A recently proposed method for the generation of relativistic electron beams with nanometer-scale current modulation requires diffracting relativistic electrons from a perfect crystal Si grating, accelerating the diffracted beam and imaging the crystal structure into the temporal dimension via emittance exchange. The relative intensity of the current modulation is limited by the ability to extinguish the transmitted beam via diffraction with a single-crystal Si membrane. In these preliminary experiments we will measure the extinction of the transmitted electron beam at zero scattering angle due to multiple Bragg scattering from a Si membrane with a uniform thickness of 340 nm at 2.35 MeV using the SLAC UED facility. The impact of beam divergence and charge density at the Si target will be quantified. The longevity of the Si membrane will also be investigated by monitoring the diffraction pattern as a function of time to observe the potential onset of damage to the crystal.