ECE340_L2_S14_Distribution

Particle is somewhere so dx dy dz 1 the expectation

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Unformatted text preview: cepts Capacitance : Loop Analysis Q Simple Form: C = V dQ dV Resistance / Conductance : Ohm's Law: V = IR dV Resistance (AC): R = dI dI Conductance (AC): G = dV A1 Bulk Resistivity: ρ = R = Lσ ⎧1i1 + 25 ( i1 − i2 ) + 50 ( i1 − i3 ) − 10 = 0 ⎪ ⎨25 ( i2 − i1 ) + 30i2 + 1( i2 − i3 ) = 0 ⎪ ⎩50 ( i3 − i1 ) + 1( i3 − i2 ) + 55i3 = 0 Differential Form: C = http://mathonweb.com/help/backgd4.htm Node Analysis i1 + i4 = i2 + i3 I = JA V V I = =σA Ohms Law R L 1L L 19 R= =ρ σA A Current- Density Equa[ons Drift Diffusion J n = qµ n nE + qDn ∇n J p = qµ p pE − qD p ∇p J cond = J n + J p •  In semiconductor, in addi[on to an electron current density there is a hole current density •  Each current consist of the dris component cause by ﬁeld and the diﬀusion component caused by the carrier concentra[on gradient 20 Con[nuity Equa[ons ∂n 1 = Gn − U n + ∇ • J n ∂t q ∂p 1 = Gp −U p − ∇ • J p ∂t q For a given volume of semiconductor, the rate change of carrier is the net effect of current flow into the volume and generation and recombination rates within the volume. Gn : electron generation rate G p : hole generation rate U n : electron recombination rate U p: hole recombination rate 21 Quantum Mechanics Heisenberg Uncertainty Principle : Position-Momentum: Energy-Time: ( Δx i Δpx ) ≥ / 2 ( ΔE i Δt ) ≥ / 2 Schrodinger's Equation : 2 2 ∂Ψ − ∇ Ψ + VΨ = − (Kinetic Energy + Potential Energy = Total Energy) 2m j ∂t Ψ ( x, y, z, t ) is continuous, finite, and single-valued The derivative in space of Ψ ( x, y, z, t ) is continuous, finite, and single-valued The...
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This note was uploaded on 03/06/2014 for the course ECE 340 taught by Professor Leburton during the Spring '11 term at University of Illinois, Urbana Champaign.

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