Number of Ions, Beam Dose and Dose Rate

Table of Contents

Number of Ions #

It is useful to know how many ions hit the sample during the scan/patterning process. The number of ions which interact with the sample can be increased by the ion beam current I or by increasing the time t. The number of ions interacting with the sample for a specific ion beam current and process time can be calculated via

N= (πΌπΌπ‘œπ‘› [𝐴]  Γ— 𝑑 [𝑠])/(π‘β„Žπ‘Žπ‘Ÿπ‘”π‘’ [𝐢])

where I is the ion beam current, NπΌπ‘œπ‘› is the number of ions, t is the time. The ion beam is assumed to have +1 charge (positive elementary charge 1.602Γ—10^(βˆ’19)C ).

Beam Dose #

The ion dose, also called areal dosage or fluence is an important concept for FIBs. It describes how many ions have hit the sample in a specific area. A lot of effects and artifacts are ion dose related, e.g. how much material is removed, beam damage occurring throughout the imaging/patterning process.

The dose is increased when either:

1.The amount of ions is increased (either higher current I or longer times t)

2.When the area is decreased (smaller patterns or field of views (FOV))

Note: There is a difference in fluence and dose per definition: Fluence is the amount of ions which are going trough an area prior to sample interaction. Dose is the amount of ions which have traveled trough the sample surface into the sample.

Example: 1 frame scan with 1Β΅s dwelltime for a field of view 1Β΅m=1Γ—10^(βˆ’4) π‘π‘š and 1pA ion beam current

=> Area: A= 1Β΅m2 = 1Γ—10^(βˆ’8) π‘π‘š2

=> Number of ions: N = 1.41Γ—10^6Β  π‘–π‘œπ‘›π‘ 

=> Dose: (1.41Γ—10^6Β  π‘–π‘œπ‘›π‘ )/(1Γ—10^(βˆ’8) π‘π‘š2”Β  ” ) = 1.41Γ—10^14Β  π‘–π‘œπ‘›π‘ /π‘π‘š2

Dose Rate #

The dose rate tells you how many ions hit the sample area per second. The dose rate remains constant for a set parameter such asΒ  beam current/aperture. Dose rates play an important role in controlling time-dependent effects such as charging or heat damage.

Example:

If the dose rate is 10 ions/cm2 per second then the dose rate will remain the same during the entire patterning time (if the ion beam current or the area is not changed). This can be seen in the top equation on the slide.

After 1 second: 10 ions have passed through the area, after 2 seconds 20 ions have passed through the area and after 10 seconds 100 ions have passed through the area. A known dose rate therefore allows to calculate, how many ions have passed through a specific area in a given amount of time.

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