Weeks10-11HWSolutions

Evaluate eqn iii and find two coupled equations for x

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: (viii) nH z The (v) becomes E x = ! n J x + ! n ( µ n rH Bz ) J y Similarly for E y : So the final result is: E x = ! n J x + ! n ( µn rH Bz ) J y E y = " ! n ( µn rH Bz ) J x + ! n J y 6) But see problem 6d). We can actually get this result without assuming a small magnetic field. This homework exercise will help you become familiar with how B –fields affect transport Consider the equation of motion for an average electron, dp Fe = − qE - qυ × B = . dt (i) Assume that the electron moves for a time, ! m , then scatters, returning the average momentum to zero, so dp p = ! . (ii) dt "m Assuming that p = m *υ , we find an equation for the average velocity as qτ qτ υ = − * E - * υ × B . (iii) m m This equation can be solved exactly for the velocity (see prob. 4.18, Lundstrom, Fundamentals of Carrier Transport, 2000), but let’s take a different approach. ECE ­656 9 Fall 2013 Mark Lundstrom 10/27/13 6a) Assume carriers move in 2D and that only a z ­directed B ­field is present. Evaluate eqn. (iii) and find two coupled equations for ! x and ! y . Solution: Assuming a z ­directed B ­field, it is straightforward to show from (iii) that q# m q# E x - *m ! y Bz * m m q# m q# m ! y = " * E y + * ! x Bz m m !x = " (*) 6b) Solve the two equations for ! x and ! y in terms of the electric field and the B ­ field. Solution: From (*), it is straightforward to show: !x = !y = 2 " µnE x + µnE y Bz 1 + (# c$ ) 2 2 " µnE y " µnE x Bz 1 + (# c$ ) Where ! c = (**) 2 qBz is the so ­called cyclotron frequency. m* 6c) Write the current densities as J x = ! nS q" x...
View Full 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