--- title: "Diffusion of carriers and conductivity" subject: "Electrical Engineering Material" chapter: 6 key: "semester_3/electrical_engineering_material:diffusion-conductivity" source: https://www.bctengineer.com/q/semester_3/electrical_engineering_material/diffusion-conductivity site: BCT Engineering --- # Diffusion of carriers and conductivity Electrical Engineering Material · Chapter 6: Semiconductors - Asked in: 2068 Chaitra, 4 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/diffusion-conductivity - Whole chapter: https://www.bctengineer.com/md/semester_3/electrical_engineering_material/chapter-6 ## Question What do you understand by diffusion of charge carriers in semiconductor? How does diffusion contribute to conductivity of a semiconductor? ## Short answer Diffusion is carrier flow from high to low concentration due to thermal motion, producing current density J_diff = eD dn/dx (electrons) or −eD dp/dx (holes). It adds a drift-independent component, crucial in concentration gradients like pn junction forward current, but does not alter uniform bulk conductivity. ## Answer **Diffusion** of charge carriers is the movement of electrons or holes from a region of **high concentration to low concentration** due to their random thermal motion, even when no electric field is present. It occurs whenever the carrier concentration is non-uniform, e.g. near a pn junction or when light injects extra carriers at one end of a bar. #### Why it happens Carriers move randomly with thermal velocity. Across any plane, more carriers cross from the crowded side than from the sparse side, so there is a net flow down the gradient. By Fick's law the flux is $$ F = -D\frac{dn}{dx} $$ where $D$ (cm² s⁻¹) is the diffusion coefficient. #### Diffusion current $$ J_{e,diff} = eD_e\frac{dn}{dx},\qquad J_{h,diff} = -eD_h\frac{dp}{dx} $$ ```text n high o o o o o o --> o o n low electrons diffuse --> electron current <-- ``` #### Contribution to conduction - Diffusion adds a second current component to the drift current, so the total is $$ J_e = en\mu_e\mathcal{E} + eD_e\frac{dn}{dx} $$ - It lets current flow where there is little or no field, e.g. minority carriers crossing the base of a transistor or the neutral regions of a forward-biased diode. The forward current of a diode is essentially a diffusion current. - $D$ and $\mu$ are linked by the Einstein relation $D/\mu = kT/e$, so carriers with high mobility also diffuse quickly. - In equilibrium (e.g. a pn junction with no bias) diffusion is balanced by an equal and opposite drift current, so the net current is zero. Thus diffusion does not change the bulk conductivity $\sigma = e(n\mu_e + p\mu_h)$ of a uniform sample, but in devices with concentration gradients it is often the main way current is carried. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is diffusion of charge carriers? A. Motion caused only by an applied field B. Motion from high to low concentration due to random thermal motion C. Motion from low to high concentration D. Motion of ions in the lattice Answer: B. Net flow down a concentration gradient arises from random thermal motion, even with no field. (Key point: Definition of diffusion) 2. Which gives the electron diffusion current density? A. e n mu_e E B. -e D_h dp/dx C. e D_e dn/dx D. e D_e E Answer: C. J_e,diff = e D_e dn/dx, from Fick's law. (Key point: Diffusion current expression) 3. Where is diffusion current the main current component? A. In a uniformly doped resistor B. In a metal wire C. In an unbiased uniform bar D. In the base of a BJT and a forward-biased diode Answer: D. Minority carriers cross neutral regions mostly by diffusion, where little field exists. (Key point: Role in devices) 4. Why is there no net current in an unbiased pn junction despite diffusion? A. An equal and opposite drift current cancels it B. Diffusion does not occur C. Carriers are absent D. The Fermi level is not flat Answer: A. The built-in field drives a drift current balancing diffusion. 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