Lecture Outline ESE 570: Digital Integrated Circuits and

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ESE 570: Digital Integrated Circuits and VLSI Fundamentals

Lec 4: January 26, 2016 MOS Transistor Theory, MOS Model

Penn ESE 570 Spring 2016 – Khanna

Lecture Outline

!  Semiconductor Physics "  Band gaps "  Field Effects

!  MOS Physics "  Cut-off "  Depletion "  Inversion "  Threshold Voltage

Penn ESE 570 Spring 2016 - Khanna 2

Review: MOSFET – N-Type, P-Type

!  N – negative carriers "  electrons

!  Switch turned on positive VGS

!  P – positive carriers "  holes

!  Switch turned on negative VGS

Vth,p < 0VGS < Vth,p to conduct

3

Vth,n > 0VGS > Vth,n to conduct

Penn ESE 570 Spring 2016 - Khanna

Semiconductor Physics

4 Penn ESE 570 Spring 2016 - Khanna

Silicon Lattice

!  Cartoon two-dimensional view


Energy State View

Valance Band – all states filled

Ene

rgy


2

Energy State View


Ene

rgy

Conduction Band– all states empty


Energy State View


Ene

rgy

Conduction Band– all states empty

Band Gap


Band Gap and Conduction

Ec

Ev

Ev

Ec

Ev

Ec

OR

Insulator Metal

8ev

Ev

Ec

Semiconductor

1.1ev


Doping

!  Add impurities to Silicon Lattice "  Replace a Si atom at a lattice site with another

!  E.g. add a Group 15 element "  E.g. P (Phosphorus)


Doping with P

!  End up with extra electrons "  Donor electrons

!  Not tightly bound to atom "  Low energy to displace "  Easy for these electrons

to move


Doped Band Gaps

!  Addition of donor electrons makes more metallic "  Easier to conduct

Ev

Ec

Semiconductor

1.1ev ED 0.045ev


3

Capacitor Charge

!  Remember capacitor charge

+ + + + + + + +

- - - - - - - - - semiconductor

gate

source drain


MOS Field?

!  What does “capacitor” field do to the Donor-doped semiconductor channel?

- -

Vgs=0 No field

- - - -


MOS Field?


+ + + +

- - - Vcap>0

- -

Vgs=0 No field

- - - -


MOS Field?


- -

Vgs=0 No field

+ + + + +

- - - - - - = Vgs>0

Conducts

+ + + +

- - - Vcap>0

- - - -


+ + + + +

- - - - - -

- - - - - -

MOS Field Effect

!  Charge on capacitor "  Attract or repel charges to form channel "  Modulates conduction "  Positive

"  Attracts carriers "  Enables conduction

"  Negative? "  Repel carriers

"  Disable conduction


Doping with B

!  End up with electron vacancies -- Holes "  Acceptor electron sites

!  Easy for electrons to shift into these sites "  Low energy to displace "  Easy for the electrons to move

"  Movement of an electron best viewed as movement of hole


4

Doped Band Gaps

!  Addition of acceptor sites makes more metallic "  Easier to conduct

Ev

Ec

Semiconductor

1.1ev EA 0.045ev


Field Effect?

!  Effect of positive field on Acceptor-doped Silicon?

Vgs=0 No field

+ + + +


Field Effect?


Vgs=0 No field + + + +

- - - Vcap>0

+ + + +


Field Effect?


Vgs=0 No field

+ + + + +

= Vgs>0

No conduction

+ + + +

- - - Vcap>0

+ + + +


Field Effect?

!  Effect of negative field on Acceptor-doped Silicon?

+ +

Vgs=0 No field +

+ + +

- - -

Vcap<0 + +


Field Effect?

!  Effect of negative field on Acceptor-doped Silicon?

+ +

Vgs=0 No field

+ + + + + =

Vgs>0 Conduction

+ + + +

- - -

Vcap<0

- - -

+ +


5

MOSFETs

!  Donor doping "  Excess electrons "  Negative or N-type material "  NFET

!  Acceptor doping "  Excess holes "  Positive or P-type material "  PFET


MOSFET

!  Semiconductor can act like metal or insulator !  Use field to modulate conduction state of

semiconductor

- - - - - -

+ + + + +


MOS Physics - nMOS


Two-Terminal MOS Structure

28

2

GATE

(Mass Action Law)

n+ n+

Si – Oxide interface


P-type Doped Semiconductor Band Gap

29

Free space

Conduction band

Intrinsic Fermi level

Fermi level

Valence band

Electron affinity of silicon

qΦS

!  qΦ and E are in units of energy = electron-volts (eV); where 1 eV = 1.6 x 10-19 J.

!  1 eV corresponds to energy acquired by a free electron that is accelerated by an electric potential of one volt.

!  Φ and V corresponds to potential difference in volts. Penn ESE 570 Spring 2016 - Khanna 30

Free space

Conduction band

Intrinsic Fermi level

Fermi level

Valence band

ΦF =EF −Ei

q→ΦFp =

kTqln niNA

Fermi potential:

qΦS = qχ + (EC −EF )

Electron affinity of silicon

qΦS

Work function (Fermi-to-space):

P-type Doped Semiconductor Band Gap

Ei =EC −EV2


6

MOS Capacitor Energy Bands


MOS Capacitor with External Bias

!  Three Regions of Operation: "  Accumulation Region – VG < 0 "  Depletion Region – VG > 0, small "  Inversion Region – VG ≥ VT, large


Accumulation Region


Accumulation Region – Energy Bands

34

VG < 0 Band bending due to VG < 0

Accumulation

qΦFp qΦ(x) qΦS

x

EFm

EFp

0

qVG= EFp− EFm

Si surface


Depletion Region

35

tox

mobile holes - - - - -


Depletion Region – Energy Bands

36

Depletion VG > 0 (small)

xd

Band bending due to VG > 0

qΦFp

qΦS

qΦ(x)

x

EFm

EFp

0

qVG= EFp− EFm

Si surface


7

Depletion Region

37

Bulk potential

tox

- - - - Surface potential

ΦFp =ΦF =kTqln niNA

< 0

ΦS

ΦFpΦ

26 mV at room T


Depletion Region

38

Bulk potential

tox



< 0

ΦS

ΦFpΦ

26 mV at room T

dQ = −qNAdx Mobile hole charge density (per unit area) in thin layer below surface

dφ = −x dQεSi

Potential required to displace dQ by distance x

dφ = q ⋅NA ⋅ xεSi

dx


Depletion Region

39

Bulk potential

tox



< 0

ΦS

ΦFpΦ

26 mV at room T

dφ = q ⋅NA ⋅ xεSi

dx

dφΦS

ΦFp

∫ =q ⋅NA ⋅ xεSi

dx0

xd

∫ =q ⋅NA ⋅ xd

2

2εSi=ΦFp −ΦS

⇒ xd =2εSi ΦFp −ΦS

q ⋅NA


Depletion Region

40

Bulk potential

tox



< 0

ΦS

ΦFpΦ

26 mV at room T

xd =2εSi ΦFp −ΦS

q ⋅NA

Q = −qNAxd

Q = −qNA

2εSi ΦFp −ΦS

q ⋅NA

= − 2qNAεSi ΦFp −ΦS


Inversion Region

41

tox

- - - - - - - - -

VG ≥ VT (threshold voltage)

(Density of mobile electrons = density of holes in bulk)


Inversion Region – Energy Bands

42

Inversion VG ≥ VT0 > 0

xdm

qΦS

qΦFp

x 0

EFm

EFp qVG= EFp− EFm

Si surface


8

Depletion Region – Energy Bands

43

Depletion VG > 0 (small)

xd

Band bending due to VG > 0

qΦFp

qΦS

qΦ(x)

x

EFm

EFp

0

qVG= EFp− EFm

Si surface


Inversion Region

44

tox

- - - - - - - - -

VG ≥ VT (threshold voltage)

(Density of mobile electrons = density of holes in bulk) Q = − 2qNAεSi ΦFp −ΦS = − 2qNAεSi 2ΦFp


45

depletion region

-

VG VS VD

2-terminal MOS Cap # 3-terminal nMOS

- - - - -- -

-

-- --


nMOS = MOS cap + source/drain

46

VSB = 0

-

- - - - - -

- - -

-

VG VD VS

xd =2εSi 2ΦFp −VSB

q ⋅NA


Threshold Voltage

47

+

)

l

[VT0 -> VT0 in SPICE] VT0n,p

work function between gate and channel

with VSB = 0. VFB VFB

- + - for nMOS and pMOS

V FB= GC−Qox

Cox≈ GC

VFB = flat band voltage

VT 0 =ΦGC −Qox

Cox

− 2ΦF −QB0

Cox

QB0 = − 2qNAεSi 2ΦF


Threshold Voltage

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for VSB = 0 VT =VT 0 =VFB − 2ΦF −QB0

Cox

for VSB != 0 VT =VFB − 2ΦF −

QB

Cox

VT =VFB − 2ΦF −QB0

Cox

−QB −QB0

Cox

VT =VT 0 −QB −QB0

Cox

−QB −QB0

Cox

=2qNAεSiCox

2ΦF −VSB − 2ΦF( )

VT =VT 0 +γ 2ΦF −VSB − 2ΦF( )

γ


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Threshold Voltage

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VSB is ≥ 0 in nMOS, ≤ 0 in pMOS $  VT0 is positive in nMOS (VT0n) , negative in pMOS (VT0p)


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|VSB|

Threshold Voltage


Big Idea

!  3 operation regions "  Cut-off "  Depletion "  Inversion

!  Doping and VSB change VT

Penn ESE 570 Spring 2016 - Khanna 51

Admin

!  HW 2 due Thursday, 1/28 !  Office hours updated on Course website

!  No Journal Thursday this week


Documents

Lecture Outline ESE 570: Digital Integrated Circuits and