Abstract
To describe a nonlinear ultrasonic wave in a semiconductor with charged dislocations, an evolution equation is obtained that generalizes the well-known equations of wave dynamics: Burgers and Korteweg de Vries. By the method of truncated decompositions, an exact analytical solution of the evolution equation with a kink profile has been found. The kind of kink (increasing, decreasing) and its polarity depend on the values of the parameters and their signs. An ultrasonic wave in a semiconductor containing numerous charged dislocations is considered. It is assumed that there is a constant electric field that creates an electric current. The situation is similar to the case of the propagation of ultrasonic waves in piezoelectric semiconductors, but in the problem under consideration, instead of the electric field due to the piezoelectric properties of the medium, the electric field of dislocations appears.
Highlights
In the one-dimensional approximation, a nonlinear system of coupled equations for displacement u, dislocation movements ξ and electric field E have the following form [1]: ρ
We assume that u~ε12, τ~ε1, N~ε19, A~ε13, B~ε12
The order of the remaining quantities follows from equations (9) - (12)
Summary
In the one-dimensional approximation, a nonlinear system of coupled equations for displacement u, dislocation movements ξ and electric field E have the following form [1]: ρ. Ρ – density of the medium; c1, Q – linear and nonlinear elastic moduli; A, B – coefficients characterizing the mass and damping of dislocation oscillations; λ – "stiffness". The equations for the components of the vector of electric current density have the following form: ji eμik Let's move on to the new coordinate τ = x − t, the system of equations for v semiconductors will take the following form:.
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