What is Effective mass: Definition and 65 Discussions
In solid state physics, a particle's effective mass (often denoted
m
∗
{\textstyle m^{*}}
) is the mass that it seems to have when responding to forces, or the mass that it seems to have when interacting with other identical particles in a thermal distribution. One of the results from the band theory of solids is that the movement of particles in a periodic potential, over long distances larger than the lattice spacing, can be very different from their motion in a vacuum. The effective mass is a quantity that is used to simplify band structures by modeling the behavior of a free particle with that mass. For some purposes and some materials, the effective mass can be considered to be a simple constant of a material. In general, however, the value of effective mass depends on the purpose for which it is used, and can vary depending on a number of factors.
For electrons or electron holes in a solid, the effective mass is usually stated in units of the rest mass of an electron, me (9.11×10−31 kg). In these units it is usually in the range 0.01 to 10, but can also be lower or higher—for example, reaching 1,000 in exotic heavy fermion materials, or anywhere from zero to infinity (depending on definition) in graphene. As it simplifies the more general band theory, the electronic effective mass can be seen as an important basic parameter that influences measurable properties of a solid, including everything from the efficiency of a solar cell to the speed of an integrated circuit.
Could somebody tell what is connection
between effective mass of electron and
its energy?
As I know rest energy of electron is about
500 KeV what is pretty big.
In some materials effective mass of electron
is one thousand of its rest mass.
Could we create some energy storage device
which...
The literature i have on the origins / need for an effective mass of electrons seems only to relate it to the explanation of heat capacity of metals but it seems like the concept has applications far beyond this. Can someone pls provide a more general summary of its derivation and applications...
Hi all,
according to textbook definition the effective mass of a particle in a periodic potential is
\frac{\hbar^2}{m*} = \frac{d^2}{d k^2} E(k)
where E(k) is the energy dispersion.
Is this definition applicable at a generic point of a band, or only at the center and edge of the Brillouin...
in indirect band gap semiconductors ,the effective mass isn't constant , because of the anisotropie of this effective mass there are (longitidinal and transversal effective mass). for calculate the optical parameters in semiconductor , i need electron and hole effective masses , what the value...
Homework Statement
In chapter 8, page 207 Kittel derives an equation for the fermi level in an intrinsic conductor:
\mu=½Eg + \frac{3}{4}kBT*ln(me/mh)
How am I to understand the ln(me/mh) part? Earlier he states that the effective mass is proportional to the curvature of the energy band...
Hello-
I feel that this is a "graduate-level" question, so I hope that this question is not found to be insultingly easy.
Can someone help me gain an understanding of why bandgap and electron effective mass in semiconductors are proportional to one another (e.g. trend of C, Si, Ge...
If effective mass in schrodinger equation takes into account for coupling by other bands or so to say by other electrons, and in this way we don't care about effect of other electrons and deal with lattice potential.
Homework Statement
Here is the problem:
http://img413.imageshack.us/img413/748/64my8.th.jpg
The Attempt at a Solution
I got the effective mass. That's trivial. My question is, what are these graphs actually of? The horizontal and vertical axes are not labeled.
Is it an energy...
could anyone elucidate on how Ashcroft and Mermin get
\sqrt{\frac{det M}{M_{zz}}}
for the cyclotron effective mass (page 571)?
Is this true for all energy contours or only certain ones? And if that's the case which because they don't seem to specify?
thanks.
Hello, I am a junior undergrad taking an advanced senior/1st yr grad lab. I've been having some difficulty with a few points in the lab materials we were given (we are analyzing the reflectance spectra for GaAs/AlGaAs quantum wells). We were given the effective mass of the electrons, heavy and...
Homework Statement
Calculate the effective mass for a free electron.
Homework Equations
The Attempt at a Solution
I know the above equation comes from, in the case of the free electron dispersion relation, .
However I'm not at all sure how to go about calculating it for a...