MOSFET – N-Type, P-Type
Lecture Outline ESE 570: Digital Integrated Circuits and VLSI Fundamentals ! Semiconductor Physics " Band gaps
" Field Effects Lec 4: January 26, 2016 ! MOS Physics
MOS Transistor Theory, MOS Model " Cut-off
" Depletion
" Inversion
" Threshold Voltage
Penn ESE 570 Spring 2016 – Khanna Penn ESE 570 Spring 2016 - Khanna 2
Review: MOSFET – N-Type, P-Type
! N – negative carriers ! P – positive carriers Semiconductor Physics " electrons " holes
! Switch turned on ! Switch turned on
positive VGS negative VGS
Vth,n > 0 Vth,p < 0 VGS > Vth,n VGS < Vth,p to conduct to conduct Penn ESE 570 Spring 2016 - Khanna 3 Penn ESE 570 Spring 2016 - Khanna 4
Silicon Lattice Energy State View
! Cartoon two-dimensional view Energy
Valance Band – all states filled
Penn ESE 570 Spring 2016 - Khanna 5 Penn ESE 570 Spring 2016 - Khanna 6
1 Energy State View Energy State View
Conduction Band– all states empty Conduction Band– all states empty
Band Gap Energy Energy
Valance Band – all states filled Valance Band – all states filled
Penn ESE 570 Spring 2016 - Khanna 7 Penn ESE 570 Spring 2016 - Khanna 8
Band Gap and Conduction Doping
! Add impurities to Silicon Lattice
" Replace a Si atom at a lattice site with another
Insulator Metal ! E.g. add a Group 15 element Ec Ec Ev " E.g. P (Phosphorus) 8ev OR E v Ev Ec
Semiconductor
Ec 1.1ev Ev
Penn ESE 570 Spring 2016 - Khanna 9 Penn ESE 570 Spring 2016 - Khanna 10
Doping with P Doped Band Gaps
! End up with extra electrons ! Addition of donor electrons makes more metallic
" Donor electrons " Easier to conduct
! Not tightly bound to atom
" Low energy to displace
" Easy for these electrons Semiconductor to move E 0.045ev c 1.1ev ED Ev
Penn ESE 570 Spring 2016 - Khanna 11 Penn ESE 570 Spring 2016 - Khanna 12
2 Capacitor Charge MOS Field?
! Remember capacitor charge ! What does “capacitor” field do to the Donor-doped semiconductor channel?
Vgs=0 + + + + + + + + gate No field - - - - drain source ------semiconductor
Penn ESE 570 Spring 2016 - Khanna 13 Penn ESE 570 Spring 2016 - Khanna 14
MOS Field? MOS Field?
! What does “capacitor” field do to the Donor-doped ! What does “capacitor” field do to the Donor-doped semiconductor channel? semiconductor channel?
Vgs=0 + + + Vgs=0 + + + No field + V >0 No field + V >0 - - - - - cap - - - - - cap ------
+ + + + + Vgs>0 Conducts = ------
Penn ESE 570 Spring 2016 - Khanna 15 Penn ESE 570 Spring 2016 - Khanna 16
MOS Field Effect Doping with B
! Charge on capacitor ! End up with electron vacancies -- Holes
" Attract or repel charges to form channel " Acceptor electron sites
" Modulates conduction ! Easy for electrons to shift into these sites
" Positive " Low energy to displace " Attracts carriers " Easy for the electrons to move " Enables conduction + + + + + " Movement of an electron best viewed as movement of hole " Negative? " Repel carriers ------" Disable conduction
------
Penn ESE 570 Spring 2016 - Khanna 17 Penn ESE 570 Spring 2016 - Khanna 18
3 Doped Band Gaps Field Effect?
! Addition of acceptor sites makes more metallic ! Effect of positive field on Acceptor-doped Silicon?
" Easier to conduct
Vgs=0 No field Semiconductor + + + + Ec 1.1ev 0.045ev EA Ev
Penn ESE 570 Spring 2016 - Khanna 19 Penn ESE 570 Spring 2016 - Khanna 20
Field Effect? Field Effect?
! Effect of positive field on Acceptor-doped Silicon? ! Effect of positive field on Acceptor-doped Silicon?
Vgs=0 Vgs=0 No field + + + + No field + + + + Vcap>0 Vcap>0 + + + + - - - + + + + - - -
+ + + + + Vgs>0 = No conduction
Penn ESE 570 Spring 2016 - Khanna 21 Penn ESE 570 Spring 2016 - Khanna 22
Field Effect? Field Effect?
! Effect of negative field on Acceptor-doped Silicon? ! Effect of negative field on Acceptor-doped Silicon?
Vgs=0 - - - Vgs=0 - - - No field + No field + Vcap<0 Vcap<0 + + + + + + + + + + + + + +
- - - Vgs>0 = Conduction + + + + +
Penn ESE 570 Spring 2016 - Khanna 23 Penn ESE 570 Spring 2016 - Khanna 24
4 MOSFETs MOSFET
! Donor doping ! Semiconductor can act like metal or insulator " Excess electrons ! Use field to modulate conduction state of " Negative or N-type material semiconductor " NFET
! Acceptor doping
" Excess holes " Positive or P-type material ------" PFET + + + + +
Penn ESE 570 Spring 2016 - Khanna 25 Penn ESE 570 Spring 2016 - Khanna 26
Two-Terminal MOS Structure
2
MOS Physics - nMOS GATE
Si – Oxide interface
n+ n+
(Mass Action Law)
Penn ESE 570 Spring 2016 - Khanna Penn ESE 570 Spring 2016 - Khanna 28
P-type Doped Semiconductor Band Gap P-type Doped Semiconductor Band Gap
Free space Free space
Electron affinity of silicon Electron affinity of silicon
Conduction band Conduction band E − E E = C V i 2 Intrinsic Fermi level Intrinsic Fermi level
Fermi level Fermi level qΦS qΦS Valence band Valence band
! qΦ and E are in units of energy = electron-volts (eV); where 1 eV = 1.6 x E − E kT n -19 Fermi potential: F i i 10 J. ΦF = → ΦFp = ln q q N A ! 1 eV corresponds to energy acquired by a free electron that is accelerated by
an electric potential of one volt. Work function (Fermi-to-space): qΦS = qχ + (EC − EF ) ! Φ and V corresponds to potential difference in volts. Penn ESE 570 Spring 2016 - Khanna 29 Penn ESE 570 Spring 2016 - Khanna 30
5 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
Penn ESE 570 Spring 2016 - Khanna 31 Penn ESE 570 Spring 2016 - Khanna 32
Accumulation Region Accumulation Region – Energy Bands
Accumulation Si surface
VG < 0 Band bending due to VG < 0
EFm qΦ qV E E S G= Fp− Fm qΦ(x) qΦFp EFp
x 0
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Depletion Region Depletion Region – Energy Bands
Depletion Si surface VG > 0 (small) Band bending due to VG > 0 tox
- - - - - mobile holes qΦ(x) qΦFp qV G= E Fp− E Fm EFp qΦS EFm
xd x 0
Penn ESE 570 Spring 2016 - Khanna 35 Penn ESE 570 Spring 2016 - Khanna 36
6 Depletion Region Depletion Region
kT ni kT ni ΦFp = ΦF = ln < 0 ΦFp = ΦF = ln < 0 q N A q N A
tox 26 mV at room T tox 26 mV at room T
ΦS Surface potential ΦS Surface potential - - - Φ - - - Φ - ΦFp Bulk potential - ΦFp Bulk potential
dQ = −qN Adx Mobile hole charge density (per unit area) in thin layer below surface dQ dφ = −x Potential required to displace dQ by distance x εSi q ⋅ N ⋅ x dφ = A dx εSi Penn ESE 570 Spring 2016 - Khanna 37 Penn ESE 570 Spring 2016 - Khanna 38
Depletion Region Depletion Region
kT ni kT ni ΦFp = ΦF = ln < 0 ΦFp = ΦF = ln < 0 q N A q N A
tox 26 mV at room T tox 26 mV at room T
ΦS Surface potential ΦS Surface potential - - - Φ - - - Φ - ΦFp Bulk potential - ΦFp Bulk potential
q ⋅ N A ⋅ x dφ = dx 2εSi ΦFp − ΦS εSi xd = q ⋅ N A
ΦFp xd 2 q ⋅ N A ⋅ x q ⋅ N A ⋅ xd dφ = dx = = Φ − Φ Q = −qN A xd ∫ ∫ 2 Fp S ΦS 0 εSi εSi 2εSi ΦFp − ΦS Q = −qN A = − 2qN AεSi ΦFp − ΦS 2εSi ΦFp − ΦS q ⋅ N A ⇒ xd = q ⋅ N A
Penn ESE 570 Spring 2016 - Khanna 39 Penn ESE 570 Spring 2016 - Khanna 40
Inversion Region Inversion Region – Energy Bands
Inversion Si surface VG ≥ VT (threshold voltage) VG ≥ VT0 > 0 tox
qΦFp ------E qΦS Fp qV G= E Fp− E Fm
EFm
xdm x (Density of mobile electrons = 0 density of holes in bulk)
Penn ESE 570 Spring 2016 - Khanna 41 Penn ESE 570 Spring 2016 - Khanna 42
7 Depletion Region – Energy Bands Inversion Region
Depletion Si surface VG ≥ VT (threshold voltage) VG > 0 (small) Band bending due to VG > 0
tox
qΦ(x) ------qΦFp qV G= E Fp− E Fm EFp qΦS EFm
xd (Density of mobile electrons = x density of holes in bulk) 0 Q = − 2qN AεSi ΦFp − ΦS = − 2qN AεSi 2ΦFp
Penn ESE 570 Spring 2016 - Khanna 43 Penn ESE 570 Spring 2016 - Khanna 44
2-terminal MOS Cap # 3-terminal nMOS nMOS = MOS cap + source/drain
VG VD VSB = 0 VS
------V G VD VS
------2εSi 2ΦFp −VSB - - - depletion region- - - xd = q ⋅ N A
Penn ESE 570 Spring 2016 - Khanna 45 Penn ESE 570 Spring 2016 - Khanna 46
Threshold Voltage Threshold Voltage
Q V [VT0 -> VT0 in SPICE] B0 T0n,p for VSB = 0 VT = VT 0 = VFB − 2ΦF − Cox Qox QB0 - VT 0 = ΦGC − − 2ΦF − - for nMOS and pMOS C C + ox ox for V != 0 + SB Q V = V − 2Φ − B VFB = flat band voltage T FB F Qox Cox V FB= 觻GC− ≈ 觻GC C ox Q Q −Q V = V − 2Φ − B0 − B B0 QB0 = − 2qN AεSi 2ΦF T FB F Cox Cox ) Q −Q V = V − B B0 with V = 0. T T 0 SB γ Cox VFB V FB Q −Q 2qN ε − B B0 = A Si 2Φ −V − 2Φ work function between gate and channel C C ( F SB F ) l ox ox V = V +γ 2Φ −V − 2Φ T T 0 ( F SB F )
Penn ESE 570 Spring 2016 - Khanna 47 Penn ESE 570 Spring 2016 - Khanna 48
8 Threshold Voltage Threshold Voltage
VSB is ≥ 0 in nMOS, ≤ 0 in pMOS |VSB| $ VT0 is positiveϨ言Ϩ in nMOS (VT0n) , negative in pMOS (VT0p)
Penn ESE 570 Spring 2016 - Khanna 49 Penn ESE 570 Spring 2016 - Khanna 50
Big Idea Admin
! 3 operation regions ! HW 2 due Thursday, 1/28 " Cut-off ! Office hours updated on Course website " Depletion
" Inversion ! No Journal Thursday this week ! Doping and VSB change VT
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