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EE216.W2010.Lecture6

EE216.W2010.Lecture6 - Lecture 6 P-N Junctions P-N junction...

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1 EE 216 Principles and Models of Semiconductor Devices (Winter 2010) K. C. Saraswat and R. T. Howe Lecture 6. P-N Junctions P-N junction structures and qualitative solutions in thermal equilibrium Depletion approximation and charge, field, potential, and energy bands in thermal equilibrium The Debye length: field penetration into the quasi- neutral regions Quantitative analysis of depletion width for abrupt and graded junctions in thermal equilibrium EE 216 Principles and Models of Semiconductor Devices (Winter 2010) K. C. Saraswat and R. T. Howe P-N Junction Formation P-N junctions, in addition to being a useful semiconductor device, form the basis for almost all other semiconductor devices. Understanding their operation is basic to understanding most devices Junction Fabrication by Epitaxy N(x) N P N a (x) N d (x) X P-type N-type Junction Fabrication by Ion Implantation IMPLANT N(x,t) = 2 π∆ R p Q e 2 R p 2 (x - R p ) 2 R p
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2 EE 216 Principles and Models of Semiconductor Devices (Winter 2010) K. C. Saraswat and R. T. Howe DRIVE-IN N(x,t) = π Dt Q e 4Dt x 2 A variety of techniques is available to fabricate P-N junctions. The two "simple" impurity profiles that result are the erfc and Gaussian. P-N Junction Formation (Cont.) PREDEP N(x,t) = N o erfc 2 Dt x N Unlimited source Limited source EE 216 Principles and Models of Semiconductor Devices (Winter 2010) K. C. Saraswat and R. T. Howe The two profiles that are encountered most often in real devices are also easiest to analyze from a device physics point of view N(x) N P N a (x) N d (x) X ) N P x N d (x) N a (x) N(x) P-N Junction Profiles Step Junction Good approximation for shallow, high concentration junctions (x j < 1μm) and epitaxially grown junctions Linearly Graded Junction Good approximation for deep junctions (x j > 3 μm)
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3 EE 216 Principles and Models of Semiconductor Devices (Winter 2010) K. C. Saraswat and R. T. Howe Thought Experiment (p, n separate) EE 216 Principles and Models of Semiconductor Devices (Winter 2010) K. C. Saraswat and R. T. Howe Thought Experiment (pn junction)
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4 EE 216 Principles and Models of Semiconductor Devices (Winter 2010) K. C. Saraswat and R. T. Howe Band Diagrams in Thermal Equilibrium If N and P type materials are brought into contact, establishment of equilibrium takes place. Both electrons and holes move to establish equilibrium. χ = electron affinity = E o - E c, an intrinsic property where E o = vacuum level Φ s = semiconductor work function Φ sp = E o - E Fp = semiconductor work function of p-type Si Φ sn = E o - E Fn = semiconductor work function of n-type Si EE 216 Principles and Models of Semiconductor Devices (Winter 2010) K. C. Saraswat and R. T. Howe Band Diagrams at Equilibrium
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5 EE 216 Principles and Models of Semiconductor Devices (Winter 2010) K. C. Saraswat and R. T. Howe
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