**GATE 2016 EC SET B QUESTION 37**

GATE 2016 EC SET B QUESTION 37 :- Consider a region of silicon devoid of electrons and holes, with an ionized donor density of N^{+}_{d}=10^{17}cm^{-3}. The electric field at x = 0 is 0 V/cm and the electric field at x = L is 50 kV/cm in the positive x direction. Assume that the electric field is zero in the y and z directions at all points.

Given q=1.6×10^{-19} coulomb, ∈_{0}=8.85×10^{-14}F/cm,∈_{r}=11.7 for silicon, the value of L in nm is______________.

## Solution

We know that, dE/dx=qN_{D}/∈ . Hence from problem statement, we get

50×10^{3}/L =(1.6×10^{-19}×10^{17})/(8.854×10^{-14}×11.7)

=> L=(50×10^{3}×8.854×10^{-14}×11.7)/(1.6×10^{-2} )

=> L=32.372×10^{-9}m

### Answer to GATE 2016 EC SET B QUESTION 37

The answer is obtained by finding the length of region of silicon devoid of electrons and holes, with given ionized donor density and for which electric field has been given to be 32.372 nm