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Semiconductors

Basic Properties

Band Structure

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

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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 ε is filled

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

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

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

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Conduction Electrons

•  If ε - EF >> kT then

•  If we measure ε 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

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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

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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

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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

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Impurity Semiconductors

•  n-type

Impurity Semiconductors

•  p-type

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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

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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

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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

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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

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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.

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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

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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

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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

ΔE

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

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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

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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 ΔE, 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

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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

ΔE + eV

Thermal current

Recombination current

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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

ΔE - eV

Thermal current

Recombination current

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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.

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Practical Diode Model •  A somewhat more realistic

model incorporates the “turn-on voltage” or knee voltage.

•  There is a minimum voltage required across the diode in the forward direction before it conducts an appreciable amount of current.

•  The turn-on voltage is approximately 0.5 to 0.7 Volts in Si and about 0.3 volts in Ge.

I

V Vturn-on

Realistic Model

•  In forward bias the diode has a resistance on the order of 10 Ω.

•  In reverse bias the resistance is on the order of 108 Ω.

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Biased pn junction

•  In terms of positive current the current vs. voltage graph for a biased pn junction:

I = I0(e+eV/kT − 1)

Breakdown •  In sufficiently large reverse bias is applied to a diode an “avalanche” occurs.

•  At the breakdown voltage charge carriers gain enough energy (from the reverse bias electric field) between collisions to break a covalent bond in the lattice and create another charge carrier.

•  These two charge carriers are accelerated and create more charge carriers leading to an “avalanche” of charge carriers.

•  This occurs very sharply at a certain voltage. •  Ordinary diodes usually fail in these conditions.

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The Diode Curve

Real Diodes

•  The schematic symbol for a diode is

•  Diodes come in many shapes, each designed for a specific set of applications.

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Diodes and Temperature

•  As temperature increases, more thermal energy is available to electrons enabling them to escape their binding atoms more readily. This causes the knee voltage (the voltage at which the diode turns on) to decrease.

Zener Diodes

•  The p-n junction diode that operates in the reverse breakdown region is usually destroyed by the excess current and the heat it produces. The zener diode is designed to successfully operate in this region.

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Zener Diode •  The characteristic curve

of the zener operating in the reverse breakdown region shows that the voltage dropped across the zener diode remains relatively constant while current through the zener current is allowed to increase dramatically.

Zener Diode •  When forward biased, the zener has a turn-on voltage of

approximately 0.7 V (like any other silicon diode.) When reverse biased, the zener can have a “zener voltage” equal to whatever amplitude it is designed (and doped) to possess (from a minimum of approximately 1.8 V to several hundred volts.)

•  The relatively constant voltage drop across the zener when it is reverse biased is the reason for to its use as a voltage regulator. A voltage regulator is a device (or circuit) designed to maintain a constant output voltage regardless of any variations in the magnitude of its input voltage or in the requirements of load current.

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Light-Emitting Diode (LED)

•  LEDs are diodes that emit light when biased properly.

•  LEDs are available in various colours: red, green, yellow, orange, blue and white.

•  Forward knee voltage does vary with LED color (from approximately 1.2 V to approximately 4.3 V.)

LEDs •  LEDs usually have clear

(or semi-clear) cases. The different colors are obtained by using different elements in the LED's construction.

•  LEDs must be forward biased to allow current to pass through them.

•  LEDs will only light up when current is sufficiently large.

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LEDs

•  Since LED cases are not labeled, a means of identifying the anode and cathode must exist.

Laser Diodes

•  Laser diodes are basically LEDs driven at higher current so that a population inversion is created to allow stimulated emission of photons.

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Photovoltaic Diode or Solar Cell

•  A photon is absorbed by a semiconductor atom promoting an electron across the energy gap to the conduction band.

•  The electron is then accelerated by the electric field in the depletion region.

•  This produces a reverse current driven by the incoming photons.

Diode Application: The Half-wave rectifier