GATE Physics Electronics Syllabus

Electronics syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Electronics in GATE Physics, not a summary of it.

1. 1

   Semiconductors in Equilibrium

   4 topics

   • Electron and Hole Statistics
   • Intrinsic and Extrinsic Semiconductors
   • Metal-Semiconductor Junctions
   • Ohmic and Rectifying Contacts
2. 2

   Electronic Devices

   3 topics

   • PN Diodes
   • Bipolar Junction Transistors
   • Field Effect Transistors
3. 3

   Circuit Theory

   4 topics

   • Negative and Positive Feedback Circuits
   • Oscillators
   • Operational Amplifiers
   • Active Filters
4. 4

   Digital Logic Circuits

   7 topics

   • Basics of Digital Logic Circuits
   • Combinational and Sequential Circuits
   • Flip-Flops
   • Timers
   • Counters
   • Registers
   • A/D and D/A Conversion

Electronics flashcards for GATE Physics

22 of 66 cards from the Electronics deck — real questions with worked answers.

1. What is the law of mass action in a semiconductor at thermal equilibrium?

   The product of electron and hole concentrations is constant and equals the square of the intrinsic concentration: $$np = n_i^{2}$$ This holds for both intrinsic and extrinsic non-degenerate semiconductors at a given temperature.

2. Write the expression for the intrinsic carrier concentration $n_i$ in terms of the effective densities of states and band gap.

   $$n_i = \sqrt{N_c N_v}\,\exp\!\left(-\frac{E_g}{2k_BT}\right)$$ where $N_c$ and $N_v$ are the effective densities of states in the conduction and valence bands and $E_g$ is the band gap.

3. How does the electron concentration $n$ relate to the conduction-band edge $E_c$ and Fermi level $E_F$ (non-degenerate case)?

   $$n = N_c\,\exp\!\left(-\frac{E_c - E_F}{k_BT}\right)$$ Similarly $p = N_v\exp\!\left(-\dfrac{E_F - E_v}{k_BT}\right)$.

4. What is the temperature dependence of the effective density of states $N_c$ (and $N_v$)?

   $$N_c = 2\left(\frac{2\pi m_e^{*}k_BT}{h^{2}}\right)^{3/2}$$ so $N_c \propto T^{3/2}$ (with $m_e^{*}$ the electron density-of-states effective mass).

5. Where does the Fermi level lie in an ideal intrinsic semiconductor, and what is its exact position?

   Near mid-gap. Exactly: $$E_{F_i} = \frac{E_c + E_v}{2} + \frac{3}{4}k_BT\ln\!\left(\frac{m_h^{*}}{m_e^{*}}\right)$$ It is shifted from mid-gap only by the effective-mass asymmetry term.

6. Define an n-type and a p-type extrinsic semiconductor in terms of dopants.

   n-type: doped with donors (group V, e.g. P, As) that supply electrons; majority carriers are electrons. p-type: doped with acceptors (group III, e.g. B, Al) that supply holes; majority carriers are holes.

7. For an n-type semiconductor with full donor ionization ($N_D \gg n_i$), give the majority and minority carrier concentrations.

   $$n \approx N_D, \qquad p \approx \frac{n_i^{2}}{N_D}$$ Electrons are majority carriers; holes are minority carriers.

8. Write the charge-neutrality equation for a doped semiconductor (both donors and acceptors, fully ionized).

   $$n + N_A^{-} = p + N_D^{+}$$ i.e. (electrons + ionized acceptors) = (holes + ionized donors).

9. How does the Fermi level shift with doping in n-type vs p-type material?

   In n-type the Fermi level moves up toward the conduction band; in p-type it moves down toward the valence band. Specifically $E_F - E_{F_i} = k_BT\ln(n/n_i)$ (positive for n-type).

10. What are the three temperature regimes of carrier concentration in an extrinsic semiconductor?

    1) Freeze-out (low T): carriers bound to dopants. 2) Extrinsic/saturation (room T): all dopants ionized, $n \approx N_D$ roughly constant. 3) Intrinsic (high T): $n_i$ dominates and $n$ rises sharply.

11. Write the conductivity of a semiconductor in terms of carrier concentrations and mobilities.

    $$\sigma = q\left(n\mu_n + p\mu_p\right)$$ where $\mu_n,\mu_p$ are electron and hole mobilities and $q$ is the elementary charge.

12. State the Einstein relation between diffusion coefficient and mobility.

    $$\frac{D}{\mu} = \frac{k_BT}{q}$$ Thus $D_n = \mu_n\,V_T$ and $D_p = \mu_p\,V_T$ where $V_T = k_BT/q$ is the thermal voltage ($\approx 25.9$ mV at 300 K).

13. What is a metal-semiconductor junction and what determines whether it is rectifying or ohmic?

    A junction between a metal and a semiconductor. The behavior is set by the relation between the metal work function $\phi_m$ and semiconductor work function/electron affinity. A barrier (Schottky barrier) gives rectifying behavior; absence of a barrier (or a very thin one allowing tunneling) gives ohmic behavior.

14. Give the ideal Schottky barrier height for a metal on an n-type semiconductor.

    $$\phi_{B} = \phi_m - \chi$$ where $\phi_m$ is the metal work function and $\chi$ is the semiconductor electron affinity (Schottky-Mott rule).

15. For a metal on n-type semiconductor, what condition gives a rectifying (Schottky) contact vs an ohmic contact?

    Rectifying when $\phi_m > \phi_s$ (metal work function larger than semiconductor's), forming a depletion barrier. Ohmic when $\phi_m < \phi_s$, forming an accumulation layer with no barrier.

16. For a metal on p-type semiconductor, what condition gives a rectifying contact?

    Rectifying when $\phi_m < \phi_s$ (opposite of the n-type case); ohmic when $\phi_m > \phi_s$.

17. How is a practical ohmic contact usually achieved regardless of work-function matching?

    By heavily doping the semiconductor surface ($n^{+}$ or $p^{+}$). This makes the depletion barrier very thin so carriers tunnel through it freely, giving a low-resistance, linear (ohmic) contact.

18. Compare a Schottky diode with a PN junction diode in terms of carrier type and switching speed.

    Schottky diode: majority-carrier device, no minority-carrier storage, so very fast switching and low forward drop ($\sim 0.2$–$0.3$ V). PN diode: minority-carrier injection causes charge storage and slower switching, higher forward drop ($\sim 0.7$ V for Si).

19. What is the built-in potential of a PN junction?

    $$V_{bi} = \frac{k_BT}{q}\ln\!\left(\frac{N_A N_D}{n_i^{2}}\right)$$ It is the equilibrium potential difference across the junction due to doping.

20. Write the depletion-region width of an abrupt PN junction under bias $V$.

    $$W = \sqrt{\frac{2\varepsilon_s}{q}\left(\frac{1}{N_A}+\frac{1}{N_D}\right)(V_{bi}-V)}$$ where $\varepsilon_s$ is the semiconductor permittivity and $V>0$ for forward bias.

21. State the ideal diode (Shockley) equation.

    $$I = I_0\left(e^{\,qV/k_BT} - 1\right) = I_0\left(e^{\,V/V_T} - 1\right)$$ where $I_0$ is the reverse saturation current and $V_T = k_BT/q$.

22. How does the reverse saturation current $I_0$ of a PN diode depend on temperature qualitatively?

    $I_0 \propto n_i^{2} \propto T^{3}\exp(-E_g/k_BT)$, so it rises strongly with temperature — roughly doubling about every 10 °C for silicon.

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