4- the semiconductor in equilibrium

7/22/2019 4- The Semiconductor in Equilibrium

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The Semiconductor in Equilibrium


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Introduction

Equilibrium (thermal equilibrium): no external forces such asvoltages, electric fields, magnetic fields, or temperature gradientacting on the semiconductor.

Intrinsic semiconductor: (undoped semiconductor), is a puresemiconductor with no impurity or defects.

The number of charge carriers is therefore determined by the

properties of the material itself instead of the amount of impurities

Extrinsic semiconductor: (doped semiconductor), electricalproperties of semiconductor can be altered in desirable way byadding controlled amounts of specific impurity atoms (dopantatoms).

Depending on the type of dopant atom added, the dominant charge

carrier in the semiconductor can be electrons in the conduction bandor holes in the valence band


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Charge Carriers in Semiconductors

In a semiconductor, current can be conducted by two types of carrier, the

electron and the hole. Since the current is determined largely by the number of electrons in

the conduction band and the number of holes in the valence band,An important characteristic of the semiconductor is the density of thesecharge carriers.

Density of states

Fermi distribution function

Density of electrons and holes=


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Distribution of Electrons and Holes in

EquilibriumThe electron density distribution at energy level E

The hole density distribution at energy level E


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Distribution of Electrons and Holes in

Equilibrium (in intrinsic semiconductor)To find the thermal-

equilibrium electron and hole

concentrations, we need to

determine the position of theFermi energy EF with respect

to the bottom of the

conduction-band energy Ec, and

the top of the valence-bandenergy Ev.For an intrinsic semiconductor,

the Fermi energy must be

somewhere between Ec, and Ev.


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Concentration of Electrons at EquilibriumThermal-equilibrium concentration of electrons (#/cm3) in the conduction band

0 ( ) ( )

c

c F

E

n g E f E dE

=

Assume that EF is within the energy bandgap and E-EF>>KT

For an intrinsic semiconductor, EF is at the middle of bandgap, so for energy

levels in the conduction band E>EC there is E-EF>>KT (KT 25 meV for

T=300K).


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Concentration of Electrons at Equilibrium

Define effective density of states in the conduction band


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Concentration of Holes at EquilibriumThermal-equilibrium concentration of holes (#/cm^3) in the conduction band

Assume that EF is within the energy bandgap and, EF-Ev >>KT

So, for energy levels in the valance band , EF- E >> KT, there is then


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Concentration of Holes at Equilibrium

Define effective density of states in the valence band


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Carrier Concentrations in Intrinsic

SemiconductorsFor an intrinsic semiconductor, the concentration of electrons in the conduction

band is equal to the concentration of holes in the valence band

EFi is the Fermi-level for the intrinsic semiconductor, i.e., intrinsic Fermi-level

For a given semiconductor, at constant temperature, ni is constant.ni for silicon at T = 300 K is approximately 1.5 X 10

10 cm-3.

Known as the Law of mass Action2

0 0 i

n p n=


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The intrinsic carrier concentration versus temperature.


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The Intrinsic Fermi-Level position

Solving for EFi


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Extrinsic Semiconductor Materials

An extrinsic semiconductor is a semiconductor that has been doped, that is,

into which dopant atoms has been introduced, giving it different electrical

properties than the intrinsic semiconductor.

Semiconductor doping is the process that changes an intrinsic

semiconductor to an extrinsic semiconductor.

During doping, impurity atoms are introduced to an intrinsic semiconductor.

N-type doping: doping pure silicon with group V elements such as

phosphorus, extra valence electrons are added and become unbonded from

individual atoms, which allows the compound to be electrically conductive.The n-type dopant is said to behave as an electron donor.

P-type doping: doping with group III elements, such as boron, which are

missing the fourth valence electron and create "broken bonds", or holes, in the

silicon lattice.

The p-type dopant is an acceptor.


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N-Type Doping


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Energy band diagram of N-Type

Semiconductor

Donor energy state

Donor being ionized


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P-Type Doping


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Energy band diagram of P-Type

Semiconductor

Acceptor energy state

Acceptor being ionized


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Fermi-energy levels in Extrinsic

Semiconductors

N-type semiconductor (donors added) P-type semiconductor (acceptors added)


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Fermi-energy levels in Extrinsic

Semiconductors

Adding dopant atoms to a semiconductor will change Fermi energy, and thus

change the electron and hole distributions

For N-type semiconductor, , EF>EFi, n0> p0

electrons are majority carrier and holes are minority carrierFor P-type semiconductor, EF


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Electron and Hole Concentrations in

Extrinsic Semiconductor

Equilibrium

condition


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Degenerate and Nondegenerate Semiconductors

In n-type semiconductor,

if EF >Ec then n0>Nc degenerate n-type semiconductor

if EF


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Ionization of Donors and Acceptors

N-type semiconductor

nd : concentration of electrons occupying the donor states

Nd: concentration of donor atoms (n-type doping density)

N+d: concentration of ionized donors

P-type semiconductor

pa: concentration of holes in the acceptor statesNa: concentration of acceptor atoms (p-type doping density)

N-a: concentration of ionized acceptors


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Partial Ionization Case

gD

= 2 for Si, GaAs, Ge and

most semiconductors

For 1017cm-3 P in Si:

N+d=0.94 Nd

gA = 4 for Si, GaAs, Ge and mostsemiconductors.

For 1014 cm-3 B in Si:

N-a = 0.9998 NaFor 1017 cm-3 B in Si:

N- a = 0.88 Na


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Complete Ionization

At room temperature, for a typical doping density of 1016 cm-3 , for n-type

semiconductor, almost all donor impurity atoms are ionized and have donated

an electron to the conduction band, i.e.,

N+d N

dfor p-type semiconductor, each acceptor atom has accepted an electron

from the valence band and a hole is created in the valence band for each

acceptor atom, i.e.,N-a Na


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Charge Neutrality

0 0[( ) ( )] 0a dq p N N n +

+ =

0 0( ) ( ) 0a dp N N n +

+ =

In thermal equilibrium, the semiconductor crystal is electrically neutral.

Electrons and holes are distributed among various energy states, but the net

charge density is zero.

anda a dN N N N +

0 0( ) ( ) 0a dp N N n + =


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Equilibrium Carrier Concentrations for ExtrinsicSemiconductors

0 0( ) ( ) 0a dp N N n + =2

0

0

( ) ( ) 0ia d

nN N n

n + =

2 20 ( ) 0d a in n N N n =

2 2

0

2 2

( )d a d ai

N N N Nn n

= + +

2 2

02 2

( )a d a d iN N N N

p n

= + +

and for P-type semiconductor

For N-type semiconductor


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Position of Fermi Energy in ExtrinsicSemiconductors

N-type semiconductor

P-type semiconductor


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Variation of Fermi-Energy with DopingConcentration


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Variation of Fermi-Energy withTemperature

4- the semiconductor in equilibrium

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