Most recently, the whole world is struggling against the virulent pandemic COVID-19. Due to the unbounded global spread of the disease, having biosensors with high performance such as high sensitivity and accuracy is of utmost importance. In this paper, the effects of various parameters on the behaviors of micro-biosensors are investigated in order to enhance their performance. These parameters are related to the geometry and material, and they are assumed to be gradually changing in the longitudinal direction of the biosensor according to a power law. Therefore, they are called functionally graded geometrical and material parameters. Another aspect is when considering microcantilever-based biosensors, the main behavior parameter is the deflection at the free end. In the analyses, the influences of the surface stress and van der Waals intermolecular forces are taken into account. Also, the total energy of the beam, which is the combination of the van der Waals energy and the elastic strain energy, is accomplished. In addition, the equivalent force causing the deflection is also evaluated using Castigliano method for two cases. These cases account for a concentrated force at the free end and a distributed load along the biosensor, respectively. Since the governing equations account for the size dependency and the considered parameters are functions of the position, the solution is too complex to be achieved analytically, and therefore, numerical methods are applied. For uniform biosensors made of homogeneous materials, or in other words when all parameters are not varying with the position, the obtained results are compared with those in the literature, and good agreement is obtained. On the other hand, the performance, which include sensitivity and limit of detection, of functionally graded biosensors can be enhanced by proper choices of the considered parameters and the corresponding exponent of the gradation function.