Materials & Atomic Structure

Q1. (4 marks)

• Bohr postulate: the energy of the $n$-th allowed orbit is $E_n = -\dfrac{13.6}{n^2}\ \text{eV}$ (energy is quantised; electrons occupy fixed orbits without radiating). (2 marks) — the quantisation/fixed-orbit idea is the core of the model.
• Maximum electrons in shell $n$ is $2n^2$. (2 marks) — standard shell-capacity rule (e.g. K=2, L=8, M=18).

Q2. (4 marks)

• Valence electrons = the electrons in the outermost shell of an atom, which participate in chemical bonding. (2 marks)
• Silicon has 4 valence electrons (1 mark) and belongs to Group IV (14) of the periodic table (1 mark).

Q3. (4 marks)

• A covalent bond is the sharing of a pair of electrons between two adjacent atoms. (2 marks)
• Each silicon atom shares one electron with each of its 4 neighbours; combined with its own 4 valence electrons, this gives an effective 8 electrons in the outer shell — a stable (filled octet) configuration. (2 marks)

Q4. (4 marks)

• Intrinsic: a pure semiconductor with no added impurities; conduction arises only from thermally generated electron–hole pairs. (1.5 marks)
• Extrinsic: a semiconductor deliberately doped with impurity atoms (donors/acceptors) to increase carrier concentration and control conductivity. (1.5 marks)
• For intrinsic material: $n = p = n_i$. (1 mark)

Q5. (5 marks)

• Mobility = drift velocity acquired by a carrier per unit applied electric field. (1.5 marks)
• SI unit: $\text{m}^2\,\text{V}^{-1}\,\text{s}^{-1}$. (1 mark)
• Calculation: $v_d = \mu_n E = 0.135 \times 500 = 67.5\ \text{m/s}$. (2.5 marks) — substitution (1) and correct result with unit (1.5).

Q6. (4 marks)

• Thermal energy breaks a covalent bond, freeing an electron and leaving behind a vacancy (a hole); the freed electron and hole form an electron–hole pair, both able to conduct. (3 marks)
• As temperature rises, more bonds break so $n_i$ increases (roughly exponentially with $T$). (1 mark)

Q7. (5 marks)

• $\sigma = q\,n_i(\mu_n + \mu_p)$. (1 mark)
• $\mu_n + \mu_p = 0.135 + 0.048 = 0.183$. (1 mark)
• $\sigma = 1.6\times10^{-19} \times 1.5\times10^{16} \times 0.183$. (1 mark)
• $= 1.6\times1.5\times0.183 \times 10^{-3} = 0.43920 \times 10^{-3} \approx 4.39\times10^{-4}\ \text{S/m}$. (2 marks)

Q8. (3 marks) — any three, 1 mark each:

• Silicon forms a stable, high-quality native oxide ($\text{SiO}_2$) essential for MOS technology.
• Higher bandgap (~1.1 eV) → lower leakage current and operation at higher temperatures than germanium (~0.66 eV).
• Abundant and cheap (from sand); mature, well-developed fabrication technology.

Q9. (3 marks) — any three, 1 mark each (semiconductor + valid application):

• GaN — LEDs, high-power/high-frequency RF and power devices.
• GaAs — high-speed microwave/RF circuits, laser diodes, solar cells.
• SiC — high-power, high-temperature power electronics (e.g. EV inverters).

Q10. (4 marks)

• Metal: conductivity decreases with rising temperature. (1 mark) — increased lattice vibrations scatter carriers, reducing mobility (carrier count is fixed). (1 mark)
• Intrinsic semiconductor: conductivity increases with rising temperature. (1 mark) — the exponential rise in thermally generated carriers ($n_i$) outweighs the fall in mobility. (1 mark)

[
  {"claim":"Q1 shell capacity 2n^2 gives L-shell (n=2) capacity of 8","code":"n=2; result = (2*n**2 == 8)"},
  {"claim":"Q5 drift velocity = mu*E = 0.135*500 = 67.5 m/s","code":"vd = 0.135*500; result = abs(vd - 67.5) < 1e-9"},
  {"claim":"Q7 conductivity approx 4.392e-4 S/m","code":"q=1.6e-19; ni=1.5e16; sigma=q*ni*(0.135+0.048); result = abs(sigma - 4.392e-4) < 1e-7"},
  {"claim":"Q7 mobility sum equals 0.183","code":"result = abs((0.135+0.048) - 0.183) < 1e-12"}
]