PHT.301 Physics of Semiconductor Devices | |
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PN diode IV characteristicsThe current-voltage characteristic of a diode is described by the diode equation, I=IS(exp(eVηkBT)−1)[A].Where I is the current, IS is the saturatuion current, e is the charge of an electron, V is the voltage, kB is Boltzmann's constant, η is the nonideality factor and T is the absolute temperature. For a real diode there is always a resistance RS in series. This modifies the diode equation to, I=IS(exp(e(V−IRS)ηkBT)−1)[A].This complicates the calculation since I now appears on both sides of the equation. However, such equations can be solved numerically, for instance by using a binary search. For a long diode, the saturation current can be written as, IS=Aen2i(DpLpNd+DnLnNa).Here A is the area of the diode perpendicular to the current flow, ni is the intrinsic carrier concentration, Nd is the donor concentration, Na is the acceptor concentration, Dn is the diffusion constant for electrons, Dp is the diffusion constant for holes, Ln=√Dnτn is the diffusion length for electrons, Lp=√Dpτp is the diffusion constant for holes, τn is the minority carrier lifetime for electrons, and τp is the minority carrier lifetime for holes. The derivation of the saturation current assumes that the dominant current mechanism is diffusion as it is in forward bias. While this equation describes forward bias well, the measured diode current in reverse bias often differs significantly from −IS. The intrinsic carrier density is a strong function of temperature, ni=√Nc(T300)3/2Nv(T300)3/2exp(−Eg2kBT).Here Nc is the effective density of states in the conduction band at 300 K, Nv is the effective density of states in the valence band at 300 K, and Eg is the band gap. The temperture dependence of the band gap can be input into the form below. The diffusion constants are related to the mobilities by the Einstein relation, Dn=μnkBTeDp=μpkBTe,where μn is the mobility of the electrons and μp is the mobility of the holes.
IS= 2.37e-17 [A]; ni= 2.66e+9 [cm-3]; Eg= 1.17 [eV]; Dn= 34.9 [cm²/s]; Dp= 12.4 [cm²/s]; Ln= 187 [μm]; Lp= 111 [μm];
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