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EE105Microelectronic Devices and Circuits:
Basic Semiconductors
Prof. Ming C. Wu
511 Sutardja Dai Hall (SDH)
Excellent Reference for Module 2:Chenming Hu, Modern Semiconductor Devices for Integrated Circuits, 2010
downloadable from:https://people.eecs.berkeley.edu/~hu/Book-Chapters-and-Lecture-Slides-download.html
EE 130
2
Silicon: Group IV Element
P-typedopant
N-typedopant
o
088
3
Resistivity of Typical Materials
• Conductors– Copper: 1.7 x 10-6 Ω-cm (or 1.7 x 10-8 Ω-m)– Aluminum: 2.8 x 10-6 Ω-cm
• Insulators– SiO2: 1018 Ω-cm
• Semiconductor– Silicon: 10-3 to 103 Ω-cm – A wide range of resistivity, – Can be controlled by “doping” of impurities or electrical
bias
o O
1024
106
e
4
From Atoms to Crystals
Decreasing atomic separation
Ener
gy
p
s
isolated atoms lattice spacing
valenceband
conductionband Pauli exclusion
principle
• Energy states of Si atom (a) expand into energy bands of Si crystal (b).
• The lower bands are filled and higher bands are empty in a semiconductor.
• The highest filled band is the valence band.• The lowest empty band is the conduction band
(a) (b)
datoe
Energy emptys
Bande a
t.IEp hybrids Ps full
A
D
5
Energy Band Diagram of Various MaterialsBoltzmannDistribution offc EET d
krs BoltzmannConseolton LBT 2GmeVFonducting Iop
0 O Yalene 4 11 14 4 VBsand
BandEg BandgapEnergy e HEY
tongue 1eV 1.6 1019 J
0180 a
ySc Eg Inter
nne EIt e F3z eaonco.ro liquid elects
or
6
SiliconCrystalline Structure
(Diamond Cubic)Schematic Two-Dimensional
Representation
At 0 Kelvin, all electrons are “locked” in covalent bondsà Behave like insulator
Simplifiedz dillustration
Sony
4 0 0 00
Topofte
7
Electrons and Holes
• At room temperature, thermal energy breaks some covalent bonds, creating free electrons and “holes”
• Hole: empty space left by electron– Hole “moves” as
adjacent electron move into its space
– Treat hole like a positively charged particle
f
O
P OO E tfBound
ThermalEnergy hrs1 26MeV
keeptrack of free electrons
free hole
8
Intrinsic SemiconductorIntrinsic semiconductor n = p = ni n : electron concentration [cm−3]p : hole concentration [cm−3]
ni = BT32e
−Eg
2kT : instrinsic carrier concentration B : material dependent constant T : temperature in Kelvin Eg : bandgap energy (=1.12 eV for Si)
k : Boltzmann's constant = 8.62x10−5 eV/KAt room temperature (T = 300K )ni =1.5×1010 [cm−3]Note: There are 5×1022 atoms/cm−3, so the number of free electrons and holes are very smallIn general, np = ni
2
electronfans conc a hole conc Hand
D00 C
MassAction LawIn semiconductornxp nexn nE
2 1020
9
N-Type SemiconductorElectron concentration can begreatly increased by replacing some Si atoms with P (phosphorus) or As (Arsenic), which have 5 shell electrons (one more than Si).P or As are called "donors" nn = ND (donor impurtiy concentration)
pn =ni
2
ND
where ni =1.5×1010 [cm−3]
Subscript n refers to n-type semiconductor(n stands for "negative", referring to the charge carried by electrons)In n-type semiconductor, nn >> ni >> pn e.g., ND =1017 cm−3, nn =1017, pn = 2.2×103
Electrons are "majority" carriers, holes are "minority" carriers
eNegativeto
o OGroupseg As.P
nn ND DonorConc
nnxpn ne 2 10 D
pn nI Y Izxw3n n ND
Pn Rn
10
P-Type SemiconductorHole concentration can begreatly increased by replacing some Si atoms with B (boron), which has 3 shell electrons (one less than Si).B is called "acceptors" pp = NA (acceptor impurtiy concentration)
np =ni
2
NA
where ni =1.5×1010 [cm−3]
The subscript p refers to p-type semiconductor(p stands for "positive", referring to the charge carried by holes)In p-type semiconductor, pp >> ni >> np
e.g., NA =1017 cm−3, pp =1017,np = 2.2×103
Holes are "majority" carriers, electrons are "minority" carriers
TossitiveHole f
D
O
Bubbleg
11
How Electron (or Hole) Move
No Electric Field
!∗# = %&'
# = %&'!∗ ∝ &
# = )&
) = %'!∗
M kBT 26meV26 153 1,6 151958P Forcetime
mean freetimeE E
T momentum
9 10348 EIFFEL 7vz 5 2012 mass of X
0
104 109 Ot
Es cIT
drifevelocity n
scattering LE mobility
ImpurityThermal electric fieldenergyoff lattice Phonon
12
Mobility of Common Semiconductors
IT IT
electronhole D
Un Up ftype n typetransistor
InAs
tr
13
Mobility vs Dopant Concentration
E
mgL
DAIEeor Don or
14
Current: Movement of Charged Particles (Electrons and Holes)
I _J Areap Ecurrent densityAmp CFJp PEf Vp FVpf_
p Vp dpE
pholevelocity
A Jn nqVnvolume1 1 9 Vn µnE
15
Current in Semiconductor (1):Drift Current
When an electrical field, E, is applied,holes moves in the direction of E, whileelectrons move opposite to E :vp−drift = µpE, µp : hole mobilityvn−drift = −µnE, µn : electron mobility
"#$
%$
In intrinsic Si, µn =1350 cm2 / V ⋅sµp = 480 cm2 / V ⋅s (Note: µn ≈ 2.5µp )
Current density, J [A/cm2 ]J = qpvp−drift + qnvn−drift = q(pµp + nµn )E =σEwhere σ = q(pµp + nµn ) is conductivity [S/cm]
Resistivity ρ= 1σ
[Ω-cm]
R f deeron 8hole tf
Jn C f n C Mnf
nqMnEI zV E 4 F N type n
P type pt o Ej gt.fr
16
Resistivity vs Dopant Concentration
Ip I
p D Insulatingconducting f f tung
17
Current in Semiconductor (2):Diffusion Current - Holes
• If hole distribution is non-uniform, holes will move from high to low concentration areas
• Flux ∝ - [conc. gradient]
• Current flows since holes carry charge:
"#$%&'' = )*# −,- .,.*#: hole diffusion coef. [cm2/s]
• Note: since hole carries positive charge, hole diffusion and hole current are in the same direction
Hole Diffusion
18
Current in Semiconductor (2):Diffusion Current - Electrons
• Similarly, electron diffusion also causes current to flow, but in opposite direction since electron carries negative charge
!"#$%&& = (−*)," −-. /-/
= *,"-. /-/
,": electron diffusion coef. [cm2/s]
!"#$%&& : [A/cm2]
• In Si, – Dn = 35 cm2/s – Dp = 12 cm2/s
Electron Diffusion
19
Einstein Relationship
Dn
µn
=Dn
µn
=VT =kTq
VT : Thermal voltageAt room temperature, VT = 26 mV
Proof: Total electron current:
Jn = Jn−drift + Jn−diff = qn(x)µnE + qDndn(x)dx
E = − dφdx
, φ : potential
n(x) = n0e−
(−qφ )kT = n0e
φVT : Boltzmann distribution
In equilibrium, no net current flow
⇒ qn(x)µnE + qDndn(x)dx
= 0
n(x)µnE +Dndn(x)dφ
dφdx
= 0
n(x)µnE +Dn1VTn(x)
#
$%
&
'( −E( ) = 0
Dn
µn
=VT
