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EE216.W2010.Lecture8

EE216.W2010.Lecture8 - 1 EE 216 Principles and Models of...

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Unformatted text preview: 1 EE 216 Principles and Models of Semiconductor Devices (Winter 2010) K. C. Saraswat and R. T. Howe Lecture 8. P-N Junctions under Forward Bias • P-N junctions in forward bias, continued – Diffusion Approximation – Solving the Continuity Equation • Long-Base Diode – Minority carrier concentrations – Minority and majority carrier currents • Short-Base Diode – Ohmic contacts as boundary conditions – Comparison with long-base solution • High- and low-forward bias effects – Ohmic drops, depletion region generation/recombination • Junction breakdown under reverse bias EE 216 Principles and Models of Semiconductor Devices (Winter 2010) K. C. Saraswat and R. T. Howe Roadmap for Finding I D vs. V D • Boundary conditions for minority, majority carriers – Depletion region (law of the junction; low-level injection) – Metal-p and metal-n ohmic contacts. • Solving for n p ( x ) and p n ( x ) in steady-state – Simplify the minority carrier current equations for two limiting cases: the long-base and the short-base diode • Find the minority carrier current densities • Figure out what the majority carriers are doing • Add up the current densities (carefully) and multiply by the area … done! 2 EE 216 Principles and Models of Semiconductor Devices (Winter 2010) K. C. Saraswat and R. T. Howe The E-feld which exists in the regions oF excess carrier concentration is given by J drift = q μ n n E For majority carriers, electrons J drift = q μ p p E For minority carriers, holes Since n >> p , the driFt current oF holes is negligible. The minority carriers move primarily by diffusion , while the majority carriers are pulled to the junction region by drift ( E ). The minority carriers control the behavior of the P-N junctions. This is in contrast to Schottky diodes (metal- semiconductor junctions) where majority carriers dominate. Carrier Transport EE 216 Principles and Models of Semiconductor Devices (Winter 2010) K. C. Saraswat and R. T. Howe We assume that the injected minority carriers move away From the depletion region only by diFFusion (i.e., driFt is negligible). This is known as the Diffusion Approximation . ¡or holes in the N-region Transport Equation Continuity Equation Similarly, For electrons in the P-region, x d dp qD J n p p − ≈ ∂ p n ∂ t = D p ∂ 2 p n ∂ x 2 − p n − p n o τ p J n ≈ qD n dn p dx ∂ n p ∂ t = D n ∂ 2 n p ∂ x 2 − n p − n p o τ n Carrier Transport 3 EE 216 Principles and Models of Semiconductor Devices (Winter 2010) K. C. Saraswat and R. T. Howe Boundary Conditions • The law of the junction determines the minority carrier concentrations at the edges of the depletion region • The ohmic contacts force the adjacent carrier concentrations to be at their equilibrium values Why? The metal can be considered a large, unchanging reservoir of holes and electrons, preventing the carrier concentrations from deviating significantly from their values at thermal equilibrium. Alternatively, the recombination...
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EE216.W2010.Lecture8 - 1 EE 216 Principles and Models of...

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