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We present calculations of the Casimir force between silicon and gold slabs of variable thickness. For silicon, the force is found to depend strongly on slab thickness and to decrease rapidly when the slab separation exceeds the thickness. For gold, Drude and plasma models give qualitatively different predictions for the Casimir force at large slab separations. We explain the influence of slab thickness by analyzing the phase factor acquired by the vacuum field when propagating inside the material slab. The present results could be interesting for nanotechnologies to eliminate an unwanted Casimir force.