# MOSFET Basics by S03OBzbO

VIEWS: 0 PAGES: 49

• pg 1
```									MOSFET I-Vs

ECE 663
Operation of a transistor
VSG > 0
n type operation

VSG
Gate               VSD
Insulator
Source Channel      Drain
More
electrons
Substrate

Positive gate bias attracts electrons into channel
Channel now becomes more conductive
Some important equations in the
inversion regime (Depth direction)

VT = fms + 2yB + yox
Gate
Insulator

yox = Qs/Cox                       Source Channel     Drain

Qs = qNAWdm                              Substrate

Wdm = [2eS(2yB)/qNA]
x
VT = fms + 2yB + [4eSyBqNA]/Cox

Qinv = -Cox(VG - VT)
MOSFET Geometry

VG

Z

VD
L

S           D
z

y

x
ECE 663
How to include y-dependent potential
without doing the whole problem over?

ECE 663
Assume potential V(y) varies slowly along
channel, so the x-dependent and y-dependent
electrostats are independent

i.e.,

Ignore ∂Ex/∂y

Potential is separable in
x and y
ECE 663
How to include y-dependent potentials?
VG = yS + [2eSySqNA]/Cox

yS = 2yB + V(y)

Need VG – V(y) > VT to invert
channel at y (V increases
threshold)

Since V(y) largest at drain end, that
end reverts from inversion to
depletion first (Pinch off) 

SATURATION [VDSAT = VG – VT]            ECE 663
So current:

j = qninvv = (Qinv/tinv)v

I = jA = jZtinv = ZQinvv

Qinv = -Cox[VG – VT - V(y)]

v = -meffdV(y)/dy

ECE 663
So current:

I = meff ZCox[VG – VT - V(y)]dV(y)/dy

Continuity implies ∫Idy = IL

I = meff ZCox[(VG – VT )VD- VD2/2]/L

ECE 663
But this current behaves like a parabola !!
I = meff ZCox[(VG – VT )VD- VD2/2]/L

ID                           IDsat

VDsat     VD

We have assumed inversion in our model (ie, always above pinch-off)

So we just extend the maximum current into saturation…

Easy to check that above current is maximum for VDsat = VG - VT

Substituting, IDsat = (CoxmeffZ/2L)(VG-VT)2
ECE 663
What’s Pinch off?

VG
0            VG
0                         VG            VG

0             0                          0            VD

Now add in the drain voltage to drive a current. Initially you get
an increasing current with increasing drain bias
When you reach VDsat = VG – VT, inversion is disabled at the drain
end (pinch-off), but the source end is still inverted

The charges still flow, just that you can’t draw more current
with higher drain bias, and the current saturates
Square law theory of MOSFETs

I = meff ZCox[(VG – VT )VD- VD2/2]/L,   VD < VG - VT

I = meff ZCox(VG – VT )2/2L,   VD > VG - VT

J = qnv
n ~ Cox(VG – VT )
v ~ meffVD /L
Ideal Characteristics of n-channel
enhancement mode MOSFET

ECE 663
Drain current for REALLY small VD
Z                    1 2
I D  m nCi  VG  VT VD  VD 
L                     2  
Z                                 Linear operation
I D  m nCi VG  VT VD 
L
VD  VG  VT 

Channel Conductance:

I D   Z
gD         m nCi (VG  VT )
VD V G
L

Transconductance:
I D   Z
gm         m nCiVD
VG V  L
D                     ECE 663
In Saturation

• Channel Conductance:

I D
gD        0
VD V
G

• Transconductance:

Z
I D sat     m nCi VG  VT 
2

2L

I D   Z
gm           m nCi VG  VT 
VG VD
L

ECE 663
Equivalent Circuit – Low Frequency AC

• Gate looks like open circuit
• S-D output stage looks like current source with channel
conductance
I D        I D
I D        VD        VG
VD VG
VG V     D

i  g Dv d  g mv g
ECE 663
Equivalent Circuit – Higher Frequency AC

• Input stage looks like capacitances gate-to-source(gate) and
gate-to-drain(overlap)

• Output capacitances ignored -drain-to-source capacitance
small

ECE 663
Equivalent Circuit – Higher Frequency AC

• Input circuit:

i in  jCgs  Cgd v g  j 2fCgatev g
• Input capacitance is mainly gate capacitance

• Output circuit:      i out  g mv g

i out     gm

i in   2fCgate

I D   Z
gm           m nCiVD
VG V  L
D

ECE 663
Maximum Frequency (not in saturation)

• Ci is capacitance per unit area and Cgate is total capacitance
of the gate
Cgate  Ci ZL

• F=fmax when gain=1 (iout/iin=1)

gm
fmax   
2Cgate

Z
m nVDCi
L           m nVD
fmax              
2Ci ZL 2L2

ECE 663
Maximum Frequency (not in saturation)

m nVD
f m ax 
2L2

1
m ax 
L/v
(Inverse transit time)
v  mVD / L
ECE 663
Switching Speed, Power Dissipation

ton = CoxZLVD/ION

Trade-off: If Cox too small, Cs and Cd take over and you lose
control of the channel potential (e.g. saturation)

(DRAIN-INDUCED BARRIER LOWERING/DIBL)

If Cox increases, you want to make sure you don’t control
immobile charges (parasitics) which do not contribute to
current.

ECE 663
Switching Speed, Power Dissipation

Pdyn = ½ CoxZLVD2f

Pst = IoffVD

ECE 663
CMOS

NOT gate
(inverter)

ECE 663
CMOS

NOT gate
Vin = 1               Vout = 0    (inverter)

Positive gate turns nMOS on

ECE 663
CMOS

NOT gate
Vin = 0              Vout = 1     (inverter)

Negative gate turns pMOS on

ECE 663
So what?

• If we can create a NOT gate
we can create other gates
(e.g. NAND, EXOR)

ECE 663
So what?

Ring Oscillator

ECE 663
So what?

• More importantly, since one is open and one is shut at steady
state, no current except during turn-on/turn-off

 Low power dissipation

ECE 663
Getting the inverter output

ON

Gain

OFF
ECE 663
I D
gD        0
VD V G

I D   Z
gm           m nCi VG  VT 
VG VD
L

What’s the gain here?

ECE 663
Signal Restoration

ECE 663
BJT vs MOSFET

• RTL logic vs CMOS logic

• DC Input impedance of MOSFET (at gate end) is infinite
Thus, current output can drive many inputs  FANOUT

• CMOS static dissipation is low!!   ~ IOFFVDD

• Normally BJTs have higher transconductance/current (faster!)

IC = (qni2Dn/WBND)exp(qVBE/kT)       ID = mCoxW(VG-VT) 2/L

gm = IC/VBE = IC/(kT/q)             gm = ID/VG = ID/[(VG-VT)/2]

• Today’s MOSFET ID >> IC due to near ballistic operation
ECE 663
What if it isn’t ideal?
• If work function differences and oxide charges are present,
threshold voltage is shifted just like for MOS capacitor:
2e s qN A (2y B )
VT  VFB    2y B 
Ci
      Qf         2e s qN A (2y B )
  fms    2y B 
      Ci               Ci

• If the substrate is biased wrt the Source (VBS) the
threshold voltage is also shifted

2e s qN A (2y B  VBS )
VT  VFB    2y B 
Ci

ECE 663
Threshold Voltage Control

• Substrate Bias:

2e s qN A (2y B  VBS )
VT  VFB    2y B 
Ci

VT  VT (VBS )  VT (VBS  0)

2e s qN A
VT                 2y B  VBS  2y B 
Ci

ECE 663
Threshold Voltage Control-substrate bias

ECE 663
It also affects the I-V
VG

The threshold voltage is increased due to the depletion region
that grows at the drain end because the inversion layer shrinks
there and can’t screen it any more. (Wd > Wdm)

Qinv = -Cox[VG-VT(y)], I = -meffZQinvdV(y)/dy

VT(y) = y + √2esqNAy/Cox

y = 2yB + V(y)
ECE 663
It also affects the I-V

IL = ∫meffZCox[VG – (2yB+V) - √2esqNA(2yB+V)/Cox]dV

I = (ZmeffCox/L)[(VG–2yB)VD –VD2/2

-2√2esqNA{(2yB+VD)3/2-(2yB)3/2}/3Cox]

ECE 663
We can approximately include this…
Include an additional charge term from the
depletion layer capacitance controlling V(y)

Q = -Cox[VG-VT]+(Cox + Cd)V(y)

where Cd = es/Wdm

Q = -Cox[VG –VT - MV(y)], M = 1 + Cd/Cox

ID = (ZmeffCox/L)[(VG-VT - MVD/2)VD]

ECE 663
Comparison between different models

Square Law Theory
Bulk Charge Theory

Body Coefficient

Still not good below threshold or above saturation   ECE 663
Mobility
• Drain current model assumed constant mobility in channel
• Mobility of channel less than bulk – surface scattering
• Mobility depends on gate voltage – carriers in inversion
channel are attracted to gate – increased surface scattering
– reduced mobility

ECE 663
Mobility dependence on gate voltage

m0
m
1  (VG  VT )

ECE 663
Sub-Threshold Behavior

• For gate voltage less than the threshold – weak inversion
• Diffusion is dominant current mechanism (not drift)

n         n(o)  n(L)
y              L

q ( y s y B ) / kT
n(0)  ni e

q ( y s  y B VD ) / kT
n(L)  ni e
ECE 663
Sub-threshold
y B / kT
ID 
L
1  e      qVD / kT
e   qy s / kT

We can approximate ys with VG-VT below threshold since all
voltage drops across depletion region

1  e               e
/ kT
q VG VT  / kT
B
qVD / kT
ID 
L

•Sub-threshold current is exponential function of applied gate voltage
•Sub-threshold current gets larger for smaller gates (L)

ECE 663
Subthreshold Characteristic

Subthreshold Swing
1
S
 log ID  VG 

ECE 663
Much of new research depends on reducing S !

Ghosh, Rakshit, Datta
Tunneling transistor                               (Nanoletters, 2004)
– Band filter like operation                     (Sconf)min=2.3(kBT/e).(etox/m)

Hodgkin and Huxley, J. Physiol. 116, 449 (1952a)
J Appenzeller et al, PRL ‘04
Much of new research depends on reducing S !

• Increase ‘q’ by collective motion (e.g. relay)
Ghosh, Rakshit, Datta, NL ‘03

• Effectively reduce N through interactions
Salahuddin, Datta

• Negative capacitance
Salahuddin, Datta

• Non-thermionic switching (T-independent)
Appenzeller et al, PRL

• Nonequilibrium switching
Li, Ghosh, Stan

• Impact Ionization
Plummer
More complete model – sub-threshold to
saturation
• Must include diffusion and drift currents
• Still use gradual channel approximation
• Yields sub-threshold and saturation behavior for long
channel MOSFETS
• Exact Charge Model – numerical integration

yV
Z esm n    VD y s
e
ID          
L LD 0 y                      np0 
F  y,V ,     
B

        pp0 
            

ECE 663
Exact Charge Model (Pao-Sah)
– Long Channel MOSFET

http://www.nsti.org/Nanotech2006/WCM2006/WCM2006-BJie.pdf
ECE 663
ECE 663

```
To top