1. Theory

Definition: A focused ion beam instrument scans a beam of gallium or other ions, typically at 30 $kV$ , to image by ion-induced secondary electrons and to remove material by sputtering, often combined with an SEM in a dual-beam system (Nellen et al.; Cantoni).
Sputtering: Each ion ejects a few atoms, about 2.1 for silicon, so the removal rate is proportional to beam current (Nellen et al.).
Damage: Ions implant and amorphize the surface to the ion range, 10 to 30 $nm$ at 30 $kV$ , reduced by low-energy final polishing (Nellen et al.; Cantoni).
Gas chemistry: Precursor gases enable local deposition of metals and dielectrics and enhanced etching (Nellen et al.).

2. Working Principle

Source and column: A liquid-metal ion source and electrostatic lenses focus the beam to about 7 to 10 $nm$ at low current (Nellen et al.; Cantoni).
Dual beam: The electron column at 52 degrees images while the ion beam mills (Nellen et al.).
Gas injection: Needles deliver precursors 100 to 200 $μ m$ from the sample (Nellen et al.).
Manipulators: Nanomanipulators lift out lamellae with precision below 10 $nm$ (Cantoni).

3. Applications

TEM lamellae: Site-specific cross-sections of devices (Nellen et al.; Cantoni; TEM page).
Cross-sections for SEM: Failure-analysis sections at defects located by EMMI or OBIRCH (my reading; Emission Microscope page).
Circuit edit: Cutting and reconnecting lines with metal deposition (my reading; Nellen et al. for deposition chemistry).
Tomography: Slice-and-view 3-D reconstructions (Cantoni; Nellen et al.).

Sputtering and Milling

Name	Formula	Related Formulae	Variables/Constants
Sputter yield and volume yield	$Y_{V} = \frac{Y _{a t o m s}}{e n _{a t}}$	$Y_{S i} = 2.1 atoms/ion \leftrightarrow 0.26 μ m^{3} /nC, Y_{C u} = 0.25 μ m^{3} /nC$	$Y_{V} : v o l u m e r e m o v e d p er u ni t c ha r g e$ $Y_{a t o m s} : a t o m s s p u tt er e d p er i o n$ $e : e l e m e n t a r y c ha r g e$ $n_{a t} : a t o mi c d e n s i t y; co n v er s i o n (co m p u t e d); N e l l e n e t a l . : 2.1 a t o m s p er i o n (0.26 μ m^{3} /nC) f or s i l i co n a t n or ma l in c i d e n ce, i o n e n er g i es t y p i c a l l y 20 t o 50 kV; C an t o ni : 0.25 μ m^{3} /nC f or C u, l i q u i d - m e t a l i o n so u r ces o f G a an d o t h er s p ec i es$ $(co m p u t e d : 2.1 a t o m s p er i o n w i t h n_{a t} = 5 \times 1 0^{22} c m^{- 3} g i v es 0.262 μ m^{3} /nC, co n f i r min g N e l l e n^{'} s p ai r o f v a l u es)$
Milling time	$t_{mi l l} = \frac{V}{Y _{V} I}$	$\dot{V} = Y_{V} I$	$t_{mi l l} : mi l l in g t im e$ $V : v o l u m e$ $I : i o n c u r r e n t; C an t o ni : 10 nA t y p i c a l hi g h c u r r e n t, a 10 b y 10 b y 5 μ m b o x (500 μ m^{3}) in C u q u o t e d a s 2000 s (33 min) (see t h e Q / A), ima g in g a t 50 pA; N e l l e n e t a l . : 300 pA sc an s w i t h 48.2 μ s d w e l l r e m o v in g ab o u t 3 nm p er p a ss, c u r r e n t s f r o m 1 pA t o 30 nA$ $(co m p u t e d : 500 μ m^{3} a t 10 nA an d 0.25 μ m^{3} /nC t ak es 200 s; o n e 300 pA, 48.2 μ s p i x e l r e m o v es 3760 n m^{3}, so a 3 nm p a ss im pl i es ab o u t 35 nm p i x e l p i t c h)$
Angle and gas enhancement	$Y (θ) rises with incidence angle to a maximum near 70 to 8 5^{\circ}$	$Y_{G A E} = (2 to 20) Y$	$θ : in c i d e n ce an g l e f r o m t h e s u r f a ce n or ma l$ $Y_{G A E} : g a s - a ss i s t e d y i e l d; N e l l e n e t a l . : ma x im u m a t r o ug h l y 70 t o 85 d e g r ees d e p e n d in g o n ma t er ia l, r e a c t i v e g a ses r ai s in g y i e l d 2 t o 20 t im es, i o d in e an d c h l or in e f or m e t a l s, f l u or in e co m p o u n d s f or d i e l ec t r i cs, w a t er v a p o u r f or c a r b o n, P t an d W p r ec u r sor s an d s i l o x an e w i t h w a t er f or d e p os i t i o n; C an t o ni : ma x im u m n e a r 75 d e g r ees$ $(co m p u t e d : a 20 - f o l d e nhan ce m e n t t u r n s t h e 200 s C u b o x in t o 10 s)$

Damage, Dose and Resolution

Name	Formula	Related Formulae	Variables/Constants
Ion range and damage	$R_{G a} (30 keV) \approx 10 to 30 nm$	$t_{a} \approx 25 to 30 nm (30 kV), t_{a} \approx 2 to 3 nm (Si, low kV)$	$R_{G a} : i o n r an g e$ $t_{a} : am or p h o u s d ama g e t hi c k n ess o n e a c h f a ce; N e l l e n e t a l . : r an g e in am or p h o u s ma tt er 10 t o 30 nm a t t h e e n er g i es u se d, l o w - e n er g y c l e anin g f r o m 7 keV d o w n t o 500 eV; C an t o ni : G a im pl an t a t i o n an d am or p hi z a t i o n u p t o 25 nm b e l o w t h e s u r f a ce f or hi g h - e n er g y p r e p a r a t i o n, l i s t e d l a y er s o f 25 t o 30, 25 t o 30 an d 5 t o 7 nm (ma pp in g t o e n er g i es u n c l e a r), 2 t o 3 nm f or S i a t l o w k V, A r i o n mi l l in g a s an a l t er na t i v e$ $(co m p u t e d : a 60 nm l am e l l a c u t a t 30 kV o n l y co u l d b e a l m os t e n t i r e l y am or p h o u s, 2 x 25 t o 30 nm)$
Gallium dose	$D = \frac{I t}{e A}$	$D \approx 1 0^{16} c m^{- 2} (onset of milling; swelling below)$	$D : im pl an t e d d ose$ $A : i r r a d ia t e d a r e a; d e f ini t i o n (co m p u t e d); N e l l e n e t a l . : d oses b e l o w ab o u t 1 \times 1 0^{16} c m^{- 2} s w e l l in g s i l i co n b y u p t o a f e w nan o m e t r es b e f or e mi l l in g s t a r t s, G a im pl an t e d a s co n t amina t i o n, G a d r o pl e t s o f a f e w h u n d r e d nan o m e t r es w h er e so l u bi l i t y i s l o w, G a A s a r t e f a c t s f r o m se l ec t i v e A s s p u tt er in g, G a m e l t in g p o in t 29.6^{\circ} C$ $(co m p u t e d : 1 pA o n 1 s q u a r e mi cr o m e t r e d e l i v er s 6.2 \times 1 0^{14} c m^{- 2} p er seco n d, r e a c hin g 1 \times 1 0^{16} c m^{- 2} in 16 s)$
Resolution and current	$d_{i o n} \approx 7 nm (1 pA) to \approx 10 nm (low current)$	$J > 10 A/c m^{2}$	$d_{i o n} : i o n - b e am r eso l u t i o n$ $J : c u r r e n t d e n s i t y in t h e p r o b e; N e l l e n e t a l . : t h ese v a l u es o n a S t r a t a 235 D B (1 pA t o 20 nA a t 30 kV), e l ec t r o n co l u mn 0.2 t o 30 kV w i t h 3 nm a t 1 keV m o u n t e d a t 52 d e g r ees, c hamb er ab o u t 1 \times 1 0^{- 6} mbar, g a s n oz z l es 100 t o 200 μ m a w a y; C an t o ni : 2 t o 3 S E p er i o n, S E M r eso l u t i o n 1 t o 2 nm, mani p u l a t or p r ec i s i o n b e l o w 10 nm$ $(co m p u t e d : 1 pA in a 7 nm s p o t i s 2.6 A/c m^{2}; r e a c hin g ab o v e 10 A/c m^{2} n ee d s a s ma l l er or b r i g h t er p r o b e, m y r e a d in g o f t h e q u o t e d f i g u r es)$

Lamellae and Tomography

Name	Formula	Related Formulae	Variables/Constants
TEM lamella sequence	$7 nA \to 300 pA \to 100 pA \to 7 keV to 500 eV$	$20 \times 10 \times 0.1 μ m (Nellen), 10 \times 5 μ m, 50 to 80 nm (Cantoni)$	$N e l l e n e t a l . : t r e n c h es a t ab o u t 7 nA, t hinnin g a t 300 pA, f ina l p o l i s hin g a t 100 pA, c l e anin g f r o m 7 keV t o 500 eV, a t y p i c a l l am e l l a o f 20 b y 10 μ m b y 100 nm, p r o t ec t i v e P t b y e l ec t r o n t h e n i o n d e p os i t i o n t o 1 t o 4 μ m; C an t o ni : l a r g e f l a t a r e a s o f 10 b y 5 μ m w i t h u ni f or m 50 t o 80 nm t hi c k n ess (see t h e Q / A)$ $(co m p u t e d : t hinnin g 20 μ m^{3} a t 300 pA t ak es ab o u t 256 s)$
FIB tomography	$N_{s l i ces} = \frac{Z _{t o t a l}}{Δ z}$	$data = N_{s l i ces} \times image size$	$N_{s l i ces} : n u mb er o f s l i ces$ $Z_{t o t a l} : d e pt h mi l l e d$ $Δ z : s l i ce t hi c k n ess; C an t o ni : 1100 s l i ces o f 20 nm, 2048 b y 1536 ima g es o f ab o u t 3 M B, ab o u t 12 GB p er d a t a se t, v o x e l s o f 10 nm c u b e d; N e l l e n e t a l . : 20 nm s l i ces, 1 nm l a y er s a t l o w c u r r e n t, c hi p m e t a l l i z a t i o n r eco n s t r u c t e d t o 1.5 μ m in 3 nm l a y er s$ $(co m p u t e d : 1100 s l i ces o f 20 nm i s 22 μ m o f d e pt h; 1100 x 3 M B = 3.3 GB p er c hann e l, so ab o u t 12 GB im pl i es se v er a l c hann e l s or l a r g er f i l es; m y r e a d in g)$

Important Questions

Ques: How does a FIB remove material, and how fast?

By sputtering: each 30 $kV$ gallium ion transfers momentum to surface atoms and ejects a few of them. Nellen et al. give 2.1 atoms per ion for silicon at normal incidence, equivalent to 0.26 $μ m^{3} /nC$ ; converting with silicon’s atomic density of $5 \times 1 0^{22}$ $c m^{- 3}$ reproduces 0.262 $μ m^{3} /nC$ (computed). Cantoni quotes 0.25 $μ m^{3} /nC$ for copper. The rate is the yield times the current, so 10 $nA$ removes about 2.5 cubic micrometres per second, and a 500 $μ m^{3}$ box takes about 200 $s$ (computed). Fine work uses lower currents for better resolution: Nellen et al. describe 300 $pA$ scans removing about 3 $nm$ per pass. Sputter yield rises steeply toward grazing incidence, with a maximum near 70 to 85 degrees. Reference: P. M. Nellen, V. Callegari and U. Sennhauser, ‘Preparative Methods for Nanoanalysis of Materials with Focused Ion Beam Instruments’, CHIMIA 60, 735 (2006) (fetch-tool summary); M. Cantoni, ‘MSE-704 3D Microscopy and FIB Nanotomography’ course slides 3.4 FIB, CIME, EPFL (fetch-tool summary).

Ques: Does Cantoni’s 10 x 10 x 5 micron copper box take 2000 s or 200 s?

Cantoni’s slide states 2000 $s$ , or 33 minutes, for a 500 $μ m^{3}$ box in copper at the typical 10 $nA$ milling current, with a yield of 0.25 $μ m^{3} /nC$ . The arithmetic gives $t = V / (Y_{V} I) = 500/ (0.25 \times 10) = 200$ $s$ (computed), ten times shorter. The 200 $s$ figure is correct for that yield and current; the slide is most likely off by a factor of ten, perhaps assuming 1 $nA$ , or it may include redeposition and overhead not stated (my reading). In practice, redeposition in deep boxes, rounding of edges and lower yields on sidewalls make real milling slower than the ideal value, so a factor of about 1.5 to 2 over the calculation is a prudent estimate (my reading). Gas-assisted etching could cut it to about 10 $s$ (computed). Reference: M. Cantoni, ‘MSE-704 3D Microscopy and FIB Nanotomography’ course slides 3.4 FIB, CIME, EPFL (fetch-tool summary); P. M. Nellen, V. Callegari and U. Sennhauser, ‘Preparative Methods for Nanoanalysis of Materials with Focused Ion Beam Instruments’, CHIMIA 60, 735 (2006) (fetch-tool summary).

Ques: How are TEM lamellae prepared, and how thin should they be?

In stages of decreasing current, then low-energy cleaning. Nellen et al. protect the site with electron-beam then ion-beam platinum totalling 1 to 4 $μ m$ , mill trenches on each side at about 7 $nA$ , thin at 300 $pA$ , polish at 100 $pA$ , and clean from 7 $keV$ down to 500 $eV$ , giving a typical lamella 20 by 10 $μ m$ and 100 $nm$ thick. Cantoni gives 10 by 5 $μ m$ areas of uniform 50 to 80 $nm$ . The values reflect different targets: about 100 $nm$ suits EELS and holography, within the thickness range on the TEM page, while 50 to 80 $nm$ suits high-resolution imaging (my reading). Thinning 20 $μ m^{3}$ at 300 $pA$ takes about 256 $s$ (computed). Reference: P. M. Nellen, V. Callegari and U. Sennhauser, ‘Preparative Methods for Nanoanalysis of Materials with Focused Ion Beam Instruments’, CHIMIA 60, 735 (2006) (fetch-tool summary); M. Cantoni, ‘MSE-704 3D Microscopy and FIB Nanotomography’ course slides 3.4 FIB, CIME, EPFL (fetch-tool summary); Transmission Electron Microscope (TEM and STEM) page of this vault.

Ques: How much damage does the beam leave, and how is it reduced?

Tens of nanometres at 30 $kV$ , a few nanometres after low-kV polishing. Nellen et al. give an ion range of 10 to 30 $nm$ in amorphous matter at the usual energies, and Cantoni reports gallium implantation and amorphization up to 25 $nm$ below the surface, with listed layers of 25 to 30 $nm$ at high energy and 2 to 3 $nm$ for silicon at low kV. A 60 $nm$ lamella cut only at 30 $kV$ could therefore be almost entirely amorphous on its two faces (computed). Final passes at 5 $kV$ down to 500 $eV$ remove most of this layer (Nellen et al.), and low-energy argon milling is an alternative (Cantoni). The mapping of Cantoni’s 5 to 7 $nm$ value to a specific energy is unclear in the slide. Reference: P. M. Nellen, V. Callegari and U. Sennhauser, ‘Preparative Methods for Nanoanalysis of Materials with Focused Ion Beam Instruments’, CHIMIA 60, 735 (2006) (fetch-tool summary); M. Cantoni, ‘MSE-704 3D Microscopy and FIB Nanotomography’ course slides 3.4 FIB, CIME, EPFL (fetch-tool summary).

Ques: What problems does gallium cause?

Implantation, swelling and droplets. Every milled surface contains implanted gallium; Nellen et al. note that below about $1 \times 1 0^{16}$ $c m^{- 2}$ , silicon swells by up to a few nanometres before net milling begins, which matters for imaging and fine polishing. Since 1 $pA$ on a square micrometre delivers $6.2 \times 1 0^{14}$ $c m^{- 2}$ per second, that dose is reached in about 16 $s$ (computed), so even ion imaging alters the surface. In materials with low gallium solubility, high fluence forms gallium droplets a few hundred nanometres across, and in GaAs selective arsenic sputtering leaves gallium-rich artefacts (Nellen et al.). Electron-beam imaging and alternative ion species reduce these effects. Reference: P. M. Nellen, V. Callegari and U. Sennhauser, ‘Preparative Methods for Nanoanalysis of Materials with Focused Ion Beam Instruments’, CHIMIA 60, 735 (2006) (fetch-tool summary).

Ques: What can gas injection add to a FIB?

Local deposition and faster, more selective etching. Nellen et al. list iodine and chlorine compounds for metal etching, fluorine compounds for dielectrics, water vapour for selective carbon removal, platinum and tungsten precursors for metal deposition and siloxane with water for insulators; reactive gases raise sputter yields 2 to 20 times, up to 20 for metal and oxide layers. Gases are delivered by nozzles 100 to 200 $μ m$ from the sample, with chamber pressure near $1 \times 1 0^{- 6}$ $mbar$ rising slightly during flow. Deposition lays protective caps for lamellae and conductive straps for circuit edit; etching speeds trenches and reduces redeposition. Unwanted reactions occur, such as InI3 islands on InP with iodine (Nellen et al.). Reference: P. M. Nellen, V. Callegari and U. Sennhauser, ‘Preparative Methods for Nanoanalysis of Materials with Focused Ion Beam Instruments’, CHIMIA 60, 735 (2006) (fetch-tool summary).

Ques: How does FIB tomography build 3-D images?

By alternating thin milled slices with SEM images. Cantoni’s example used 1100 slices of 20 $nm$ , 22 $μ m$ of depth (computed), with 2048 by 1536 images of about 3 MB, giving about 12 GB per dataset, and voxels down to 10 $nm$ cubed. Nellen et al. report slices as thin as 20 $nm$ in tomography and 1 $nm$ layers at low current, and reconstructed chip metallization to 1.5 $μ m$ depth in 3 $nm$ layers. The dual-beam geometry, with the electron column at 52 degrees, images each fresh face without moving the sample. Resolution is limited by slice thickness, SEM resolution of 1 to 2 $nm$ (Cantoni), and drift. Curtaining from uneven milling and charging must be controlled for clean stacks (my reading). Reference: M. Cantoni, ‘MSE-704 3D Microscopy and FIB Nanotomography’ course slides 3.4 FIB, CIME, EPFL (fetch-tool summary); P. M. Nellen, V. Callegari and U. Sennhauser, ‘Preparative Methods for Nanoanalysis of Materials with Focused Ion Beam Instruments’, CHIMIA 60, 735 (2006) (fetch-tool summary); Emission Microscope, OBIRCH and Lock-In Thermography page of this vault.

References

P. M. Nellen, V. Callegari and U. Sennhauser, “Preparative Methods for Nanoanalysis of Materials with Focused Ion Beam Instruments,” CHIMIA, vol. 60, no. 11, pp. 735-741, 2006. Available: https://chimia.ch/chimia/article/download/2006_735/3529/14214
M. Cantoni, “3.4 FIB,” MSE-704 3D Microscopy and FIB Nanotomography course slides, CIME, EPFL. Available: https://www.epfl.ch/research/facilities/cime/wp-content/uploads/2019/05/3_4-FIB.pdf
Transmission Electron Microscope (TEM and STEM), page in this vault.
Emission Microscope, OBIRCH and Lock-In Thermography, page in this vault.

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Focused Ion Beam (FIB)