Semiconductor Electronics Set-3

Q1. An n-type silicon bar has cross-sectional area $A=1.0\ \text{mm}^2$ and donor concentration $N_D=5\times10^{15}\ \text{cm}^{-3}$ (assume full ionisation). Electron mobility is $\mu_n=1350\ \text{cm}^2\text{V}^{-1}\text{s}^{-1}$. A uniform electric field $E=20\ \text{V/cm}$ is applied. Using $q=1.6\times10^{-19}\ \text{C}$, the magnitude of the drift current is closest to:

Q2. Two diodes A and B follow $I=I_s\exp\!\left(\dfrac{qV}{n k T}\right)$. At $T=300\ \text{K}$ they have equal forward currents at $V_1=0.20\ \text{V}$. At $V_2=0.60\ \text{V}$, diode A's forward current is $100$ times that of diode B. The value of $\left(\dfrac{1}{n_A}-\dfrac{1}{n_B}\right)$ (dimensionless) is approximately:

Q3. For an intrinsic semiconductor $\sigma(T)\propto\exp\!\left(-\dfrac{E_g}{2kT}\right)$. Measured conductivities are $\sigma(300\ \text{K})=1.0\times10^{-4}\ \text{S/m}$ and $\sigma(400\ \text{K})=1.0\times10^{-2}\ \text{S/m}$. Estimate the band gap $E_g$ (in eV). (Take $k$ in SI units; give answer to two significant figures.)

Q4. An abrupt p–n junction in silicon ($\varepsilon_r=11.7$) has $N_A=10^{17}\ \text{cm}^{-3}$ (p-side) and $N_D=10^{16}\ \text{cm}^{-3}$ (n-side). The built-in potential is $\phi_0=0.70\ \text{V}$. Using

compute the total depletion width $W$ and the depletion portion on the n-side $x_n$ (give answers in $\mu\text{m}$). The closest values are:

Q5. Statement (I): For an n-type silicon sample at $300\ \text{K}$ with $N_D\gg n_i$, the majority electron concentration satisfies $n\approx N_D$.
Statement (II): The electron mobility $\mu_n$ is independent of donor concentration $N_D$ at all doping levels.
Choose the correct option:

Q6. Using the Einstein relation $D_n=\mu_n kT/q$ and diffusion length $L_n=\sqrt{D_n\tau_n}$, find $L_n$ for electrons if $\mu_n=1350\ \text{cm}^2\text{V}^{-1}\text{s}^{-1}$ and $\tau_n=1.0\ \mu\text{s}$ at $T=300\ \text{K}$. Give the result in $\mu\text{m}$ (nearest whole number):

Q7. Statement (I): The small‑signal (dynamic) resistance $r_d$ of a forward‑biased diode carrying DC current $I_D$ is $r_d=\dfrac{nV_T}{I_D}$ where $V_T=\dfrac{kT}{q}$.
Statement (II): For the exponential diode law, a small change $\delta V$ produces $\delta I\approx \dfrac{I_D}{nV_T}\,\delta V$, so $r_d=\delta V/\delta I=nV_T/I_D$.
Choose the correct option:

Q8. A full‑wave bridge rectifier is fed by an AC source with peak voltage $V_m=10\ \text{V}$. Each diode has forward drop $0.7\ \text{V}$. The filtered output uses $C=220\ \mu\text{F}$ and a load $R_L=1.0\ \text{k}\Omega$. The mains frequency is $50\ \text{Hz}$. Approximate the peak-to-peak ripple voltage $\Delta V$ at the output (assume capacitor charges to $V_m-2V_D$ and use small-ripple approximation):

Q9. For a silicon diode with $N_D=10^{16}\ \text{cm}^{-3}$ on the n-side and $N_A=10^{18}\ \text{cm}^{-3}$ on the p-side, intrinsic concentration $n_i=1.5\times10^{10}\ \text{cm}^{-3}$. Under forward bias $V=0.60\ \text{V}$ (at $T=300\ \text{K}$), the minority hole concentration at the n-side edge of the depletion region is

Estimate $p_n(0)$ and state whether low‑level injection ($p_n(0)\ll N_D$) holds.

Q10. For a one‑sided abrupt p+–n junction the Mott–Schottky relation gives

so the slope $m=\dfrac{d(1/C^2)}{dV}=\dfrac{2}{q\varepsilon A^2 N_D}$. A diode has area $A=1.0\ \text{cm}^2$, $\varepsilon_r=11.7$, and the measured slope is $m=1.20\times10^{15}\ \text{F}^{-2}\text{V}^{-1}$. Calculate the donor concentration $N_D$ (in $\text{cm}^{-3}$). (Take $\varepsilon_0=8.85\times10^{-12}\ \text{F/m}$, $q=1.6\times10^{-19}\ \text{C}$; convert units as needed.)