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The effects of 10-keV X-rays and 400-keV endpoint-energy bremsstrahlung X-rays on MOS capacitors with SiO2 or HfO2 gate dielectrics and Al and TaSi gate metallization have been studied using the Monte Carlo simulator, MRED. We compare these calculations with previous results in the literature obtained with other Monte Carlo and discrete ordinates codes, and with experiments on devices with SiO2 gate dielectrics, and find generally good agreement. There is a significant dose reduction in thin HfO2 layers exposed to 10-keV X-rays, when the HfO2 is surrounded by lower-Z materials (e.g., Si, Al). This dose reduction does not occur in a medium-energy bremsstrahlung X-ray environment; in that case, the dose in a HfO2 gate dielectric can be ~10 times higher than the dose in a SiO2 dielectric, for the same incident X-ray fluence. These results demonstrate the capability of MRED to assist in the evaluation of dose enhancement and reduction in regions including or nearby high-Z materials in microelectronic materials and devices.