Temperature Dependence of the Fermi Level −=kTEEExpNnCFc −=kTEEExpNpFVv =−CCFNnLnkTEE * =−VFVNpLnkTEE * For an n-type semiconductor at room temperature, DNn ≈ For an p-type semiconductor at room temperature, ANp ≈ As T increases, the doping becomes less important than the thermal generation of carriers FE tends to IE For an n-type, 0<∂∂TEF For an p-type, 0>∂∂TEF EI EC ED EA EV T p-type n-type EF(T)Thermoelectric Effect )(TEEFF= → A temperature gradient induces a Fermi Level Gradient N-type Semiconductor with a gradient of Temperature TEqVF∆=∆=∆−α1 α: Thermoelectric power, Seebeck Coefficient For n-type, 0<α, The induced electric field and the gradient of temperature are in the same direction. For p-type, 0>α, The induced electric field and the gradient of temperature are in opposite direction. ∆EF EC EV EI EF EC EV EI T T+∆T T∇E-+∆V>0Seebeck Coefficient For 0=∇T: xEqxEnJFnFnn∂∂=∂∂=1σµ For 0≠∇T: ∂∂−∂∂=xTxEqJFnnασ1 022)(<+−=+−−=nNLnqkqTkTEECFcnα 022)(>+=+−=pNLnqkqTkTEEvVFpα The Seebeck effect depends on carrier concentration and therefore depends on resistivity. For pratical purposes, Ω≈−mLnqksi610*56.2ρα Typically, for semiconductors, αis a few 100µV/KThermocouples TVba∆−=∆ )(αα T∇aEbE0>aα 0<bαThermoelectric Generation Efficiency: inLQIR2=η inQ: Thermal Power Input The efficiency is a function of Z: Figure of merit for Thermoelectric Material: ρκα2=Z ρ : Electrical resistivity κ : Thermal ConductivityPeltier Effect Opposite to Seebeck effect: Applied Voltage induces heat flow At a junction between two material A and B IQababΠ= With abΠthe Peltier coefficient ababTα=Π TITIQbaabab)(ααα−== Application: Thermoelectric