ECE 874: Physical Electronics Prof. Virginia Ayres Electrical & Computer Engineering Michigan State University ayresv@msu.edu

Lecture 06, 18 Sep 12 VM Ayres, ECE874, F12

Atomic hydrogen can only radiate or absorb energy in discreet packets: Heat hydrogen gas, get atomic hydrogen (not H2) = 1 proton + 1 electron. Atomic hydrogen can only radiate or absorb energy in discreet packets: En = -13.6 eV/n2, n = 1, 2, 3, …… This formula can also be used as an approximation for systems that are like hydrogen, such as excitons. VM Ayres, ECE874, F12

Quantization of angular momentum Ln = m0vrn = nhbar, n = 1, 2, 3, …… Charge: Coulomb force Motion: Centripetal force Eliminate v, get expression for rn in terms of integer n VM Ayres, ECE874, F12

Now get an expression for total energy En: Energy due to motion Get v in terms of rn from force balance (not L quantization). Reason: that’s how PE is written. Energy due to charge Now substitute for rn on previous slide to get En in terms of integer n VM Ayres, ECE874, F12

VM Ayres, ECE874, F12

VM Ayres, ECE874, F12

This is the predicated ground state energy level. What you can observe are transitions, e.g., E2 – E1: VM Ayres, ECE874, F12

VM Ayres, ECE874, F12

http://www.matter.org.uk/diffraction/geometry/geometry_of_diffraction_braggs_law_2.htm VM Ayres, ECE874, F12

VM Ayres, ECE874, F12

VM Ayres, ECE874, F12

Chp. 02: 3 important examples of electron showing wavelike properties Free electron An electron between scattering events during transport in a semiconductor is often nearly free Motivation: low heat transisotrs Electron in an infinite potential well Electron in a finite potential well Pr. 2.7: Electrons in a triangular well = realistic Motivation: these are all about Quantum well lasers: Arai article: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4265925 Transitions between quantized energy levels DE = hc/l : what you see is light of precise wavelength l VM Ayres, ECE874, F12

Approach: conservation of energy applied to wavelike electrons VM Ayres, ECE874, F12

Approach: conservation of energy applied to wavelike electrons/particles: VM Ayres, ECE874, F12

Approach: conservation of energy applied to wavelike electrons VM Ayres, ECE874, F12

Approach: conservation of energy applied to wavelike electrons VM Ayres, ECE874, F12