  We propose two novel experiments on the measurement of the Casimir force
acting between a gold coated sphere and semiconductor plates with markedly
different charge carrier densities. In the first of these experiments a
patterned Si plate is used which consists of two sections of different dopant
densities and oscillates in the horizontal direction below a sphere. The
measurement scheme in this experiment is differential, i.e., allows the direct
high-precision measurement of the difference of the Casimir forces between the
sphere and sections of the patterned plate or the difference of the equivalent
pressures between Au and patterned parallel plates with static and dynamic
techniques, respectively. The second experiment proposes to measure the Casimir
force between the same sphere and a VO${}_2$ film which undergoes the
insulator-metal phase transition with the increase of temperature. We report
the present status of the interferometer based variable temperature apparatus
developed to perform both experiments and present the first results on the
calibration and sensitivity. The magnitudes of the Casimir forces and pressures
in the experimental configurations are calculated using different theoretical
approaches to the description of optical and conductivity properties of
semiconductors at low frequencies proposed in the literature. It is shown that
the suggested experiments will aid in the resolution of theoretical problems
arising in the application of the Lifshitz theory at nonzero temperature to
real materials. They will also open new opportunities in nanotechnology.
