ECEE 302: Electronic Devices

1. 28 October 2002 ECEE 302: Electronic Devices Lecture 4. Effect of Excess Carriers in Semi-Conductors

2. 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

3. 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

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

5. 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)

6. Example: Absorption (Example 4-1) (2 of 2)

7. 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

8. Direct Recombination of Electrons and Holes (1 of 2) • Direct Recombination of an electron and hole occurs spontaneously

9. Direct Recombination of Electrons and Holes (2 of 2)

10. Steady State Carrier Generation

11. Example 4-2 (Textbook, Page 121)

12. 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

13. Example, Text page 122

14. 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

15. 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

16. 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 • • • • • • • • • • • •

17. Diffusion Equation (1 of 2) L n1 n2 L L x0 n1 >n2

18. Diffusion Equation (2 of 2)Particles and Current

19. 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)

20. Built in Electric Fields

21. Einstein Relationship

22. Example, Text page 130 EC n(x) E(x) N0 EF Ei EV ni x x

23. Continuity Equation

24. Diffusion Length: Steady State Carrier Injection

25. Diffusion Length

26. Haynes-Shockley Experiment • The Haynes-Shockley Experiment results in the independent determination of minority carrier mobility (m) and the minority carrier diffusion constant (D)

27. Example, Text Page 136-137

28. 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

29. 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

30. 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