Post on 19-Mar-2022
Lundstrom ECE 305 S16
ECE-305: Spring 2016
Intgroduction to
PN Junctions I:
Professor Mark Lundstrom Electrical and Computer Engineering
Purdue University, West Lafayette, IN USA lundstro@purdue.edu
2/16/16
Pierret, Semiconductor Device Fundamentals (SDF) pp. 195-209
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2 Lundstrom ECE 305 S16
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ECE 305: Spring 2016: Exam 2
Out of 75 points:
Lundstrom ECE-305 S15 3
N: 22 Mean: 74.8% (56.1/75) SD: 17.5% Min: 26.7% Max: 96% Median: 80.7% (60.5/75)
20 30 40 50 60 70 80 90 1000
1
2
3
4
5
6
7
8
9
10
Count
E X AM 2 P erc ent %
How to succeed in ECE 305
Lundstrom ECE-305 S15 4
1) Do the assigned reading before class.
2) Listen to lecture, ask questions.
3) Review the lecture notes and reading afterwards.
4) Work the HW problems, then look at solutions.
5) Ask questions.
https://www.edx.org
NP junction (equilibrium)
5
N P
p0 ! NA
ρ ! 0 n0 ! ND
ρ ! 0
Lundstrom ECE 305 S16
“the semiconductor equations”
6
∂ p∂t
= −∇i
!Jpq
⎛
⎝⎜⎞
⎠⎟+Gp − Rp
∂n∂t
= −∇i!Jn−q
⎛⎝⎜
⎞⎠⎟+Gn − Rn
0 = −∇i ε
!E( ) + ρ
Three equations in three unknowns:
p!r( ), n !r( ), V !r( )
ρ = q p − n + N D
+ − N A−( )
!
E !r( ) = ∇V !r( )Lundstrom ECE 305 S16
equilibrium
NP junction
7
N P
p0 ! NA
ρ ! 0 n0 ! ND
ρ ! 0
transition region
Find: electric field, electrostatic potential, n(x), p(x), rho(x)
xp−xn 0
+
-
EVL > VR
ρ < 0NA
−
ρ > 0ND
+
Lundstrom ECE 305 S16
energy band approach
8
EC
EVEF
Ei V = 0
EC
EV
Ei
1) Fermi-level must be constant in equilibrium. 2) Positive electrostatic potentials lower the electron energy 3) Left side must develop a positive potential, Vbi.
EF
qVbiV = Vbi
Lundstrom ECE 305 S16
eq. energy band diagram
9
EFEF
1) Begin with EF 2) Draw the E-bands where you know the carrier density 3) Electrostatic potential by flipping E-band upside down. 4) E-field from slope 5) n(x), p(x) from the E-band diagram 6) rho(x) from n(x) and p(x) 7) diffusion current from (5) or from (6)
EC x( ) = EC− ref − qV x( )
E x( ) = 1
qdEC x( ) dx
Lundstrom ECE 305 S16
energy band diagram
10
EF
EC
EV
x
E
Ei
x = xpx = 0x = −xnLundstrom ECE 305 S16
“read” the e-band diagram
11
1) Electrostatic potential vs. position
2) Electric field vs. position
3) Electron and hole densities vs. position
4) Space-charge density vs. position
Lundstrom ECE 305 S16
electrostatics: V(x)
12
V
x
N P
xp−xn
Vbi
Lundstrom ECE 305 S16
NP junction
13
N P
p0 ! NA
ρ ! 0 n0 ! ND
ρ ! 0
transition region
Find: electric field, electrostatic potential, n(x), p(x), rho(x)
xp−xn 0
+
-
EVL > VR
ρ < 0NA
−
ρ > 0ND
+
Lundstrom ECE 305 S16
electrostatics: E (x)
14
E
xN P xp−xn
Lundstrom ECE 305 S16
NP junction
15
N P
p0 ! NA
ρ ! 0 n0 ! ND
ρ ! 0
transition region
Find: electric field, electrostatic potential, n(x), p(x), rho(x)
xp−xn 0
+
-
EVL > VR
ρ < 0NA
−
ρ > 0ND
+
Lundstrom ECE 305 S16
carrier densities vs. x
16
log10 n x( ), log10 p x( )
xN P xp−xn
p0P = NA
p0N = ni2 ND
n0N = ND
n0 p = ni2 NA
n0N << ND p0P << NA
Lundstrom ECE 305 S16
NP junction
17
N P
p0 ! NA
ρ ! 0 n0 ! ND
ρ ! 0
transition region
Find: electric field, electrostatic potential, n(x), p(x), rho(x)
xp−xn 0
+
-
EVL > VR
ρ < 0NA
−
ρ > 0ND
+
Lundstrom ECE 305 S16
electrostatics: rho(x)
18
ρ
x
N P
xp−xn
qND
−qNA
Lundstrom ECE 305 S16
NP junction
19
N P
p0 ! NA
ρ ! 0 n0 ! ND
ρ ! 0
transition region
Find: electric field, electrostatic potential, n(x), p(x), rho(x)
xp−xn 0
+
-
EVL > VR
ρ < 0NA
−
ρ > 0ND
+
Lundstrom ECE 305 S16
the built-in potential
20
EC
EVEFP
Ei V = 0
EC
EV
Ei
EFN
qVbiV = Vbi
n0 = nieEFN −Ei( ) kBT p0 = nie
Ei−EFP( ) kBT
n0p0 = NDNA = ni2e EFN −EFP( ) kBT = eqVbi kBT
Vbi =kBTqln NDNA
ni2
⎛⎝⎜
⎞⎠⎟
NP junction electrostatics
21
How do we calculate rho(x), E(x), and V(x)?
Lundstrom ECE 305 S16