Diffusion current

Diffusion Current is a current in a semiconductor caused by the diffusion of charge carriers (holes and/or electrons). This is the current which is due to the transport of charges occurring because of non-uniform concentration of charged particles in a semiconductor. The drift current, by contrast, is due to the motion of charge carriers due to the force exerted on them by an electric field. Diffusion current can be in the same or opposite direction of a drift current. The diffusion current and drift current together are described by the drift–diffusion equation. J = q n μ E + q D d n d x {displaystyle J=qnmu E+qD{frac {dn}{dx}}}     (1) J e − Φ / V t = q D ( − n V t ∗ d Φ d x + d n d x ) e − Φ / V t = q D d d x ( n e − Φ / V t ) {displaystyle Je^{-Phi /V_{t}}=qDleft({frac {-n}{V_{t}}}*{frac {dPhi }{dx}}+{frac {dn}{dx}} ight)e^{-Phi /V_{t}}=qD{frac {d}{dx}}(ne^{-Phi /V_{t}})}     (2) J = q D N c e − Φ B / V t [ e V a / V t − 1 ] ∫ 0 x d e − Φ ∗ / V t d x {displaystyle J={frac {qDN_{c}e^{-Phi _{B}/V_{t}}left}{int _{0}^{x_{d}}e^{-Phi ^{*}/V_{t}}dx}}}     (3) Φ ∗ = q N d x E s ( x d − x 2 ) = ( Φ i − V a ) x x d {displaystyle Phi ^{*}={frac {qN_{d}x}{E_{s}}}left(x_{d}-{frac {x}{2}} ight)=(Phi _{i}-V_{a}){frac {x}{x_{d}}}}     (4) J = q 2 D N c V t [ 2 q E s ( Φ i − V a ) N d ] 1 / 2 e − Φ B / V t ( e V a / V t − 1 ) {displaystyle J={frac {q_{2}DN_{c}}{V_{t}}}left^{1/2}e^{-Phi _{B}/V_{t}}(e^{V_{a}/V_{t}}-1)}     (5) E m a x = [ 2 q E s ( Φ i − V a ) N d ] 1 / 2 {displaystyle E_{mathrm {max} }=left^{1/2}}     (6) J = q μ E m a x N c e − Φ B / V t ( e V a / V t − 1 ) {displaystyle J=qmu E_{mathrm {max} }N_{c}e^{-Phi _{B}/V_{t}}(e^{V_{a}/V_{t}}-1)}     (7) Diffusion Current is a current in a semiconductor caused by the diffusion of charge carriers (holes and/or electrons). This is the current which is due to the transport of charges occurring because of non-uniform concentration of charged particles in a semiconductor. The drift current, by contrast, is due to the motion of charge carriers due to the force exerted on them by an electric field. Diffusion current can be in the same or opposite direction of a drift current. The diffusion current and drift current together are described by the drift–diffusion equation. It is necessary to consider the part of diffusion current when describing many semiconductor devices. For example, the current near the depletion region of a p–n junction is dominated by the diffusion current. Inside the depletion region, both diffusion current and drift current are present. At equilibrium in a p–n junction, the forward diffusion current in the depletion region is balanced with a reverse drift current, so that the net current is zero. The diffusion constant for a doped material can be determined with the Haynes – Shockley experiment. Alternatively, if the carrier mobility is known, the diffusion coefficient may be determined from the Einstein relation on electrical mobility.