Introduction / Context:
Diffusion length is a key transport parameter indicating the average distance a minority carrier travels before recombining. It is widely used in device design and analysis (e.g., BJTs, solar cells).
Given Data / Assumptions:
- Minority-carrier lifetime τ = 100 μs = 1.0e-4 s.
- Diffusion constant D = 100 cm^2/s.
- Isotropic, low-level injection conditions.
Concept / Approach:
The diffusion length L is defined by L = sqrt(D * τ). This comes from the solution of the diffusion-recombination equation for minority carriers.
Step-by-Step Solution:
Step 1: Write formula: L = sqrt(D * τ).Step 2: Substitute: D = 100 cm^2/s, τ = 1.0e-4 s.Step 3: Compute product: D * τ = 100 * 1.0e-4 = 1.0e-2.Step 4: Take square root: L = sqrt(1.0e-2) = 0.1 cm.
Verification / Alternative check:
Order-of-magnitude check: If D is large and τ is modest, L is typically in the sub-millimeter to centimeter range; 0.1 cm is reasonable.
Why Other Options Are Wrong:
0.01 cm and 0.0141 cm: Result from incorrect arithmetic or unit mishandling.1 cm and 0.316 cm: Overestimates due to using D or τ alone or taking incorrect square roots.
Common Pitfalls:
Mixing SI and cgs units; forgetting to convert μs to seconds; taking sqrt(D/τ) instead of sqrt(D*τ).
Final Answer:
0.1 cm
Discussion & Comments