Introduction / Context:
Understanding how carrier mobility varies with temperature is fundamental in solid-state electronics and device modeling. Mobility directly impacts conductivity, transconductance, and speed of diodes, bipolar junction transistors, and MOSFETs. The question probes your grasp of scattering mechanisms that dominate at different temperature ranges in a typical doped semiconductor.
Given Data / Assumptions:
- Material context: a standard doped semiconductor (e.g., silicon).
- Temperature increase is considered above cryogenic/very-low ranges so that lattice (phonon) scattering is the dominant mechanism.
- We focus on mobility trend with temperature, not on carrier concentration changes that affect conductivity.
Concept / Approach:
Carrier mobility μ is limited by scattering. At moderate and high temperatures, acoustic phonon (lattice) scattering dominates, and mobility approximately follows μ ∝ T^(-m), with m around 1.5 to 2 for many semiconductors. As temperature rises, lattice vibrations intensify, increasing the collision rate and reducing the average drift velocity per unit field, hence reducing mobility.
Step-by-Step Solution:
Identify dominant scattering: at elevated temperatures → lattice (phonon) scattering.Relate temperature to mobility: higher T → more phonons → higher scattering probability.Conclude trend: electron mobility decreases with temperature due to increased scattering.
Verification / Alternative check:
At low temperature, ionized impurity scattering can dominate and mobility can increase with T, but this is not the usual operating region for most electronics. In standard ranges (room temperature upward), the phonon-limited model explains the observed decrease of μ with T.
Why Other Options Are Wrong:
Option b: States an increase in mobility for a reason that is physically incorrect at normal temperatures.Option c: Mobility does vary with temperature; it is not constant.Option e: Ionized-impurity scattering does not dominate at high temperatures; it is more significant at low temperatures.
Common Pitfalls:
Confusing conductivity (which depends on μ and carrier concentration) with mobility alone; assuming that more carriers always implies better conduction regardless of mobility.
Final Answer:
Decreases because lattice-scattering collisions increase with temperature
Discussion & Comments