1. Theory

Definition: A beamline ion implanter ionizes a dopant gas, accelerates the ions, selects one mass and charge with an analyzing magnet, and scans the beam over the wafer to place a measured dose at a chosen depth (Jaeger; Doolittle).
Profile: The implanted profile is roughly Gaussian about the projected range, with Pearson IV used for accurate work (Stanford; Doolittle).
Stopping: Ions lose energy by nuclear collisions and electronic drag, with crossover near 17 $keV$ for boron and 150 $keV$ for phosphorus (Stanford).
Damage: Each ion displaces hundreds to thousands of atoms, so an anneal is required to repair the lattice and activate dopants (Stanford; Jaeger).

2. Working Principle

Source and extraction: Source material is ionized in vacuum and extracted by high voltage, with acceleration of tens of kV or more (Matsusada).
Mass analysis: A magnetic sector separates ions by mass-to-charge ratio (Jaeger; Matsusada).
Acceleration and scan: Post-acceleration sets energy; electrostatic, magnetic or mechanical scanning spreads the dose (dose-uniformity patent).
Dosimetry: Faraday cups integrate the beam current to stop at the target dose (Doolittle; dose-uniformity patent).

3. Applications

Implanter classes: Medium-current tools at 260 keV or below with microampere beams, high-current tools with milliampere beams, and high-energy tools from 250 keV to 7 MeV (Matsusada).
Power devices: Deep p-columns of superjunction MOSFETs, IGBT field-stop layers and SiC doping (Matsusada).
Image sensors and detectors: Photodiode regions of CMOS image sensors and deep junctions of X-ray detectors (Matsusada).

Beam Formation and Dose

Name	Formula	Related Formulae	Variables/Constants
Analyzing magnet	$r = \frac{1}{B} \frac{2 mV}{n q}$	$\frac{Δ r}{r} = \frac{1}{2} \frac{Δ m}{m}$	$r : b e n d r a d i u s$ $B : ma g n e t i c f i e l d$ $m : i o n ma ss$ $V : e x t r a c t i o n v o l t a g e$ $n : c ha r g e s t a t e; J a e g er : ma g n e t i c f i e l d s l i d e w i t h m, v, V an d r; r e l a t i o n f r o m t h e f or ce ba l an ce o n t ha t s l i d e (co m p u t e d : q v B = m v^{2} / r w i t h q V = m v^{2} /2); M a t s u s a d a : se p a r a t i o n b y ma ss - t o - c ha r g e r a t i o in ma g n e t i c sec t or ana l y z er s$ $(a ss u m e d : r = 0.5 m, 30 kV; co m p u t e d : 0.17 T f or B^{+}, 0.28 T f or P^{+}, 0.35 T f or B F_{2}^{+} an d 0.43 T f or A s^{+})$
Dose integration	$Q = \frac{1}{n q A} \int I d t$	$t = \frac{Q n q A}{I}$	$Q : d ose$ $A : sc ann e d a r e a$ $I : b e am c u r r e n t m e a s u r e d in a F a r a d a y c u p; D oo l i ttl e an d J a e g er : d ose f r o m in t e g r a t e d c u r r e n t; J a e g er : d ose co n t r o l o f a f e w p er ce n t a g ain s t 20 t o 30 p er ce n t f or p r e - d e p os i t i o n; d ose - u ni f or mi t y p a t e n t : F a r a d a y s am pl e d ab o v e 1 kHz (t y p i c a l l y 5 kHz), w h ee l 200 t o 1250 rpm, s l o w sc an 2 t o 4 s, e a c h p o in t s w e pt a h u n d r e d t im es or m or e, n or ma l s u pp or t - t o - s u pp or t v a r ia t i o n b e l o w 1 p er ce n t, g l i t c h es ab o v e 10 p er ce n t$ $(a ss u m e d : 1 \times 1 0^{15} c m^{- 2} o n a 300 mm w a f er o f 707 c m^{2}; co m p u t e d : 113 s a t 1 m A, an d 4.5 m A f or D oo l i ttl e^{'} s 25 s m o d er a t e - d ose c a se)$
Molecular ion energy	$E_{B} = \frac{M _{B}}{M _{B F_{2}}} E$	$\frac{M _{B}}{M _{B F_{2}}} = \frac{11}{49}$	$M : ma sses (B 11, B F_{2} 49)$ $E : b e am e n er g y; D oo l i ttl e : m o l ec u l a r B F_{2} s ha r es e n er g y b y ma ss$ $(co m p u t e d : a 50 keV B F_{2} b e am d e l i v er s b or o n a t 11.2 keV, ma ss r a t i o 0.224)$

Implant Profiles and Masking

Name	Formula	Related Formulae	Variables/Constants
Gaussian profile	$C (x) = C_{p} exp [- \frac{( x - R _{p} ) ^{2}}{2Δ R _{p}^{2}}]$	$Q = 2 π Δ R_{p} C_{p} \Rightarrow C_{p} \approx \frac{0.4 Q}{Δ R _{p}}$	$R_{p} : p r o j ec t e d r an g e$ $Δ R_{p} : s t r a g g l e$ $C_{p} : p e ak co n ce n t r a t i o n; S t an f or d han d o u t e q u a t i o n s 1 an d 2; D oo l i ttl e : m o m e n t s d escr i pt i o n (s k e w n ess, k u r t os i s 3 f or G a u ss ian, β ab o u t 2.8 + 2.4 γ^{2}), P e a r so n I V u se d f or r e a l im pl an t s; J a e g er : d e v ia t i o n f r o m G a u ss ian ab o v e ab o u t 200 keV$ $(B er k e l ey E E 143 so l u t i o n : P a t 200 keV w i t h R_{p} = 0.254 μ m, Δ R_{p} = 0.0775 μ m; co m p u t e d f or 1 \times 1 0^{13} c m^{- 2} : C_{p} = 5.15 \times 1 0^{17} c m^{- 3}, ma t c hin g t h e so l u t i o n^{'} s 5.2 \times 1 0^{17})$
Junction depth	$x_{j} = R_{p} + Δ R_{p} 2 ln \frac{C _{p}}{N _{B}}$	$σ_{p}^{'} = σ_{p}^{2} + 2 D t$	$N_{B} : ba c k g r o u n d d o p in g$ $D : d i f f u s i v i t y d u r in g ann e a l; J a e g er : j u n c t i o n d e pt h a s w r i tt e n; D oo l i ttl e : s t r a g g l e b r o a d e nin g b y ann e a l$ $(co m p u t e d f or t h e e x am pl e an d N_{B} = 1 \times 1 0^{16} c m^{- 3} : x_{j} = 0.036 an d 0.472 μ m, a g ain s t t h e so l u t i o n^{'} s 0.032 an d 0.474 μ m)$
Mask thickness	$x_{m} = R_{p}^{} + m Δ R_{p}^{}, m = 2 ln \frac{C _{p}^{*}}{C _{B}}$	$\frac{Q _{p a ss}}{Q} = \frac{1}{2} erfc (\frac{x _{m} - R _{p}^{}}{2 Δ R _{p}^{}})$	$* : r an g e p a r am e t er s in t h e ma s k ma t er ia l$ $C_{B} : t o l er a t e d co n ce n t r a t i o n; S t an f or d han d o u t e q u a t i o n s 5 an d 6; C o h er e n t : minim u m r es i s t t hi c k n ess R_{p} + 5Δ R_{p}, t hi c k er f or hi g h d oses t ha t s h r ink r es i s t; U W E E 486 h o m e w or k : 1 \times 1 0^{14} c m^{- 2} B a t 5 keV w i t h a t m os t 2 \times 1 0^{12} c m^{- 2} p a ss in g$ $(co m p u t e d : m = 5 cor r es p o n d s t o C_{p} / C_{B} = 2.7 \times 1 0^{5} an d a p a ss in g f r a c t i o n o f 2.9 \times 1 0^{- 7}; t h e h o m e w or k l imi t o f 2 p er ce n t n ee d s o n l y m = 2.05)$

Stopping, Damage and Channeling

Name	Formula	Related Formulae	Variables/Constants
Stopping power	$\frac{d E}{d x} = - N (S_{n} + S_{e}), R = \int_{0}^{E_{0}} \frac{d E}{N ( S _{n} + S _{e} )}$	$S_{e} = k E$	$N : t a r g e t a t o m d e n s i t y$ $S_{n}, S_{e} : n u c l e a r an d e l ec t r o ni c s t o pp in g cr oss sec t i o n s; S t an f or d han d o u t e q u a t i o n s 12 an d 13, k ab o u t 0.2 \times 1 0^{- 15} (u ni t s g a r b l e d in t h e e x t r a c t i o n), cr osso v er S_{n} = S_{e} a t ab o u t 17 keV f or B, 150 keV f or P, ab o v e 500 keV f or A s an d S b$ $(m y r e a d in g : l i g h t b or o n l oses e n er g y m os tl y e l ec t r o ni c a l l y an d t r a v e l s f a r w i t h l i ttl e d ama g e, w hi l e a r se ni c s t o p s b y co l l i s i o n s)$
Displacement damage	$n_{d} = \frac{E}{2 E _{d}}$	$E_{d} \approx 15 eV$	$n_{d} : d i s pl a ce d a t o m s p er i o n$ $E_{d} : d i s pl a ce m e n t e n er g y; S t an f or d han d o u t : 30 keV A s g i v es ab o u t 1000 d i s pl a ce d a t o m s, 300 keV S i in S i t u r n s am or p h o u s b e tw ee n 1 \times 1 0^{15} an d 1 \times 1 0^{16} c m^{- 2}, + 1 m o d e l f or t r an s i e n t e nhan ce d d i f f u s i o n w i t h C_{I} / C_{I}^{*} ab o v e 1 \times 1 0^{5} a t 750^{\circ} C; D oo l i ttl e : ab o u t 5 eV t o annihi l a t e d e f ec t s, 2.3 eV f or so l i d - p ha se e p i t a x y, 3 t o 4 eV f or d o p an t d i f f u s i o n$ $(co m p u t e d : 30000/ (2 x 15) = 1000, a s in t h e han d o u t)$
Channeling control	$θ_{t i l t} \approx 7^{\circ}$	$θ_{t i l t} = 7. 4^{\circ} (Doolittle)$	$θ_{t i l t} : w a f er t i l t f r o m t h e b e am; S t an f or d : 7 d e g r ee t i l t co mm o n, scr ee n o x i d es an d r o t a t i o n r e d u ce b u t d o n o t r e m o v e c hann e l in g; D oo l i ttl e : 7.4 d e g r ees q u o t e d, cr i t i c a l - an g l e p r e f a c t or 9.73 (f or m g a r b l e d); U W h o m e w or k : c hann e l e d 20 keV b or o n w i t h e l ec t r o ni c s t o pp in g$ $(m y r e a d in g : t h e 7 an d 7.4 d e g r ee f i g u r es a r e t h e s am e p r a c t i ce, 7 d e g r ees w i t h a tw i s t c h ose n t o a v o i d maj or pl an es)$

Important Questions

Ques: How does a beamline implanter select ions and control dose?

An analyzing magnet bends ions on a radius $r = 2 mV / n q / B$ , so only one mass-to-charge ratio passes (Jaeger; Matsusada; computed from the force balance). For an assumed 0.5 m radius at 30 $kV$ , boron needs 0.17 T and arsenic 0.43 T (computed). Dose is the Faraday-cup current integrated over time and divided by charge state and area (Doolittle; Jaeger). A $1 0^{15}$ $c m^{- 2}$ implant over a 300 mm wafer takes 113 $s$ at 1 $mA$ , and Doolittle’s 25 $s$ moderate-dose case needs about 4.5 $mA$ (computed). Jaeger notes dose control of a few per cent, against 20 to 30 per cent for diffusion pre-deposition. The dose-uniformity patent samples the Faraday current at about 5 $kHz$ and sweeps each point a hundred times or more, so one beam glitch has little effect. Reference: R. C. Jaeger, Introduction to Microelectronic Fabrication, 2nd ed., chapter 5 ‘Ion Implantation’ lecture slides (Pearson 2002), hosted by KMITL (fetch-tool summary); Matsusada Precision, ‘Ion implantation’ technical column: implanter classes and applications (fetch-tool summary); W. A. Doolittle, ECE 6450 Lecture 5, ‘Ion Implantation’, Georgia Institute of Technology (fetch-tool summary); US patent 6,965,116, ‘Method of determining dose uniformity of a scanning ion implanter’ (USPTO full text; assignee not shown in the fetched text) (fetch-tool summary).

Ques: How are the peak concentration and junction depth of an implant found?

From the Gaussian profile. Integrating $C_{p} exp [- (x - R_{p})^{2} /2Δ R_{p}^{2}]$ gives $Q = 2 π Δ R_{p} C_{p}$ , so the peak is about $0.4 Q /Δ R_{p}$ (Stanford). A Berkeley EE143 exam solution uses phosphorus at 200 $keV$ with $R_{p}$ = 0.254 $μ m$ and $Δ R_{p}$ = 0.0775 $μ m$ ; a $1 0^{13}$ $c m^{- 2}$ dose then peaks at $5.15 \times 1 0^{17}$ $c m^{- 3}$ (computed), matching its $5.2 \times 1 0^{17}$ . The junctions lie where the profile meets the background, $R_{p} \pm Δ R_{p} 2 ln (C_{p} / N_{B})$ (Jaeger), at 0.036 and 0.472 $μ m$ for $1 0^{16}$ $c m^{- 3}$ (computed), against the solution’s 0.032 and 0.474 $μ m$ . Real profiles are skewed, and channeling and anneal diffusion broaden them, $σ^{'} = σ^{2} + 2 D t$ (Doolittle), so these numbers are first estimates (my reading). Doolittle describes profiles by four moments, range, straggle, skewness and kurtosis, with Pearson IV distributions fitted for accurate work, and Jaeger notes that curves deviate from a Gaussian above about 200 $keV$ . Reference: J. D. Plummer, M. D. Deal and P. B. Griffin, EE 212 class handout 14, chapter 8 ‘Ion Implantation’ (Stanford, 1999-2000), hosted on the University of Washington EE 528 site (fetch-tool summary); UC Berkeley EE143 Spring 2003 Midterm 1 solutions (HKN exam archive): 200 keV P with R_p = 0.254 um and Delta R_p = 0.0775 um, C_p = 5.2e17 cm-3, x_j = 0.032 and 0.474 um for N_B = 1e16 cm-3 (fetch-tool summary); R. C. Jaeger, Introduction to Microelectronic Fabrication, 2nd ed., chapter 5 ‘Ion Implantation’ lecture slides (Pearson 2002), hosted by KMITL (fetch-tool summary); W. A. Doolittle, ECE 6450 Lecture 5, ‘Ion Implantation’, Georgia Institute of Technology (fetch-tool summary).

Ques: Should a mask be Rp plus 5 straggles thick, or thickness from the tolerated dose?

The sources state the rule differently. Coherent recommends a minimum resist thickness of $R_{p} + 5Δ R_{p}$ , while the Stanford handout sets $x_{m} = R_{p}^{*} + m Δ R_{p}^{*}$ with $m = 2 ln (C_{p}^{*} / C_{B})$ , the depth where the profile falls to a tolerated level. Five straggles corresponds to a peak-to-tolerated ratio of $2.7 \times 1 0^{5}$ and lets through only $2.9 \times 1 0^{- 7}$ of the dose (computed). The UW homework case, where 2 per cent of a $1 0^{14}$ $c m^{- 2}$ boron dose may pass, needs only $m$ = 2.05 (computed). The Stanford criterion is more likely the right design rule, because it ties thickness to the device requirement, while $R_{p} + 5Δ R_{p}$ is a safe default when no limit is given (my reading). Coherent adds that high doses shrink resist, so thicker resist may be needed. Reference: Coherent (II-VI), ‘Ion Implantation Projected Range Statistics’ datasheet (SRIM 2013 based) (fetch-tool summary); J. D. Plummer, M. D. Deal and P. B. Griffin, EE 212 class handout 14, chapter 8 ‘Ion Implantation’ (Stanford, 1999-2000), hosted on the University of Washington EE 528 site (fetch-tool summary); University of Washington, EE486 Integrated Circuit Fabrication, Homework 4 (Spring 2017) (fetch-tool summary).

Ques: Why does boron travel far but arsenic cause heavy damage?

Because their stopping mechanisms differ. Energy loss is $N (S_{n} + S_{e})$ , and electronic stopping rises as $E$ while nuclear stopping peaks at low energy (Stanford). The two are equal at about 17 $keV$ for boron, 150 $keV$ for phosphorus and above 500 $keV$ for arsenic and antimony. Light boron at typical energies therefore slows mainly by electronic drag, going deep with little displacement damage, while arsenic loses energy in nuclear collisions (my reading). A 30 $keV$ arsenic ion displaces about $E /2 E_{d}$ = 1000 atoms with $E_{d}$ of 15 $eV$ (Stanford; computed), and silicon becomes amorphous at $1 0^{15}$ to $1 0^{16}$ $c m^{- 2}$ . Damage releases interstitials that cause transient enhanced diffusion during anneal, more than $1 0^{5}$ times at 750 $^{\circ} C$ (Stanford). Reference: J. D. Plummer, M. D. Deal and P. B. Griffin, EE 212 class handout 14, chapter 8 ‘Ion Implantation’ (Stanford, 1999-2000), hosted on the University of Washington EE 528 site (fetch-tool summary).

Ques: Is the standard anti-channeling tilt 7 or 7.4 degrees?

Both appear. The Stanford handout calls a 7 degree tilt common and notes that screen oxides and tilting or rotating the wafer reduce but do not eliminate channeling, while Doolittle quotes 7.4 degrees. Doolittle’s critical-angle relation, with a prefactor of 9.73, depends on the ion and target atomic numbers, the ion energy and the atomic spacing along the row, though its exact form was garbled in extraction. The two values describe the same practice; 7 degrees is more likely the general rule, with the exact tilt and twist chosen per tool to avoid major planes (my reading). Tilt causes shadowing at tall mask edges, which is why Doolittle notes dense thin masks such as tungsten (Doolittle). The UW homework asks for the range of channeled 20 $keV$ boron assuming only electronic stopping, showing how deep channeled tails reach. Reference: J. D. Plummer, M. D. Deal and P. B. Griffin, EE 212 class handout 14, chapter 8 ‘Ion Implantation’ (Stanford, 1999-2000), hosted on the University of Washington EE 528 site (fetch-tool summary); W. A. Doolittle, ECE 6450 Lecture 5, ‘Ion Implantation’, Georgia Institute of Technology (fetch-tool summary); University of Washington, EE486 Integrated Circuit Fabrication, Homework 4 (Spring 2017) (fetch-tool summary).

References

R. C. Jaeger, Introduction to Microelectronic Fabrication, 2nd ed., Pearson, 2002, chapter 5 lecture slides. Available: https://www.ami.kmitl.ac.th/wp-content/uploads/2018/05/12026118_Lecture8.pdf
University of California, Berkeley, EE143 Spring 2003 Midterm 1 Solutions, HKN exam archive. Available: https://hkn.eecs.berkeley.edu/examfiles/ee143_sp03_mt1_sol.pdf
Matsusada Precision, “Ion implantation,” technical column. Available: https://www.matsusada.com/column/ion-implantation.html
W. A. Doolittle, “Lecture 5: Ion Implantation,” ECE 6450, Georgia Institute of Technology. Available: https://alan.ece.gatech.edu/ECE6450/Lectures/ECE6450L5-Ion%20Implantation.pdf
“Method of determining dose uniformity of a scanning ion implanter,” US Patent 6,965,116. Available: https://image-ppubs.uspto.gov/dirsearch-public/print/downloadPdf/6965116
J. D. Plummer, M. D. Deal and P. B. Griffin, EE 212 Handout 14, “Chapter 8: Ion Implantation,” Stanford University, 1999-2000. Available: https://dunham.ece.uw.edu/ee528/notes/Chapter8.pdf
University of Washington, EE486 Integrated Circuit Fabrication, Homework 4, Spring 2017. Available: https://dunham.ece.uw.edu/ee486/hw4_2017.pdf
Coherent, “Ion Implantation Projected Range Statistics,” datasheet. Available: https://www.coherent.com/content/dam/coherent/site/en/resources/datasheet/materials/ion-implantation-projected-range-statistics-ds.pdf

Quartz 5

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Beamline Ion Implanter