Semiconductor carrier transport: Given minority-carrier lifetime τ = 100 μs and diffusion constant D = 100 cm^2/s, compute the diffusion length L of the carriers.

Introduction / Context:The diffusion length L characterizes how far minority carriers can diffuse before recombining. It is a key parameter for device dimensions in photodiodes, solar cells, and bipolar transistors, linking material quality (lifetime) and transport (diffusion constant).

Given Data / Assumptions:

• Minority-carrier lifetime τ = 100 μs = 100 × 10^-6 s = 1 × 10^-4 s.
• Diffusion constant D = 100 cm^2/s.
• One-dimensional steady-state diffusion–recombination model.

Concept / Approach:

The diffusion length is L = sqrt(D * τ). Substituting the given values gives L in centimeters because D is in cm^2/s and τ in seconds.

Step-by-Step Solution:

Verification / Alternative check:

Units: sqrt(cm^2) = cm, consistent. Orders of magnitude are typical for high-quality materials with long lifetimes.

Why Other Options Are Wrong:

• 0.01 cm and 0.0141 cm correspond to smaller D or τ; not matching the given data.
• 1 cm is an order of magnitude too large for the stated parameters.
• 0.32 cm would require D * τ ≈ 0.1024 cm^2, not given here.

Common Pitfalls:

• Mistaking μs for ms, which would inflate L by sqrt(10).

Final Answer:

0.1 cm