# Chemical Sciences: A Manual for CSIR-UGC National Eligibility Test for Lectureship and JRF/Faraday cup

A Faraday cup is a metal (conductive) cup designed to catch charged particles in vacuum. The resulting current can be measured and used to determine the number of ions or electrons hitting the cup. The Faraday cup is named after Michael Faraday who first theorized ions around 1830.

## How it works

When a beam or packet of Ions hits the metal it gains a small net charge while the ions are neutralized. The metal can then be discharged to measure a small current equivalent to the number of impinging ions. Essentially the faraday cup is part of a circuit where ions are the charge carriers in vacuum and the faraday cup is the interface to the solid metal where electrons act as the charge carriers (as in most circuits). By measuring the electrical current (the number of electrons flowing through the circuit per second) in the metal part of the circuit the number of charges being carried by the ions in the vacuum part of the circuit can be determined. For a continuous ion beam of ions (each with a single charge)

${\frac {N}{t}}={\frac {I}{e}}$ where N is the number of ions observed in a time t (in seconds), I is the measured current (in amperes) and e is the elementary charge (about 1.60 × 10−19 C). Thus, a measured current of one nanoamp (10−9 A) corresponds to about 6 billion ions striking the faraday cup each second.

Similarly, a Faraday cup can act as a collector for electrons in a vacuum (for instance from an electron beam). In this case electrons simply hit the metal plate/cup and a current is produced. Faraday cups are not as sensitive as electron multiplier detectors, but are highly regarded for accuracy because of the direct relation between the measured current and number of ions.

## Error sources

The counting of charges collected per unit time is impacted by two error sources: 1) the emission of low-energy secondary electrons from the surface struck by the incident charge and 2) backscattering (~180 degree scattering) of the incident particle, which causes it to leave the collecting surface, at least temporarily. Especially with electrons, it is fundamentally impossible to distinguish between a fresh new incident electron and one that has been backscattered or even a fast secondary electron.