반도체 기초 이론Vol. I Semiconductor Fundamentals

by R. F. PierretModular Series on Solid State Devices

서강대학교 기계공학과최 범규

반도체 재료• 원소

– Si, Ge

• III-V 화합물– GaAs, GaP, AlP, AlAs, etc.

• II-VI 화합물 반도체– ZnO, ZnS, ZnSe, CdS, etc.

• 합금– AlxGa1-xAs, GaAs1-xPx, etc.

주기율표와 고체의 분류• 주기율표 • 고체의 분류

Semiconductor Models• Schematic representation of an isolated Si atom

Semiconductor Models

• The bonding model • Freeing of an electron

Energy Band Model• Conceptual development of the energy band model

Visualization of carriers

• The electron • The hole

Material Classification

Manipulation of Carrier nos.-Doping(1)

• Carrier numbers in intrinsic material– n = no. of electrons/cm3

– p = no. of holes/cm3

• Equilibrium condition– No external voltages, magnetic fields, stresses, o

r other perturbing forces

– n = p = ni

– ni = 1×1010/cm3 in Si at room temperature

Manipulation of Carrier nos.-Doping(2)• Common Si dopants. Arrows indicate the most widely employed dopan

ts

•Visulization of a donor and acceptor in the bonding model

Visualization of carriers in the energy band model

• Donor

• Acceptor

Density of States

• How many states at any given energy in the bands

• gc(E)dE represents the no. of conduction band states/cm3 lying in the energy range between E and E+dE

The Fermi Function• The probability that an available state at an energy E will b

e occupied by an electron– EF = Fermi energy or Fermi level

– k = Boltzmann constant (8.62E-5 eV/K)

– T = temperature in Kelvin (K)kTEEe

Ef/)( F1

1)(

Distribution of Carriers• n type

• p type

Carrier Concentrations

• Formulas for n and p • Nondegenerate semiconductor

Etop

E cc

dEEfEgn )()(

Ev

E vbottom

dEEfEgp )(1)(

kTEEi

iFenn / kTEE

iFienp /

2innp

Carrier Concentration Calculations

• Charge Neutrality Relationship– charge/cm3

• Formulas for n and p

0 AD qNqNqnqp

0 AD NNnp

0 AD NNnp

3

3

atoms/cmdonor ionized of no. total:

atoms/cmdonor ionized ofnumber :

D

D

N

N

2/1

22

22

iADAD n

NNNNn

2/1

22

22

iDADA n

NNNNp

Special cases for semiconductors

• Intrinsic semiconductor (NA= 0, ND= 0)

• Doped semiconductor with

• Doped semiconductor with

• Compensated semicond.– Intrinsic-like material by ma

king ND - NA = 0

– When NA and ND are comparable & nonzero, the material is “compensated”.

iDAD nNNN

ADi NNn

inpn

Di

D

Nnp

Nn

/2

inpn

Carrier Action• The three primary action

– drift: charged-particle motion in response to an applied electric field

– diffusion: process whereby particles tend to spread out as a result of their difference of concentrations

– recombination-generation: • Generation is a process whereby carriers are created.

• Recombination is a process whereby carriers are destroyed.

Drift Current

• Hole drift current

– vd: drift velocity

• Hole mobility, p, is the proportional constant between vd and

• Current density

AqpvI dP|drift pq pP|driftJ

pd v

nq n|driftNJ

Diffusion Currents• Diffusion coefficients

– DP, DN are proportional constants

• Total carrier currents

• Visualization of diffusion– hole

– electron

pqD PP|diffJ

nqD N|diffNJ

pqDpq PpP -εμJ

nqDnq NnN εμJ

Recombination-generation

• Direct thermal R-G • Indirect thermal R-G– bonding model

– energy band model