2.6 The Isothermal Approximation

Although the present thesis deals with the full modeling of magnetic effects in semiconductor devices also at low temperatures, the available experimental data and simulation results show an excellent agreement when (2.16) is applied to the isothermal case. Literature shows that the thermomagnetic effects are orders of magnitude smaller than the Hall voltage [38].

The mathematical model that reproduces the Lorentz force on carriers in semiconductors for the electrons can therefore be simplified to

$$\mathbf{J_n} = -\sigma_n(\nabla\phi_n) -\sigma_n\frac{1}{1+(\mu^*... ..._n\mathbf{B})^2} \{\mu^*_n\mathbf{B} \times (\mathbf{B} \times \nabla\phi_n) \}$$ (2.18)

For holes, the mathematical model reads

$$\mathbf{J_p} = -\sigma_p(\nabla\phi_p) -\sigma_p\frac{1}{1+(\mu^*... ...*_p\mathbf{B})^2} \{\mu^*_p\mathbf{B} \times (\mathbf{B} \times \nabla\phi_p)\}$$ (2.19)

Along with the Poisson and continuity equations, a device under the presence of a magnetic field can be properly simulated with the drift-diffusion approximation if the device is sufficiently large [19].