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ECE216-Lecture-02-Semiconductor-Physics

ECE216-Lecture-02-Semiconductor-Physics - ECE 216 DEVICE...

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ECE 216 DEVICE PHYSICS FOR INTEGRATED CIRCUITS Lecture 02 Chapter 2 – SEMICONDUCTOR PHYSICS Professor Hisham Z. Massoud Department of Electrical and Computer Engineering Fitzpatrick Building, Room 3521 Duke University, Durham, NC 27708–0291 [email protected] https://courses.duke.edu/webapps/portal/frameset.jsp ECE 216 Chapter 2 – Semiconductor Physics Lecture 02.1
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TOPICS 1. Introduction 2. The Hydrogen Atom 3. The Schr¨ odinger Wave Equation 3.1. The Wave Equation 3.2. The Free-Electron Solution 4. Electrons in a Crystal 4.1. Crystal Structure 4.2. Energy Bands in Solids 4.3. E ( ~ k ) Relationship of a One-Dimensional Crystal 4.4. The Band Structure of Silicon ECE 216 Chapter 2 – Semiconductor Physics Lecture 02.2
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1. INTRODUCTION The properties of electrons in atoms and solids are described by the Schr¨ odinger Wave Equation. The properties of semiconductors are derived from applying Schr¨ odinger’s Equation to electrons in a crystal. The solution of Schr¨ odinger’s equation leads to the concepts of con- duction and valence energy bands in solids, energy band gaps, dis- persion relationships E ( ~ k ), electron effective masses, and the density of electron states. Carrier statistics are described by the Fermi-Dirac distribution func- tion and the effective density of states. ECE 216 Chapter 2 – Semiconductor Physics Lecture 02.3
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1. INTRODUCTION An intrinsic semiconductor is defined as a pure semiconductor with neither defects nor dopants, with each lattice site occupied by a Si atom. The intrinsic carrier concentration n i and its dependence on temperature are calculated. The motion of electrons is described in terms of wave packets and their effective masses. The concentrations of electrons and holes in a semiconductor are controlled by doping it with donor and acceptor atoms. The con- centrations of majority and minority carriers are calculated using the Fermi level. ECE 216 Chapter 2 – Semiconductor Physics Lecture 02.4
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2. THE HYDROGEN ATOM The motion of an electron in a hydrogen atom results from the balance between the centrifugal force and the Coulomb force written as m 0 v 2 r = q 2 4 π 0 r 2 , (1) where m 0 is the free electron mass, v its velocity, r its orbit radius, q its charge, and 0 the dielectric permittivity of free space. Bohr postulated that an electron can only exist in certain orbits E n and that a photon with frequency ν is emitted when an electron transitions from an orbit at energy E 2 to an orbit at a lower energy E 1 , such that E 2 - E 1 = h ν , (2) where h is Planck’s constant. ECE 216 Chapter 2 – Semiconductor Physics Lecture 02.5
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2. THE HYDROGEN ATOM Louis de Broglie postulated that particles acts as a wave. He introduced the concept that a particle with momentum ~ p is assigned a wavelength λ given by λ = h | ~ p | .
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