Temperature dependence of resistance: metal vs semiconductor A copper sample and a germanium sample are cooled from 30 °C down to 80 K. How do their resistances change?

Introduction / Context:Electrical resistance varies with temperature in different classes of materials. Metals and semiconductors show opposite trends because the dominant scattering and carrier mechanisms differ. This behavior is central to cryogenics, sensors, and device physics.

Given Data / Assumptions:

• Copper (a typical metal) and germanium (a semiconductor).
• Cooling from ~303 K to 80 K.
• No phase changes or magnetic transitions considered.

Concept / Approach:

In metals, conduction is by a high density of electrons; resistivity is dominated by phonon scattering that decreases strongly as temperature drops. In intrinsic or lightly doped semiconductors, the number of thermally generated carriers falls steeply upon cooling, increasing resistivity despite reduced scattering. Hence, metals get more conductive at low T, while intrinsic semiconductors become less conductive.

Step-by-Step Solution:

Verification / Alternative check:

Residual resistivity ratios for high-purity copper are large, confirming strong decrease with T; intrinsic germanium at cryogenic temperatures becomes highly resistive, necessitating doping for device operation.

Why Other Options Are Wrong:

Options B and C ignore opposite trends; D reverses the true behaviors; E contradicts strong temperature dependence.

Common Pitfalls:

Assuming all materials behave like metals; overlooking the exponential carrier freeze-out in semiconductors.

Final Answer:

copper decreases and germanium increases