1. Theory

Definition: A plasma immersion ion implanter (PIII, or plasma doping, PLAD) places the wafer in a dopant-containing plasma and pulses it to a negative high voltage, so ions from the surrounding sheath are accelerated into the whole surface at once (Linder; Varian patent).
Sheath dynamics: Each pulse first forms an ion matrix sheath, which expands toward a Child-law sheath as ions are drawn out (Linder; Kostov et al.; Gupta et al.).
Dose rate: Because the whole wafer is implanted simultaneously, current densities above 1 $mA/c m^{2}$ are possible against about 0.14 $mA/c m^{2}$ for a beamline (Linder).
Conformal reach: The sheath wraps three-dimensional parts, giving homogeneous and conformal implantation, though edges collect more ions than holes and trenches (Kostov et al.).

2. Working Principle

Plasma: B2H6, BF3, PH3 or AsH3 diluted in helium or neon is excited by RF or microwave power (Sharp patent; Linder).
Pulsing: Negative pulses of a few kV and about 1 $μ s$ are applied at kHz rates (Linder; Varian patent).
Dose control: Pulse width, frequency, partial pressure and time set the dose, with corrections for secondary electrons (Sharp patent; Linder).
Uniformity: A separately biased ring around the wafer shapes the sheath edge (Varian patent).

3. Applications

Ultra-shallow junctions: Low-energy, high-dose source and drain extensions (Sharp patent; Varian patent).
Three-dimensional parts: Conformal implantation of non-planar structures (Kostov et al.).
Large-area substrates: Panels and non-planar parts where beam scanning is impractical (Linder).

Sheath Physics

Name	Formula	Related Formulae	Variables/Constants
Matrix sheath	$s_{0} = \frac{2 ε _{0} V _{0}}{e n _{0}}$	$t \sim ω_{p i}^{- 1} (ions still at rest)$	$s_{0} : ini t ia l s h e a t h t hi c k n ess w h e n e l ec t r o n s a r e e x p e l l e d$ $V_{0} : p u l se v o l t a g e$ $n_{0} : pl a s ma d e n s i t y$ $ω_{p i} : i o n pl a s ma f r e q u e n cy; L in d er : ma t r i x s h e a t h f r o m P o i sso n^{'} s e q u a t i o n w i t h u ni f or m i o n s p a ce c ha r g e (e q u a t i o n 4 - 1 g a r b l e d); K os t o v e t a l . e q u a t i o n 1 a s w r i tt e n; G u pt a e t a l . : s am e r e l a t i o n (c i t in g L i e b er man), pl a s ma d e n s i t y 1 \times 1 0^{16} m^{- 3}, - 15 kV p u l ses; L in d er : r i se t im e b e l o w 50 ns, i o n t r an s i t ab o u t 100 ns$ $(u s in g G u pt a^{'} s 1 \times 1 0^{10} c m^{- 3} a t 10 kV; co m p u t e d : s_{0} = 1.05 c m)$
Child-law sheath and current	$J_{C} = \frac{4}{9} ε_{0} \frac{2 e}{M} \frac{V _{0}^{3/2}}{s ^{2}}$	$Q = \frac{1}{e} \int_{0}^{t} j_{i} (t^{'}) d t^{'}$	$J_{C} : s p a ce - c ha r g e - l imi t e d i o n c u r r e n t d e n s i t y$ $M : i o n ma ss$ $s : s h e a t h w i d t h$ $Q : d ose; K os t o v e t a l . e q u a t i o n 3 (pl ana r C hi l d l a w, o n ce a s t e a d y s h e a t h f or m s) w i t h s h e a t h e x p an d in g t o ab o u t 6 c m a t - 10 kV, 1 \times 1 0^{9} c m^{- 3} an d 3 eV; G u pt a e t a l . : d ose a s t h e t im e in t e g r a l o f c u r r e n t d e n s i t y, p e ak A r c u r r e n t 240 A / m^{2}; L in d er : q u a s i - s t a t i c C hi l d - l a w s h e a t h g i v es t h e im pl an t c u r r e n t, ma x im u m s h e a t h 2.4 c m f or a 10 kV 1 μ s p u l se, d ose r a t e ab o v e 1 mA/c m^{2} o v er t h e w a f er a g ain s t 0.14 mA/c m^{2} f or a co n v e n t i o na l 300 mm im pl an t er$ $(co m p u t e d f or a r g o n a t 10 kV : J_{C} = 1.5 mA/c m^{2} a t t h e 2.4 c m s h e a t h, co n s i s t e n t w i t h L in d e r^{'} s f i g u r e)$
Bohm flux at the sheath edge	$u_{B} = \frac{e T _{e}}{M}$	$Γ_{i} = n_{s} u_{B} \approx 0.61 n_{0} u_{B}$	$u_{B} : B o hm v e l oc i t y$ $n_{s} : d e n s i t y a t t h e s h e a t h e d g e; L in d er : s h e a t h v e l oc i t y t i e d t o t h e B o hm v e l oc i t y b y a ma c hin e f a c t or K = 1.1 f or t h e B er k e l ey P I I I t oo l, co l l a p se r a t e l imi t e d b y u_{B}; B o hm v e l oc i t y an d e d g e - d e n s i t y f a c t or 0.61 a s o n t h e L an g m u i r P r o b e p a g e, w hi c h co m p a r es t h e 0.5 an d 0.61 v a l u es$ $(co m p u t e d w i t h K os t o v^{'} s 3 eV : u_{B} = 2.7 k m / s f or a r g o n an d 5.1 k m / s f or b or o n)$

Dose and Uniformity

Name	Formula	Related Formulae	Variables/Constants
Dose from pulses	$Q = \frac{J ˉ _{i}}{e} f τ t$	$D_{f} = f τ$	$\overset{ˉ}{J}_{i} : i o n c u r r e n t d e n s i t y d u r in g t h e p u l se$ $f : r e p e t i t i o n r a t e$ $τ : p u l se w i d t h$ $t : p r ocess t im e$ $D_{f} : d u t y f a c t or; L in d er : e x am pl e d u t y f a c t or 2.25 p er ce n t (2.25 kHz, 1 μ s), 100 m A s u ppl y l imi t, 6 kV 25 kHz m o d u l a t or; S ha r p p a t e n t : p u l se w i d t h, f r e q u e n cy, d o p an t p a r t ia l p r ess u r e an d t im e co n t r o l d ose, v o l t a g e se t s d e pt h$ $(co m p u t e d : 1 mA/c m^{2} a t 2.25 p er ce n t d u t y i s 8.4 \times 1 0^{15} c m^{- 2} p er min u t e o f s in g l y c ha r g e d i o n s)$
Secondary-electron correction	$I_{m e a s} = I_{i} (1 + γ_{se})$	$γ_{se} (10 keV) \approx 7 (A l)$	$γ_{se} : seco n d a r y e l ec t r o n s p er i o n; L in d er : seco n d a r y c u r r e n t e x cee d s i o n c u r r e n t ab o v e ab o u t 200 V o n a l u mini u m, y i e l d ab o u t 7 a t 10 keV, e m p i r i c a l f i t k ab o u t 0.0696; V a r ian p a t e n t : hi g h seco n d a r y - e mi ss i o n coe f f i c i e n t o f a l u mini u m a p r o b l e m f or t h e r in g$ $(co m p u t e d : w i t h γ = 7 o n l y o n e e i g h t h o f t h e m e a s u r e d c u r r e n t i s i o n s, so 8.4 \times 1 0^{15} b eco m es ab o u t 1.05 \times 1 0^{15} c m^{- 2} p er min u t e)$
Dose uniformity	$\frac{σ _{Q}}{Q ˉ} ≲ 2 per cent (1 σ)$	$38.5 per cent (grounded ring) \to 2.17 per cent (biased ring)$	$σ_{Q} / \overset{ˉ}{Q} : r e l a t i v e s t an d a r d d e v ia t i o n o f d ose; V a r ian p a t e n t : t a r g e t 2 p er ce n t or l ess, p r i or a r t ab o v e 10 p er ce n t, g r o u n d e d r in g 38.5 p er ce n t, se p a r a t e l y bia se d r in g 2.17 p er ce n t, f e w - k V n e g a t i v e p u l ses, d ose r a t es o f 1 \times 1 0^{15} c m^{- 2} p er min u t e$ $(m y r e a d in g : t h e bia se d r in g f l a tt e n s t h e s h e a t h e d g e o v er t h e w a f er r im, so i o n s a r r i v e n or ma l t o t h e s u r f a ce e v er y w h er e)$

Pulse, Heating and Gas

Name	Formula	Related Formulae	Variables/Constants
Pulse fall time	$t_{f a l l} = 16.22, 0.12, 0.88, 0.36 μ s$	$t_{f a l l} ≪ t_{p u l se}$	$L in d er t ab l e 2 - 1 : n o s h u n t 16.22 μ s, 50 Ω 0.12 μ s, 270 Ω w i t h ma t c hin g 0.88 μ s, 270 Ω w i t h o u t 0.36 μ s; f a l l t im e d e f in e d t o 500 V in o n e c ha pt er an d - 50 V in an o t h er; s l o w f a l l im pl an t s i o n s a t l o w er e n er g y$ $(m y r e a d in g : a 16 μ s f a l l o n a 1 μ s p u l se w o u l d d e l i v er m os t o f t h e d ose a t r e d u ce d e n er g y, b r o a d e nin g t h e p r o f i l e)$
Wafer heating	$P_{w} \approx V_{0} \overset{ˉ}{I}_{i} (1 + γ_{se})$	$P_{pl a s ma} \approx 2 W, P_{6 k V, 5 k H z} \approx 55 W$	$P_{w} : p o w er in t o t h e w a f er f r o m im pl an t a t i o n; L in d er : 900 W, 1 mTorr A r pl a s ma d e p os i t s ab o u t 2 W o n a 4 in c h w a f er (b e l o w 200^{\circ} C), 6 kV p u l s in g a t 5 kHz ab o u t 55 W (ab o v e 450^{\circ} C w i t h o u t coo l in g), g a t e - o x i d e d ama g e r o ug h l y d o u b l es p er 50^{\circ} C$ $(m y r e a d in g : t h e p u l se p o w er, n o t t h e pl a s ma, se t s t h e coo l in g r e q u i r e m e n t)$
Gas dilution	$\frac{F _{d o p an t}}{F _{d i l}} = \frac{25}{75} to \frac{5}{95}$	$dopants: B_{2} H_{6}, B F_{3}, P H_{3}, A s H_{3}$	$F : g a s f l o w s; S ha r p p a t e n t : d i l u t i o n r an g e, n eo n or h e l i u m p r e f er r e d, a r g o n d ama g es p h o t or es i s t, osc i l l a t in g p r ess u r e r e d u ces d ose co n t r o l, p h o t or es i s t ma t er ia l c an r e d e p os i t; L in d er : a r g o n a t 1 mTorr w i t h an E C R so u r ce a t 875 G an d 2.45 GHz, 1500 W$ $(m y r e a d in g : l i g h t d i l u t an t s s p u tt er l ess, w hi c h h e l p s b o t h r es i s t in t e g r i t y an d r e t ain e d d ose)$

Important Questions

Ques: How does the plasma sheath deliver the implant in PIII?

When the wafer is pulsed to a negative voltage, electrons are pushed away within nanoseconds, leaving a matrix sheath of uniform ion space charge $s_{0} = 2 ε_{0} V_{0} / e n_{0}$ (Linder; Kostov et al.). For Gupta’s $1 0^{10}$ $c m^{- 3}$ plasma at 10 $kV$ that is about 1.05 cm (computed). Ions are then accelerated into the wafer and the sheath expands toward a Child-law sheath; Kostov’s simulation reaches about 6 cm at -10 $kV$ in a thinner $1 0^{9}$ $c m^{- 3}$ plasma. Linder reports a maximum sheath of 2.4 cm for a 10 $kV$ , 1 $μ s$ pulse, larger than the matrix sheath as expected for an expanding sheath (my reading). The Child-law current density at 2.4 cm is about 1.5 $mA/c m^{2}$ for argon (computed), matching Linder’s figure of above 1 $mA/c m^{2}$ . Reference: B. P. Linder, ‘Investigation of Plasma Implantation and Gate Oxide Charging during Plasma Processing’, PhD dissertation, UC Berkeley, Memorandum UCB/ERL M99/8 (February 1999) (fetch-tool summary); K. G. Kostov, J. J. Barroso and M. Ueda, ‘Two dimensional computer simulation of plasma immersion ion implantation’, Brazilian Journal of Physics 34, 1689 (2004) (fetch-tool summary); D. Gupta, J. Jogi and P. J. George, ‘Analytical Estimation of Doping in a Microwave based PIII System, Implementing Sheath Models’, Proceedings of the World Congress on Engineering 2013 (fetch-tool summary).

Ques: Do the PLAD dose-rate figures of Linder and Varian disagree?

The two sources quote rates that differ by more than a hundredfold. Linder gives a PIII dose rate above 1 $mA/c m^{2}$ over the wafer, which for singly charged ions is $3.7 \times 1 0^{17}$ $c m^{- 2}$ per minute (computed), while Varian’s patent quotes about $1 0^{15}$ $c m^{- 2}$ per minute. They agree once two corrections are applied. The current flows only during pulses, so at Linder’s 2.25 per cent duty factor the average is $8.4 \times 1 0^{15}$ per minute (computed). Secondary electrons then add about seven electrons per ion at 10 $keV$ , so only one eighth of the measured current is ions, giving about $1.05 \times 1 0^{15}$ per minute (computed). Varian’s time-averaged figure is therefore the more likely throughput value, and Linder’s is the in-pulse current (my reading). Reference: B. P. Linder, ‘Investigation of Plasma Implantation and Gate Oxide Charging during Plasma Processing’, PhD dissertation, UC Berkeley, Memorandum UCB/ERL M99/8 (February 1999) (fetch-tool summary); D. L. Chapek, S. B. Felch, M. W. Kissick, S. M. Malik and T. T. Sheng, ‘Apparatus for obtaining dose uniformity in plasma doping (PLAD) ion implantation processes’, US patent 5,711,812, Varian Associates (filed June 1995) (fetch-tool summary).

Ques: How is PLAD dose uniformity achieved across the wafer?

By shaping the sheath at the wafer edge. Varian’s patent targets a dose standard deviation of about 2 per cent or less (1 sigma). Its prior-art configuration exceeded 10 per cent, a grounded ring around the wafer gave 38.5 per cent, and a separately biased ring reduced it to 2.17 per cent. The biased ring probably extends the flat part of the sheath beyond the wafer rim, so ions arrive at normal incidence and with even flux at the edge (my reading). Aluminium parts are a problem because of their high secondary-electron emission, which distorts the measured current. In the beamline implanter, uniformity comes instead from scanning the beam over the wafer many times, with Faraday sampling at kHz rates (Beamline Ion Implanter page). Reference: D. L. Chapek, S. B. Felch, M. W. Kissick, S. M. Malik and T. T. Sheng, ‘Apparatus for obtaining dose uniformity in plasma doping (PLAD) ion implantation processes’, US patent 5,711,812, Varian Associates (filed June 1995) (fetch-tool summary); B. P. Linder, ‘Investigation of Plasma Implantation and Gate Oxide Charging during Plasma Processing’, PhD dissertation, UC Berkeley, Memorandum UCB/ERL M99/8 (February 1999) (fetch-tool summary); Beamline Ion Implanter page of this vault.

Ques: Why do pulse fall time and wafer heating matter?

Because ions keep arriving while the voltage falls. Linder measured fall times of 16.22 $μ s$ with no shunt resistor, but 0.12 $μ s$ with a 50 ohm shunt and 0.36 to 0.88 $μ s$ with 270 ohm. With a 1 $μ s$ pulse, a 16 $μ s$ fall would deliver most of the dose at reduced energy and broaden the profile (my reading). His fall time is defined to 500 V in one chapter and to -50 V in another, so the values are not directly comparable. Heating comes mostly from the pulses: the 900 W argon plasma at 1 $mTorr$ deposits about 2 W on a 4 inch wafer, but 6 $kV$ pulsing at 5 $kHz$ deposits about 55 W, driving the wafer above 450 $^{\circ} C$ without cooling. Gate-oxide damage roughly doubles per 50 $^{\circ} C$ rise. Reference: B. P. Linder, ‘Investigation of Plasma Implantation and Gate Oxide Charging during Plasma Processing’, PhD dissertation, UC Berkeley, Memorandum UCB/ERL M99/8 (February 1999) (fetch-tool summary).

Ques: Why are dopant gases diluted in helium or neon?

To control dose and protect the mask. Sharp’s patent dilutes B2H6, BF3, PH3 or AsH3 to dopant-to-dilutant ratios of 25:75 to 5:95, preferring neon or helium because argon damages photoresist, and notes that resist material can redeposit on the wafer. Pressure oscillations reduce dose control, since dopant partial pressure is one of the dose-setting parameters with pulse width, frequency and time. Since a PLAD chamber has no mass analyzer, hydrogen and fluorine fragments from these gases are presumably implanted too (my reading). Light dilutants sputter less, which helps retained dose (my reading). The plasma itself can be characterized with a Langmuir probe, whose electron temperature and density set the sheath (Langmuir Probe page). Reference: Y. Ono, Y. Ma and S. T. Hsu, ‘Dose control technique for plasma doping in ultra-shallow junction formations’, US patent 6,403,453 B1, Sharp Laboratories of America (filed July 2000) (fetch-tool summary); Langmuir Probe page of this vault.

References

B. P. Linder, “Investigation of Plasma Implantation and Gate Oxide Charging during Plasma Processing,” PhD dissertation, University of California, Berkeley, Memorandum UCB/ERL M99/8, 1999. Available: https://www2.eecs.berkeley.edu/Pubs/TechRpts/1999/ERL-99-8.pdf
K. G. Kostov, J. J. Barroso and M. Ueda, “Two dimensional computer simulation of plasma immersion ion implantation,” Brazilian Journal of Physics, vol. 34, no. 4B, pp. 1689-1695, 2004. Available: https://www.redalyc.org/pdf/464/46434833.pdf
D. Gupta, J. Jogi and P. J. George, “Analytical Estimation of Doping in a Microwave based PIII System, Implementing Sheath Models,” Proceedings of the World Congress on Engineering, 2013. Available: https://www.iaeng.org/publication/WCE2013/WCE2013_pp1133-1135.pdf
D. L. Chapek, S. B. Felch, M. W. Kissick, S. M. Malik and T. T. Sheng, “Apparatus for obtaining dose uniformity in plasma doping (PLAD) ion implantation processes,” US Patent 5,711,812, Varian Associates, 1998. Available: https://patents.google.com/patent/US5711812
Beamline Ion Implanter page of this vault.
Y. Ono, Y. Ma and S. T. Hsu, “Dose control technique for plasma doping in ultra-shallow junction formations,” US Patent 6,403,453 B1, Sharp Laboratories of America, 2002. Available: https://patents.google.com/patent/US6403453
Langmuir Probe page of this vault.

Quartz 5

Explorer

Plasma Immersion Ion Implanter