A charged particle streaks through a silicon sensor, leaving behind a trail of free electrons. The time it takes for this charge to be collected at the electrode depends on how deep in the crystal it was born. A particle entering head-on carves identical paths through neighboring pixels: their signals arrive almost simultaneously. But tilt it, and one pixel sees the start of the track near the surface while another sees it at the far edge. The difference in response time can reach hundreds of picoseconds (trillionths of a second).

The authors of the study put this feature to work. They used silicon avalanche diodes with low gain — sensitive elements capable of recording time to within tens of picoseconds. By simulating particles passing through an array of such pixels, they noticed that when a track crosses three or more cells at an angle, the delays between them form a clear pattern. It turns out that these delays can be used to compute the angle without adding extra detector layers. A simple linear formula links the time difference to the tangent of the track's tilt angle.

The main enemy of accuracy is random fluctuations in energy loss (the so-called Landau fluctuations). When a particle slows down in matter, it loses energy unevenly: sometimes a bit more, sometimes a bit less. This smears the timing marks and limits both the angular resolution and the fraction of tracks for which the angle can be recovered at all. Interestingly, the simple linear model comes close to the theoretical limit set by these fluctuations. This means that it is not algorithmic cleverness but the very geometry of charge collection that determines how well we can measure a particle's direction.