Questions: Electrical Properties of Materials

Question 1

A material's electrical resistance increases as it is heated from room temperature to 200°C. What type of material is this most likely to be?

• A. A semiconductor, because thermally excited carriers always reduce resistance
• B. An insulator, because high temperatures promote electron trapping
• C. A metal, because increasing temperature creates more phonon scattering that impedes electron flow
• D. A superconductor, because superconductivity breaks down above a critical temperature

Answer: (C)

In metals, the conduction band is already partially filled — electrons can conduct readily. As temperature rises, increased lattice vibrations (phonons) scatter conduction electrons more frequently, reducing their mean free path and decreasing conductivity (increasing resistance). This is the diagnostic signature of metallic behavior: resistance rises with temperature. Semiconductors behave oppositely — their resistance falls as temperature rises, because the dominant effect is exponential increase in thermally excited carriers across the band gap. Option A describes semiconductor behavior and is the common confusion this question is designed to catch.

Question 2

Silicon is doped with phosphorus atoms substituted into the crystal lattice. How does this primarily increase the conductivity of the silicon?

• A. Phosphorus atoms widen the band gap, allowing more electrons to participate in conduction
• B. Phosphorus provides extra electrons with energy levels just below the conduction band, easily excited into it at room temperature
• C. Phosphorus replaces silicon-silicon bonds with metallic bonds, increasing electron mobility
• D. Phosphorus creates holes in the valence band by accepting electrons from silicon atoms

Answer: (B)

Phosphorus has 5 valence electrons; silicon has 4. When phosphorus substitutes into the silicon lattice, 4 electrons form bonds with neighboring silicon atoms, but the 5th is only loosely bound — its energy level sits just below the conduction band. At room temperature, thermal energy is sufficient to excite this electron into the conduction band, creating a free electron carrier. This is n-type doping. The key insight is that doping creates energy levels near the band edge, dramatically reducing the activation energy needed to generate carriers. Option D describes p-type doping (with boron or other trivalent atoms), not phosphorus.

Question 3

A material that becomes more electrically conductive as temperature rises is behaving as a semiconductor rather than a metal.

• T. True
• F. False

Answer: True

The contrasting temperature dependence is the clearest diagnostic for distinguishing metals from semiconductors. In semiconductors, the dominant effect of rising temperature is exponential increase in carriers thermally excited across the band gap — which overwhelms the increased phonon scattering that also occurs. In metals, there are already enough carriers (the band is partially filled), so the scattering effect dominates and conductivity decreases. This temperature signature is used in practice to identify and classify materials: if resistance falls when you heat a sample, it's behaving semiconductingly.

Question 4

Semiconductors are simply 'weak conductors' that behave like metals with fewer charge carriers — just a less conductive version of the same mechanism.

• T. True
• F. False

Answer: False

The conduction mechanisms are fundamentally different, not just quantitatively different. In a metal, charge carriers (electrons) are always present in partially filled bands and available to conduct at any temperature. In a semiconductor, the valence band is completely full at absolute zero — there are no carriers and it is a perfect insulator. Carriers only appear when electrons are thermally (or photonically) excited across the band gap into the conduction band, leaving behind mobile holes in the valence band. This gap-crossing mechanism explains why semiconductor conductivity is temperature-sensitive and light-sensitive (photovoltaic effect), while metallic conductivity is neither. It also explains why doping with tiny impurity concentrations can change conductivity by many orders of magnitude — something impossible in a true metal.

Question 5

Explain why the conductivity of a metal decreases with increasing temperature while the conductivity of a semiconductor increases, even though both effects involve temperature.

Model answer: In a metal, the conduction band is already partially filled — there are always free electrons available to carry current. As temperature rises, lattice vibrations (phonons) increase, scattering electrons more frequently and shortening their mean free path. More scattering means lower mobility, lower conductivity. In a semiconductor, the valence band is full and the conduction band is empty at low temperatures — there are no free carriers. As temperature rises, thermal energy excites electrons across the band gap into the conduction band (and creates holes in the valence band). The number of carriers increases exponentially with temperature, which more than compensates for the increased scattering. The net effect is rising conductivity. The key is that metals are carrier-saturated (more temperature just adds scatter), while semiconductors are carrier-starved (more temperature primarily adds carriers).

This distinction is also why semiconductors can be light-sensitive: photons can supply the energy to excite electrons across the band gap just as thermal energy does, creating carriers and increasing conductivity. Metals don't exhibit photoconductivity for the same reason they don't show thermally activated conductivity — the carriers are already there.