GATE 2014 EC (EC2) – Question 44
Given $q=1.6\times10^{-19}$ C, $kT/q=25$ mV and $\mu_n=1000$ cm²/(V·s), electrons injected into p-type silicon have concentration gradient $10^{21}$ cm⁻⁴. Find diffusion-current-density magnitude (A/cm²).
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Correct answer: 3990 to 4010
Explanation
Einstein’s relation gives Dn=µnVT=1000×0.025=25cm²/s. The diffusion-current magnitude is qDn|dn/dx|=1.6×10⁻¹⁹×25×10²¹=**4000A/cm²**. The gradient is per fourth power of length, so the resulting current density is per square centimetre.