Minimum Size and Maximum Packing Density of Nonredundant Semiconductor Devices

It is shown that there exists an absolute lower limit to device size and an absolute upper limit to packing density of nonredundant semiconductor devices, whether integrated or nonintegrated, based on fundamental physical phenomena such as statistical variations in impurity distribution, maximum resolution of semiconductor fabrication methods, power density and influence of cosmic rays. The influence of these phenomena falls in two categories, namely failures that appear during the fabrication of the devices (impurity distribution, dividing operation) and failures that appear during use. The latter may be temporary failures (cosmic ray ionization, carrier fluctuations) or permanent failures (atomic displacements by cosmic rays, heat generation). For a medium size computer (105 components) with a reasonable life expectancy (1 month mean time between failures), the minimum device size under reasonable conditions is approximately (10¿)3, which is not far from devices now in the planning stage and within reach with eidsting techniques. It is within a factor of 2-5 of the dimensions of the active region of many devices of today. As microminiaturization by mere reduction in size appears headed for a not too distant limit it appears necessary from a device point of view to consider remedies which also have been suggested from a system point of view, namely redundancy, self-organizing systems, negative feedback, etc.