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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
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Silicon Lattice
! Cartoon two-dimensional view
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Energy State View
Valance Band – all states filled
Ene
rgy
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Energy State View
Valance Band – all states filled
Ene
rgy
Conduction Band– all states empty
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Energy State View
Valance Band – all states filled
Ene
rgy
Conduction Band– all states empty
Band Gap
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Band Gap and Conduction
Ec
Ev
Ev
Ec
Ev
Ec
OR
Insulator Metal
8ev
Ev
Ec
Semiconductor
1.1ev
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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)
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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
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Doped Band Gaps
! Addition of donor electrons makes more metallic " Easier to conduct
Ev
Ec
Semiconductor
1.1ev ED 0.045ev
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Capacitor Charge
! Remember capacitor charge
+ + + + + + + +
- - - - - - - - - semiconductor
gate
source drain
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MOS Field?
! What does “capacitor” field do to the Donor-doped semiconductor channel?
- -
Vgs=0 No field
- - - -
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MOS Field?
! What does “capacitor” field do to the Donor-doped semiconductor channel?
+ + + +
- - - Vcap>0
- -
Vgs=0 No field
- - - -
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MOS Field?
! What does “capacitor” field do to the Donor-doped semiconductor channel?
- -
Vgs=0 No field
+ + + + +
- - - - - - = Vgs>0
Conducts
+ + + +
- - - Vcap>0
- - - -
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+ + + + +
- - - - - -
- - - - - -
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
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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
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Doped Band Gaps
! Addition of acceptor sites makes more metallic " Easier to conduct
Ev
Ec
Semiconductor
1.1ev EA 0.045ev
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Field Effect?
! Effect of positive field on Acceptor-doped Silicon?
Vgs=0 No field
+ + + +
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Field Effect?
! Effect of positive field on Acceptor-doped Silicon?
Vgs=0 No field + + + +
- - - Vcap>0
+ + + +
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Field Effect?
! Effect of positive field on Acceptor-doped Silicon?
Vgs=0 No field
+ + + + +
= Vgs>0
No conduction
+ + + +
- - - Vcap>0
+ + + +
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Field Effect?
! Effect of negative field on Acceptor-doped Silicon?
+ +
Vgs=0 No field +
+ + +
- - -
Vcap<0 + +
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Field Effect?
! Effect of negative field on Acceptor-doped Silicon?
+ +
Vgs=0 No field
+ + + + + =
Vgs>0 Conduction
+ + + +
- - -
Vcap<0
- - -
+ +
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MOSFETs
! Donor doping " Excess electrons " Negative or N-type material " NFET
! Acceptor doping " Excess holes " Positive or P-type material " PFET
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MOSFET
! Semiconductor can act like metal or insulator ! Use field to modulate conduction state of
semiconductor
- - - - - -
+ + + + +
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MOS Physics - nMOS
Penn ESE 570 Spring 2016 - Khanna
Two-Terminal MOS Structure
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2
GATE
(Mass Action Law)
n+ n+
Si – Oxide interface
Penn ESE 570 Spring 2016 - Khanna
P-type Doped Semiconductor Band Gap
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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
Penn ESE 570 Spring 2016 - Khanna
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MOS Capacitor Energy Bands
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MOS Capacitor with External Bias
! Three Regions of Operation: " Accumulation Region – VG < 0 " Depletion Region – VG > 0, small " Inversion Region – VG ≥ VT, large
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Accumulation Region
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Accumulation Region – Energy Bands
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VG < 0 Band bending due to VG < 0
Accumulation
qΦFp qΦ(x) qΦS
x
EFm
EFp
0
qVG= EFp− EFm
Si surface
Penn ESE 570 Spring 2016 - Khanna
Depletion Region
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tox
mobile holes - - - - -
Penn ESE 570 Spring 2016 - Khanna
Depletion Region – Energy Bands
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Depletion VG > 0 (small)
xd
Band bending due to VG > 0
qΦFp
qΦS
qΦ(x)
x
EFm
EFp
0
qVG= EFp− EFm
Si surface
Penn ESE 570 Spring 2016 - Khanna
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Depletion Region
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Bulk potential
tox
- - - - Surface potential
ΦFp =ΦF =kTqln niNA
< 0
ΦS
ΦFpΦ
26 mV at room T
Penn ESE 570 Spring 2016 - Khanna
Depletion Region
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Bulk potential
tox
- - - - Surface potential
ΦFp =ΦF =kTqln niNA
< 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
Penn ESE 570 Spring 2016 - Khanna
Depletion Region
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Bulk potential
tox
- - - - Surface potential
ΦFp =ΦF =kTqln niNA
< 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
Penn ESE 570 Spring 2016 - Khanna
Depletion Region
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Bulk potential
tox
- - - - Surface potential
ΦFp =ΦF =kTqln niNA
< 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
Penn ESE 570 Spring 2016 - Khanna
Inversion Region
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tox
- - - - - - - - -
VG ≥ VT (threshold voltage)
(Density of mobile electrons = density of holes in bulk)
Penn ESE 570 Spring 2016 - Khanna
Inversion Region – Energy Bands
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Inversion VG ≥ VT0 > 0
xdm
qΦS
qΦFp
x 0
EFm
EFp qVG= EFp− EFm
Si surface
Penn ESE 570 Spring 2016 - Khanna
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Depletion Region – Energy Bands
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Depletion VG > 0 (small)
xd
Band bending due to VG > 0
qΦFp
qΦS
qΦ(x)
x
EFm
EFp
0
qVG= EFp− EFm
Si surface
Penn ESE 570 Spring 2016 - Khanna
Inversion Region
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tox
- - - - - - - - -
VG ≥ VT (threshold voltage)
(Density of mobile electrons = density of holes in bulk) Q = − 2qNAεSi ΦFp −ΦS = − 2qNAεSi 2ΦFp
Penn ESE 570 Spring 2016 - Khanna
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depletion region
-
VG VS VD
2-terminal MOS Cap # 3-terminal nMOS
- - - - -- -
-
-- --
Penn ESE 570 Spring 2016 - Khanna
nMOS = MOS cap + source/drain
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VSB = 0
-
- - - - - -
- - -
-
VG VD VS
xd =2εSi 2ΦFp −VSB
q ⋅NA
Penn ESE 570 Spring 2016 - Khanna
Threshold Voltage
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+
)
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
Penn ESE 570 Spring 2016 - Khanna
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
Penn ESE 570 Spring 2016 - Khanna
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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)
Penn ESE 570 Spring 2016 - Khanna
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|VSB|
Threshold Voltage
Penn ESE 570 Spring 2016 - Khanna
Big Idea
! 3 operation regions " Cut-off " Depletion " Inversion
! Doping and VSB change VT
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Admin
! HW 2 due Thursday, 1/28 ! Office hours updated on Course website
! No Journal Thursday this week
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