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This invention provides an extremely accurate way to characterize the Young's modulus of thin film materials with thicknesses in the nanometer range. It takes advantage of a recently developed high Q silicon Young's modulus resonator (YMR), which has a record high quality factor of about fifty million in operation at temperatures below 10 degrees Kelvin (10K). Because of the high Q of the YMR, the temperature stability of the YMR's resonance frequency below 1K, and the extremely high degree of vibration isolation inherent in the inventive design, the relative resolution of the resonant frequency is typically in 2×10−7. This is enough to resolve a resonant frequency shift after a deposition of a thin film onto the sensitive part of the resonator, and to compute the Young's modulus of thin film materials of even a few monolayers thickness.