1 Introduction to quantum mechanics (Chap.2) Quantum theory for semiconductors (Chap. 3) Allowed and forbidden energy bands (Chap. 3.1) What Is An Energy Band And How Does It Explain The Operation Of Semiconductor Devices? To Answer These Questions, We Will Study:

2 Classical Mechanics and Quantum Mechanics Mechanics: the study of the behavior of physical bodies when subjected to forces or displacements Classical Mechanics: describing the motion of macroscopic objects. Macroscopic: measurable or observable by naked eyes Quantum Mechanics: describing behavior of systems at atomic length scales and smaller.

33 Photoelectric Effect T max 0 ν νoνo Inconsistency with classical light theory According to the classical wave theory, maximum kinetic energy of the photoelectron is only dependent on the incident intensity of the light, and independent on the light frequency; however, experimental results show that the kinetic energy of the photoelectron is dependent on the light frequency. Metal Plate Incident light with frequency ν Emitted electron kinetic energy = T The photoelectric effect ( year1887 by Hertz) Experiment results Concept of “energy quanta”

4 Planck’s constant: h = 6.625× J-s Photon energy = hν Work function of the metal material = hν o Maximum kinetic energy of a photoelectron: T max = h(ν-ν o ) Energy Quanta Photoelectric experiment results suggest that the energy in light wave is contained in discrete energy packets, which are called energy quanta or photon The wave behaviors like particles. The particle is photon

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6 Electron’s Wave Behavior Electron beam Nickel sample Detector Scattered beam θ θ =0 θ =45º θ =90º Davisson-Germer experiment (1927) Electron as a particle has wave-like behavior

7 Wave-Particle Duality Particle-like wave behavior (example, photoelectric effect) Wave-like particle behavior (example, Davisson-Germer experiment) Wave-particle duality Mathematical descriptions: The momentum of a photon is: The wavelength of a particle is: λ is called the de Broglie wavelength

8 The Uncertainty Principle The Heisenberg Uncertainty Principle (year 1927): It is impossible to simultaneously describe with absolute accuracy the position and momentum of a particle It is impossible to simultaneously describe with absolute accuracy the energy of a particle and the instant of time the particle has this energy The Heisenberg uncertainty principle applies to electrons and states that we can not determine the exact position of an electron. Instead, we could determine the probability of finding an electron at a particular position.

9 Quantum Theory for Semiconductors How to determine the behavior of electrons in the semiconductor? Mathematical description of motion of electrons in quantum mechanics ─ Schrödinger’s Equation Solution of Schrödinger’s Equation energy band structure and probability of finding a electron at a particular position

10 Schr ӧ dinger’s Equation One dimensional Schr ӧ dinger’s Equation: Wave function Potential function Mass of the particle, the probability to find a particle in ( x, x+dx ) at time t, the probability density at location x and time t