Last time: Concentration of electrons in conduction band

ESE 372 / Spring 2013 / Lecture 6 Last time: Concentration of electrons in conduction band Top of conduction band Volume concentration of  electrons...
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ESE 372 / Spring 2013 / Lecture 6

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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ESE 372 / Spring 2013 / Lecture 6

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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ESE 372 / Spring 2013 / Lecture 6

Electron and hole concentrations.

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Intrinsic semiconductors

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Doped Semiconductors N-type

P-type

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ESE 372 / Spring 2013 / Lecture 6

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.

Richardson constant Current will flow:

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ESE 372 / Spring 2013 / Lecture 6

Schottky diode Current‐Voltage (IV) Characteristics. Cathode

Anode

In our example considered

+

small

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ESE 372 / Spring 2013 / Lecture 6

Ohmic contact. Metal

n+ - semiconductor Heavily doped

Almost linear very steep IV.

Depletion region is  Depletion region is very thin (