lecture 13: part i: mos small-signal models
DESCRIPTION
Lecture 13: Part I: MOS Small-Signal Models. Prof. Niknejad. Lecture Outline. MOS Small-Signal Model (4.6) Diode Currents in forward and reverse bias (6.1-6.3). Total Small Signal Current. Trans conductance. C onductance. Role of the Substrate Potential. - PowerPoint PPT PresentationTRANSCRIPT
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 13
Lecture 13:
Part I: MOS Small-Signal Models
Prof. Niknejad
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 13 Prof. A. Niknejad
Lecture Outline
MOS Small-Signal Model (4.6) Diode Currents in forward and
reverse bias (6.1-6.3)
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 13 Prof. A. Niknejad
Total Small Signal Current
( )DS DS dsi t I i
DS DSds gs ds
gs ds
i ii v v
v v
1ds m gs ds
o
i g v vr
TransconductanceConductance
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 13 Prof. A. Niknejad
Role of the Substrate Potential
Need not be the source potential, but VB < VS
Effect: changes threshold voltage, which changes the drain current … substrate acts like a “backgate”
QBS
D
QBS
Dmb v
i
v
ig
Q = (VGS, VDS, VBS)
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 13 Prof. A. Niknejad
Backgate Transconductance
Result:2 2
Tn mD Dmb
BS Tn BS BS pQ Q Q
V gi ig
v V v V
0 2 2T T SB p pV V V
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 13 Prof. A. Niknejad
Four-Terminal Small-Signal Model
1ds m gs mb bs ds
o
i g v g v vr
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 13 Prof. A. Niknejad
MOSFET Capacitances in Saturation
Gate-source capacitance: channel charge is not controlled by drain in saturation.
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 13 Prof. A. Niknejad
Gate-Source Capacitance Cgs
Wedge-shaped charge in saturation effective area is (2/3)WL(see H&S 4.5.4 for details)
ovoxgs CWLCC )3/2(
Overlap capacitance along source edge of gate
oxDov WCLC
(Underestimate due to fringing fields)
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 13 Prof. A. Niknejad
Gate-Drain Capacitance Cgd
Not due to change in inversion charge in channel
Overlap capacitance Cov between drain and sourceis Cgd
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 13 Prof. A. Niknejad
Junction Capacitances
Drain and source diffusions have (different) junctioncapacitances since VSB and VDB = VSB + VDS aren’t the sameComplete model (without interconnects)
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 13 Prof. A. Niknejad
P-Channel MOSFET
Measurement of –IDp versus VSD, with VSG as a parameter:
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 13 Prof. A. Niknejad
Square-Law PMOS Characteristics
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 13 Prof. A. Niknejad
Small-Signal PMOS Model
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 13 Prof. A. Niknejad
MOSFET SPICE Model
Many “levels” … we will use the square-law “Level 1” modelSee H&S 4.6 + Spice refs. on reserve for details.
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 13
Part II: Currents in PN Junctions
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 13 Prof. A. Niknejad
Diode under Thermal Equilibrium
Diffusion small since few carriers have enough energy to penetrate barrier Drift current is small since minority carriers are few and far between: Only
minority carriers generated within a diffusion length can contribute current Important Point: Minority drift current independent of barrier! Diffusion current strong (exponential) function of barrier
p-type n-type
DN AN
-
-
-
-
-
-
-
-
-
-
-
-
-
+++++++++++++
0E
biq
,p diffJ
,p driftJ
,n diffJ
,n driftJ
−
−
+
+
−
−
ThermalGeneration
Recombination Carrier with energybelow barrier height
Minority Carrier Close to Junction
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 13 Prof. A. Niknejad
Reverse Bias
Reverse Bias causes an increases barrier to diffusion
Diffusion current is reduced exponentially
Drift current does not change Net result: Small reverse current
p-type n-type
DN AN
-
-
-
-
-
-
-
+++++++
( )bi Rq V
+−
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 13 Prof. A. Niknejad
Forward Bias
Forward bias causes an exponential increase in the number of carriers with sufficient energy to penetrate barrier
Diffusion current increases exponentially
Drift current does not change Net result: Large forward current
p-type n-type
DN AN
-
-
-
-
-
-
-
+++++++
( )bi Rq V
+−
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 13 Prof. A. Niknejad
Diode I-V Curve
Diode IV relation is an exponential function
This exponential is due to the Boltzmann distribution of carriers versus
energy
For reverse bias the current saturations to the drift current due to minority
carriers
1dqV
kTd SI I e
dqV
kT
d
s
I
I
1
( )d d SI V I
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 13 Prof. A. Niknejad
Minority Carriers at Junction Edges
Minority carrier concentration at boundaries of depletion region increase as barrier lowers … the function is
)(
)(
pp
nn
xxp
xxp (minority) hole conc. on n-side of barrier
(majority) hole conc. on p-side of barrier
kTEnergyBarriere /)(
(Boltzmann’s Law)
kTVq DBe /)(
A
nn
N
xxp )(
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 13 Prof. A. Niknejad
“Law of the Junction”
Minority carrier concentrations at the edges of thedepletion region are given by:
kTVqAnn
DBeNxxp /)()(
kTVqDpp
DBeNxxn /)()(
Note 1: NA and ND are the majority carrier concentrations on the other side of the junction
Note 2: we can reduce these equations further by substituting
VD = 0 V (thermal equilibrium)Note 3: assumption that pn << ND and np << NA
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 13 Prof. A. Niknejad
Minority Carrier Concentration
The minority carrier concentration in the bulk region for forward bias is a decaying exponential due to recombination
p side n side
-Wp Wn xn -xp
0
AqV
kTnp e
0 0( ) 1A
p
xqVLkT
n n np x p p e e
0np0pn
0
AqV
kTpn e
Minority CarrierDiffusion Length
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 13 Prof. A. Niknejad
Steady-State Concentrations
Assume that none of the diffusing holes and electrons recombine get straight lines …
p side n side
-Wp Wn xn -xp
0
AqV
kTnp e
0np0pn
0
AqV
kTpn e
This also happens if the minority carrier diffusion lengths are much larger than Wn,p
, ,n p n pL W
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 13 Prof. A. Niknejad
Diode Current Densities
0 1A
p
qVpdiff n kT
n n ppx x
dn DJ qD q n e
dx W
0 0( )( )
AqV
kTp p p
p p
dn n e nx
dx x W
p side n side
-Wp Wn xn -xp
0
AqV
kTnp e
0np
0pn
0
AqV
kTpn e
0 1A
n
qVpdiff n kT
p p nx x n
DdpJ qD q p e
dx W
2 1AqV
pdiff n kTi
d n a p
D DJ qn e
N W N W
2
0i
pa
nn
N
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 13 Prof. A. Niknejad
Fabrication of IC Diodes
Start with p-type substrate Create n-well to house diode p and n+ diffusion regions are the cathode and annode N-well must be reverse biased from substrate Parasitic resistance due to well resistance
p-type
p+
n-well
p-type
n+
annodecathode
p
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 13 Prof. A. Niknejad
Diode Small Signal Model
The I-V relation of a diode can be linearized
( )
1d d d dq V v qV qv
kT kT kTD D S SI i I e I e e
( )1 d d
D D D
q V vI i I
kT
2 3
12! 3!
x x xe x
dD d d
qvi g v
kT
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 13 Prof. A. Niknejad
Diode Capacitance
We have already seen that a reverse biased diode acts like a capacitor since the depletion region grows and shrinks in response to the applied field. the capacitance in forward bias is given by
But another charge storage mechanism comes into play in forward bias
Minority carriers injected into p and n regions “stay” in each region for a while
On average additional charge is stored in diode
01.4Sj j
dep
C A CX
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 13 Prof. A. Niknejad
Charge Storage
Increasing forward bias increases minority charge density By charge neutrality, the source voltage must supply equal
and opposite charge A detailed analysis yields:
p side n side
-Wp Wn xn -xp
( )
0
d dq V v
kTnp e
0np0pn
( )
0
d dq V v
kTpn e
1
2d
d
qIC
kT
Time to cross junction(or minority carrier lifetime)
Department of EECS University of California, Berkeley
EECS 105 Fall 2003, Lecture 13 Prof. A. Niknejad
Diode Circuits
Rectifier (AC to DC conversion) Average value circuit Peak detector (AM demodulator) DC restorer Voltage doubler / quadrupler /…