Semiconductor Electronics Set-2

Q1. An abrupt silicon PN junction at $T=300\,$K has $N_A=10^{16}\,\text{cm}^{-3}$ and $N_D=10^{18}\,\text{cm}^{-3}$. Using $n_i=1.5\times10^{10}\,\text{cm}^{-3}$ and $kT/q\approx0.02585\,$V, compute the built‑in potential $V_{bi}$ from $V_{bi}=\dfrac{kT}{q}\ln\!\left(\dfrac{N_A N_D}{n_i^2}\right)$. (Nearest value)

Q2. Statement‑I: Under steady uniform optical illumination of an intrinsic semiconductor the excess carrier concentrations satisfy $\Delta n=\Delta p$, and the conductivity increment is $\Delta\sigma=q(\mu_n+\mu_p)\Delta n$.
Statement‑II: Photons create equal electron–hole pairs but since $\mu_n>\mu_p$ in most semiconductors the numerical change in conductivity is dominated by electrons even though $\Delta n=\Delta p$.

Q3. A silicon diode at $300\,$K has reverse saturation current $I_s=10^{-12}\,$A. Using the Shockley equation $I=I_s\left(e^{\frac{qV}{kT}}-1\right)$ with $kT/q\approx0.02585\,$V, estimate the forward current at $V=0.65\,$V. (Closest)

Q4. On a semilog plot (natural log) of forward current $I$ vs forward voltage $V$ at $T=300\,$K, two diodes P and Q show linear regions with slopes $s_P=19.35\ \text{V}^{-1}$ and $s_Q=38.70\ \text{V}^{-1}$ where $s=d(\ln I)/dV$. Using $s=\dfrac{q}{n k T}$, identify $n_P$, $n_Q$ and the dominant transport mechanism in P and Q.

Q5. Two reverse‑biased silicon diodes X and Y show sharp breakdowns at approximately $5.6\,$V and $60\,$V respectively. Experimentally, when temperature increases, $V_{BR,X}$ decreases while $V_{BR,Y}$ increases. Which statement best explains the observations?

Q6. For the circuit: $V_{CC}=12\,$V, $R_1=120\,$k$\Omega$ (to base from $V_{CC}$), $R_2=30\,$k$\Omega$ (base to ground), $R_C=4\,$k$\Omega$ (collector to $V_{CC}$). Take $V_{BE}=0.7\,$V and $\beta=50$. Using Thevenin for the base divider, determine the operating condition and approximate collector current.

Q7. Statement‑I: For an $n$‑type semiconductor, increasing temperature moves the Fermi level $E_F$ toward the mid‑gap (away from the conduction band edge).
Statement‑II: As temperature rises the intrinsic concentration $n_i$ increases, making the dopant contribution relatively less important; thus $E_F$ approaches the intrinsic level $E_i$, explaining the shift.

Q8. An intrinsic semiconductor sample shows conductivities $\sigma_1=1.0\times10^{-6}\ \text{S m}^{-1}$ at $T_1=300\,$K and $\sigma_2=2.5\times10^{-6}\ \text{S m}^{-1}$ at $T_2=330\,$K. Assuming intrinsic conduction with $\sigma\propto e^{-E_g/(2kT)}$, estimate the band gap $E_g$ (use $k=8.617\times10^{-5}\ \text{eV K}^{-1}$). (Nearest)

Q9. A diode biased at $V_D=0.7\,$V has DC current $I_D=1.0\,$mA and ideality factor $n=1$. It is in series with $R=100\ \Omega$. Using $V_T\approx0.02585\,$V and small‑signal resistance $r_d=nV_T/I_D$, a small increment $\Delta V_s=10\,$mV is applied to the source. Using the small‑signal model, estimate the incremental diode current $\Delta I$.

Q10. Two diodes D1 and D2 are in series and share the same forward current $I$. For $T=300\,$K the parameters are: D1: $n_1=1$, $I_{01}=10^{-12}\,$A; D2: $n_2=2$, $I_{02}=10^{-9}\,$A. They are forward biased together so that $V_{D1}+V_{D2}=0.80\,$V. Neglecting the “−1” in the diode equation, solve approximately for $I$ and determine which diode drops the larger voltage.