Analysis of a semiconductor die having silicon-on-insulator (SOI) structure is enhanced by operating a die and detecting a response that is used to analyze selected characteristics of the die. According to an example embodiment of the present invention, a die having a thinned backside is provided for analysis. The die is operated so that one or more portions of circuitry in the die are near a state-changing transition between a failed mode and a recovered mode. An electron-beam probe is directed to the thinned backside, and the probe electrically couples a capacitance load to underlying circuitry via the insulator of the SOI structure. The capacitance load alters the timing margin of a portion of the circuitry and, thereby, causes the circuitry to undergo a state-changing transition. A response from the circuitry related to the transition is detected and used to analyze the die. In this manner, portions of the die being affected by altered timing margins can be detected.