ese 570: digital integrated circuits and vlsi …ese 570: digital integrated circuits and vlsi...

ESE 570: Digital Integrated Circuits and VLSI Fundamentals

Lec 4: January 23, 2018 MOS Transistor Theory, MOS Model

Penn ESE 570 Spring 2018 – Khanna

Lecture Outline

!  CMOS Process Enhancements !  Semiconductor Physics

"  Band gaps "  Field Effects

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

Penn ESE 570 Spring 2018 - Khanna 2

CMOS Layers

!  “Standard” n-Well Process "  Active (Diffusion) (Drain/Source regions) "  Polysilicon (Gate Terminals) "  Metal 1, Metal 2, Metal3 "  Poly Contact (connects metal 1 to polysilicon) "  Active Contact (connects metal 1 to active) "  Via (connects metal 2 to metal 1) "  nWell (PMOS bulk region) "  n Select (used with active to create n-type diffusion) "  p Select (used with active to create p-type diffusion)

3 Penn ESE 570 Spring 2018 - Khanna

CMOS Process Enhancements

!  Interconnect "  Metal Interconnect (up to 8 metal levels) "  Copper Interconnect (upper two or more levels) "  Polysilicon (two or more levels, also for high quality capacitors) "  Stacked contacts and vias

!  Circuit Elements "  Resistors "  Capacitors "  BJTs





!  Devices "  Multiple thresholds (High and low Vt) "  High-k gate dielectrics "  FinFET


High-K dielectric


SiO2 Dielectric Poly gate MOSFET High-K Dielectric Metal gate MOSFET

Dielectric constant=3.9 Dielectric constant=20

High-K dielectric Survey

Wong/IBM J. of R&D, V46N2/3P133—168, 2002 Penn ESE 570 Spring 2018 - Khanna 7

22nm 3D FinFET Transistor

8

Tri-Gate transistors with multiple fins connected together

increases total drive strength for higher performance

http://download.intel.com/newsroom/kits/22nm/pdfs/22nm-Details_Presentation.pdf

High-k gate

dielectric

Penn ESE 570 Spring 2018 - Khanna




!  Devices "  Multiple thresholds (High and low Vt) "  High-k gate dielectrics "  FinFET

!  Silicon on insulator process (SOI) "  Fabricate on insulator for high speed/low leakage

9

Semiconductor Physics


Silicon Lattice

!  Cartoon two-dimensional view


Energy State View

Valance Band – all states filled

Ene

rgy


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


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


Doped Band Gaps

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

Ev

Ec

Semiconductor

1.1ev EA 0.045ev


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 "  Depends on doping

!  Use field to modulate conduction state of semiconductor

- - - - - -

+ + + + +


MOS Capacitor Charge

!  MOS gate-to-substrate capacitor "  Charge across MOS cap induce e-field

+ + + + + + + +

- - - - - - - - - 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

+ + + +

- - - Vcap>0

- - - -


+ + + + +

- - - - - -

- - - - - -

MOS Field Effect

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

"  Attracts carriers

"  Negative? "  Repel carriers


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

+ + + +

- - -

Vcap<0

- - -

+ +


MOS Physics - nMOS

MOS capacitor


Two-Terminal MOS Structure

34

2

GATE

n+ n+

Si – Oxide interface



!  Equilibrium (Mass action law) "  Product of hole and electron densities is constant at

equilibrium "  n0p0=ni

2 ni=1.45x1010 cm-3


35

2

GATE

n+ n+



!  n0p0=ni2 ni=1.45x1010 cm-3

!  Let substrate be uniformly doped with concentration NA


36

2

GATE

n+ n+



!  n0p0=ni2 ni=1.45x1010 cm-3


"  pp0=NA # np0=ni2/NA


37

2

GATE

n+ n+



!  n0p0=ni2 ni=1.45x1010 cm-3


"  pp0=NA # np0=ni2/NA


38

2

GATE

n+ n+


If N-type doped substrate: nn0=ND # pn0=ni

2/ND

P-type Doped Semiconductor Band Gap

39

Free space

Conduction band

Intrinsic Fermi level

Fermi level

Valence band

Electron affinity of silicon

!  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 2018 - Khanna

40

Free space

Conduction band


Fermi level

Valence band


Ei =EC −EV2


41

Free space

Conduction band


Fermi level

Valence band

ΦFp =EF − Eiq

→ΦFp =kTqlnniNA

Fermi potential:


Ei =EC −EV2


MOS Capacitor Energy Bands


MOS System Band Diagram

!  Three components put in physical contact "  Fermi levels must line up


MOS Capacitor with External Bias

!  Three Regions of Operation (w/ VB=0): "  Accumulation Region – VG < 0 "  Depletion Region – VG > 0, small "  Inversion Region – VG ≥ VT, large


Accumulation Region

!  Holes "  Accumulate at the

silicon-oxide interface

!  Electrons "  Near surface repelled

into silicon bulk

!  Interface accumulated with mobile carriers (holes)


Accumulation Region – Energy Bands

46

VG < 0 Band bending due to VG < 0

Accumulation

qΦFp qΦ(x) qΦS

x

EFm

EFp

0

qVG= EFp− EFm

Si surface


Depletion Region

47

tox

- - - - -


!  Holes "  Near silicon-oxide

interface repelled into silicon bulk

!  Electrons "  Left behind at interface

!  Interface depleted of mobile carriers (holes)

Depletion Region – Energy Bands

48

Depletion VG > 0 (small)

xd

Band bending due to VG > 0

qΦFp qΦS

qΦ(x)

x

EFm

EFp

0

qVG= EFp− EFm

Si surface


Depletion Region

49

Bulk potential

tox

- - - - Surface potential

ΦFp =ΦF =kTqln niNA

< 0

ΦS

ΦFpΦ

26 mV at room T


Depletion Region

50

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


Depletion Region

51

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

52

Bulk potential

tox



< 0

ΦS

ΦFpΦ

26 mV at room T


dx

dφΦS

ΦFp

∫ =q ⋅NA ⋅ xεSi

dx0

xd

∫ =q ⋅NA ⋅ xd

2

2εSi=ΦFp −ΦS

⇒ xd =2εSi ΦFp −ΦS

q ⋅NA


Depletion Region

53

Bulk potential

tox



< 0

ΦS

ΦFpΦ

26 mV at room T


dx

dφΦS

ΦFp

∫ =q ⋅NA ⋅ xεSi

dx0

xd

∫ =q ⋅NA ⋅ xd

2

2εSi=ΦFp −ΦS

⇒ xd =2εSi ΦFp −ΦS

q ⋅NA


Depletion Region

54

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

55

tox

- - - - - - - - -

VG ≥ VT


!  Holes "  Repelled deeper into silicon

bulk

!  Electrons "  Attracted to silicon-oxide

interface

!  Inversion condition "  When ΦS

= −ΦF

"  Density of mobile electrons at surface = density of mobile carriers in bulk

Inversion Region – Energy Bands

56

Inversion VG ≥ VT0 > 0

xdm

qΦS

qΦFp

x 0

EFm

EFp qVG= EFp− EFm

Si surface


Inversion Region

57

tox

- - - - - - - - -

VG ≥ VT


Q = − 2qNAεSi ΦFp −ΦS = − 2qNAεSi 2ΦFp

xdm =2εSi ΦFp −ΦS

q ⋅NA=2εSi 2ΦFp

q ⋅NA

!  Inversion condition

"  When ΦS= −ΦF

"  Density of mobile electrons at surface = density of mobile carriers in bulk

Band Diagram Demo


http://demonstrations.wolfram.com/AppliedVoltageOnAnIdealMOSCapacitor/

- - - - -

MOS Capacitor with External Bias

!  Three Regions of Operation: "  Accumulation Region – VG < 0 (Cut-off) "  Depletion Region – VG > 0, small (Subthreshold) "  Inversion Region – VG ≥ VT, large (Above Threshold)


- - - - -

Cut-off/Subthreshold Above threshold

VG ≥ VT

60

depletion region

-

VG VS VD

2-terminal MOS Cap # 3-terminal nMOS

- - - - -- -

-

-- --


nMOS = MOS cap + source/drain

61

VSB = 0

-

- - - - - -

- - -

-

VG VD VS


Threshold Voltage

!  For VSB=0, the threshold voltage is denoted as VT0 or VT0n,p

"  ΦGC : Work function difference between gate and channel "  Metal Gate: ΦGC=ΦF(substrate) –ΦM "  Poly Gate: ΦGC =ΦF(substrate) –ΦF(gate)

"  QOX : Fixed positive charge density at interface "  QOX= qNOX C/cm2

"  COX : Gate oxide capacitance per unit area "  COX=εOX/tox

"  ΦGC : Bulk fermi potential "  QB0 : Depletion region charge density at inversion

" 


62

VT 0 =ΦGC −Qox

Cox

− 2ΦF −QB0

Cox

QB0 = − 2qNAεSi 2ΦF

Threshold Voltage

!  For VSB=0, the threshold voltage is denoted as VT0 or VT0n,p

"  ΦGC : Work function difference between gate and channel "  Metal Gate: ΦGC=ΦF(substrate) –ΦM "  Poly Gate: ΦGC =ΦF(substrate) –ΦF(gate)

"  QOX : Fixed positive charge density at interface "  QOX= qNOX C/cm2

"  COX : Gate oxide capacitance per unit area "  COX=εOX/tox

"  ΦGC : Bulk fermi potential "  QB0 : Depletion region charge density at inversion

" 


63

VT 0 =ΦGC −Qox

Cox

− 2ΦF −QB0

Cox

QB0 = − 2qNAεSi 2ΦF

Threshold Voltage

64

for VSB = 0

for VSB != 0 VT =ΦGC −

QoxCox

− 2ΦF −QBCox

VT =ΦGC −QoxCox

− 2ΦF −QB0Cox

−QB −QB0Cox

VT =VT 0 −QB −QB0Cox


VT =VT 0 =ΦGC −QoxCox

− 2ΦF −QB0Cox

Threshold Voltage

65

for VSB = 0

for VSB != 0 VT =ΦGC −

QoxCox

− 2ΦF −QBCox

VT =ΦGC −QoxCox

− 2ΦF −QB0Cox

−QB −QB0Cox

VT =VT 0 −QB −QB0Cox

−QB −QB0

Cox

=2qNAεSiCox

2ΦF −VSB − 2ΦF( )

VT =VT 0 +γ 2ΦF −VSB − 2ΦF( )

γ


VT =VT 0 =ΦGC −QoxCox

− 2ΦF −QB0Cox

Q = − 2qNAεSi ΦF −ΦS

Threshold Voltage

N-channel P-channel ϕF negative positive QB0,QB negative positive ϒ positive negative VSB ≥0 ≤0 VT0 positive (VT0n) negative (VT0p)


66

!  Be careful with signs!

67

|VSB|

Threshold Voltage


Big Idea

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

!  Threshold voltage "  Defined by onset of inversion "  Doping and VSB change VT


Admin

!  HW 2 due Thursday, 1/25 "  Submit in canvas


ese 570: digital integrated circuits and vlsi …ese 570: digital integrated circuits and vlsi...

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