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The simulated results of a silicon-based microstrip patch antenna are presented. The antenna structure includes an additional layer of low permittivity material sandwiched between the antenna and the silicon substrate. The simulations are performed using two in-house computer codes that make use of the multi-resolution time domain (MRTD) and the finite difference time domain (FDTD) methods to solve for the electromagnetic fields. These techniques are used for the modeling and optimization of various silicon-based antennas.