Lundstrom ECE 305 S16
ECE-305: Spring 2016
M-S diodes: The essentials
Professor Mark Lundstrom
Electrical and Computer Engineering Purdue University, West Lafayette, IN USA
3/22/16
Pierret, Semiconductor Device Fundamentals (SDF) pp. 477-501
two types of MS diodes
2
semiconductor or device
V
I
rectifying V
I
ohmic
Lundstrom ECE 305 S16
E-band diagrams
3
EC
EV
EFN
metal
EFM
E0
ΦMχ
EG
V = 0 VLundstrom ECE 305 S16
Metal WF > semiconductor WF
ΦS
E-band diagrams
4
EC
EVEFP
metal
EFM
E0
ΦMχ
EG
V = 0 VLundstrom ECE 305 S16
Metal WF < semiconductor WF
ΦS
Built-in potential: PN junctions
5 Lundstrom ECE 305 S16
EC
EVEF
Ei V = 0
EC
EV
Ei
EF
qVbiV = Vbi
Potential on the left must be larger than the potential on the right.
How much larger? qVbi = EFN − EFP = kBT lnNAND
ni2
⎛⎝⎜
⎞⎠⎟
Built-in potential: MS junctions
6 Lundstrom ECE 305 S16
qVbi = EFM − EFS
EC
EVEFP
Ei
metal
EFM
E0
ΦM ΦS
qVbi = ΦS −ΦM( )
ΦM is a known material parameter
Built-in potential: MS vs. PN junctions
7 Lundstrom ECE 305 S16
EC
EVEFP
Ei
metal
EFM
E0
ΦM ΦSTypically, Vbi for an MS diode is less than Vbi for a PN diode
Electrostatics
8 Lundstrom ECE 305 S16
EC
EVEF
Ei
metal
EF
ΦBP
qVbi
W ρ
x
metal P
W
ρ = −qNA
DA Results
9 Lundstrom ECE 305 S16
E x( )
x
P
E 0( )
W
W = 2KSε0qNA
Vbi⎡
⎣⎢
⎤
⎦⎥
1/2
E 0( ) = 2qNAVbi
Ksε0
dEdx
=ρ x( )KSε0
Vbi = E x( )∫ dx
metal
12E 0( )W = Vbi
dEdx
= − qNA
KSε0
→E 0( ) = qNA
KSε0W
MS vs. PN electrostatics
10 Lundstrom ECE 305 S16
W = 2KSε0q
NA + ND
NDNA
⎛⎝⎜
⎞⎠⎟Vbi
⎡
⎣⎢
⎤
⎦⎥
1/2
→ 2KSε0qNA
Vbi⎡
⎣⎢
⎤
⎦⎥
1/2
E 0( ) = 2Vbi
W
xn =NA
NA + ND
W ≈ 0
xp =ND
NA + ND
W ≈W
N P
ND = 1018
depletion region xp−xn0
E x( )
Vbi =kBTqln NDNA
ni2
⎛⎝⎜
⎞⎠⎟
⎛
⎝⎜⎞
⎠⎟
W NA = 1015
Vbi =ΦM −ΦS( )
q
Metal wf > N-type semconductor wf
11
EC
EV
EFN
metal
EFM
E0
ΦMχ
EG
V = 0 VLundstrom ECE 305 S16
Equilibrium band diagram
12
EC
EV
EF
Ei
metal
EF
qVbiΦBP = ΦM − χ
Lundstrom ECE 305 S16
IV characteristics
13 Lundstrom ECE 305 S16
EC
EV
FNEi
metal
EF
q Vbi −VA( )ΦBN = ΦM − χ
J ≈ JS→M ∝ e−q Vbi−VA( ) kBT = e−qVbi kBT eqVA kBT
JS→M
J = J0eqVA kBT J0 ∝ e
−qVbi kBT
IV characteristics
14 Lundstrom ECE 305 S16
J0 = A*T 2e−ΦBP kBT
A* = 4πqmn*kB
2
h3
J = J0 eqVA /kBT −1( ) A = 4πqm0kB
2
h3= 120 A
cm2-K2
A* = mn*
m0
qVbi = ΦBP − EFS − EV( )bulk
qVbi = ΦS −ΦM( )
ΦBP = χ + EG − ΦM
IV characteristics: MS vs. PN
15
VA
J = J0 eqVA /kBT −1( )
I mA( )
0.6 V
Si
0.3V
MS
J0 = A*T 2e−ΦBN kBT
J0 MS( ) >> J0 NP( )
Strongly controlled by SB height.
two types of MS diodes
16
semiconductor or device
V
I
rectifying V
I
ohmic
Lundstrom ECE 305 S16
Ohmic contacts
17
EC
EV
EF
Ei
metal
EF
ΦBN qVbi
W
Dope the semiconductor very heavily to promote quantum mechanical tunneling.
W = 2KSε0qND
Vbi⎡
⎣⎢
⎤
⎦⎥
1/2
ND >1020cm-3
Small signal model
18 Lundstrom ECE 305 S16
VDC
υ t( )
R1
ID + i t( ) VA +υa
1) Compute the DC bias current 2) Replace the diode with the s.s. a.c. model and do the
a.c. analysis.
Small signal model
19 Lundstrom ECE 305 S16
υ t( )
R1
i t( )
Gd
CJ VA( ) = KSε0AW VA( )
CJ
Gd =dIDdVD
No diffusion capacitance!
summary
20 Lundstrom ECE 305 S16
1) M-S junctions can be diodes or ohmic contacts
2) M-S diodes typically have much high saturation current densities (much lower turn on voltages) than PN junctions.
3) The Schottky barrier height, ΦB, is a key parameter.
4) Schottky diodes are majority carrier devices – no diffusion capacitance due to minority carriers. (Leads to high speed).
