Thermodynamics of a quasi-two-dimensional electron gas: Effects of magnetic fields, temperature and finite width

The effects of nonzero temperature, finite thickness and magnetic fields on an electron gas confined in a quasi-two-dimensional (Q2DEG) region are studied. Finite values of the thickness allow the existence of energy bands and give new characteristics to the system. Here we study some thermodynamic and transport properties to get a better understanding of these effects. For electronic densities of the order of 1012 electrons per cm2, and temperatures lower than 4 K, it is found that the chemical potential, free energy, magnetization, magnetic susceptibility and the inverse of Hall conductivity are independent of the thickness up to it reaches a threshold value. Systems with thicknesses a little above of the critical value lose the two-dimensional character, but they do not have the properties of a three-dimensional electron gas.