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

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
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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
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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
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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)
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6. Example: Absorption (Example 4-1) (2 of 2)
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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
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8. Direct Recombination of Electrons and Holes (1 of 2)
Direct Recombination of an electron and hole occurs spontaneously
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9. Direct Recombination of Electrons and Holes (2 of 2)
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10. Steady State Carrier Generation
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11. Example 4-2 (Textbook, Page 121)
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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 Electrons
Excess Holes
ECONDUCTION Fn
EFERMI Fp
EVALANCE
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13. Example, Text page 122
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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
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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
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16. 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 • • • • • • • • • • • •
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17. Diffusion Equation (1 of 2)L n1 n2 L L x0
n1 >n2
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18. Diffusion Equation (2 of 2) Particles and Current
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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)
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20. Built in Electric Fields
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21. Einstein Relationship
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22. Example, Text page 130 EC
n(x)
E(x) N0 EF Ei EV ni x x
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23. Continuity Equation
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24. Diffusion Length: Steady State Carrier Injection
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25. Diffusion Length
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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)
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27. Example, Text Page
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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
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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
28 October 2002

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
28 October 2002