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A conceptual model of an X-ray source based on a field emission cathode and a transmission-type target combined with a silicon X-ray window is suggested. By numerical simulation, it is shown that the proposed structure can generate a substantial emission current. It is possible to obtain a small focal spot at the target and, therefore, a high resolution. The parameters of targets providing the maximum X-ray emission intensity are determined. It is shown that effective generation is reached in a 0.25-μm-thick tungsten film and a 0.13-μm-thick molybdenum film. The transparency of a 1–2-μm-thick silicon membrane to X-rays and sufficient mechanical strength of the membrane against a pressure drop on the order of 2 atm are demonstrated, which indicates the possibility of its application as an X-ray window.