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半导体物理
半导体
物理
英文
课件
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《半导体物理》英文课件,半导体物理,半导体,物理,英文,课件
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To understand the operation and characteristics of semiconductor devices, we need some knowledge of electron behavior in a semiconductor when the electron is subjected to various potential functions. The behavior and characteristics of electrons in a semiconductor can be described by the formulation of quantum mechanics called wave mechanics. The essential elements of this wave mechanics, using Schrodingers wave equation, are presented in this chapter. 1 Chapter 2 Introduction to Quantum Mechanics Contents of Chapter 2 Principles of Quantum Mechanics Schrodingers Wave Equation Applications of Schrodingers Wave Equation Extensions of the Wave Theory to Atoms 2 The principle of energy quanta The waveparticle duality principle The uncertainty principle 3 2.1 Principles of Quantum Mechanics 4 Classical physics If the light intensity is large enough, the work function of the material will be overcome and an electron will be emitted from the surface of the material independent on the incident frequency of light. Condition of Photoelectric effect: 0Experimental results At a constant incident intensity, the maximum kinetic energy of the photoelectrons varies linearly with frequency. There is a limiting frequency o, below which no photoelectron is produced. 2.1.1 Energy Quanta Photon: particle-like packet of energy Ephoton= hv The maximum kinetic energy of the photoelectron: 002max 21hhmvT5 Energy quanta : E = hv Postulated by Planck in 1900 that thermal radiation is emitted from a heated surface in discrete packets of energy h = 6.62510-34J-s, known as Plancks constant v is the frequency of the radiation h 0 : work function of the material Energy quanta 6 Example 2.1 photo energy Calculate the photon energy corresponding to a particular wavelength. Consider an x-ray with a wavelength of = 0.708108 cm. Solution The energy is This value of energy may be given in the more common unit of electron-volt. We have 7 In the photoelectric effect, light waves behave as if they are particles. In 1924, de Broglie postulated the existence of matter waves. He suggested that since waves exhibit particle-like behavior, particles should be expected to show wave-like properties. 2.1.2 WaveParticle Duality the momentum of photon the wavelength of particle (de Broglie wavelength) khpph8 The DavissonGermer experiment The existence of a peak in the density of scattered electrons can be explained as a constructive interference of waves scattered by the periodic atoms in the planes of the nickel crystal. The angular distribution is very similar to an interference pattern produced by light diffracted from a grating. 9 10 Example 2.2 de Broglie wavelength Calculate the de Broglie wavelength of a particle. Consider an electron traveling at a velocity of 107 cm/s= 105 m/s. Solution The momentum is given by Then, the de Broglie wavelength is Typical de Broglie wavelength of electron 100 11 In some cases, electromagnetic waves behave as if they are particles (photons) and sometimes particles behave as if they are waves. The waveparticle duality principle of quantum mechanics applies primarily to small particles such as electrons, but it has also been shown to apply to protons and neutrons. For very large particles, we can show that the relevant equations reduce to those of classical mechanics. The waveparticle duality principle is the basis on which we will use wave theory to describe the motion and behavior of electrons in a crystal. Understanding of the Wave-particle duality principle 12 2.1.3The uncertainty Principle (1927, Heisenberg) It is stated that we cannot describe with absolute accuracy the behavior of subatomic particles. A fundamental relationship between conjugate variables Position vs. Momentum Energy vs. Time tExpsJh3410054. 1213 One way to visualize the uncertainty principle is to consider the simultaneous measurement of position and momentum, and the simultaneous measurement of energy and time. The uncertainty principle implies that these simultaneous measurements are in error to a certain extent. However, the modified Plancks constant is very small; the uncertainty principle is only significant for subatomic particles. The uncertainty principle is a fundamental statement and does not deal only with measurements. Understanding of the uncertainty Principle 14 2.2 Schrodingers wave equation Schrodinger in 1926 provided a formulation called wave mechanics which incorporated Based on the wave-particle duality principle, we will describe the motion of electrons in a crystal by wave theory The principle of quanta (Planck) Wave-particle duality (de Broglie) Classical physics ExVmp)(22Wave mechanics tjExjp Schodingers wave equation ttxjtxxVxtxm),(),()(),(2222(x,t): wave function V(x): potential function m: mass of the particle 15 Assume the position and time parameters in wave function is separable )()(),(txtxttxjtxxVxxtm)()()()()()()(2222tttjxVxxxm)()(1)()()(12222)()(bydevidetxa function of position x only a function of time t only Each side of the equation must be equal to a same constant )constant()()(1)()()(12222tttjxVxxxm16 )constant()()(1tttjtjet)/()(The position-independent wave function is the classical exponential form of a sinusoidal wave tj-e/EEThe separation constant is the total energy E of the particle Wave equation can be written as tEj-extxtx)/()()()(),(Time-independent portion of Schrodinger wave equation ExVxxxm)()()(12222tje17 Write the equation in the equivalent form 0)()(2)(222xxVEmxxThis time-independent Schrodingers wave equation can also be justified on the basis of the classical wave equation as shown in Appendix E 18 2.2.2 Physical meaning of the wave equation A complex function. Not represent a real physical quantity. Max Born postulated in 1926 that the wave function (x,t)2dx is the probability of finding the particle between x and x+dx at a given time, or that (x,t)2 is a probability density function. 2)/()/(2)()()()()(),(),(),(xxxexextxtxtx*tEj*tEj-*tEj-extxtx)/()()()(),( The probability density function is independent of time. In classical mechanics, the position of a particle can be determined precisely, while in quantum mechanics, the position of a particle is found in term of a probability. Since it is independent of time, we will, in general, only be concerned with the time-independent wave function. 19 2.2.3 Boundary condition The probability of finding the particle over the entire space must be equal to 1 (x): finite, single-valued, continuous. (x)/x: finite, single-valued, (continuous if E and V(x) are finite) 1)(2-dxx If the probability density were to become infinite at some point in spa
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