Register to reply

Effective Electron Mass

by roam
Tags: effective, electron, mass
Share this thread:
roam
#1
Aug18-13, 07:59 AM
P: 895
I am trying to find the effective mass of the electron within the first Brillouin zone in a particular direction in a crystal where the energy of the electron varies with some wave vector ##E(k)=Ak^2+Bk^4##. But I need to express this as a fraction of the electron rest mass.

I know that the effective mass (from Newton's 2nd law) is given by:

##m^* = \frac{\hbar^2}{d^2E/dk^2}##

At the first Brillouin zone boundary we have ##k =\pi / a##. Also the second derivative of the E(k) is ##\frac{d^2E}{dk^2}=2A+12Bk^2##.

Substituting these in I think the effective mass is:

##m^* = \frac{\hbar^2}{2A+12B (\frac{\pi}{a})^2}##

Now, how does one express this as a fraction of the electron rest mass m (511 KeV)?

Any suggestion or correction is appreciated.
Phys.Org News Partner Physics news on Phys.org
Working group explores the 'frustration' of spin glasses
New analysis of oxide glass structures could guide the forecasting of melt formation in planetary interiors
Scientists characterize carbon for batteries
fzero
#2
Aug18-13, 04:04 PM
Sci Advisor
HW Helper
PF Gold
P: 2,606
The obvious answer is to divide by ##m_e## so that you have an expression for ##m_*/m_e##. This doesn't make too much sense unless you've been given numerical values for ##A,B,a## though.
erst
#3
Aug19-13, 09:39 PM
P: 21
Yup, you're done if that's all the information provided. Put m_0 in the denominator.

roam
#4
Aug20-13, 01:41 AM
P: 895
Effective Electron Mass

Thank you very much for your inputs. Here is what I've got then for effective mass as a fraction of the electron rest mass:

##m^* = \frac{\hbar^2}{(2A+12B (\pi /a)^2) m_e}##
ZapperZ
#5
Aug22-13, 03:32 PM
Emeritus
Sci Advisor
PF Gold
ZapperZ's Avatar
P: 29,239
Quote Quote by roam View Post
Thank you very much for your inputs. Here is what I've got then for effective mass as a fraction of the electron rest mass:

##m^* = \frac{\hbar^2}{(2A+12B (\pi /a)^2) m_e}##
Don't you mean m*/m_e for the LHS of the equation?

Zz.


Register to reply

Related Discussions
Is the mass conferred by Higgs an 'effective' mass? Beyond the Standard Model 1
Electron/Hole Effective Mass vs Solar Cell efficiency Quantum Physics 1
Effective mass of Dirac electron increased by electrostatic potential? Quantum Physics 2
Electron's effective cyclotron mass Atomic, Solid State, Comp. Physics 0
Energy of electron and its effective mass Quantum Physics 11