Questions tagged [density-of-states]
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Density of States, Photoemission and Integrating the Number of States
I'm reading Fowler's theory on photoemission. I'm stuck on a part which Fowler helpfully identifies as "obvious". Fowler sets up the free electron model, suggesting that electrons need a ...
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Density of states - as a function of electron velocity
A condensed matter textbook states that in a 3D gas of electrons obeying the Fermi-Dirac statistics the number of electrons per unit volume having velocity components in the ranges $u, u+d u$, $v, v+d ...
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What causes bands to shift in energy or become narrow?
This is the density of states for pure palladium in bulk :
This is the density of states of palladium hydride :
clearly the d bands are shifting and becoming narrow. The narrowing of bands is said ...
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Relationship between Density of States and the Fermi level
My understanding is that given the DOS of a material we find the fermi level by filling electrons into those energy levels and when we run out of electrons we reach close to the fermi level (or ...
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Change in internal chemical potential of electrons in the 2DEG
I was reading about quantum capacitance and came across the following formula:
$$\Delta \mu = \frac{N}{\rho}$$ where N is the number of electrons moved from the metal to the low-density-of-states ...
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Volume occupied by mechanical states, and density of states
Suppose we express the phase space volume occupied by all mechanical states $(\mathbf{q},\mathbf{p})$ with energy equal to or less than mechanical energy $E$ as:
\begin{equation}\Phi(E,\lambda)=\int\...
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Is the inverse relation between the DOS and the energy gradient in $k$-space only valid in 1D systems?
In my solid state course, I was taught that Van Hove singularities can be explained because the DOS follows:
$$\mathrm{DOS} \propto \frac{1}{\nabla_k E} .$$
However, the DOS of a 3D system is ...
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Recover non-relativistic density of state
The density of state of a non-relativistic particle ($E = \hbar^2k^2/2m$) in 3D is:
$$\rho_{class}(E) = \dfrac{V}{4\pi^2}\left(\dfrac{2m}{\hbar^2}\right)^{3/2}E^{1/2}.$$
The density of state of an ...
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What does energy density state for holes in valence band mean and how is this equation applicable there?
Equation 1 is the energy density function for free particles confined in a 3D box. Now we could apply this equation to conduction band of a semiconducting material taking the electrons present there ...
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Density of states for non-interacting Bosons
I am tasked with calculating the density of states in terms of the angular frequency given the dispersion relation. But I couldn't help but think: why can't we calculate the density of states by ...
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The dimension of Spectral Function
For a free electron gas model with volume $V$, the spectral function is
$$A(k,\epsilon)=2\pi\delta(\epsilon-\epsilon_k)$$
so the density of states,
$$D(\epsilon)=\frac{1}{V}\sum_k\delta(\epsilon-\...
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How to compute the Auger transition rate?
I've been working on computing the Auger transition rate for an exotic atom, one where an electron has been replaced by a particle of arbitrary mass and (integer) charge. I've been closely following ...
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Boundary condition for density of state in momentum space
I am working on fermions in metal, where you need
$\frac{2}{V}\int_{0}^{P_{f}}\frac{L^{3}}{(2\pi\hbar)^{3}}dP$
to get the total number of occupied states, where the coefficient $\frac{L^{3}}{(2\pi\...
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Quasiparticle Density of States
In this paper we have the following:
The corresponding quasiparticle density is given by the equation
$$n_{qp} = 4N_0 \int_\Delta ^\infty dE \frac{E}{\sqrt{E^2 - \Delta^2}} f(E),$$
where $N_0$ is the ...
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Degeneracy in a 2D planar cavity (box potential)
Assume a finite 2D planar cavity. One can write the energy of a photon in this cavity as
$$
\begin{equation}
E(k_x, k_y)=\hbar c \sqrt{k_x^2+k_y^2+k_z^2},
\end{equation}
$$
where $k_z$ is fixed (hence ...
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