The GATE Grind

GATE 2017 EC – Question 46

Electronic Devices · Carrier Transport · 2 marks · Numerical answer

The dependence of drift velocity of electrons on electric field in a semiconductor is shown below. The semiconductor has a uniform electron concentration of $n = 1 \times 10^{16}$ cm$^{-3}$ and electronic charge $q = 1.6 \times 10^{-19}$ C. If a bias of 5 V is applied across a 1 $\mu$m region of this semiconductor, the resulting current density in this region, in kA/cm$^2$, is ________.

Drift velocity against electric field. The velocity rises linearly from 0 up to $10^7$ cm/s at an electric field of $5 \times 10^5$ V/cm, and then stays constant.

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: 1.59 to 1.61

Explanation

The field is $\frac{5\ \text{V}}{10^{-4}\ \text{cm}} = 5 \times 10^4$ V/cm, which is on the linear part of the curve. The velocity there is $10^7 \times \frac{5 \times 10^4}{5 \times 10^5} = 10^6$ cm/s. The current density is $J = qnv = 1.6 \times 10^{-19} \times 10^{16} \times 10^6 = 1.6 \times 10^3$ A/cm$^2$, which is 1.6 kA/cm$^2$.