Carrier Action: I - nanoHUBCarrierActionI_S15.pdfCarrier Action: I Professor Mark Lundstrom...
10
ECE-305: Spring 2015 Carrier Action: I Professor Mark Lundstrom Electrical and Computer Engineering Purdue University, West Lafayette, IN USA [email protected] 2/2/15 Pierret, Semiconductor Device Fundamentals (SDF) pp. 74-89 carrier concentration review Fig. 2.22 from R.F. Pierret, Semiconductor Device Fundamentals Freeze out Extrinsic Intrinsic n i = N C N V e − E G /2 k B T n 0 = N D + = N D p 0 = n i 2 n 0
Transcript of Carrier Action: I - nanoHUBCarrierActionI_S15.pdfCarrier Action: I Professor Mark Lundstrom...
Lundstrom ECE 305 S15
ECE-305: Spring 2015
Carrier Action: I
Professor Mark Lundstrom Electrical and Computer Engineering
Purdue University, West Lafayette, IN USA [email protected]
2/2/15
Pierret, Semiconductor Device Fundamentals (SDF) pp. 74-89
carrier concentration review
2 Fig. 2.22 from R.F. Pierret, Semiconductor Device Fundamentals
Freeze out
Extrinsic
Intrinsic ni = NCNV e−EG /2kBT
n0 = N D+ = N D
p0 = ni2 n0
key equations in equilibrium
3
p0 = NVeEV −EF( ) kBT
NV = 2mp*kBT( )2π!2
⎡
⎣⎢⎢
⎤
⎦⎥⎥
3/2
n0 = NCeEF−EC( ) kBT
NC = 2
mn*kBT( )2π!2
⎡
⎣⎢⎢
⎤
⎦⎥⎥
3/2
n0 = ni eEF−Ei( ) kBT
p0 = nieEi−EF( ) kBT
n0p0 = ni2
ni = NCNV e−EG /2kBT
ni = 1.00 ×1010 cm-3
p − n + ND+ − NA
− = 0
f0 E( ) = 11+ e E−EF( ) kBT
Question: Why does np = ni2 ?
4
n0 = N D+ = N D
p0 = ni2 n0
n0 = ni eEF−Ei( ) kBT
p0 = nieEi−EF( ) kBT
Why is np = ni2 ?
5
E
x
EC
EV
Ei
G T( ) cm-3-s-1
G = R
R = Cnp
np = GC
= ni2
Lundstrom ECE 305 S15 6
outline
1. Current (drift)
2. Mobility, resistivity, etc.
Lundstrom ECE 305 S15 7
outline
1. Current (drift)
2. Mobility, resistivity, etc.
semiconductor in equilibrium
8
uniform n-type semiconductor
Lcross-sectional
area, A
“ideal” contacts
KE =
32
kBT
υ 2 = υrms =
3kBTmn
*
KE =
12
mn* υ 2
υrms ≈ 107 cm/s
current flow
9
uniform n-type semiconductor
Lcross-sectional
area, A
“ideal” contacts
−V +
I
1) random walk with a small bias from left to right
2) assume that electrons “drift” to the right at an average velocity, υd
3) what is I ?
drift current and velocity
10
I = −Q tt
Q = −qnAL
tt = L υd
I = nqυd An-type semiconductor
Lcross-sectional
area, A
“ideal” contacts
−V +
I
υd = −µnE x Jnx = −nqυdx A/cm2
J px = pqυdx A/cm2
x
velocity and electric field
11
υdn = −µnE
µn =
qτmn
*
⎛
⎝⎜⎞
⎠⎟cm2 V-s
υdp = +µ pE
µ p =
qτmp
*
⎛
⎝⎜
⎞
⎠⎟ cm2 V-s
“high-field transport” υdn
E
υdn = µn E
“low-field” or “near-equilibrium” or “linear” transport
velocity vs. field
12
from R.F. Pierret, Semiconductor Device Fundamentals, Fig. 3.4
drift current
13
υdn = −µnE
υdp = +µ pE
Jnx = −nqυdx A/cm2
J px = pqυdx A/cm2
Jnx = nqµnE x A/cm2
J px = pqµ pE x A/cm2
mobility vs. doping
14
from R.F. Pierret, Semiconductor Device Fundamentals, Fig. 3.5 (a)
µ = qτ
m*
⎛
⎝⎜⎞
⎠⎟cm2 V-s
mobility vs. temperature
15
µn
increasing mobility suggests the presence of charged impurity scattering
decreasing mobility suggests the presence of lattice scattering.
µn ∝T 3/ 2
µn ∝T −3/ 2
T µ = qτ
m*
⎛
⎝⎜⎞
⎠⎟cm2 V-s
re-cap
16
Jn = −nqυd A/cm2
J p = + pqυd A/cm2
υdn = −µnE
υdp = +µ pE
n-type semiconductor
L
−V +
I
υd = −µnE x
x
E = − dV
dxV/cm
E = −V
LV/cm
current, conductivity, resistivity
17
Jnx = nqµnE x A/cm2
J px = pqµ pE x A/cm2
Jnx =σ nE x A/cm2
σ n = nqµn units?( )
σ p = pqµ p
J px =σ pE x A/cm2
E x =
1σ
Jx = ρJx V/cm
Jx = Jnx + J px = σ n +σ p( )E x =σE x A/cm2
Jx =σE x A/cm2
ρ = 1
σ= 1σ n +σ p
= 1nqµn + pqµ p
Ω-cm
resistivity vs. doping density
18 from R.F. Pierret, Semiconductor Device Fundamentals, Fig. 3.8
ρ = 1
nqµn + pqµ p
Ω-cm
resistance
19
n-type semiconductor
L
−V +
I
υd = −µnE x
Jn = σ nE A/cm2
I = −AJn =σ n AE Amps
I = σ n AV
L
I = σ n
AL
⎛⎝⎜
⎞⎠⎟
V = GV =1R
V
R = ρn
LA
Lundstrom ECE 305 S15 20
outline
1. Current (drift)
2. Mobility, resistivity, etc.
✓
✓
