EECS 105 Spring2005 Lecture 2 R. T. Howe EECS 105 Spring2005 Lecture 2 R. T. Howe Lecture 2 Thermal Equilibrium Rapid, random motion of holes and electrons at 7 • Last time: “thermal velocity” vth = 10 cm/s with collisions every τ = 10-13 s. – Course introduction c – Start: semiconductor properties of Si Apply an electric field E and charge carriers accelerate … for τc seconds • Today : zero E field – Drift velocity v – Drift current density th (hole case) – Resistivity and resistance; the IC resistor positive E aτ c v x th Dept. of EECS University of California, Berkeley Dept. of EECS University of California, Berkeley EECS 105 Spring2005 Lecture 2 R. T. Howe EECS 105 Spring2005 Lecture 2 R. T. Howe Drift Velocity and Mobility Mobility vs. Doping in Silicon at 300 K F qE qτ v = a ⋅τ = e τ = τ = c E dr c c c mp mp mp vdr = µ p E For electrons: “default” values: Dept. of EECS University of California, Berkeley Dept. of EECS University of California, Berkeley 1 EECS 105 Spring2005 Lecture 2 R. T. Howe EECS 105 Spring2005 Lecture 2 R. T. Howe Velocity Saturation Drift Current Density (Holes) Hole case: drift velocity is in same direction as E hole drift current density J dr p v dp E x The hole drift current density is: J dr = q p µ E p p Dept. of EECS University of California, Berkeley Dept. of EECS University of California, Berkeley EECS 105 Spring2005 Lecture 2 R. T. Howe EECS 105 Spring2005 Lecture 2 R. T. Howe Drift Current Density (Electrons) Resistivity Electron case: drift velocity is in opposite direction as E Bulk silicon: uniform doping concentration, away electron drift from surfaces current density J dr n-type example: in equilibrium, no = Nd . n v dn When we apply an electric field, n = Nd . E dr Jn = x Jn = qµnnE = qµn Nd E The electron drift current density is: Conductivity σn = dr -2 -1 -2 Jn = (-q) n vdn units: Ccm s = Acm Resistivity ρn = Dept. of EECS University of California, Berkeley Dept. of EECS University of California, Berkeley 2 EECS 105 Spring2005 Lecture 2 R. T. Howe EECS 105 Spring2005 Lecture 2 R. T. Howe Ohm’s Law Sheet Resistance • Current I in terms of J n • IC resistors have a specified thickness – not • Voltage V in terms of electric field under the control of the circuit designer • Eliminate t by absorbing it into a new parameter: the sheet resistance ρL ρ L L R = = = Rsq Wt t W W – Result for R Dept. of EECS University of California, Berkeley Dept. of EECS University of California, Berkeley EECS 105 Spring2005 Lecture 2 R. T. Howe EECS 105 Spring2005 Lecture 2 R. T. Howe Using Sheet Resistance Idealizations • Ion-implanted (or “diffused”) IC resistor • Why does current density Jn “turn”? • What is the thickness of the resistor? • What is the effect of the contact regions? Dept. of EECS University of California, Berkeley Dept. of EECS University of California, Berkeley 3.