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.

Top of conduction bandTotal volume concentration of electrons:

Volume concentration of allowed energy

Fermi-Dirac distribution

gylevels with energy ~E in interval of energies dE.

Probability of having electron at state with energy E

Density of states

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at state with energy E.

ESE 372 / Spring 2013 / Lecture 6

Boltzmann’s approximation

Can not be taken l ti llanalytically

Fortunately fory for

for

Effective density of states at band edge

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g

ESE 372 / Spring 2013 / Lecture 6

Electron and hole concentrations.

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ESE 372 / Spring 2013 / Lecture 6

Intrinsic semiconductors

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ESE 372 / Spring 2013 / Lecture 6

Doped SemiconductorsN-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)

Work

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 if Φ > Φ certain number of electrons will leave

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For instance, if ΦM > ΦS certain number of electrons will leave semiconductor and move to metal.

ESE 372 / Spring 2013 / Lecture 6

Metal – Semiconductor Junction – Schottky contact.Wh ilib i i t bli h d th i t d F i l l i fl t

Metal N-Semiconductor

When new equilibrium is established there is no current and Fermi level is flat.

Built-in potential(energy barrier that stopped electron transfer)Schottky

barrier

Depletion regionDepletion region(region with dramatically reduced concentration of mobile electrons)

Surface charge concentration on

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Surface charge concentration on semiconductor side of junction.(Depletion region charge)

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 i bl t i t dhence, no appreciable current is expected.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 fromn-semiconductor to metal.

Barrier for electron transport from n-semiconductor to metal is reduced. Depletion region width decreases.

Richardson constant

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Current will flow:

ESE 372 / Spring 2013 / Lecture 6

Schottky diode Current‐Voltage (IV) Characteristics.

Anode Cathode

In our example considered + -In our example considered +

small

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ESE 372 / Spring 2013 / Lecture 6

Ohmic contact.

Metal n+ - semiconductorHeavily doped

Almost linear

Depletion region is

Almost linear very steep IV.

Depletion region is very thin (<<100 nm)

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ESE 372 / Spring 2013 / Lecture 6

More realistic diode IV.

--

++

B+ -Becomes

linear at large currents

Junction IV

“Load” line

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ESE 372 / Spring 2013 / Lecture 6

Diode models.

Ideal diode:Ideal diode:

Constant voltage drop model. Battery + resistance model.

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ESE 372 / Spring 2013 / Lecture 6

Diode small‐signal model.

Differential resistanceDifferential resistance

Differential resistance depends on bias.

1. Large currents::

2. Small currents:

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Diodes also have small-signal capacitances.We already know junction capacitance.

ESE 372 / Spring 2013 / Lecture 6

Diode‐based limiting circuits.Di d t k f llDiode takes care of all extra current and thus limits output voltage.Example 1:

Clipper

Example 2:Double clipper

Example 3:Example 3:protection

15Limits maximum negative VBE

ESE 372 / Spring 2013 / Lecture 6

Clamped capacitor.

Circuit restores DC component of the signal –measure of duty cycle.

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ESE 372 / Spring 2013 / Lecture 6

pn ‐ Junction.

When these two materials are brought into contact the electrons will go from n to p and holes from p to n regions by diffusion.

They will be leaving behind immobile charges of ionized donors and acceptors

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They will be leaving behind immobile charges of ionized donors and acceptors. The corresponding electric field will eventually stop diffusion currents.

ESE 372 / Spring 2013 / Lecture 6

pn – Junction band diagram.

Donor concentration

Acceptor concentration

Surface charge densities on both

Built-in potential

densities on both sides of pn-junction

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ESE 372 / Spring 2013 / Lecture 6

pn – Junction under reverse bias.

External field is trying to move electrons from p to n and holes from n to p.

Almost no current can flow since there is smallAlmost no current can flow since there is small number of electrons in p and holes in n regions

Junction capacitance decreases

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ESE 372 / Spring 2013 / Lecture 6

pn – Junction under forward bias.

External field is trying to move electrons from n to p and holes from p to n.Current should be expected.

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ESE 372 / Spring 2013 / Lecture 6

Current of pn–junction under forward bias.

Reverse saturation current

21Observe accumulation of mobile charges on both sides on pn-junction under forward bias

ESE 372 / Spring 2013 / Lecture 6

IV of pn‐junction diode.

Nonideality factor

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