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An in-depth analysis of carrier transport mechanisms in semiconductors, focusing on diffusion current and drift current. Dr. Gargi Raina from VIT Chennai explains the concepts of diffusion, drift, mobility of carriers, and current density equation. The document also covers the continuity equation and the Haynes-Shockley experiment.
What you will learn
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Diffusion of Carriers
A pulse of excess electrons injected at x = 0 at t = 0 It will spread out in time due to diffusion Eventually n(x) becomes a constant, when no more net motion takes place. n(x) Electron concentration in x-direction
Division of n(x) into segments of length 𝒍ҧ (Mean free path) Consider any arbitrary distribution n(x) Where x divided into 𝑙 segments (mean free path) wide n(x) evaluated at center of each segment. Expanded view of two of the segments centered at x 0 In 𝑡 , half of the electrons in segment 1 (left of x 0 ) segment 2 (right of x 0 ) Net number of electrons moving from segment (1) to segment (2) through x 0 within a mean free time, tҧ)
Similarly, holes diffuse from a region of higher concentration to a region of lower concentration with a diffusion coefficient DP Thus, Electron Flux Density Hole Flux Density Diffusion Current Density Note: electrons and holes move together in a carrier gradient, however, the resulting currents are in opposite directions because of the opposite charges of the particles.
Drift and diffusion of a hole pulse in an n-type bar Sample Geometry Position and shape of the pulse for several times during its drift down the bar
the p distribution after time td. 𝐞 −𝟏 𝛅𝐩ෝ = 𝛅𝐩𝐞 −(𝐱/𝟐) 𝟐 /𝟒𝐃𝐩𝐭𝐝
𝟐
Activity
1. Video on drift diffusion based simulation https://nanohub.org/resources/21156/download/11_27_10_Mehrotra_DriftDiffus ion_Demo_810x608.mp