Ellipsoids of constant electron energy

• biketol
In summary: The exact shape and orientation of the ellipsoid depends on the type and amount of strain applied. However, this diagram does not explain how the ellipsoids were derived.
biketol
I'm an analog microelectronics designer who wants to know a little more about why strain modifies the mobility of semiconductors. I've found a paper by Nidhi Mohta and Scott Thompson where they show a three-dimensional coordinate system where the axis are labelled Kx, Ky and Kz. In addition, they have drawn ellipsoids whose shapes are modified when the semiconductor is strained. Unfortunately, they don't say anything about how this figure has been derived. I've tracked down other papers on the same subject, but they also start with this rather nice drawing without telling how they arrived at it. Can someone please explain without resorting to difficult equations the diagram with the ellipsoids? An intuitive explanation on what happens to a semiconductor when it is strained would also be greatly appreciated. Thanks a lot in advance.

Strain modifies the mobility of semiconductors by changing the conduction band structure. This is due to the fact that strain alters the crystal lattice structure and thus affects the energy levels of the electrons in the conduction band. As electrons move from one energy level to another, they gain or lose momentum depending on their direction.The diagram with the ellipsoids represents the electron wave functions in the conduction band for different strains. The three axes Kx, Ky and Kz represent the three directions in which the electrons can move (along x-axis, y-axis and z-axis). When a semiconductor is strained, the energy levels in the conduction band change, and this affects the shape of the ellipsoid. For example, if the semiconductor is stretched along the x-axis, the ellipsoid will become more elongated in the x-direction and shorter in the other two directions. This affects the mobility of electrons as they can move further in the x-direction, resulting in higher mobility. Similarly, if the semiconductor is compressed along the x-axis, the ellipsoid will become more compressed in the x-direction and more elongated in the other two directions. This reduces the mobility of electrons as they can move less far in the x-direction, resulting in lower mobility.

1. What are ellipsoids of constant electron energy?

Ellipsoids of constant electron energy are three-dimensional surfaces that represent the probability of finding an electron at a specific energy level in an atom. They are used to visualize the distribution of electrons in an atom and are an important concept in quantum mechanics.

2. How are ellipsoids of constant electron energy related to electron orbitals?

Ellipsoids of constant electron energy are related to electron orbitals in that they represent the region of space where an electron is most likely to be found. Each electron orbital has a specific shape and orientation, which can be visualized using ellipsoids of constant electron energy.

3. What is the significance of ellipsoids of constant electron energy?

Ellipsoids of constant electron energy are significant because they help us understand the behavior and properties of electrons in atoms. They also provide a visual representation of the complex mathematical equations used to describe the behavior of electrons in quantum mechanics.

4. Can ellipsoids of constant electron energy be observed in experiments?

While ellipsoids of constant electron energy cannot be directly observed, they are an important theoretical concept that helps scientists understand the behavior of electrons in atoms. However, recent advancements in imaging techniques have allowed scientists to indirectly visualize these ellipsoids in some cases.

5. Are all electrons in an atom confined to a specific ellipsoid of constant energy?

No, not all electrons are confined to a specific ellipsoid of constant energy. The shape and orientation of an electron's orbital can change depending on its energy level and the presence of other electrons in the atom. However, ellipsoids of constant electron energy provide a useful way to visualize the probability of finding an electron at a specific energy level in an atom.

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