---
title: "Drift and diffusion current density"
subject: "Electrical Engineering Material"
chapter: 6
key: "semester_3/electrical_engineering_material:drift-diffusion-current-density"
source: https://www.bctengineer.com/q/semester_3/electrical_engineering_material/drift-diffusion-current-density
site: BCT Engineering
---

# Drift and diffusion current density

Electrical Engineering Material · Chapter 6: Semiconductors

- Asked in: 2074 Asoj, 6 marks
- Video: [Drift Current and Diffusion Current in Semiconductor Materials | Drift Velocity](https://www.youtube.com/watch?v=eZudDU944mo) — Engineering Funda
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/electrical_engineering_material/drift-diffusion-current-density
- Whole chapter: https://www.bctengineer.com/md/semester_3/electrical_engineering_material/chapter-6

## Question

The current density in semiconductor devices is affected both by diffusion and drifting of electrons and holes, justify.

## Short answer

Semiconductors have non-uniform carrier concentrations, so diffusion driven by gradients produces currents J_diff = ± e D dC/dx. Drift due to electric fields gives J_drift = e n μ E. Total current sums both, linked by D/μ = kT/e.

## Answer

In a semiconductor, current is carried by electrons and holes, and each carrier can move by **two independent mechanisms**: **drift** (due to an electric field) and **diffusion** (due to a concentration gradient). Metals have only drift current because their electron density is uniform; in semiconductors carrier concentrations can vary strongly with position (doping profiles, junctions, light injection), so both terms matter.

#### 1. Drift current

When a field $\mathcal{E}$ is applied, electrons drift opposite to it and holes along it with velocities $v_d = \mu\mathcal{E}$:

$$
J_{e,drift} = en\mu_e\mathcal{E},\qquad J_{h,drift} = ep\mu_h\mathcal{E}
$$

#### 2. Diffusion current

Carriers in random thermal motion spread from high to low concentration (Fick's law: flux $= -D\,dn/dx$):

$$
J_{e,diff} = eD_e\frac{dn}{dx},\qquad J_{h,diff} = -eD_h\frac{dp}{dx}
$$

(The signs differ because electrons are negative.)

```text
 high n  ======>  low n     diffusion (no field)
 e- <---  E --->           drift (field)
```

#### 3. Total current density

$$
\begin{aligned}
J_e &= en\mu_e\mathcal{E} + eD_e\frac{dn}{dx}\\
J_h &= ep\mu_h\mathcal{E} - eD_h\frac{dp}{dx}\\
J &= J_e + J_h
\end{aligned}
$$

The two mechanisms are linked by the **Einstein relation** $D/\mu = kT/e$, because both come from the same random thermal motion and scattering.

#### Justification with examples

| Situation | Dominant current |
|---|---|
| Uniformly doped resistor | Drift only ($dn/dx = 0$) |
| pn junction in equilibrium | Drift and diffusion equal and opposite, net J = 0 |
| Forward-biased diode | Diffusion of injected minority carriers |
| Base of a BJT | Diffusion |
| Non-uniformly doped region | Built-in field: both |

So the current density in semiconductor devices is set by both drift and diffusion of electrons and holes.

## Check yourself

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

1. What drives drift current and diffusion current respectively?
   A. Concentration gradient; electric field
   B. Electric field; concentration gradient
   C. Temperature; electric field
   D. Electric field; electric field
   Answer: B. Drift is due to an applied field, diffusion is due to non-uniform carrier concentration. (Key point: Cause of drift and diffusion)

2. Why do metals usually show only drift current?
   A. Their electrons have no charge
   B. Their mobility is zero
   C. Their electron density is uniform, so there is no gradient
   D. They have holes only
   Answer: C. Diffusion needs a concentration gradient, which semiconductors can have through doping, junctions or injection. (Key point: Why metals lack diffusion)

3. Which expression is the total electron current density?
   A. e n mu_e E - e D_e dn/dx
   B. e n mu_e E + e D_e dn/dx
   C. e p mu_h E + e D_e dn/dx
   D. e D_e E + e n mu_e dn/dx
   Answer: B. J_e = e n mu_e E + e D_e dn/dx. (Key point: Total electron current)

4. In an unbiased pn junction in equilibrium, what is true of drift and diffusion?
   A. Only diffusion exists
   B. Only drift exists
   C. Both are zero
   D. They are equal and opposite so net current is zero
   Answer: D. The built-in field produces drift that exactly cancels diffusion. (Key point: Equilibrium pn junction)

## Related in Electrical Engineering Material

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- [Drift mobility of electrons in potassium](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Apotassium-drift-mobility-39-5) — Electrical Engineering Material, chapter 2, asked 2×
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