Last time: Concentration of electrons in conduction band Top of conduction band
Volume concentration of electrons with energy ~E in interval of energies dE. Total volume concentration of electrons: Top of conduction band
Fermi-Dirac distribution Volume concentration of allowed energy gy levels with energy ~E in interval of energies dE. Density of states
Probability of having electron at state with energy E E.
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Boltzmann’s approximation
Can not be taken analytically l ti ll
Fortunately y
for
for
Effective density of g states at band edge
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Electron and hole concentrations.
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Intrinsic semiconductors
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Doped Semiconductors N-type
P-type
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Metal – Semiconductor Junction Metal
N-Semiconductor
Vacuum level (minimum energy of electron that is free from crystal) Electron affinity
Work function
When these two materials are brought into contact the electrons will try to lower their energy by going to material with bigger work function. This will continue until electric field created by separated charges stops this charge transfer. For instance instance, if ΦM > ΦS certain number of electrons will leave semiconductor and move to metal.
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ESE 372 / Spring 2013 / Lecture 6
Metal – Semiconductor Junction – Schottky contact. Wh new equilibrium When ilib i is i established t bli h d there th is i no currentt and d Fermi F i level l l is i flat. fl t
Metal
N-Semiconductor Built-in potential (energy barrier that stopped electron transfer)
Schottky barrier
Depletion region (region with dramatically reduced concentration of mobile electrons)
Surface charge concentration on semiconductor side of junction. (Depletion region charge)
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ESE 372 / Spring 2013 / Lecture 6
Schottky contact under reverse bias. The external voltage is trying to move electrons from metal to n-semiconductor. BUT Schottky barrier prevents electrons from going, h hence, no appreciable i bl currentt is i expected. t d Only depletion region width increases:
Junction capacitance per unit area decreases:
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ESE 372 / Spring 2013 / Lecture 6
Schottky contact under forward bias. The external voltage is trying to move electrons from n-semiconductor to metal. Barrier for electron transport from n-semiconductor to metal is reduced. Depletion region width decreases.