High-level carrier generation events, such as heavy-ion strikes, can produce carrier den- sities that are orders of magnitude greater than the background doping density. The charge- collection process at a reverse-biased device junction in response to such a condition is complex and dynamic. In [16], device level simulations were used to assert that the electric field along the track of charge produced by a ion passing through a junction and into the device substrate is weak, and, in cases where the ion does not pass all the way through the device, the field that was initially supported by the reverse-biased depletion region is pushed down to the track end. A key conclusion of [16] is that understanding the physical mechanisms of charge collection requires considerations of the entire device structure, and not just regions near the junction. This was discussed briefly in Section 2.3.
Previous theoretical work has leveraged similar ideas in the development of an analyti- cal model for charge collection [18, 19, 40, 41]. This model is built around the observation that, for carrier-generating events of sufficient intensity, the device substrate can be parti- tioned into regions that can be characterized by their relative carrier densities, potentials, and electric fields [18, 19, 40], [48], [49]. A schematic of this partitioning and the rel- evant physical properties of each region are shown in Figure 3.1, which is discussed in greater detail in Section 3.3. This regional partitioning could be considered a similar phys- ical framework to that of funneling in response to a heavy ion strike through the depletion region of a device [15, 34, 50]. However, where the funnel model places emphasis on a region of potential modulation surrounding the ion track (i.e., the funnel), regional parti- tioning focuses on the electric field established directly beneath the region of high carrier density generated by the radiation event. This electric field is due to the reduction in voltage
Figure 3.1: Schematic showing individual region names (a) and relevant physical charac- teristics of those regions (b) for a reverse-biased p-n junction during high-level conditions.
These regions are described mathematically by the ADC model. For early times during the charge-collection process, the ambipolar region boundary corresponds approximately to the bottom of the generated carrier density.
that is typically supported by the depletion region.
In some analytical charge collection models (the funnel model of [15], for instance), tracks passing through a device are considered to be “infinitely long”. In other words, those models describe charge collection due to a particle that passes completely through the device. This might lead to some confusion when discussing the electric field “beneath the region of high carrier density”. However, many cases of practical interest involve particles that are relatively short range. Several examples of short-range phenomena were mentioned in Section 2.3. The concepts presented in this work are certainly not limited to short-track phenomena, but such phenomena do provide good example cases for the ideas discussed here.
The ambipolar diffusion with a cutoff (ADC) model is a first-principles, analytical charge collection model that is based on the regional partitioning concepts discussed above [18, 19, 40] and illustrated in Figure 3.1. As has been discussed using device-level simu- lations [40], and is shown experimentally in this work through charge-collection measure- ments for the first time, the ADC model is capable of producing reasonably accurate values for total collected charge without many of the assumptions required by other analytical
charge collection models, which are discussed in Section 3.5. The ADC model focuses on the physical mechanisms of charge collection during high-level carrier generation events.
This allows the ADC model to bridge the gap between simple analytical charge collec- tion models, which provide little physical insight into the charge-collection process, and comprehensive device-level simulations (e.g., TCAD tools).
Analytical charge collection models could also be advantageous to other modeling ef- forts. There is recent and growing interest in simulation codes that use Monte-Carlo meth- ods to analyze the interaction of radiation with matter (such as the MRED tools [51, 52]).
This analysis is then combined with information regarding charge collection and circuit analysis methods to predict the circuit-level response of a device exposed to radiation.
Due to the computationally intensive nature of Monte-Carlo techniques, it is desirable to use analytical models (as opposed to TCAD simulations) whenever possible to reduce the computational overhead.
The charge-collection measurements described throughout this chapter were made via high-speed transient capture [53] on a bulk silicon diode during exposure to high-irradiance laser pulses. The pulse was at a sub-bandgap wavelength, so carrier generation was pro- duced by TPA [39]. The data show that, for sufficiently high-energy laser pulses, nearly all of the generated charge is collected, even when substantial carrier generation occurs only well below the depletion region boundary. The ADC model is able to predict trends in col- lected charge that are in good qualitative agreement with experimentally measured values in this situation, which is an experimental condition that cannot be described accurately by other analytical charge-collection models. Models that consider only certain device regions (the depletion region, or a “funnel region” for example) can predict correct values for col- lected charge in some cases. However, for the more general case of predicting the collected charge due to an arbitrary carrier density near a reverse-biased junction during a high-level carrier generation event, the response of the entire device must be considered.
Section 3.2 describes the experimental setup and measurement process. To aid in the
Figure 3.2: An illustrative diagram of the diode and measurement procedure. Relative sizes are not to scale. Exact doping levels can be seen in Figure 3.4. The device overlayers are not shown.
understanding of the model used to analyze the experimental work, an overview of regional partitioning is discussed in Section 3.3, which includes new device-level simulations, while Section 3.4 discusses how the ADC model was applied to the experimental data. The experimental results are discussed in Section 3.5. Appendix A contains a more detailed derivation of the ADC model. The derivation shown in the appendix is intended to be a summary of the more salient characteristics of the model, it has been compiled from various works that discuss the model in even greater detail [17–19].