Calculation of Charge Carrier Concentration Profile in a Wide Potential Well with Electric and Magnetic Fields

We investigated an equilibrium state of Fermi electrons in modulation doped structures with a wide quantum well in a strong parallel magnetic field. We studied the charge carrier system with a sufficiently high density, such that the de Broglie wavelength of electrons is smaller than the potential well width. We have formulated hydrodynamic equations for this carrier system both in the absence of magnetic field and in a parallel magnetic field. We have obtained analytical solutions for the charge carrier concentration as a function of coordinates in the potential well. In a quantum area near the interface, we carried out quantum mechanical calculations taking into account the effect of electric and magnetic fields. The concentration profile is presented for modulation doped Si/SiGe/Si heterostructures. We discuss large positive magnetoresistance in a strong parallel magnetic field in these structures.