Semiconductors Handout

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It descibes the basics of semiconductor theory

Text of Semiconductors Handout

• 1

Semiconductors

Basic Properties

Band Structure

Eg = energy gap Silicon ~ 1.17 eV Ge ~ 0.66 eV

• 2

Intrinsic Semiconductors

Pure Si, Ge are intrinsic semiconductors. Some electrons elevated to conduction band

by thermal energy.

Fermi-Dirac Distribution

The probability that a particular energy state is filled

is just the F-D distribution. For intrinsic conductors at room temperature the

chemical potential, , is approximately equal to the Fermi Energy, EF.

The Fermi Energy is in the middle of the band gap.

• 3

Conduction Electrons

If - EF >> kT then

If we measure from the top of the valence band and remember that EF lies in the middle of the band gap then

Conduction Electrons

A full analysis taking into account the number of states per energy (density of states) gives an estimate for the fraction of electrons in the conduction band of

• 4

Electrons and Holes

When an electron in the valence band is excited into the conduction band it leaves behind a hole.

Holes

The holes act like positive charge carriers in the valence band.

Electric Field

• 5

Holes

In terms of energy level electrons tend to fall into lower energy states which means that the holes tends to rise to the top of the valence band.

Photon Excitations

Photons can excite electrons into the conduction band as well as thermal fluctuations

• 6

Impurity Semiconductors

An impurity is introduced into a semiconductor (doping) to change its electronic properties.

n-type have impurities with one more valence electron than the semiconductor.

p-type have impurities with one fewer valence electron than the semiconductor.

Impurities

For silicon n-type is pentavalent: As, P p-type is trivalent: Al, Ga, B

• 7

Impurity Semiconductors

n-type

Impurity Semiconductors

p-type

• 8

Band Structure of N-type

Valence band

Donor impurity levels Fermi Energy

For Si(As): Econduction - Edonor = 0.049 eV

T = 0K

Conduction band

Band Structure of N-type

Donor impurity levels Fermi Energy

For Si(As): Econduction - Edonor = 0.049 eV

T = 300 K

Valence band

Conduction band

Remember kT = 0.025 eV

• 9

Band Structure of P-type

Valence band

Acceptor impurity levels Fermi Energy

For Si(Ga): Eacceptor - Edvalence = 0.065 eV

T = 0 K

Conduction band

Band Structure of P-type

Acceptor impurity levels Fermi Energy

For Si(Ga): Eacceptor - Edvalence = 0.065 eV

T = 300 K

Valence band

Conduction band

Remember kT = 0.025 eV

• 10

The pn junction

Forming a pn junction

p-type and n-type semiconductors are placed in contact. electrons in the conduction band in the n-type diffuse across

the junction into the p-type.

Valence band

Conduction band

Valence band

Conduction band

p n

• 11

Valence band

Conduction band

Forming a pn junction

p-type and n-type semiconductors are placed in contact electrons in the conduction band in the n-type diffuse across

the junction into the p-type.

Valence band

Conduction band

p n

Valence band

Conduction band

Forming a pn junction

once in the p-type they can drop down into the valence band and to fill up one of the hole states.

Valence band

Conduction band

p n

• 12

Valence band

Conduction band

Forming a pn junction

once in the p-type they can drop down into the valence band and to fill up one of the hole states.

Valence band

Conduction band

p n

Forming a pn junction

Electrons continue to diffuse across the junction. The area of the p-type near the junction becomes more

negative due to the excess electrons while the n-type becomes more positive due to the excess of holes (or deficit of electrons).

This creates an electric field in the region of the junction that eventually prevents any further significant diffusion of electrons.

This region is essentially free of mobile charge carriers and is called the depletion region.

• 13

Depletion Region The depletion region is free of mobile charge carriers. The typical thickness of the depletion region is about

1 micron or 10-4 cm.

- - - - - - - - - - - -

+ + + + + + + + + + + +

Depletion region: Mobile holes and electrons have combined leaving charged ions.

Formation of the depletion region

1 2

3 4

• 14

Depletion Region Characteristics The fixed charges in the depletion region create an electric

field that points from the n-type to the p-type. This field tends to sweep any mobile electrons in the region back to the n-type and any mobile holes back to the p-type.

-

+

= mobile hole

= mobile electron

= fixed ionized donor atom

= fixed ionized acceptor atom

p n

- - - - -

- - - - -

- - - - -

- - - - -

+ + + + +

+ + + + + + + + + +

+ + + + +

Ed

Depletion region

Energy Diagram for pn junction In equilibrium the Fermi energy must be the same everywhere,

otherwise electrons could reduce the energy of the system by flowing to unoccupied states in a region of lower Fermi energy.

- - - -

+ + + +

EF

p n

Conduction band

Valence band

Electron Energy

• 15

Energy Diagram for pn junction The potential energy difference between the two sides of the

junction is given by electric field in the depletion region.

- - - -

+ + + +

EF

p n

Conduction band

Valence band

Electron Energy

d

E

Equilibrium Currents for pn junction

In equilibrium there are still small currents flowing across the junction though there is no net electron current.

- - - -

+ + + +

EF

p n

Conduction band

Valence band

Electron Energy Thermal Current

Recombination Current

• 16

Thermal Current Electrons in the valence band of the p-type can acquire enough thermal

energy to jump into the conduction band. They diffuse into the depletion region and are swept into n-type by the E-field.

- - - -

+ + + +

EF

p n

Conduction band

Valence band

Electron Energy

Recombination Current Electrons in the conduction band of the n-type can acquire enough thermal

energy to rise higher in the conduction band. They can then diffuse across the depletion region to the p-type and drop into the valence band filling a hole.

- - - -

+ + + +

EF

p n

Conduction band

Valence band

Electron Energy

• 17

Currents in equilibrium pn junctions

The thermal current cancels out the recombination current in the equilibrium state.

The thermal current is dependent on the width of the energy gap in the semiconductor and the temperature.

The recombination current is dependent on E, the size of energy difference between the p-type and n-type bands and the temperature.

Biasing pn junctions

Apply a voltage across a pn junction:

p n

V

+

p n

V

+

Forward Bias Reverse Bias

• 18

Reverse bias

A negative voltage is applied to the p-region. The energy of the electrons in the p-region will increase.

The potential energy difference between the two regions will increase by (-e)(-V) = eV

This will reduce the recombination current which depends on the potential difference but leave the thermal current unchanged.

A small net electron current will flow from p to n.

Reverse bias The increase in the potential energy difference reduces the

recombination current.

- - - -

+ + + +

EF

p n

Conduction band

Valence band

Electron Energy

d

E + eV

Thermal current

Recombination current

• 19

Forward bias

A positive voltage is applied to the p-region. The energy of the electrons in the p-region will decrease.

The potential energy difference between the two regions will be reduced: (-e)(V) = -eV

This will greatly increase the recombination current which depends on the potential difference but leave the thermal current unchanged.

A large net electron current will flow from n to p.

Forward bias The increase in the potential energy difference greatly

increases the recombination current.

- - - -

+ + + +

EF

p n

Conduction band

Valence band

Electron Energy

d

E - eV

Thermal current

Recombination current

• 20

Diodes

Diodes

The pn junction is used an electronic circuit element called the diode or rectifier.

The diode is the most basic electronic component.

An ideal diode would have zero resistance when forward biased and an infinite resistance when reverse biased.

• 21

Practical Diode Model A somewhat more realistic

model inco

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