Modeling diffusion and collection of charge from ionizing radiation in silicon devices

A simplified model for the diffusion and collection of the charge generated along the track of a fast ionizing particle in Si is developed and used to discuss "soft failures" due to α-particles from radioactive elements. Several examples are worked out in detail. A scaling analysis shows that the charge collected by a device struck by an α-particle decreases less rapidly as all dimensions are scaled down than does the critical charge required to cause an error. Thus the charge margins preventing soft failures in most current devices will vanish if the devices are made smaller without significant redesign.