ECE340_L8_S14_Distribution - M,W,F 12:00 12:50(X 165 Everi5...

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M,W,F 12:00-­‐12:50 (X), 165 Everi5 Lab MWF 13:00-­‐13:50 (E), 135 Mechanical Engineering Building Lecture #8, 2/7/14 Professor John Dallesasse Department of Electrical and Computer Engineering 2114 Micro and Nanotechnology Laboratory Tel: (217) 333-­‐8416 E-­‐mail: [email protected] Office Hours: Mon, Wed 14:00 – 15:00
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Reminders Homework Due Today DRES Accommoda‘on: Contact me ASAP Excused Absence Policy Review the policy No‘fy me ASAP if you plan to be out for reasons that might qualify as an excused absence
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Tenta‘ve Schedule [1] JAN 22 Course overview JAN 24 Intro to semiconductor electronics JAN 27 Materials and crystal structures JAN 29 Bonding forces and energy bands in solids JAN 31 Metals, semiconductors, insulators, electrons, holes FEB 3 Intrinsic and extrinsic material FEB 5 Distribu‘on func‘ons and carrier concentra‘ons FEB 10 Temperature dependence, compensa‘on FEB 12 Conduc‘vity and mobility FEB 14 Resistance, temperature, impurity concentra‘on FEB 17 Invariance of Fermi level at equilibrium FEB 19 Op‘cal absorp‘on and luminescence FEB 21 Genera‘on and recombina‘on 3 **Subject to Change**
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Today’s Discussion Calcula‘on of Carrier Concentra‘on (Con‘nued) Temperature Dependence of Carrier Concentra‘ons Assignments Topics for Next Lecture 4
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A Few Last Comments
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Metal Fermi Energy In a metal, the Fermi Energy referenced to the vacuum level is the metal work func‘on E m = hv q Φ Vacuum Level
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Electrochemical Poten‘al Electrochemical Poten/al: a measure of the amount of energy needed to add or remove an incremental amount of a given charged species from a defined locus that may be under the influence of an electric field, incorpora‘ng both chemical poten/al and electrosta/cs The Fermi Energy is equal to the electrochemical poten‘al in a semiconductor
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Other Defini‘ons Chemical Poten/al: The incremental change in the Gibbs Free Energy of the system per par‘cle (fixed temperature, pressure, etc.). Gibbs Free Energy: In a chemical system, the enthalpy of the system minus the product of the temperature and entropy (at constant pressure/volume) μ = G n G = H TS = U + PV TS U = internal energy, S = entropy, H = enthalpy
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Fermi Level Versus Doping Type Intrinsic n-Type p-Type
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Addi‘onal Informa‘on
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Conduc‘on Band Density of States Consider a cube of material having sides of length "L" A free electron in this material has a wavefunction given by: ψ = Ae j k x x + k y y + k z z ( ) where k x = n x 2 π L , k y = n y 2 π L , k z = n z 2 π L We also know: E = p 2 2 m * = 2 k 2 2 m * = 2 π 2 2 m * L 2 n x 2 + n y 2 + n z 2 ( ) The constant energy surface is therefore the the surface of a sphere of radius "n" where: n = n x 2 + n y 2 + n z 2 ( ) 1 2 The total number of states within the sphere is: N = 4 3 π n 3 2D 3D 11 Note: Other variants of this derivation get the same result
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Conduc‘on Band Density of States (2) Including spin, the total number of states up to a given energy is therefore: N ( n ) = 2 × 4 3 π n 3 = 8 3 π n 3
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