GATE E&C Engineering Electronic Devices Syllabus

Electronic Devices syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Electronic Devices in GATE E&C Engineering, not a summary of it.

1. 1

   Energy Bands in Semiconductors

   5 topics

   • Energy bands in intrinsic semiconductors
   • Energy bands in extrinsic semiconductors
   • Equilibrium carrier concentration
   • Direct band-gap semiconductors
   • Indirect band-gap semiconductors
2. 2

   Carrier Transport

   7 topics

   • Diffusion current
   • Drift current
   • Mobility and resistivity
   • Generation of carriers
   • Recombination of carriers
   • Poisson equations
   • Continuity equations
3. 3

   Semiconductor Devices

   8 topics

   • P-N junction
   • Zener diode
   • BJT (Bipolar Junction Transistor)
   • MOS capacitor (Metal-Oxide-Semiconductor capacitor)
   • MOSFET (Metal-Oxide-Semiconductor Field-Effect Transistor)
   • LED (Light Emitting Diode)
   • Photo diode
   • Solar cell

Electronic Devices flashcards for GATE E&C Engineering

25 of 59 cards from the Electronic Devices deck — real questions with worked answers.

1. In an intrinsic semiconductor at $T=0\,K$, how are the valence and conduction bands occupied?

   The valence band is completely full and the conduction band is completely empty, separated by the band gap $E_g$, so the material behaves as a perfect insulator at $0\,K$.

2. What is the position of the Fermi level $E_F$ in an intrinsic semiconductor, and what is its expression?

   It lies near the middle of the band gap: $$E_F = \frac{E_c + E_v}{2} + \frac{kT}{2}\ln\!\left(\frac{N_v}{N_c}\right)$$ At $T=0$ (or when $N_c=N_v$) it sits exactly at midgap.

3. Define the intrinsic carrier concentration $n_i$ and give its temperature dependence.

   $n_i$ is the equal electron and hole concentration in a pure semiconductor: $$n_i = \sqrt{N_c N_v}\;e^{-E_g/2kT}$$ It increases strongly with temperature ($n_i \propto T^{3/2}e^{-E_g/2kT}$).

4. What is the value of $n_i$ for silicon, germanium and GaAs at $300\,K$?

   Si: $n_i \approx 1.5\times10^{10}\,\text{cm}^{-3}$; Ge: $n_i \approx 2.5\times10^{13}\,\text{cm}^{-3}$; GaAs: $n_i \approx 2\times10^{6}\,\text{cm}^{-3}$.

5. How does doping with a donor (Group V) impurity create an n-type extrinsic semiconductor?

   Donor atoms (e.g. P, As, Sb in Si) introduce a shallow donor level just below $E_c$, each contributing one extra electron. Electrons become majority carriers and holes minority carriers.

6. How does doping with an acceptor (Group III) impurity create a p-type semiconductor?

   Acceptor atoms (e.g. B, Al, Ga in Si) introduce a shallow acceptor level just above $E_v$, each accepting an electron and creating a hole. Holes become majority carriers and electrons minority carriers.

7. How does the Fermi level shift in n-type and p-type extrinsic semiconductors?

   In n-type, $E_F$ moves up toward the conduction band $E_c$; in p-type, $E_F$ moves down toward the valence band $E_v$. The shift increases with doping concentration.

8. State the mass-action law relating $n$, $p$ and $n_i$ in a semiconductor at equilibrium.

   $$np = n_i^{2}$$ This holds in thermal equilibrium for any doping level (non-degenerate).

9. For an n-type semiconductor with donor concentration $N_D \gg n_i$, give the equilibrium electron and hole concentrations.

   $$n \approx N_D, \qquad p = \frac{n_i^{2}}{N_D}$$

10. For a p-type semiconductor with acceptor concentration $N_A \gg n_i$, give the equilibrium hole and electron concentrations.

    $$p \approx N_A, \qquad n = \frac{n_i^{2}}{N_A}$$

11. Write the charge-neutrality equation used to find equilibrium carrier concentrations.

    $$p + N_D^{+} = n + N_A^{-}$$ With full ionization: $p + N_D = n + N_A$.

12. Express the equilibrium carrier concentrations in terms of the Fermi level using $E_c$ and $E_v$.

    $$n = N_c\,e^{-(E_c - E_F)/kT}, \qquad p = N_v\,e^{-(E_F - E_v)/kT}$$

13. What characterizes a direct band-gap semiconductor in terms of $E$ vs $k$?

    The conduction-band minimum and valence-band maximum occur at the same crystal momentum $k$ (typically $k=0$, the $\Gamma$ point). Electron-hole recombination needs no phonon, so radiative transitions are efficient.

14. Give two examples of direct band-gap semiconductors and a typical application.

    GaAs and InP (also GaN). Used in LEDs, laser diodes and optoelectronic emitters because of efficient radiative recombination.

15. What characterizes an indirect band-gap semiconductor?

    The conduction-band minimum and valence-band maximum occur at different values of $k$. Recombination requires a phonon to conserve momentum, making radiative emission inefficient.

16. Give two examples of indirect band-gap semiconductors.

    Silicon (Si) and Germanium (Ge). They are poor light emitters but excellent for electronic devices.

17. Why are direct band-gap materials preferred for light emission over indirect ones?

    In direct-gap materials recombination conserves momentum without a phonon, giving fast, efficient radiative recombination. Indirect-gap materials need a phonon, making radiative transitions slow and dominated by non-radiative paths.

18. Define diffusion current and state its physical cause.

    Diffusion current arises from a concentration gradient of carriers; carriers move from high to low concentration regions due to random thermal motion, independent of any electric field.

19. Write the diffusion current density equations for electrons and holes.

    $$J_{n,\text{diff}} = q D_n \frac{dn}{dx}, \qquad J_{p,\text{diff}} = -q D_p \frac{dp}{dx}$$ where $D_n, D_p$ are diffusion coefficients.

20. Define drift current and write its current-density expressions.

    Drift current is carrier motion due to an applied electric field $E$: $$J_{n,\text{drift}} = q n \mu_n E, \qquad J_{p,\text{drift}} = q p \mu_p E$$

21. Write the total current density in a semiconductor including both drift and diffusion.

    $$J = J_n + J_p$$ $$J_n = q n \mu_n E + q D_n \frac{dn}{dx}, \quad J_p = q p \mu_p E - q D_p \frac{dp}{dx}$$

22. State the Einstein relation linking diffusion coefficient and mobility.

    $$\frac{D_n}{\mu_n} = \frac{D_p}{\mu_p} = \frac{kT}{q} = V_T$$ where $V_T \approx 25.9\,\text{mV}$ at $300\,K$.

23. Define carrier mobility $\mu$ and give its units.

    Mobility is the drift velocity per unit electric field: $\mu = \frac{v_d}{E}$, with units $\text{cm}^2/(V\cdot s)$. It measures how easily carriers move under a field.

24. Compare electron and hole mobility in silicon and explain.

    In Si, $\mu_n \approx 1350\,\text{cm}^2/Vs$ and $\mu_p \approx 480\,\text{cm}^2/Vs$. Electrons are more mobile than holes because of their smaller effective mass, so $\mu_n > \mu_p$.

25. How do mobility and conductivity depend on temperature and doping at high doping?

    At high doping/low temperature, ionized-impurity scattering dominates ($\mu \propto T^{3/2}$, rising with T); at high temperature, lattice (phonon) scattering dominates ($\mu \propto T^{-3/2}$, falling with T). Mobility decreases with increasing doping.

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