Lecture8-EquilibreumAndEinstienRelationships

Lecture8-EquilibreumAndEinstienRelationships - ECE 3040 -...

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Unformatted text preview: ECE 3040 - Dr. Alan Doolittle Georgia Tech Lecture 8 Equations of State, Equilibrium and Einstein Relationships and Generation/Recombination Reading: Pierret 3.3-3.4 ECE 3040 - Dr. Alan Doolittle Georgia Tech Equilibrium Concept Consider a non-uniformly doped semiconductor. E c-E f varies with position x Ln(N D ) x Energy E c E v E i E f Since the electrons (or holes) are free to move anywhere in the material, the average energy of the electrons can not change. If the average energy did change from one position to another, there would be a net motion of electrons from high energy toward low energy. E f must be constant when no current flows! Fewer electrons, but higher energy More electrons, but lower energy ECE 3040 - Dr. Alan Doolittle Georgia Tech Equilibrium Concept •Remember: •No net current can flow otherwise we have a “perpetual motion machine”. •But dEc/dx is nonzero so we have a drift current component. •The drift current component MUST be balanced by a diffusion current component! x E c E v E i E f x Ln(N D ) J n | Diffusion J n | Drift E ECE 3040 - Dr. Alan Doolittle Georgia Tech Equilibrium Concept Additionally, since electrons and holes operate “independently of each other”, J n | Diffusion + J n | Drift =0 and J p | Diffusion + J p | Drift =0 •Thus, for non-uniform doping in equilibrium, we have: •E f is constant •No net current •Carrier Concentration gradients that result in a diffusion current component. •A “Built in” electric field that result in a drift current component. •BOTH electron and hole components must sum to zero. I.E. J n =J p =0 ECE 3040 - Dr. Alan Doolittle Georgia Tech Equilibrium Concept Consider the case for electrons: ( ) ( ) ( ) q kT D holes for Likewise q kT D or kT q D qnE qnE becomes Thus nE kT q dx dE e kT n dx dn dx dE dx dE e kT n dx dn n of derivative the taking Thus dx dE and e n n and dx dE q E but dx dn qD nE q J J p p n n n n i kT Ei Ef i i f kT Ei Ef...
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This note was uploaded on 08/23/2011 for the course ECE 3040 taught by Professor Doolittle during the Spring '11 term at University of Florida.

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Lecture8-EquilibreumAndEinstienRelationships - ECE 3040 -...

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