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tnho
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Can anyone explains the concept of effective mass in solid state physics to me?
Thanks a lot~
Thanks a lot~
tnho said:Can anyone explains the concept of effective mass in solid state physics to me?
Thanks a lot~
tnho said:Can anyone explains the concept of effective mass in solid state physics to me?
Thanks a lot~
marlon said:Intuitively, effective mass is a concept that uncouples one many body problem into a set of one body problems that are more easu to solve (i mean, of which the Schrödinger equation, ie the SE, is easier to solve).
Suppose you have 100 electrons mutually interacting through a coulombic potential. The SE cannot be solved exactly because of the mutual coupling between all the electrons (electron 1 interacts with electron 2,3, etc). To uncouple this many body system, we convert it into a system where you have "new electrons" interacting in a background potential. So, you look at the problem as if the new electrons are no longer interacting with each other but with some background potential. Since both systems need to be equivalent (ie you need to describe the same physical reality) you need to compare both systems : the original system as mutually interacting electrons, the new system has non interacting electrons in a certain potential well. To make sure that both systems are equivalent, we change the mass of the electrons in the second system, in such a way that both SE are describing the same reality. This new mass is the effective mass, which can be defined as the electron mass + some interactions (ie energy of those interactions) to uncouple the many body problem into many one body problems.
That is the philosophy behind effective mass.
marlon
tnho said:Introducing the concept of effective mass, is it a kind of renormalization method?? =)
marlon said:To make sure that both systems are equivalent, we change the mass of the electrons in the second system, in such a way that both SE are describing the same reality. This new mass is the effective mass, which can be defined as the electron mass + some interactions (ie energy of those interactions) to uncouple the many body problem into many one body problems.
That is the philosophy behind effective mass.
marlon
To explain what i said i will show you the actual calculation of the effective mass : http://www.tf.uni-kiel.de/matwis/amat/semi_en/kap_2/backbone/r2_3_1.htmlneu said:so the effective mass is the mass that the electron/hole appears to posses in the field at the band gap.
What do you mean by real mass ? I suppose you are referring to the mass of a free particle. Electrons in the vacuum have mass m and electrons in a crystal have effective mass m'. m' exists exactly because the electrons have energylevels E determined by the symmetry (ie periodicity) of the crystal. This is also why some materials have band gaps and others do not.what interactions are causing the apparent mass to be less than the real mass?
As the effective mass is related to the band curviture, are electrons near the tip of the gap curve 'lighter' than those at the lower part of the band curve?
rewebster said:Z---
The photo on p.157 looks like your 'image'/avatar---how closely are the two related?
rewebster said:Is the sloping curve of the intensity due to any aspect of the magnetic field/forces?
Effective mass refers to the apparent mass of an electron or hole in a crystalline solid, which reflects the influence of the crystal lattice on the particle's motion. It is a measure of the particle's mobility in the solid and is crucial for understanding the electronic and optical properties of materials.
Effective mass is typically calculated using the band structure of a solid, which describes the allowed energy levels for electrons in the material. The curvature of the energy bands near the top or bottom of the band structure determines the effective mass, which can be calculated using specialized mathematical equations.
The effective mass of a particle in a solid is influenced by several factors, including the material's crystal structure, the strength of the electron-lattice interactions, and the presence of impurities or defects in the material. Additionally, external factors such as temperature and magnetic fields can also affect the effective mass.
Effective mass is a crucial concept in solid state physics because it helps explain and predict the behavior of electrons and holes in materials. It is used to calculate various properties of a material, such as its electrical conductivity and optical properties. Understanding effective mass is essential for developing new materials for electronic and optoelectronic devices.
The effective mass of particles in a solid has a significant impact on the material's properties. For example, a lower effective mass means that electrons or holes can move more easily, resulting in higher electrical conductivity. Additionally, the effective mass affects the material's response to external stimuli, such as light or magnetic fields, and can significantly influence its optical and magnetic properties.