ECE-305: Spring 2015 MOS Fundamentals Professor Mark Lundstrom Electrical and Computer Engineering Purdue University, West Lafayette, IN USA lundstro@purdue.edu Pierret, Semiconductor Device Fundamentals (SDF) pp. 525-530, 563-571 Lundstrom ECE 305 S15 3/29/15 MOS Fundamentals 1) MOSFET and MOS capacitors 2) E-bands and workfunctions 3) Bandbending in ideal MOS-C’s Lundstrom ECE 305 S15 2 MOSFETs S G D source drain silicon SiO2 gate electrode (Texas Instruments, ~ 2000) gate oxide EOT ~ 1.1 nm 3 channel ~ 20 nm MOSFET (off) VD L 0 ID = 0 VG < VT n+-Si n+-Si p-Si 4 Lundstrom ECE 305 S15 MOSFET (on) VD L 0 ID > 0 VG > VT n+-Si n+-Si p-Si Lundstrom ECE 305 S15 5 MOSFET and MOS C n+-Si n+-Si p-Si 6 MOS capacitor MOS capacitor SiO 2 VG t ox ≈ 1− 2 nm p-Si or n-Si 7 Lundstrom ECE 305 S15 oxide scaling 8 metal or heavily doped “polysilicon” e-band diagram E0 χi ΦM EC χS EC EFM EG = 1.12 eV Ei metal EF EG ≈ 8.9 eV EV Si SiO 2 EV 9 recall the MS junction E0 Φ M = 4.08 eV χ S = 4.05 eV ΦS EC EFM Ei aluminum 10 Lundstrom ECE 305 S15 Ei EFP EV built-in potential E0 χ S = 4.05 eV Φ M = 4.08 eV ΦS EC EFM Ei EFS EV aluminum potential = Vbi 11 Vbi = −Φ MS = −φms q qVbi = ( EFM − EFS ) = ( Φ S − Φ M ) = − ( Φ M − Φ S ) = −Φ MS example: Aluminum metal and p-type Si N A = 1016 cm -3 Φ M = 4.08 eV p0 = NV e( EV − EFS ) / kB T cm -3 Φ S = χ S + EG − ( EFS − EV ) q ⎛N ⎞ EFS − EV = kBT ln ⎜ V ⎟ ⎝ NA ⎠ Φ S = 4.97 eV ( 12 ⎡ m *p kBT NV = 2 ⎢ 2 ⎢⎣ 2π ! EFS − EV = 0.2 q ) ⎤⎥ ⎥⎦ 3/2 = 1.83 × 10 cm 19 -3 φ ms = ( Φ M − ΦS ) = − 0.9 V q Vbi = −φ ms = + 0.9 V now the band diagram E0 Φ M = 4.5 ΦS EC EFM Ei metal EFS EV Lundstrom ECE 305 S15 13 the band diagram EC qVbi Ei EF φM 14 EF EV metal Lundstrom ECE 305 S15 MOS e-band diagram E0 χi ΦM EC χS EC EFM EG = 1.12 eV Ei metal EF EV EG ≈ 8.9 eV Si SiO 2 15 EV MOS e-band diagram 1) Built-in potential is exactly the same. 2) But part of the voltage drop occurs across the semiconductor and part across the oxide. 16 Lundstrom ECE 305 S15 Ei equilibrium e-band diagram φS ΔVox V ( metal) = ΔVox + φS EC ΔVS Ei EF EV Vbi = −φms φ ( x ) = 0 in the bulk metal φ ( x = 0 ) = φS surface potential V ( metal) = Vbi 17 Question 1) Which of the following statements is true about the electric field in the semiconductor (near the oxidesemiconductor interface). a) b) c) d) e) It is 0 V/cm It is > 0 V/cm and constant It is < 0 V/cm and constant It is > 0 V/cm and non-constant It is < 0 V/cm and non-constant metal 18 EC Ei EF EV Question 2) Which of the following statements is true about the electric field in the oxide. a) b) c) d) e) It is 0 V/cm It is > 0 V/cm and constant It is < 0 V/cm and constant It is > 0 V/cm and non-constant It is < 0 V/cm and non-constant EC Ei EF EV metal 19 equilibrium e-band diagram ρ ( x) dE = dx ε constant electric field EC Ei EF EV metal V ( metal) = Vbi 20 monotonically decreasing electric field equilibrium e-band diagram Dox = DS K ox ε 0E ox = K S ε 0E S E ox = ΔVOX E S = E (0+ ) KS ES K OX EC ΔVS E ox E ox ≈ 3E S Ei EF EV Vbi metal 21 potential vs. position φ ( x) φS > 0 V ( metal) = Vbi = −φms = ΔVox + ΔVS φ=0 −xox 22 0 Lundstrom ECE 305 S15 x from the e-band diagram: e-field EC Ei EF EV metal V ( metal) = Vbi 23 electric field vs. position E ( x) E ox ES φ=0 −xox 0 Lundstrom ECE 305 S15 x 24 from the e-band diagram: charge density EC Ei EF EV Vbi 25 metal Lundstrom ECE 305 S15 space charge density vs. position ρ ( x) W 0 −xox x −qN A depletion charge Lundstrom ECE 305 S15 26 apply a voltage to the gate ΔVOX What happens if we apply a voltage to the gate? EC ΔVS Ei EF EV Si metal V ( metal) = Vbi + VG V ( metal) = Vbi = ΔVox + ΔVS → VG + Vbi = VG − φms = ΔVox + ΔVS → 27 e-band under “flat band” conditions What happens if we apply a negative voltage = φ ms ? MOS–C at the flat band voltage. EC Ei VG = −Vbi EF metal EV Si VG + Vbi = ΔVox + ΔVS → 0 = ΔVox + ΔVS 28 “ideal” MOS structure E0 χi EC χS ΦM EFM EC EG = 1.12 eV Ei EF EV EG ≈ 8 eV Si hypothetical metal SiO 2 29 Ei Vbi = 0 EV flat band conditions For an ideal MOS structure, flat band occurs for: VG = VFB = 0 For a real MOS structure, flat band occurs for: VG′ = VG − VFB = VG + Vbi = VG − φms VFB = φms 30 Lundstrom ECE 305 S15 VG = VFB = φms in Chapter 16 of SDF by Pierret VG means V’G; i.e. an ideal MOS structure with NO metal-semiconductor workfunction difference is assumed. 31 Lundstrom ECE 305 S15 band banding in an MOS device 32 Fig. 16.6, Semiconductor Device Fundamentals, R.F. Pierret next: band-bending and depletion approximation 1) V’G < 0: Accumulation (No depletion region) 2) 0 < V’G < VT: Depletion (depletion region) 3) V’G < VT: Inversion (depletion region + inversion layer) N-channel MOS (p-type substrate) 33 Lundstrom ECE 305 S15
