# Lecture 5 MSJ

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Step Potential Function Assume a flux of particles is incident on the potential barrier.

Classical physics: particles are not absorbed or transmitted through the potential barrier.

Quantum physics: there is a finite probability that the incident particles will penetrate

the potential barrier and exist in region II. Since the reflection coefficient in region I isunity, the particle in region II must eventually turn around and move back into region I.

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The Potential Barrier & Tunneling Classical physics: particles can not pass

potential barrier wall in Region II, therefore,there is not particle in Region III.

Quantum physics: there is a finite probability that a particle impinging a potential barrier will penetrate the barrier andwill appear in region III. This phenomenon iscalled tunneling.

The tunneling probability may appear

to be small value, but not zero.If a large number of particles

impinging on potential barrier, asignificant number can penetratethe barrier.

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Fermi Energy Level

The Fermi energy level in n-type is higher than the Fermi energy level in p-type.

Does the Fermi energy level change ever?

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Effect of Temperature on Fermi Energy Level forVarious Doping Concentration

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Fermi Energy Level BalancingIf two different materials A and B with different number of electrons in the

allowed energy states, are brought into contact, the electrons in the entiresystem will tend to seek the lowest possible energy.

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Fermi Energy Level in pn Junction

Electrons from higher energy statemove into the lower energy state (like

connecting two water tanks withdifferent water levels) .

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Is it possible to make a device

with pn junction properties butusing only one of the junctions

(either p or n)?

Metal-Semiconductor Junctions

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The Photoelectric Effect A photon with sufficient energy, can knock an electron from the surface of the material. The minimum energy required to remove an electron is called the work function of the

material and any excess photon energy goes into the kinetic energy of the photoelectron.

hv E =2

21

mvT =

== hvmvT 221

Where hv is the incident photon energy and is theminimum energy or work function , required to remove anelectron from the surface of the material.

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Work Function of Different Materials

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Schottky Barrier or Schottky Barrier Diode

An energy work function is required to remove an electron at the Fermilevel to the vacuum outside the metal.

When negative charges are brought near the metal surface, positive (image)charges are induced in the metal.

When this image force is combined with an applied electric field (e.g. voltagesource), the effective work function is somewhat reduced.

Such barrier lowering is called the Schottky effect , and this terminology is

carried over to the discussion of potential barriers arising in metal-semiconductor contacts, and generally, rectifying contacts are referred to asSchottky barrier diodes .

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Metal-n-Semiconductor Junction

Assuming m > s . This means, before

contact, the Fermi level in thesemiconductor is above that in the metal.

When a metal with work function of m is brought

in contact with a semiconductor having a workfunction of s, charge transfer occurs until theFermi levels align at equilibrium.

In order for the Fermi level to become aconstant through the system in thermalequilibrium, electrons from the semiconductorflow into the lower energy states in the metal.

Positively charged donor atoms remain in thesemiconductor, creating a space charge region.

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Metal-n-Semiconductor Junction The Schottky barrier B0 is the potential

barrier seen by electrons in the metal tryingto move into semiconductor, and given as:

On the semiconductor side, V bi is the built-in potential barrier. This barrier, similar to the

case of the pn junction, is the barrier seen byelectrons in the conduction band trying tomove into the metal calculate as:

)(0 = m B

n BbiV = 0

where is known as the electron affinity .

V bi is slight function of semiconductor doping

where n is potential difference between E c and E F

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Metal-n-Semiconductor Junction: Reverse Bias

If we apply a positive voltage to the semiconductor with respect to the metal, thesemiconductor-to-metal barrier height increases, while B0 is remains constant inideal case.

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Metal-n-Semiconductor Junction: Forward Bias

If a positive voltage is applied to the metal with respect to the semiconductor, thesemiconductor-to-metal barrier V bi is reduced while B0 again remains essentiallyconstant.

In this situation, electrons can more easily flow from the semiconductor into the

metal since the barrier has been reduced.

Unlike pn junction, the current mechanism here is due to the flow of majority carrierelectrons. In forward bias, the barrier seen by the elctrons in the semiconductor is

reduced, so majority carrier electrons flow more easily from the semiconductor intothe metal.

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Example: Determine the theoretical barrier height, built-in potential barrier, and maximum

electric field in a metal-semiconductor diode for zero applied bias. Consider a contact between tungsten and n-type silicon doped to N d = 10 16 cm -3 T = 300 K.

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Schottky Barrier Diode and pn Junction DiodeComparison

The current in a pn junction is determined by the diffusion of minority carriers whilethe current in a Schottky barrier diode is determined by thermionic emission ofmajority carriers over a potential barrier.

=kT

eT A J Bn sT

exp2*

p

no p

n

pon s L

peD L

neD J +=

Another difference between a Schottky

barrier diode and a pn junction is in thefrequency response or switchingcharacteristics. A typical switching timefor a Schottky diode is in the picosecond

range, while for a pn junction it is in thenanosecond range.

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