We can describe Drude model for electrons, but, can we also write the equation for holes? Does it fail?
In Drude model, wp=(ne2/ ε0m)1/2 where n is electron concentration, e is charge, m is effective mass, ε0 is free space permittivity.
charge has a square dependence so, weather charge is positive or negative, the results are going to be the same.
We need 3 inputs in order to define the Drude model in a system; plasma frequency, mobility and permittivity. Wp will be the same for holes like electrons depending on the hole concentration.
Mobility is defined as qt/m, where q is elementary charge, t is relaxation time, m is the effective mass. Is it going to be negative for holes? If it is negative, it means it will behave like a gain medium because imaginary part of permittivity will be negative.
Permittivity will depend on the material.
What are your ideas?
Thanks
From Wikipedia,
Drude model electrons (shown here in blue) constantly bounce between heavier, stationary crystal ions (shown in red).
The Drude model of electrical conduction was proposed in 1900[1][2] by Paul Drude to explain the transport properties ofelectrons in materials (especially metals). The model, which is an application of kinetic theory, assumes that the microscopic behavior of electrons in a solid may be treated classically and looks much like a pinball machine, with a sea of constantly jittering electrons bouncing and re-bouncing off heavier, relatively immobile positive ions.
The two most significant results of the Drude model are an electronic equation of motion,
and a linear relationship between current density J and electric field E,
Here t is the time and p, q, n, m, and τ are respectively an electron's momentum, charge, number density, mass, and mean free time between ionic collisions (that is, the mean time an electron has traveled since the last collision, not the average time between collisions). The latter expression is particularly important because it explains in semi-quantitative terms why Ohm's law, one of the most ubiquitous relationships in all of electromagnetism, should be true.[3][4][5]
The model was extended in 1905 by Hendrik Antoon Lorentz (and hence is also known as the Drude–Lorentz model) and is a classical model. Later it was supplemented with the results of quantum theory in 1933 by Arnold Sommerfeld and Hans Bethe, leading to the Drude–Sommerfeld model.
In solid-state physics, the free electron model is a simple model for the behaviour of valence electrons in a crystal structure of a metallicsolid. It was developed principally by Arnold Sommerfeld who combined the classical Drude model with quantum mechanical Fermi–Dirac statistics and hence it is also known as the Drude–Sommerfeld model.
The free electron empty lattice approximation forms the basis of the band structure model known as nearly free electron model. Given its simplicity, it is surprisingly successful in explaining many experimental phenomena, especially
the Wiedemann–Franz law which relates electrical conductivity and thermal conductivity;
the temperature dependence of the heat capacity;
the shape of the electronic density of states;
the range of binding energy values;
electrical conductivities;
thermal electron emission and field electron emission from bulk metals.
If I understand your question, isn't possible because model is classical. It not explain about hall effect and heat capacity of metal. The holes is a concept started just hall effect. The limitation of the model, that is good but limited, went overcome with quantum consideration.
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