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Thomas Fermi (TF) approach was used to represent a model for the n-type quadruple δ-doped (QDD) system in GaAs. This is the first physical model in the literature for the QDD system. The energies, the wave functions and the Fermi energy (EF) were calculated. These calculations were performed for different density of impurities in the doped layer (N2D) and for different separation distances (d) between the doped layers. Preliminary results show that the value of the Fermi level for the first proposed model is well below its expected value. This observation is exploited for a second model consistent with the expected values of the EF. Our results indicate that there is a limit at the bottom of the potential profile for a multilayered doped delta system. This has a great importance for calculations in optoelectronic and transport properties