GATE EC 2025 Question Paper (15-Feb-2025) (Shift 2)

The intrinsic carrier concentration of a semiconductor is $2.5\times 10^{16}/m^3$ at $300K$. If the electron and hole mobilities are $0.15m^2/Vs$ and $0.05m^2/Vs$, respectively, then the intrinsic resistivity of the semiconductor (in $k\Omega .m$) at $300K$ is __________.
(Charge of an electron $e=1.6\times 10^{-19}C$.)

In the circuit shown, the identical transistors $Q1$ and $Q2$ are biased in the active region with $\beta =120$. The Zener diode is in the breakdown region with $V_Z=5V$ and $I_Z=25mA$. If $I_L=12mA$ and $V_{EB1}=V_{EB2}=0.7V$, then the values of $R_1$ and $R_2$ (in $k\Omega$, rounded off to one decimal place) are __________ respectively.

The electron mobility ${\mu }_n$ in a non-degenerate germanium semiconductor at $300K$ is $0.38m^2/Vs$.

The electron diffusivity $D_n$ at $300K$ (in $c{m}^2/s$, rounded off to the nearest integer) is __________.
(Consider the Boltzmann constant $k_B=1.38\times 10^{-23}J/K$ and the charge of an electron $e=1.6\times 10^{-19}C$.)

A square metal sheet of $4m\times 4m$ is placed on the x-y plane as shown in the figure below.

If the surface charge density (in $\mu C/m^2$) on the sheet is ${\rho }_s(x,y)=4|y|$, then the total charge (in $\mu C$, rounded off to the nearest integer) on the sheet is __________.

An electric field of $0.01V/m$ is applied along the length of a copper wire of circular cross-section with diameter $1mm$. Copper has a conductivity of $5.8\times 10^{7}S/m$. The current (in Amperes, rounded off to two decimal places) flowing through the wire is __________.