The resulting current can be measured and used to determine the number of ions or electrons hitting the cup.

Faraday cups can also be used to measure charged aerosol particles.

When a beam or packet of ions or electrons (e.g. from an electron beam) hits the metallic body of the cup, the apparatus gains a small net charge.

The cup can then be discharged to measure a small current proportional to the charge carried by the impinging ions or electrons.

For a continuous beam of ions (assumed to be singly charged) or electrons, the total number N hitting the cup per unit time (in seconds) is where I is the measured current (in amperes) and e is the elementary charge (1.60 × 10−19 C).

Thus, a measured current of one nanoamp (10−9 A) corresponds to about 6 billion singly charged particles striking the Faraday cup each second.

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.

The Faraday cup uses a physical principle according to which the electrical charges delivered to the inner surface of a hollow conductor are redistributed around its outer surface due to mutual self-repelling of charges of the same sign – a phenomenon discovered by Faraday.

[2] The conventional Faraday cup is applied for measurements of ion (or electron) flows from plasma boundaries and comprises a metallic cylindrical receiver-cup – 1 (Fig.

1) closed with, and insulated from, a washer-type metallic electron-suppressor lid – 2 provided with the round axial through enter-hollow of an aperture with a surface area

Both the receiver cup and the electron-suppressor lid are enveloped in, and insulated from, a grounded cylindrical shield – 3 having an axial round hole coinciding with the hole in the electron-suppressor lid – 2.

The electron-suppressor lid is connected by 50 Ω RF cable with the source

The receiver-cup is connected by 50 Ω RF cable through the load resistor

enables an observer to acquire an I-V characteristic of the Faraday cup by oscilloscope.

is the Faraday cup I-V characteristic which can be observed and memorized by oscilloscope In Fig.

can be measured at the absence of the ion flow and can be subtracted further from the total current

measured with plasma to obtain the actual Faraday cup I-V characteristic

All of the Faraday cup elements and their assembly that interact with plasma are fabricated usually of temperature-resistant materials (often these are stainless steel and teflon or ceramic for insulators).

For processing of the Faraday cup I-V characteristic, we are going to assume that the Faraday cup is installed far enough away from an investigated plasma source where the flow of ions could be considered as the flow of particles with parallel velocities directed exactly along the Faraday cup axis.

of the Faraday cup can be calculated by integrating Eq.

(3), where the lower integration limit is defined from the equation

(4) represents the I-V characteristic of the Faraday cup.

of ions arriving into the Faraday cup and their average energy

can be calculated (under the assumption that we operate with a single type of ion) by the expressions where

in the ion flow at the Faraday cup vicinity can be calculated by the formula which follows from Eq.

, and from the conventional condition for distribution function normalizing Fig.

installed at output of the Inductively coupled plasma source powered with RF 13.56 MHz and operating at 6 mTorr of H2.

The value of the electron-suppressor voltage (accelerating the ions) was set experimentally at

, near the point of suppression of the secondary electron emission from the inner surface of the Faraday cup.

[3] 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.