Beam Current Is Counted, Not Amplified

Measuring the current of every beam in a multi-beam electron writer can become a significant bottleneck, particularly when sub-percent precision is required. While a Faraday cup provides an accurate reference measurement, its associated electrometer introduces noise and settling-time penalties that can substantially extend measurement time.

This article examines where the true limit lies: not in the measurement electronics, but in the beam itself. Because electrons arrive according to counting statistics, shot noise establishes a fundamental averaging time for achieving a specified relative precision. For a 4.00 pA beam, for example, a silicon detector requires 42.7 ms to reach 0.1% precision, approaching the beam's counting-statistics limit.

The analysis compares a Faraday cup and electrometer with a silicon photodiode detector that provides approximately 12,000× current gain at 50 keV. That gain does not eliminate shot noise; instead, it reduces the impact of noise and settling in the electronics that follow the detector. At 1 pF feedback capacitance, the optimized electrometer penalty is 2.98× at 0.1% precision and 24.3× at 1% precision, while the detector operates much closer to the shot-noise floor.

For a 262,144-beam map, the modeled detector completes measurements in 112 seconds at 1% precision and 3.11 hours at 0.1%. The article also explains why detector gain must be calibrated against a Faraday cup and outlines a test for separating beam fluctuations from measurement-chain noise.