SolidStatePhysics
Thebasicsofsemiconductors
ShayanHemma7yan
April4th,2016
Thebasicsofsolidstatephysics:
Thebasicproper7esofsemiconductors
Semiconductors'conductanceis
betweenthatofconductorsand
insulators.
Conduc7vityofsemiconductors
unlikemetalsincreasesasa
func7onoftemperature
Themostimportantsemiconductors
Monocrystallineorsingle-crystalmaterials:
• Semiconductorelements:Si(silicon),Ge(germanium)
Theyareusedinintegratedcircuitsandsemiconduc7ng
devices.
• Compoundsemiconductors:GaAs(galliumarsenide),
GaAsP(galliumarsenidephosphide)
TheyareusedtocreateLEDs.
Amorphoussemiconductors:
• amorphousSimainly
TFTs,solarcellsaremadeofthem.
• Organicsemiconductors:OLEDs(OrganicLEDs)
Thebandstructureofmaterials:
Recall:Semiconductors,
§  Weassumeµfarfrombandedges,|µ-εc,v|>>kT.
§  Carriersactasclassicalgas,occupa:onfunc:on<<1.
gc(ε)
gv(ε)
Electrons(exaggerated)
Holes
εv
⎡ VN 2m*m* m* ⎤
gc (ε ) = ⎢ m 3 12 2 3 ⎥ ε − εc
!π
⎢⎣
⎥⎦
εc
−1
⎡
⎛ ε −µ ⎞
ε −µ ⎤
⎟⎟
f (ε ) = ⎢exp
+ 1⎥ ≈ exp⎜⎜ −
k BT
⎣
⎦
⎝ k BT ⎠
Intrinsicdensi+es:
Generalcase,
independentofµ
n = N c (T )e − (ε c − µ ) / kT
np = N c (T ) Pv (T )e
p = Pv (T )e − ( µ −ε v ) / kT
− ( ε g ) / kT
Silicon,RTNcPv=(2.8×1.0)×1038cm-6
§  Intrinsic:ultra-pure(noimpurityeffects)
§  n=pbychargeconservaIon.
§  µnearmid-gapposiIon.
ni = N c (T ) Pv (T )e
− ( ε g ) / 2 kT
Silicon,RTni=1.5×1010cm-3
Lawofmassac*on:
Independentofµ
np = N c (T ) Pv (T )e
Silicon,RTni=1.5×1010cm-3
So,e.g.ifn=1.5×1015cm-3(“n-type”)
thenp=1.5×105cm-3
− ( ε g ) / kT
≡ ni2
Donors/acceptors
AssumeionizedintoC.B.
Groundstate:localized“Bohrorbit”,composedofCBstates.
(Resultshowsthisisconsistent)
2
e
U=
4πε o r ⋅ κ
!
r = * κ ≈ 60ao
mc e
silicon
mc* / m 1 20meV
En = 13.6eV
≈
2
2
2
n
κ n
N-Pdoping!
Donors/acceptors:
Typical:allionized
overconsiderableTrange
(concentra6onnottoobig)
µ
T