An n-p-n silicon transistor has a neutral base of width

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Electronics, Instrumentation & Communication · Semiconductor devices and analogue circuits

Solid State Physics, Ch Junctions and devices, finished

Problem

An n-p-n silicon transistor has a neutral base of width WB=0.50 μmW_B=0.50\,\mu\mathrm{m}, doped NA=5.0×1016 cm−3N_A=5.0\times10^{16}\,\mathrm{cm^{-3}}, in which minority electrons have mobility μn=1000 cm2 V−1s−1\mu_n=1000\,\mathrm{cm^2\,V^{-1}s^{-1}} and lifetime τn=0.50 μs\tau_n=0.50\,\mu\mathrm{s}. The collector is doped ND=5.0×1015 cm−3N_D=5.0\times10^{15}\,\mathrm{cm^{-3}} and the collector-base junction is reverse biased at VCB=3.0 VV_{CB}=3.0\,\mathrm{V}. Take ni=1.0×1010 cm−3n_i=1.0\times10^{10}\,\mathrm{cm^{-3}}, εs=11.7\varepsilon_s=11.7 and kBT/e=25.85 mVk_BT/e=25.85\,\mathrm{mV}. ((a)) Find the base-transport gain β\beta. ((b)) Show that, at fixed emitter-base bias, the collector current varies as 1/WB1/W_B, and hence that its Early voltage is VA=WB/∣dWB/dVCB∣V_A=W_B/|dW_B/dV_{CB}|. ((c)) Find VAV_A.

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