ECEE 302: Electronic Devices 28 October 2002 ECEE 302: Electronic Devices Lecture 4. Effect of Excess Carriers in Semi-Conductors 28 October 2002

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 28 October 2002

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 28 October 2002

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 28 October 2002

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) 28 October 2002

Example: Absorption (Example 4-1) (2 of 2) 28 October 2002

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 28 October 2002

Direct Recombination of Electrons and Holes (1 of 2) Direct Recombination of an electron and hole occurs spontaneously 28 October 2002

Direct Recombination of Electrons and Holes (2 of 2) 28 October 2002

Steady State Carrier Generation 28 October 2002

Example 4-2 (Textbook, Page 121) 28 October 2002

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 Electrons Excess Holes ECONDUCTION Fn EFERMI Fp EVALANCE 28 October 2002

Example, Text page 122 28 October 2002

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 28 October 2002

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 28 October 2002

Clustered Group of Particles Uniformly Distributed Group of Particles 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 • • • • • • • • • • • • 28 October 2002

Diffusion Equation (1 of 2) L n1 n2 L L x0 n1 >n2 28 October 2002

Diffusion Equation (2 of 2) Particles and Current 28 October 2002

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) 28 October 2002

Built in Electric Fields 28 October 2002

Einstein Relationship 28 October 2002

Example, Text page 130 EC n(x) E(x) N0 EF Ei EV ni x x 28 October 2002

Continuity Equation 28 October 2002

Diffusion Length: Steady State Carrier Injection 28 October 2002

Diffusion Length 28 October 2002

Haynes-Shockley Experiment The Haynes-Shockley Experiment results in the independent determination of minority carrier mobility (m) and the minority carrier diffusion constant (D) 28 October 2002

Example, Text Page 136-137 28 October 2002

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 28 October 2002

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 28 October 2002

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 28 October 2002