When phosphorus (group 15) is doped into silicon (group 14), each P atom contributes one extra electron to the conduction band. Why does this make the material n-type rather than simply changing the lattice energy?
Think about your answer, then reveal below.
Model answer: Phosphorus has 5 valence electrons versus silicon's 4. Four of P's electrons participate in covalent bonds with neighboring Si atoms, mimicking Si. The fifth electron is only weakly bound to the P+ core (binding energy ~45 meV, far less than kT at room temperature), so it ionizes into the conduction band at room temperature. This creates a free electron without creating a hole in the valence band, making the material n-type. The donor level sits just below the conduction band edge in the band diagram.
The key chemistry insight is that aliovalent substitution in a covalent crystal creates localized states near the band edges. Donors (extra electrons) create states just below the conduction band; acceptors (missing electrons) create states just above the valence band. The shallow binding energy (~40-50 meV for common dopants in Si) means complete ionization at room temperature, giving precise control over carrier concentration through dopant concentration. This is why semiconductor purity and controlled doping are central to the entire electronics industry.
Question 2 Multiple Choice
GaAs is a direct band gap semiconductor (1.42 eV) while Si has an indirect band gap (1.12 eV). Which statement correctly explains why GaAs is preferred for LEDs and laser diodes?
AGaAs has a larger band gap, so it emits higher-energy photons
BIn GaAs, electrons and holes recombine directly by emitting a photon without requiring a phonon, making radiative recombination far more efficient
CGaAs has higher electron mobility, which increases the rate of photon emission
DSilicon cannot emit light under any circumstances due to its crystal structure
In a direct gap material, the conduction band minimum and valence band maximum are at the same point in k-space (both at the Gamma point for GaAs). An electron can drop from the conduction band to the valence band by emitting a photon that carries away the energy — momentum is automatically conserved because Delta-k is approximately zero. In silicon's indirect gap, the band extrema are at different k-values, so recombination requires a phonon to conserve momentum. This three-particle process (electron + hole + phonon) is far less probable than the two-particle radiative process, making Si a very inefficient light emitter.
Question 3 True / False
Compound semiconductors like GaAs offer tunable band gaps not available from elemental semiconductors.
TTrue
FFalse
Answer: True
Elemental semiconductors are limited to the band gaps of Si (1.12 eV), Ge (0.67 eV), and diamond (5.5 eV). Compound semiconductors span a continuous range: InSb (0.17 eV) through GaAs (1.42 eV) to GaN (3.4 eV) to AlN (6.2 eV). Moreover, ternary and quaternary alloys (e.g., Al_xGa_{1-x}As, In_xGa_{1-x}N) allow continuous tuning of the band gap by varying composition x. This tunability is essential for designing materials that absorb or emit at specific wavelengths — the basis of LEDs, lasers, detectors, and multi-junction solar cells.
Question 4 True / False
Silicon's dominance in the electronics industry is primarily due to its superior electronic properties compared to all other semiconductors.
TTrue
FFalse
Answer: False
Silicon's dominance is primarily due to the exceptional quality of its native oxide (SiO2), the abundance of silicon in the Earth's crust, and decades of manufacturing optimization — not superior intrinsic electronic properties. GaAs has ~6x higher electron mobility; GaN has superior breakdown voltage and thermal stability; Ge has higher hole mobility. But SiO2 forms a near-perfect, stable, electrically insulating gate dielectric on Si surfaces, which was critical for MOSFET technology. The entire semiconductor industry was built on this fortunate chemical property.