Topics MOSFET Gate as Capacitor ! Derivation of transistor characteristics. ! Basic structure of gate is parallel-plate capacitor: gate + xox Vg SiO2 - substrate Slides courtesy Modern VLSI Design, 3rd Edition Slides courtesy Modern VLSI Design, 3rd Edition Parallel Plate Capacitance Threshold Voltage ! Formula for parallel plate capacitance: Components of threshold voltage Vt: C = ε /x ox ox ox ! Vfb = flatband voltage; depends on difference in work ! Permittivity of silicon: function between gate and substrate and on fixed surface ε -13 2 ox = 3.46 x 10 F/cm charge. φ φ ! Gate capacitance helps determine charge in channel which ! s = surface potential (about 2 f). forms inversion region. ! Voltage on parallel plate capacitor. ! Additional ion implantation. Slides courtesy Modern VLSI Design, 3rd Edition Slides courtesy Modern VLSI Design, 3rd Edition Example: Threshold Voltage of a Body Effect Transistor φ ! Reorganize threshold voltage equation: Vt0 =Vfb + s +Qb/Cox + VII ∆ Vt = Vt0 + Vt = -0.91 V + 0.58 V + (1.4E-8/1.73E-7) + 0.92 V ! Threshold voltage is a function of source/substrate = 0.68 V voltage V . γ ε sb Body effect n =sqrt(2q SiNA/Cox) = 0.1 ! Body effect γ is the coefficienct for the V dependence ∆ γ φ sb Vt = n[sqrt( s +Vsb) - sqrt(Vs)] factor. = 0.16 V Slides courtesy Modern VLSI Design, 3rd Edition Slides courtesy Modern VLSI Design, 3rd Edition Channel Length Modulation Length More Device Parameters Parameter µ λ ! Process transconductance k’ = Cox. ! describes small dependence of drain corrent on Vds in ! Device transconductance β =k’W/L. saturation. ! Factor is measured empirically. ! New drain current equation: 2 λ ! Id = 0.5k’ (W/L)(Vgs -Vt) (l - Vds) ! Equation has a discontinuity between linear and saturation regions---small enough to be ignored. Slides courtesy Modern VLSI Design, 3rd Edition Slides courtesy Modern VLSI Design, 3rd Edition Gate Voltage and the Channel Leakage and Subthreshold Current gate ! A variety of leakage currents draw current away from the current source drain main logic path. Vds < Vgs -Vt I d ! The subthreshold current is one particularly important type of leakage current. gate current source drain Vds = Vgs -Vt Id gate current source drain Vds > Vgs -Vt Id Slides courtesy Modern VLSI Design, 3rd Edition Slides courtesy Modern VLSI Design, 3rd Edition Types of Leakage Current. Subthreshold Current ! Weak inversion current (a.k.a. subthreshold current). ! Subthreshold current: [(Vgs - Vt)/(S/ln 10)] -qVds/kT ! Reverse-biased pn junctions. ! Isub=ke [1-e ] ! Drain-induced barrier lowering. ! Subthreshold slope S characterizes weak inversion current. ! Gate-induced drain leakage; ! Subthreshold current is a function of V . ! Punchthrough currents. t ! Can adjust Vt by changing the substrate bias to control leakage. ! Gate oxide tunneling. ! Hot carriers. Slides courtesy Modern VLSI Design, 3rd Edition Slides courtesy Modern VLSI Design, 3rd Edition The Modern MOSFET Circuit Simulation Features of deep submicron MOSFETs: ! Circuit simulators like Spice numerically solve device ! epitaxial layer for heavily-doped channel; models and Kirchoff’s laws to determine time-domain ! reduced area source/drain contacts for lower capacitance; circuit behavior. ! lightly-doped drains to reduce hot electron effects; ! Numerical solution allows more sophisticated models, non- ! silicided poly, diffusion to reduce resistance. functional (table-driven) models, etc. Slides courtesy Modern VLSI Design, 3rd Edition Slides courtesy Modern VLSI Design, 3rd Edition Some (by no means all) Spice Model Spice MOSFET Models Parameters ! Level 1: basic transistor equations of Section 2.2; not very ! L, W: transistor length width. accurate. ! KP: transconductance. ! Level 2: more accurate model (effective channel length, ! GAMMA: body bias factor. etc.). ! AS, AD: source/drain areas. ! Level 3: empirical model. ! CJSW: zero-bias sidewall capacitance. ! Level 4 (BSIM): efficient empirical model. ! CGBO: zero-bias gate/bulk overlap capacitance. ! New models: level 28 (BSIM2), level 47 (BSIM3). Slides courtesy Modern VLSI Design, 3rd Edition Slides courtesy Modern VLSI Design, 3rd Edition.