MatSci 152: Principles of Electronic Materials and Devices Stanford University MatSci 152: Principles of Electronic Materials and Devices Practice Midterm Exam 2011 This is a closed book, closed notes exam. You are allowed one double-sided sheet of paper with your own notes, as well as a calculator and a writing utensil. You should not have any other materials on your desk. The exam is composed of 4 parts. Exam duration: 50 minutes Maximum Score: 100 points Please do not discuss the content of this exam with others until you have received your exam grade. Useful Constants: h = 6.626x10-34 J∙s ħ = 1.054x10-34 J∙s c = 3x108 m/s 1 eV = 1.602x10-19 J Name:

Part 1: Qualitative questions about electronic materials (30 points total) (a) Why do materials generally expand when they are heated? Your answer should at least include a plot of energy versus bond length and the expression for kinetic energy from Maxwell’s principle of equipartition of energy.

Part 1 Continued (b) Draw the Maxwell-Boltzmann distribution function for a collection of particles at temperature T1. As the temperature of the particles is increased to T2, how does this distribution change? Draw the new distribution at T2. Describe an experiment that would allow this distribution to be determined.

Part 2: Bonding (20 points) In general, the potential energy E per atom, or per ion pair, in a crystal as a function of interatomic (interionic) separation r can be written as the sum of an attractive PE and a repulsive PE, where A and n are constants characterizing the attractive PE and B and m are constants characterizing the repulsive PE. This energy is minimum when the crystal is in equilibrium. The magnitude of the minimum energy and its location ro define the bonding energy and the equilibrium interatomic (or interionic) separation respectively. Show that the bond energy Ebond and equilibrium separation r0 are given by:

Part 3: Quantum Wires (20 points) Consider a one-dimensional free electron gas (i.e., a quantum wire). Assume that the length of the wire extends from x=0 to x=L. Outside these dimensions, the potential V=∞. (a) Draw the first four wavefunctions corresponding to the lowest four energy levels of the electron. (b) Using the time independent Schrodinger equation, determine an expression for the energy of the electron.

Part 4: Photoexcitation & Scanning Tunneling Microscopy (30 points) In nanoscale materials studies, there is increasing interest in studying the photoexcitation of atoms and molecules with scanning tunneling microscopy. In a particular experiment, a sharp tungsten STM tip is scanned over a clean cesium surface and the tunneling current is measured. The sample is then illuminated with λ=450 nm light over an area A with intensity Io. Knowing the work function of tungsten is 4.5 eV and the work function of Cesium is 1.9 eV: Write an expression for the tunnelling current in the dark (no illumination), assuming a wide, tall potential barrier. Under illumination of the cesium, determine the kinetic energy of the photoemitted electrons. Determine the measured photocurrent under illumination in terms of A and Io assuming the quantum efficiency is 100%. What bias would need to be applied to recover the tunneling current measured without illumination (i.e., to extinguish the photoemission current)? Vapplied fiber optic Tungsten tip Imeas a Cesium sample