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 Penn ESE 570 Spring 2016 - Khanna 33 Penn ESE 570 Spring 2016 - Khanna 34 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 Penn ESE 570 Spring 2016 - Khanna 51 Penn ESE 570 Spring 2016 - Khanna 52 9 .