EE105 – Fall 2015
Microelectronic Devices and Circuits
Prof. Ming C. Wu
[email protected]
511 Sutardja Dai Hall (SDH)
5-1
Silicon: Group IV Element
P-type
dopant
N-type
dopant
5-2
1
Silicon
Crystalline Structure
(Diamond Cubic)
Schematic Two-Dimensional
Representation
At 0 Kelvin, all electrons are
“locked” in covalent bonds
à Behave like insulator
5-3
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
5-4
2
Intrinsic Semiconductor
Intrinsic semiconductor
n = p = ni
n : electron concentration [cm −3 ]
p : hole concentration [cm −3 ]
3
ni = BT 2 e
−
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/K
At room temperature (T = 300K )
ni = 1.5 ×1010 [cm −3 ]
Note: There are 5 ×10 22 atoms/cm −3, so the
number of free electrons and holes are very small
In general, np = ni2
5-5
N-Type Semiconductor
Electron 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 = N D (donor impurtiy concentration)
ni2
where ni = 1.5 ×1010 [cm −3 ]
ND
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
pn =
e.g., N D = 1017 cm −3, nn = 1017, pn = 2.2 ×10 3
Electrons are "majority" carriers,
holes are "minority" carriers
5-6
3
P-Type Semiconductor
Hole 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"
p p = N A (acceptor impurtiy concentration)
np =
ni2
where ni = 1.5 ×1010 [cm −3 ]
NA
The subscript p refers to p-type semiconductor
(p stands for "positive", referring to the
charge carried by holes)
In p-type semiconductor, p p >> ni >> n p
e.g., N A = 1017 cm −3, p p = 1017, n p = 2.2 ×10 3
Holes are "majority" carriers,
electrons are "minority" carriers
5-7
Current in Semiconductor (1):
Drift Current
When an electrical field, E, is applied,
holes moves in the direction of E, while
electrons move opposite to E :
"$v p−drift = µ p E, µ p : hole mobility
#
%$vn−drift = −µ n E, µ n : electron mobility
In intrinsic Si, µ n = 1350 cm 2 / V ⋅ s
µ p = 480 cm 2 / V ⋅ s
(Note: µ n ≈ 2.5µ p )
Current density, J [A/cm 2 ]
J = qpv p−drift + qnvn−drift = q( pµ p + nµ n )E = σ E
where σ = q( pµ p + nµ n ) is conductivity [S/cm]
Resistivity ρ =
1
[Ω-cm]
σ
5-8
4
Current in Semiconductor (2):
Diffusion Current
Hole Diffusion
Diffusion: particles move from high to
low concentrations. As electrons and holes
diffuse, currents flow because they carry charges
dp(x)
dx
dn(x)
dn(x)
J n−diff = −(−q)Dn
=qDn
dx
dx
where Dp and Dn are hole and electron diffusion
J p−diff = −qDp
Electron Diffusion
coefficients [cm 2 /s]
In instrinsic Si, Dp = 12cm 2 /s, Dn = 35cm 2 /s
Total diffusion current density, J diff [A/cm 2 ]
J diff = −qDp
dp(x)
dn(x)
+ qDn
dx
dx
5-9
Einstein Relationship
Dn Dn
kT
=
= VT =
µn µn
q
VT : Thermal voltage
At room temperature, VT = 26 mV
Proof: Total electron current:
J n = J n−drift + J n−diff = qn(x)µ n E + qDn
E =−
dφ
,
dx
n(x) = n0 e
dn(x)
dx
φ : potential
−
(−qφ )
kT
φ
= n0 e VT : Boltzmann distribution
In equilibrium, no net current flow
dn(x)
⇒ qn(x)µ n E + qDn
=0
dx
dn(x) dφ
n(x)µ n E + Dn
=0
dφ dx
#1
&
n(x)µ n E + Dn % n(x)( (−E ) = 0
$ VT
'
Dn
= VT
µn
5-10
5