Lecture handout including QS - Department of Materials Science ...

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BH46 Course B: Materials for Devices BH46 (b) Drift current (due to an electric field) energy Addition of an electric field field, E → (E, direction of positive charge flow) ⇒ reduction of Q in one direction (& equivalent increase in the opposite direction) energy barrier = (Q – y) € The current density is governed by the conductivity (the ease of motion) & the electric field (the driving force), and is given by the microscopic form of Ohm’s law. If σ = conductivity: drift current density, € j = −σ ∂V ∂x E = − ∂V ∂x , current flow (+ve charge) V j → from high to low potential E → and so The number € of diffusing ions in an electric potential follows Boltzmann’s statistics: Therefore € j drift = σE ⎛⎛ n = n o exp⎜⎜ −qV ⎞⎞ ⎟⎟ and the differential gives the concentration gradient: ⎝⎝ kT⎠⎠ ∂n ∂x = −q ⎛⎛ ⎛⎛ n 0 exp −qV ⎞⎞⎞⎞ ⎜⎜ ⎜⎜ ⎟⎟⎟⎟ × ∂V kT ⎝⎝ ⎝⎝ kT ⎠⎠⎠⎠ ∂x ∂n ∂x = −nq ∂V kT ∂x = nqE kT Voltage, i.e. the electric field leads to a concentration gradient Distance, x At equilibrium the diffusion current density (BH45) j diffusion = − qD ∂n , due to this resultant ∂x concentration gradient, must be equal to the drift current density, i.e. - j diffusion = j drift : qD ∂n ∂x = σE ⇒ ⎛⎛ qD nqE ⎞⎞ ⎜⎜ ⎟⎟ = σE ⎝⎝ kT ⎠⎠ € σ € D = nq2 kT Nernst-Einstein equation €
BH47 Course B: Materials for Devices BH47 since D = D o exp( −Q kT) (BH45) and ⎛⎛ n = n o exp⎜⎜ −qV ⎞⎞ ⎝⎝ kT⎠⎠ ⎟⎟ (BH46) Nernst-Einstein (BH46): σ = Dnq2 kT € Therefore, ⎛⎛ lnσ ≈ lnσ 0 − Q ⎞⎞ ⎜⎜ ⎟⎟ 1 ⎝⎝ k ⎠⎠ T ≈ D n o o q2 exp −Q kT kT € ( ) for small E, where € where σ 0 = D n 0 0 q2 kT qV
Page 1 and 2: Natural Sciences Tripos Part IA MAT
Page 3 and 4: BH1 Course B: Materials for Devices
Page 13 and 14: BH11 Course B: Materials for Device
Page 47: BH45 Course B: Materials for Device
Page 61 and 62: Qu. Sheet 5 MATERIALS SCIENCE BQ1 C
Page 67 and 68: Qu.Sheet 8 MATERIALS SCIENCE BQ4 Co

Lecture handout including QS - Department of Materials Science ...

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