{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

3Q3%20assignment%20solution_modif

3Q3%20assignment%20solution_modif - 6 February 2006 MTLS...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
6 February 2006, MTLS 3Q3 Materials for Electronic Applications Assignment 1, Due Feb 13 th at Class time (SOLUTION) In all answers use diagram and concise explanations. 1) Free electron theory and energy distribution electrons in solids. a) For solid Al, draw a schematic diagram of the energy distributions of valence electrons indicating the position of the Fermi energy E F at a temperature T = 0 K. b) Draw the same diagram at a finite temperature T>0K and T >> 0 K. c) What energy distribution would you need to use to calculate the probability of finding an electron with an energy E>E F at T > 0 K. d) Sketch a density of states diagram for a non free-electron metal such as Fe. (5 points) Answer: (a) and (b) T=0 (c) The probability of finding an electron with an energy E > E F at T>0 K is represented by the Fermi-Dirac distribution: F ( E ) = {(exp( E - E F ) /kT )+1} -1 which is the function of energy, E , for a given kT . The occupancy probability of electron at T = 0 K and T > 0 K are shown in figures below. E F Energy 2p electrons Bands full 3 s electrons Parabolic band. Sharp transition at T = 0K but for T>>0 we have electrons at E > E F . T > 0 K T >> 0 K
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
(d) Sketch of density of states diagram for Fe: 2) Band theory and properties of solids. a) Using the Ziman model of band theory, explain the origin of the gap in solids. b) What distinguishes metals and insulators in a simple one-dimensional Ziman model. (Hint, discuss the trends as a function of number of valence electrons).
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern