# Search results for query: *

1. ### I Fermi distribution interpretation

I know that, in Quantum Mechanics, talking about "actual" quantities is inappropriate. Anyway, it is common to compute the number of electrons in conduction band, for example, in a semiconductor (e.g. here, penultimate formula). During the computation, Fermi distribution and density of states...
2. ### I Number of electrons in conduction band

Ok, that's right now, so thank you both!
3. ### I Planck formula and density of photons

TeethWhitener, I agree with you, the refractive index is at the same power as c and in different media photons have different velocities. Henryk, it was difficult because the book spoke about "density" without specifying anything else; so I thought it was per unit frequency. Thank you both!
4. ### I Planck formula and density of photons

Hello! Let's consider again a system of atoms with only two permitted energy levels E_1 and E_2 > E_1. When electrons decay from E_2 level to E_1, they generate a photon of energy E_{21} = E_2 - E_1 = h \nu. The number of photons (per unit frequency, per unit volume) emitted by such a system in...
5. ### I Volume in K space occupied per allowed state

:wink: Yes, exactly! I understand what you are meaning and yes, it is correct. Obviously, very often you are not interested in counting just the number of states between two available modulus values k_1 and k_2: instead, you will be interested in counting the total number of states, so...
6. ### I Fermi distribution interpretation

Did you deduce this from my post or by your own? The first post was maybe not clear about this. Don't consider my problem as real and don't take its numbers as absolute: it was just an example to show how the Fermi distribution is used to count the electrons in a band of energies. The strange...
7. ### I Fermi distribution interpretation

Hello! Let E_1, E_2, \ldots, E_n be n allowed energy levels for a system of electrons. This system can be described by the Fermi-Dirac distribution f(E). Each of those levels can be occupied by two electrons if they have opposite spins. Suppose that E_1, E_2, \ldots, E_n are such that...
8. ### I Volume in K space occupied per allowed state

1) If you read again my answer, I didn't say that dk has not a physical meaning. I said instead that dk is not related to the spacing between the states Be careful: the \mathbf{k}-space is a vector space. Your variable \mathbf{k} = k_x \mathbf{x} + k_y \mathbf{y} + k_z \mathbf{z}, is in fact a...
9. ### I Volume in K space occupied per allowed state

You're welcome :). Yes, it is. If \mathbf{k} is a vector with components k_x, k_y, k_z, the minimum spacing between two adjacent values of k_x (or k_y, or k_z) is \pi / L. So, each of the acceptable values of \mathbf{k} result to be "alone" inside a volume (\pi / L)^3 (and then you obtain the...
10. ### I Volume in K space occupied per allowed state

Ok, and so first of all you can say now that the density of the allowed states in the K-space is \displaystyle \frac{1}{\left( \displaystyle \frac{\pi}{L} \right)^3} that is (volume of k-space of one octant of a spherical shell)*(density of allowed states in K-space.) No, absolutely, for...
11. ### I Number of electrons in conduction band

Yes, a factor of 2 is included in the density of states. My question is: if an energy level E_1 is such that (for example) f(E_1) = 0.1 and there are two possible states with opposite spins for the electrons at E = E_1: will both the states have the same 0.1 probability of being occupied? Or...
12. ### I Number of electrons in conduction band

Hello! In order to obtain the number of actual electrons in the conduction band or in a range of energies, two functions are needed: 1) the density of states for electrons in conduction band, that is the function g_c(E); 2) the Fermi probability distribution f(E) for the material at its...
13. ### I Fermi sphere and density of states

To marcusl: maybe this can help you. Go to page 86 and to the beginning of paragraph 6.1.
14. ### I Fermi sphere and density of states

To DrClaude: ok, now it is more clear, thank you. To marcusl: I think the "particle in a box" is the simplest representation of an electron into a lattice; it is good as a first approximation. The effective mass includes the effects of lattice and so the electrons can be treated as free...
15. ### I Fermi sphere and density of states

Remember that we are counting states in the Fermi sphere in order to derive the state density. States are acceptable solutions of the Schrödinger equation for this problem. So, should they also be linearly independent?
16. ### I Fermi sphere and density of states

In the Wikipedia page you linked, it is stated that negative values of p, q, r are neglected because "they give wavefunctions identical to the positive" p, q, r "solutions except for a physically unimportant sign change". It is what thephystudent mentioned: \sin(x) =? \sin(-x). So I would like...
17. ### I Fermi sphere and density of states

To marcusl: no, it is general, but referred to semiconductor materials. To navrit: I think it is related to the wavefunctions more than the symmetry of the Fermi sphere. To thephystudent: no, \sin(x) = - \sin(-x) and so they seem to be not equivalent. I think the approach to be followed is the...
18. ### I Fermi sphere and density of states

Hello! When computing the density of states of electrons in a lattice, a material with dimensions L_x, L_y, L_z can be considered. The allowed \mathbf{k} vectors will have components k_x = \displaystyle \frac{\pi}{L_x}p k_y = \displaystyle \frac{\pi}{L_y}q k_z = \displaystyle \frac{\pi}{L_z}r...
19. ### I Double heterostructure junction in forward and zero bias

I know that my questions were very specific. More simply, do you know some books that talk about heterostructures?
20. ### I Double heterostructure junction in forward and zero bias

Hi! When dealing with a pn homojunction, it is easy to see the features it has at equilibrium, and also the features it has with forward/reverse bias. Plots show the constant Fermi level at equilibrium and the different Fermi levels for a forward bias; moreover, examples show how much the bands...
21. ### I Built-in potential in pn junction

Ok, thank you. By "vacuum level" I mean the energy of a free electron outside the crystal, as stated http://ecee.colorado.edu/~bart/book/book/chapter2/ch2_3.htm, par. 2.3.3.2. Anyway, maybe the vacuum level is bent like the energy bands across the junction due to the electric field.
22. ### I Built-in potential in pn junction

Hello! The (potential) energy of an electron in a solid structure is always negative; also the E_c and E_v levels (conduction band and valence band limits) are negative, in the band diagram of a pn junction. When the junction is built and thermal equilibrium is reached, the depletion region...
23. ### I Diffusion of carriers in a double heterostructure

Ok and thank you! As far as you know, which could be a typical height choosen for barriers in heterostructures? (For example, in the case of AlGaAs - GaAs - AlGaAs)
24. ### I Diffusion of carriers in a double heterostructure

For example, let's refer to this document, page 7, figure (a). If electrons migrated from the right (n-AlGaAs) region to the central (GaAs) region, overstepping that high barrier potential, how can we be sure that they won't also overstep the barrier between the central and the left (p-AlGaAs)...
25. ### I Diffusion of carriers in a double heterostructure

Hello! Double heterostructures are used in LEDs and lasers to provide both the confinement of the charge carriers and the confinement of the generated light. This image is a comparison between a homojunction and a heterojunction. As regards the unbiased junctions, when the n region and the p...
26. ### I Pn junction to reach thermal equilibrium

Thank you for your clarifications. But in particular during the transient just after the contact between the n region and the p region, how can electrons increase their energy and move to the conduction band of the p side? It is not for thermal energy. May the charge concentration gradient be...
27. ### I Pn junction to reach thermal equilibrium

Hello! Some of the processes caused by a pn junction are not clear for me. Just after the contact between the p and the n region, a migration of charges happens in a semiconductor junction in order to reach an equilibrium condition. A valence band and a conduction band are present in both...