반도체 기초 이론 vol. i semiconductor fundamentals by r. f. pierret modular series on solid...
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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