit of an LED 6.2 The laser diode 6.2.1 Emission, Absorption and modal gain 6.2.2 Principle of operation of a laser diode 6.2.3 Longitudinal modes in the laser cavity. 6.2.4 Waveguide modes 6.2.5 The confinement factor 6.2.6 The rate equations for a laser diode. a) DC solution to the rate equations b) AC solution to the rate equations c) Small signal equivalent circuit 6.2.7 Threshold current of multi-quantum well laser 6.2.8 Large signal switching of a laser diode

6.4 6.5 6.5 6.10 6.10 6.11 6.12 6.12 6.13 6.14 6.15 6.16 6.17

7. The Bipolar Junction Transistor 7.1 Emitter efficiency and current gain 7.2 Transit time of a bipolar transistor 7.3 Microwave equivalent circuit 7.4 Bipolar transistor design

7.1 7.1 7.4 7.6 7.7

Appendices

A1.1

A.1 Quantum wells and density of states A.1.1 Density of states A.1.2 An infinite quantum well A.1.3 A finite rectangular well A.1.3 A triangular well A.1.4 Quantum well with an applied electric field

A1.1 A1.1 A1.2 A1.3 A1.4 A1.5

A.2 Semiconductor Equations

A2.1

A.3 Physical constants

A3.1

A.4 Material Constants

A4.1

A.5 List of symbols

A5.1

A.6 Exact solution of the MOS capacitor A.6.1 Low frequency capacitance A.6.2 Deep depletion capacitance A.6.3 High frequency capacitance A6.4 The body effect

A6.1 A6.2 A6.3 A6.4 A6.6

A.7 Some useful optics related issues A.7.1 Transmission and reflection at a dielectric interface A.7.2 Transmission and reflection of a multi-layer dielectric structure A.7.2.1 Example: a Distributed Bragg Reflector (DBR) A.7.2.2 Spreadsheet solution to an arbitrary layer structure A.7.2.3 Reflection and transmission through multiple layers A.7.3 Fabry-Perot cavity A.7.4 Ellipsometer Equations A.7.5 Interference colors of thin transparent films

A7.1 A7.1 A7.3 A7.3 A7.4 A7.5 A7.7 A7.9 A7.12


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A.7.6 Interference microscope with a broad band (white light) source A.8 Micromechanics A8.1 Cantilevers A8.2 Beam bending due compressive stress A8.3 Material parameters A8.4 Moment of inertia A8.4.1 Rectangular beam A8.4.2 I-shaped beam


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A7.14 A8.1 A8.1 A8.1 A8.3 A8.5 A8.6 A8.6
