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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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1 2.3 Application of Schrodingers wave equation Electron in free space Electron in the infinite potential wall Electron in the potential barrier 2 2.3.1 Electron in free space Electron in free space = no force acting on the electron V(x) is constant We must have E V(x) to assure the motion of electron Time-independent Schrodinger wave equation 0)()(2)(222xxVEmxxFor simplicity, let V(x) = 0 0)(2)(222xmExx(Free space) )exp()()(jkxBjkxexpAxWhere 22mEk 3 tj-tEj-eet)/()()(exp)()(),(tkxj-Bt-kxjexpAextxtj- This wave function solution is a traveling wave, which means that a particle moving in free space is represented by a traveling wave. The first term, with the coefficient A, is a wave traveling in the x direction, while the second term, with the coefficient B, is a wave traveling in the -x direction. The value of these coefficients will be determined from boundary conditions. 4 )(),(t-kxjexpAtxWhere k is the wave number given by or Assume, for a moment, that we have a particle traveling in the x direction, which will be described by the x traveling wave. The coefficient B = 0. We can write the traveling wave solution in the form p2phAlso recall that the de Broglies wavelength was given by kpk2 A free particle with a well-defined energy will also have a well-defined wavelength and momentum. *2),(),(),(AAtxtxtxA free particle with a well-defined momentum can be found anywhere with equal probability. xpa constant independent of position 6 2.3.2 Infinite potential well (bound electrons) V ( x) for x 0, x a 0)()(2)(222xxVEmxxRegion I & III (V (x) ) (x) = 0 Region II (V (x) 0 ) 0)(2)(222xmExxA particle cannot penetrate these infinite potential barriers, so the probability of finding the particle in regions I and III is zero. E is finite. Where 22mEk 7 boundary condition: (x) is continuous at boundaries. ( n =1,2,3,.) the normalization boundary condition Finally, the time-independent wave solution is given by This wave solution is a standing wave solution, which means that the bound electrons (electrons in an infinite potential well) is represented by a standing wave. 8 22mEk The total energy of the particle can only have discrete values. The energy of the electron is quantized, contrary to results from classical physics which would allow the electron to have continuous energy values. Quantization of energy levels 9 Electrons in an infinite potential well energy levels wave functions probability functions 10 Example 2.3 energy levels of bound electrons Calculate the first three energy levels of a bound electron. Infinite potential well with width of 5 11 2.3.3 The step potential function 0)()(2)(222xxVEmxxRegion I (V (x) 0 ) 0)(2)(222xmExx22mEk1Where The first term - a wave traveling in the x direction that represents the incident wave The second term - a wave traveling in the -x direction that represents a reflected wave. As in the case of a free particle, the incident and reflected particles are represented by traveling waves. See text for more detailed analysis. 2.3.4 The potential barrier and tunneling The potential barrier function Tunneling effect Pauli exclusion principle In any given system (an atom, molecule, or crystal), no two electrons may occupy the same quantum state. In an atom, no two electrons may have the same set of quantum numbers The electron has an intrinsic angular momentum, or spin, which is quantized and may take on one of two possible values. s =1/2 or s= -1/2 . Electron spin 2.4 Extensions of the wave theory to atoms Before the nature of atomic electron states was clarified by the application of quantum mechanics, spectroscopists saw evidence of distinctive series in the spectra of atoms and assigned letters to the characteristic spectra. In terms of the quantum number designations of electron states, the notation is as follows: Spectroscopic Notation The quantum numbers associated with the atomic electrons along with the Pauli exclusion principle provide insight into the building up of atomic structures and the periodic properties observed. The order of filling of electron energy states is dictated by energy, with the lowest available state consistent with the Pauli principle being the next to be filled. Periodic table of elements 16 For helium, two electrons may exist in the lowest energy state. For this case, l = m =0, so now both electron spin states are occupied and the lowest energy shell is full. The chemical activity of an element is determined primarily by the valence, or outermost, electrons. Since the valence energy shell of helium is full, helium does not react with oth
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