Negative Effect Mass Explained - Gradient & Standing Waves

In summary, the Energy versus K curve shows band gaps and the mass is equal to h^2 divided by the curvature of the graph. The negative mass concept arises under the influence of a periodic potential and affects the motion of electrons as they approach the zone boundary. This concept simplifies the understanding of how electrons respond to external forces in semiconductors. The effective mass takes into account the complex internal forces due to the periodic potential and allows for the prediction of electron behavior without knowing the details of these forces.
  • #1
oddiseas
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We have been shown that the Energy versus K curve has band gaps, and at the brillouin zone is where the standing waves occur.We were also shown the the mass is equal to h^2 divided by the gradient of this graph,but i have no idea what the negative effect mass actually means. Everything i have found on the net seems very complicated compared to what we are studying.Can anyone explain this concept to me?
 
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  • #2
Under the influence of periodic potential this negative mass concept does arise.
When an electron goes to zone boundary, it collides with crystal ions and loses its momentum.An energetic electron then loses momentum due to collision. So d/dE(dE/dK) becomes -ve and m comes out to be so.
As e- moves towards zone bondary it leaves back a vacant site-hole.More e- move toward boundary, more will be creation of holes, which then contributes to current. Remember after reaching zone boundary there will be no conduction of e- further.
 
  • #3
The effective mass concept takes all the complex internal forces due to the periodic potential, and sweeps them under the rug allowing you to relate an external force (eg an electric field) to the acceleration of a charge.

Consider an electron in a semiconductor under the influence of a field in the negative x-direction. The force on the electron is F=-eE, so the external force is in the positive x-direction.

Far from the zone boundary, the effective mass is positive, so by Fext = m*a, the acceleration is also positive. The electron accelerates in the positive x-direction towards the zone boundary.

As the electron approaches the zone boundary, the effective mass becomes negative (this can be seen from the curvature of the dispersion relation). The external force is still positive, which means that the electron acceleration now becomes negative, ie the electron decelerates. The negative effective mass tells you that the electron responds to the field opposite to how a free electron would.

Physically, the fact that the electron accelerates opposite to the direction of the force is because the electron must reflect off the zone boundary. As it approaches the boundary, it must decelerate. This behavior is of course due to the complex interaction with the periodic potential, but the effective mass serves as a convenient tool to understand how the electron will behave without knowing the details of these internal forces.P.S. In case you didn't learn it this way, a standing wave can be written as the sum of an equal forward and backward traveling wave, so it's just the same as saying the electron reflects from the boundary. And this may have just been a typo on your part, but it's the second derivitive and not the gradient of the dispersion relation that determines m*.
 
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1. What is negative mass?

Negative mass is a hypothetical concept in physics where an object has a negative value for its mass. This means that the object's acceleration would be in the opposite direction of the applied force.

2. How does negative mass affect gravity?

Negative mass would have a repulsive effect on other objects with positive mass. This means that instead of being pulled towards each other, two objects with negative and positive mass would push away from each other.

3. What is the gradient of negative mass?

The gradient of negative mass refers to the change in its strength or value over a distance. Negative mass has a negative gradient, meaning that its strength decreases as the distance increases.

4. What are standing waves in relation to negative mass?

Standing waves are a phenomenon that occurs when two waves with equal amplitudes and frequencies travel in opposite directions and interfere with each other. In the context of negative mass, standing waves can be created when a negative mass interacts with a positive mass, resulting in a stable equilibrium.

5. What are the potential practical applications of negative mass?

Negative mass is a theoretical concept and has not been observed in nature. However, if it were to exist, it could have potential applications in fields such as propulsion and energy generation. It could also help in understanding the behavior of exotic particles and dark matter.

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