Semiconductor Electronics Set-4

Q1. A silicon sample at $300\ \text{K}$ has intrinsic carrier concentration $n_i=1.5\times10^{16}\ \text{m}^{-3}$ and is doped n-type with donor concentration $N_D=1.0\times10^{20}\ \text{m}^{-3}$. Electron mobility $\mu_n=0.14\ \text{m}^2\text{V}^{-1}\text{s}^{-1}$ and hole mobility $\mu_p=0.05\ \text{m}^2\text{V}^{-1}\text{s}^{-1}$. Assuming complete ionization and $q=1.6\times10^{-19}\ \text{C}$, use $n\approx N_D$ and $p=\dfrac{n_i^2}{N_D}$ to estimate the conductivity $\sigma=q(n\mu_n+p\mu_p)$ of the sample (in S/m) approximately.

Q2. At $T=300\ \text{K}$ an abrupt silicon p–n junction has doping $N_A=8\times10^{22}\ \text{m}^{-3}$ and $N_D=2\times10^{24}\ \text{m}^{-3}$. Intrinsic concentration $n_i=1.5\times10^{16}\ \text{m}^{-3}$, $\epsilon_r=11.7$, $\epsilon_0=8.85\times10^{-12}\ \text{F/m}$ and $q=1.6\times10^{-19}\ \text{C}$. Using $V_{bi}=\dfrac{kT}{q}\ln\!\left(\dfrac{N_A N_D}{n_i^2}\right)$ with $kT/q\approx0.02585\ \text{V}$ and the depletion width formula for an abrupt junction $W=\sqrt{\dfrac{2\epsilon_s V_{bi}}{q}\left(\dfrac{1}{N_A}+\dfrac{1}{N_D}\right)}$ where $\epsilon_s=\epsilon_r\epsilon_0$, calculate the total depletion width $W$ (in $\mu$m) and the maximum electric field $E_{\max}$ (in MV/m) at zero bias. Choose the closest pair.

Q3. An NPN transistor in common-emitter configuration has current gain $\beta=100$. Circuit: $V_{CC}=12\ \text{V}$, collector resistor $R_C=1.5\ \text{k}\Omega$, base resistor $R_B=240\ \text{k}\Omega$ connected between $V_{CC}$ and base, emitter grounded. Take $V_{BE}\approx0.7\ \text{V}$. Using $I_B=\dfrac{V_{CC}-V_{BE}}{R_B}$ and $I_C=\beta I_B$, determine the transistor's region of operation and give the approximate collector current $I_C$ and collector voltage $V_C$ (w.r.t ground).

Q4. A semiconductor diode at $300\ \text{K}$ follows $I=I_S\exp\!\left(\dfrac{V}{nV_T}\right)$ with $V_T=kT/q\approx0.02585\ \text{V}$. Measured forward currents: $I=0.10\ \text{mA}$ at $V=0.60\ \text{V}$ and $I=1.00\ \text{mA}$ at $V=0.70\ \text{V}$. Assuming the same ideality factor $n$, determine $n$ and estimate the forward current at $V=0.75\ \text{V}$.

Q5. Two diodes of the same area at the same temperature carry the same forward current. One diode is silicon with $E_{g,\mathrm{Si}}=1.12\ \text{eV}$ and the other is germanium with $E_{g,\mathrm{Ge}}=0.67\ \text{eV}$. Ignoring prefactors in the saturation current, the approximate difference in their forward voltages $V_{\mathrm{Si}}-V_{\mathrm{Ge}}$ is:

Q6. In an n-type silicon sample at room temperature the intrinsic carrier concentration is $n_i=1.5\times10^{10}\ \mathrm{cm^{-3}}$ and the donor concentration is $N_D=1.0\times10^{16}\ \mathrm{cm^{-3}}$. Using the mass-action law, the minority hole concentration $p$ (in $\mathrm{cm^{-3}}$) is approximately:

Q7. A half-wave rectifier with an ideal diode (forward drop $0.7\ \text{V}$) is fed from a transformer secondary of RMS voltage $12\ \text{V}$. The rectified output charges a smoothing capacitor $C=100\ \mu\mathrm{F}$ which supplies a load resistor $R=1\ \mathrm{k\Omega}$. If the mains frequency is $50\ \mathrm{Hz}$, estimate the peak-to-peak ripple voltage $\Delta V$ across the load. (Use $V_m=12\sqrt{2}\ \mathrm{V}$ and approximate $\Delta V\approx I_{\text{load}}/(fC)$ for half-wave.)

Q8. A silicon NPN transistor has a voltage-divider bias from $V_{CC}=12\ \text{V}$ with $R_1=100\ \text{k}\Omega$ (to $V_{CC}$) and $R_2=40\ \text{k}\Omega$ (to ground). The emitter resistor $R_E=1\ \text{k}\Omega$ and $\beta=50$. Taking $V_{BE}=0.7\ \text{V}$ and using the Thevenin equivalent of the base bias, the collector current $I_C$ is approximately:

Q9. Assertion (A): For a silicon p–n junction diode, at a fixed forward current the forward voltage drop decreases as temperature increases. Reason (R): Increasing temperature raises the intrinsic carrier concentration $n_i$ and hence the saturation current $I_s$; from the diode equation $I=I_s e^{V/V_T}$ (with $V_T=kT/q$) a larger $I_s$ requires a smaller $V$ to keep $I$ constant. Which of the following is correct?

Q10. Two diodes of the same area at the same temperature carry the same forward current. One diode is silicon with $E_{g,\mathrm{Si}}=1.12\ \text{eV}$ and the other is germanium with $E_{g,\mathrm{Ge}}=0.67\ \text{eV}$. Ignoring prefactors in the saturation current, the approximate difference in their forward voltages $V_{\mathrm{Si}}-V_{\mathrm{Ge}}$ is:

Q11. (A silicon diode at $T=300\ \text{K}$ has a reverse saturation current $I_0=10^{-12}\ \text{A}$. Using the ideal diode equation $I=I_0\left(e^{qV/kT}-1\right)$ and $kT/q\approx 25.85\ \text{mV}$, estimate the forward current when the diode is biased at $V=0.60\ \text{V}$.)

Q12. (An NPN transistor has $\beta=40$. It is connected in a common-emitter fixed-bias arrangement with $V_{CC}=12\ \text{V}$, $R_C=3.0\ \text{k}\Omega$, base resistor $R_B$ connected to $V_{CC}$, $V_{BE}=0.7\ \text{V}$ and $V_{CE(\text{sat})}=0.2\ \text{V}$. Find the maximum value of $R_B$ (approx.) for which the transistor just reaches saturation when base is driven by $V_{CC}$.)

Q13. (A diode with forward drop $0.7\ \mathrm{V}$ is in series with a large resistance and driven by $v(t)=10\sin\omega t + 3\ \mathrm{V}$. For what fraction of each cycle does the diode conduct? (Hint: find range of $\omega t$ for which $10\sin\omega t+3>0.7$.) )

Q14. (For a PN junction at fixed temperature and intrinsic concentration $n_i$, the built-in potential and depletion width are given by $V_{bi}=(kT/q)\ln\left(\dfrac{N_A N_D}{n_i^2}\right)$ and

and the reverse saturation current roughly scales as $I_S\propto n_i^2\left(\dfrac{1}{N_A}+\dfrac{1}{N_D}\right)$. If both doping concentrations $N_A$ and $N_D$ are increased by a factor of $100$ (keeping $T$ and $n_i$ constant), which of the following is correct? )

Q15. (A CE amplifier has $V_{CC}=20\ \mathrm{V}$, $R_C=2.0\ \mathrm{k}\Omega$ and is biased so that $I_{CQ}=2.0\ \mathrm{mA}$ and $V_{CEQ}=10\ \mathrm{V}$ (emitter at 0V). Assuming $V_{CE(\text{sat})}=0.2\ \mathrm{V}$, what is the maximum symmetrical undistorted peak amplitude (single-sided peak) of the collector output voltage $v_c$ about its Q-point? )