---
title: "Diffusion coefficient of electrons at 300 K"
subject: "Electrical Engineering Material"
chapter: 6
key: "semester_3/electrical_engineering_material:diffusion-coefficient-300k"
source: https://www.bctengineer.com/q/semester_3/electrical_engineering_material/diffusion-coefficient-300k
site: BCT Engineering
---

# Diffusion coefficient of electrons at 300 K

Electrical Engineering Material · Chapter 6: Semiconductors

- Asked in: 2082 Kartik (new course), 3 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/electrical_engineering_material/diffusion-coefficient-300k
- Whole chapter: https://www.bctengineer.com/md/semester_3/electrical_engineering_material/chapter-6

## Question

Calculate the diffusion coefficient of electrons at 300 K in n-type silicon semiconductor with 10¹⁵ arsenic atoms per cm³. (μ = 1300 cm² V⁻¹ s⁻¹)

## Short answer

Using Einstein relation De = μe kT/e, with kT/e = 0.02586 V at 300 K. De = 1300 cm²/V·s × 0.02586 V = 33.6 cm² s⁻¹.

## Answer

The diffusion coefficient is related to mobility by the **Einstein relation**. With $N_d = 10^{15}$ cm⁻³ the semiconductor is non-degenerate, so the relation applies, and electrons are the majority carriers.
$$
\begin{aligned}
\frac{D_e}{\mu_e} &= \frac{kT}{e} = \frac{1.381\times10^{-23} \times 300}{1.602\times10^{-19}} = 0.02586\ \text{V} \\
D_e &= \mu_e \frac{kT}{e} = 1300 \times 0.02586 \\
&= 33.6\ \text{cm}^2\,\text{s}^{-1}
\end{aligned}
$$
**Answer:** $D_e \approx 33.6$ cm² s⁻¹ $= 3.36\times10^{-3}$ m² s⁻¹.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What links D and mu?
   A. D = mu kT
   B. D mu = kT/e
   C. D = e/(mu kT)
   D. D/mu = kT/e
   Answer: D. Einstein relation. (Key point: Relation used)

2. kT/e at 300 K is about:
   A. 0.02586 V
   B. 0.26 V
   C. 2.586 V
   D. 0.0026 V
   Answer: A. 1.381e-23 x 300/1.602e-19 = 0.02586 V. (Key point: Thermal voltage)

3. D_e for mu = 1300 cm^2/Vs:
   A. 3.36 cm^2/s
   B. 33.6 cm^2/s
   C. 336 cm^2/s
   D. 1300 cm^2/s
   Answer: B. 1300 x 0.02586 = 33.6 cm^2/s. (Key point: Result)

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