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28 October 2002. ECEE 302: Electronic Devices. Lecture 4. Effect of Excess Carriers in Semi-Conductors. Outline. Optical Absorption Luminescence Photo-Luminenscence Cathodoluminescence Electroluminescence Carrier Lifetime and Photoconductivity
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28 October 2002 ECEE 302: Electronic Devices Lecture 4. Effect of Excess Carriers in Semi-Conductors
Outline • Optical Absorption • Luminescence • Photo-Luminenscence • Cathodoluminescence • Electroluminescence • Carrier Lifetime and Photoconductivity • Direct Re-Combination of electrons and holes • Indirect Combination; Trapping • Steady State Carrier Generation: Quasi-Fermi Levels • Photoconductive Devices • Diffusion of Carriers • Diffusion Process • Diffusion and Drift of Carriers, (built in fields) • Continuity Equation (Diffusion and Recomination) • Steady State Carrier Injection and Diffusion Length • Haynes-Shockley Experiment • Gradients in the Quasi-Fermi levels
Optical Absorption • Optical Absorption Process Text, Figure 4-1 • Absorption Experiment Text, Figure 4-2 & 4-3 • Band Gaps of common semi-conductors Text, Figure 4-4
Luminescence • Luminescence refers to light emission from solids • Types of Luminescence • Photoluminescence Text, Figures 4-5 & 4-6 • Direct excitation and recombination of an EHP • Trapping • Color is determined by impurities that create different energy levels within the solid • Florescence • fast luminescence process • Phosphorescence (phosphors) • slow luminescence process • mulitple trapping process • Electroluminescence • mechanism for LEDs • electric current causes injection of minority carriers to regions where they combine with majority carriers to produce light
Example: Absorption (Example 4-1) (1 of 2) Problem: GaAs with t=.46mm. Illumination=monochromatic light =hn=2eV, a=5x104 cm-1. Pincident=10mW (a) Find the total energy absorbed by the sample per sec (J/s) (b) Find the rate of excess thermal energy given up to the electrons in the lattice prior to recombination (J/s) (c) Find the number of photons per second given off from recombination events (assume 100% quantum efficiency)
Carrier Lifetime and Photoconductivity • Excess electrons and holes increase conductivity of semi-conductors • When excess carriers are produced from optical luminescence, the resulting increase in conductivity is called photoconductivity • This is the primary mechanism in the operation of solar cells • Mechanisms • Direct Recombination Text, Figure 4- 7 • Indirect Recombination, Trapping Text, Figure 4- 8 • Impurity Energy Levels Text, Figure 4- 9 • Photo-conductive decay Text, Figure 4-10 • Steady State Carrier Generation; Quasi-Fermi Levels Text, Fig 4-11 • Photo-conductive Devices
Direct Recombination of Electrons and Holes (1 of 2) • Direct Recombination of an electron and hole occurs spontaneously
Quasi-Fermi Levels • Fermi Level is valid only when there are no excess carriers present • We define the “quasi-Fermi” level for electrons (Fn) and holes (Fp) to describe steady state carrier concentrations Excess Holes Excess Electrons ECONDUCTION Fn EFERMI Fp EVALANCE
Optical Sensitivity of a Photo conductor • Photo-conductors are conductors that change their conductivity when illuminated by light • Applications are electric eyes, exposure meters for photography, solar cells, etc • Sensitivity to specific light color (frequency) is determined by the energy gap
Diffusion of Carriers • Diffusion Process Text, Figure 4-12 & 4-13 • motion of carriers from high density to low density states • Diffusion and Drift - Built in Fields Text, Figure 4-14 & 15 • Continuity Equation (Diffusion and Recombination) Text, Fig 4-16 • Steady State Carrier Injection (Diffusion Length) Text, Fig 4-17 • Haynes-Shockley Experiment Text, Figure 4-18 & 4-19 • Gradients in the Quasi-Fermi Levels
Diffusion Process • Diffusion refers to the process of particles moving from areas of high density to areas of low density • The diffusion rate is driven by the concentration at a point Before Clustered Group of Particles After Uniformly Distributed Group of Particles • • • • • • • • • • • •
Diffusion Equation (1 of 2) L n1 n2 L L x0 n1 >n2
Diffusion and Drift of Carriers • Forces that can cause electron (hole) drift are • Diffusion - driven by carrier concentration • Electro-Motive Force - driven by an Electric Field (F=qE)
Example, Text page 130 EC n(x) E(x) N0 EF Ei EV ni x x
Haynes-Shockley Experiment • The Haynes-Shockley Experiment results in the independent determination of minority carrier mobility (m) and the minority carrier diffusion constant (D)
Gradients in the Quasi-Fermi Levels • Equilibrium implies no gradient in the Fermi level • Combination of drift (due to Electric Field) and diffusion implies there is a gradient in the “quasi” Fermi Level
Summary • We described methods of calculating carrier concentrations under equilibrium conditions in the previous lecture • This lecture we discussed carrier concentrations under non-equilibrium conditions • Mechanisms (Optical Absorption-Direct and Indirect Recombination) • Quasi-Fermi Levels to describe non-equilibrium carrier concentrations • Diffusion Process • Current Density Mechanisms • Diffusion • Electric Field • Einstein Relation • Continuity Equation • Diffusion Length • Haynes-Shockley Experiment • Generalized Ohm’s Law (Quasi-Fermi Levels) • Photo conductive devices
Next Time - Semi-conductor Junctions • Fabrication of p-n junctions • p-n Junction equilibrium conditions • contact potential • Fermi Level • Space Charge • Forward and Reverse Biased Junctions • Steady State Conditions • Reverse Bias Breakdown • A-C conditions • Diode Operation • Capacitance of the p-n junction • Varactor Diode • Shottky Barriers