ese 570 mos transistor theory – part 1ese570/spring2015/ese570_mos... · 2015. 2. 5. · ese 570...

Kenneth R. Laker, University of Pennsylvania, updated 5Feb15

ESE 570 MOS TRANSISTOR THEORY – Part 1

2Kenneth R. Laker, University of Pennsylvania, updated 5Feb15

2

GATE

Mass Action Law

Two-Terminal MOS Structure

VB

n+ n+

Si – Oxide interface


Acc

epto

rs

Don

ors

MetalloidsChemical Periodic Table

American Chemical Society (ACS)


Gate

Oxi

deVG

= 0

Si surface

qΦM

Ideal Equilibrium MOS Capacitor Energy Bands

NOTE: 1. qΦ and E are in units of energy = electron-volts (eV); where 1 eV = 1.6 x 10 -19 J. 2. 1 eV corresponds to energy acquired by a free electron that is accelerated by an electric potential of one volt. 3. Φ and V corresponds to potential difference in volts.

Work Functions qΦM, qΦSi = energy required to move an electron from EF to Evacuum for metal gate, Si respectively.

EC, EFm

p doped Si

met

al

EFp

q/Si=q3Si(,E C−EV -

E i=EC−EV

2


MOS Capacitor with External BiasThree Regions of Operation:1. Accumulation Region – VG < 02. Depletion Region – VG > 0, small3. Inversion Region – VG ≥ VT, large


VG < 0

Surface potential: q/S=q/,0-)0

Band bending due to VG < 0

Si surface

Accumulation

qΦFp

q/Fp=E Fp−E i−bulk)0

q/, x -=E Fp−E i , x -

qΦ(x)qΦS

Band bending: .E i ,x -=E i ,x -−E i−bulk*0

x

Energy Bands - Accumulation Region

EFm

EFp

0

qV G=E Fp−E Fm


MOS Capacitor - Depletion Region

tox

mobile holes- - - - -


DepletionVG > 0 (small)

xd

Surface Potential:

Si surface

Band bending due to VG > 0

qΦFp

qΦS

qΦ(x)

q/Fp=E Fp−E i−bulk)0q/, x -=E Fp−E i , x -

q/S=q/,0-*0

Band bending: .E i ,x -=E i ,x -−E i−bulk)0

x

Energy Bands - Depletion Region

EFm

EFp

0

qV G=E Fp−E Fm


Bulk or Fermi potential

MOS Capacitor - Depletion Region

2Fp=2F=kTq

lnni

N A)0

26 mV at room T

22S

2Fp

Mobile hole charge density (per unit area) in thin layer parallel to Si-Oxide interfaceDepletion region potential needed to displace dQ by distance x into bulk (Poisson Eq.)

tox

∣2S−2F∣∣2S−2F∣

2Fp−2S2S

2Fp

- - - -

NOTE

surface potential (Fermi potential at surface)

Q=−q N A xd=−+2 q N A1Si∣2Fp−2S∣xd=+ 21Si∣2Fp−2S∣q N A


Si surface

/S=−/Fp @ V G=V T0

InversionVG ≥ VT0 > 0

xdm

qΦS

qΦFp

q/Fp=E Fp−E i−bulk)0q/, x -=E Fp−E i , x -

Surface Potential: q/S=q/,0-=−q/Fp*0Band bending: .E i ,x -=E i ,x -−E i−bulk)0

x

Energy Bands - Inversion Region

0

EFm

EFpqV G=E Fp−E Fm


MOS Capacitor - Inversion Region

tox

∣−22F∣

∣2S−2F∣2S=−2F

2S=−2F,2S=−2F-

2Fp=2F=kTq

lnni

N A

2Fn=2F=kTq

lnN D

ni

xdm=xd l2S=−2F=+ 21Si∣−22F∣

qN A

- - - -- - - - -

VG = VT for φS = - φFp

VG ≥ VT (threshold voltage)

2S=−2Fp

xdm=+ 21Si∣22Fp∣q N A

.=−+q N A1Si∣22Fp∣


MOS Capacitor - Inversion Region

INVERSION CONDITION – Key Equations2S=−2F

2F=2Fp=kTq

lnni

N A

n-Sub2F=2Fn=kTq

lnN D

ni

QB0=−+qN A1Si∣22F∣ c/cm2p-Sub

Where 1Si≈31ox F/cm

when n = NA Depletion region charge density

V

V

VG ≥ VT (threshold voltage)

VG = VFB for φS = φF → flat band (FB) condition, i.e. no band bending.


nMOS layout


G


Two-Terminal MOS Structure -> nMOS Transistor

depletion region

-

- --

- - - - -

- - -

-

VGV

S

VD


nMOS Transistor = MOS Capacitor + source/drain

where

VSB

= 0

xdm=+ 21Si∣22Fp−V SB∣q N A

where

NOTE: In CadenceSPICE = Spectre

NOTE: Since NA >> n

i : φ

Fp < 0

-

- - -- - - -

- -

-

1Si≈31ox

VG

VD

VS

m


+

)

l

for p-sub 2F=2Fp

[VT0

-> VT0 in SPICE]VT0n,p

work function between gate and channel

with VSB

= 0.V

FBV

FB

-+- for nMOS and pMOS

V FB=/GC−Qox

C ox≈/GC

V T0=/GC−Qox

C ox−22F−

QB0

Cox

VFB = flat band voltage

QB0=−+q N A1Si∣22F∣


Adjusting VT0

Using and an Added Channel Implant

V T0=V FB−22F−QB0

C ox

Intrinsic VT0

- no channel implant adjustment

.V T0=±q N I

Cox

Adjusted V'T0

– due to channel implant adjustment with carrier concentration N

I

V T0' =V T0(.V T0=V FB−22F−

QB0

C ox±

q N I

Cox

for p-type implant(q N I

C ox

−q N I

C ox

for n-type implant

NOTE: When channel implant adjustment NI is done as a step in the CMOS process,

the SPICE parameter VT0 refers to the adjusted threshold voltage V'T0

.


−QB−QB0

Cox=+2q N A1Si

C ox,+∣22F−V SB∣−+∣22F∣-

V T=V FB−22F−QB

Cox(

QB0

Cox−

QB0

Cox

V T=V FB−22F−QB0

Cox−

QB−QB0

Cox

VT0

V T0=V FB−22F−QB0

C ox

for VSB

= 0

units = V1/2

QB=−+q N A1Si∣22F−V SB∣ QB0=−+q N A1Si∣22F∣

V T=V T0(0,+∣22F−V SB∣−+∣22F∣-


VSB

is ≥ 0 in nMOS, ≤ 0 in pMOS

∣0∣● VT0 is positive in nMOS (V

T0n) , negative in pMOS (V

T0p)QOX is negative for nMOS and pMOS


|VSB

|


for

1

1

φF

2Fp=k Tq

lnni

N A=0.26V ln ,1.45 x 1010

1016 -=−0.35V

V T0n=V FB−22Fp−QB0

Cox

1 A=10−10 m


1 V T0n=V FB−22Fp−QB0

Cox

2Fp=−0.35 V

QB0=−+2q N A1Si∣22Fp∣

F = C/V

.=−+2 ,1.6 x 10−19 C -,1016 cm−3-,1.06 x 10−12 F cm−1-∣−0.70 V∣

V T0n=−1.04V −2 ,−0.35V -−,−0.72 V -=0.38V


Example 12

+C 2 cm−4 V−1

C cm−2V −1 =V 1/2

Units Calc.

V1/2

2Fp=−0.35V

V Tn=V T0n(0,+∣22Fp−V SB∣−+∣22F∣-

bulk potential

.=5.824 x 10−8 C /,V 1/2 cm2-6.8 x 10−8 C /,V cm2-

=0.85V 1/2


2

1

V Tn=V T0n(0,+∣22Fp−V SB∣−+∣22F∣-

V Tn=0.38V (0,+∣0.70V −V SB∣−+∣0.70V∣-

V T0n=0.38 V0=0.85V 1/2

2Fp=−0.35V

where

ese 570 mos transistor theory – part 1ese570/spring2015/ese570_mos... · 2015. 2. 5. · ese 570...

Documents