1. Theory

Definition: E-beam inspection scans a patterned wafer with a focused electron beam to find physical and electrical defects, and a defect-review SEM revisits defects found by inspection to image and classify them at high magnification (low-voltage patent; Hitachi patent).
Voltage contrast: At landing energies between the two crossover energies, floating conductors charge differently from grounded ones, so opens and shorts below the surface change the secondary-electron signal (low-voltage patent; Applied Materials patent).
Physical contrast: Topography and material contrast reveal residues, bridges and missing patterns at nanometre resolution (Scanning Electron Microscope (SEM) page).
Speed limit: Shot noise sets the electrons needed per pixel, so beam current limits area per hour (Du and Jacobsen; KLA patent).

2. Working Principle

Column: Field-emission source, low landing energy set by wafer bias, energy-filtered secondary detection (low-voltage patent).
Charge control: Flood or defocused pre-charge before imaging sets the surface potential (low-voltage patent; Applied Materials patent).
Multi-beam: Arrays of beamlets with separate detectors raise total current (KLA patent).
Review: Low-magnification relocation, defect detection against a reference, high-magnification imaging, then classification (Hitachi patent).

3. Applications

Contacts and vias: Under-etched or unlanded vias and contact opens found by voltage contrast (Applied Materials patent; low-voltage patent).
Gate and metal shorts: Leakage paths and bridges in logic and memory arrays (low-voltage patent).
Defect review and Pareto: Imaging and classifying optical inspection hits (Hitachi patent).

Charging and Voltage Contrast

Name	Formula	Related Formulae	Variables/Constants
Total electron yield and charging	$σ (E_{L}) = δ + η, I_{n e t} = I_{p} (1 - σ)$	$E_{1} < E_{L} < E_{2} \Rightarrow σ > 1 (positive charging)$	$σ : t o t a l y i e l d$ $δ : seco n d a r y e l ec t r o n y i e l d$ $η : ba c k sc a tt er coe f f i c i e n t$ $E_{L} : l an d in g e n er g y$ $I_{p} : p r ima r y c u r r e n t$ $I_{n e t} : n e t c u r r e n t in t o t h e s u r f a ce$ $E_{1}, E_{2} : cr osso v er e n er g i es; l o w - v o l t a g e p a t e n t : o p er a t i o n b e tw ee n tw o cr osso v er v o l t a g es w h er e seco n d a r y e mi ss i o n e x cee d s t h e p r ima r y c u r r e n t, l an d in g e n er g y 500 eV t o 1.5 keV; T h o m so n e t a l . : S E an d B S E y i e l d s, u ni t y t o t a l y i e l d a t t h e cr osso v er s, n e t p os i t i v e c ha r g in g b e tw ee n t h e m; t o t a l y i e l d a s t h e i r s u m an d I_{n e t} (co m p u t e d)$ $(m y r e a d in g : b e l o w E_{2} an i so l a t e d co n d u c t or l oses m or e e l ec t r o n s t han i t r ece i v es an d d r i f t s p os i t i v e u n t i l i t s o w n f i e l d r e t u r n s t h e s l o w seco n d a r i es)$
Landing energy with wafer bias	$E_{L} = E_{0} + e V_{w}$	$V_{w} < 0 \Rightarrow E_{L} < E_{0}$	$E_{0} : b e am e n er g y in t h e co l u mn$ $V_{w} : w a f er bia s; l o w - v o l t a g e p a t e n t : l an d in g e n er g y a d j u s t ab l e b y w a f er bia s, l o w l an d in g e n er g y f or t hin s i l i c i d e t o a v o i d p u n c h - t h r o ug h l e ak a g e; r e t a r d in g r e l a t i o n (co m p u t e d)$ $(a ss u m e d : E_{0} = 10 keV, V_{w} = - 9.5 kV; co m p u t e d : E_{L} = 0.5 keV)$
Floating-conductor charging	$Δ V = \frac{Q}{C _{f}}, t_{c} = \frac{C _{f} Δ V}{I _{p} ( σ - 1 )}$	$Δ V > Δ E_{S E} / e for energy-filter separation$	$C_{f} : c a p a c i t an ce o f t h e f l o a t in g s t r u c t u r e$ $Q : d e p os i t e d c ha r g e$ $t_{c} : t im e t o c ha r g e b y Δ V$ $Δ E_{S E} : seco n d a r y - e l ec t r o n e n er g y s p r e a d; A ppl i e d M a t er ia l s p a t e n t : a c ha r g in g d i f f er e n ce b e tw ee n d e f ec t i v e s t r u c t u r e an d s u r r o u n d in g s, w hi c h m u s t e x cee d t h e seco n d a r y - e l ec t r o n e n er g y w i d t h f or e n er g y f i l t er in g; l o w - v o l t a g e p a t e n t : f i l t er co l l ec t in g r o ug h l y 0 t o 15 eV; c a p a c i t or r e l a t i o n (co m p u t e d)$ $(a ss u m e d : C_{f} = 0.1 fF, n e t c u r r e n t 10 nA; co m p u t e d : 624 e l ec t r o n s an d 10 ns f or 1 V)$

Signal, Noise and Throughput

Name	Formula	Related Formulae	Variables/Constants
Rose criterion and electrons per pixel	$N_{p} \geq \frac{1}{ε} (\frac{k}{C})^{2}$	$S N R = C ε N_{p}$	$N_{p} : p r ima r y e l ec t r o n s p er p i x e l$ $ε : d e t ec t e d e l ec t r o n s p er p r ima r y$ $C : co n t r a s t$ $k : r e q u i r e d S N R (ab o u t 5); D u an d J a co b se n : R ose cr i t er i o n S N R = 5 an d n = S N R^{2} / Θ^{2} q u an t a p er p i x e l, w i t h t h e d e t ec t i o n e f f i c i e n cy a dd e d h er e (co m p u t e d)$ $(a ss u m e d : C = 0.1, k = 5, ε = 0.5; co m p u t e d : N_{p} = 5000)$
Pixel rate	$f_{p i x} = \frac{I _{p}}{N _{p} e}$	$τ_{p i x} = \frac{1}{f _{p i x}}$	$f_{p i x} : p i x e l r a t e$ $τ_{p i x} : d w e l l t im e$ $e : e l e m e n t a r y c ha r g e; l o w - v o l t a g e p a t e n t : b e am c u r r e n t ab o u t 500 pA t o 10 nA, u p t o 25 t o 50 nA in t o a s p o t b e l o w 0.1 μ m, p i x e l a c q u i s i t i o n 1 t o 100 MHz; r e l a t i o n (co m p u t e d)$ $(a ss u m e d : I_{p} = 100 nA; co m p u t e d : 8.0 ns d w e l l an d 125 MHz)$
Area rate and wafer time	$\dot{A} = n_{b} f_{p i x} p^{2}, t_{w a f er} = \frac{A _{in s p}}{A ˙}$	$n_{b} = 25 (5 by 5 beamlets)$	$\dot{A} : in s p ec t e d a r e a p er seco n d$ $n_{b} : n u mb er o f b e am s$ $p : p i x e l s i z e$ $A_{in s p} : in s p ec t e d a r e a; K L A p a t e n t : 25 b e am l e t s in a 5 b y 5 a r r a y (r an g e 2 t o 200), 10 t o 25 t im es t h e s in g l e - b e am c u r r e n t a t t h e s am e s p o t s i z e, r o a d ma p o f m or e t han 0.1 w a f er p er h o u r; r e l a t i o n (co m p u t e d)$ $(a ss u m e d : p = 10 nm; co m p u t e d : 45 m m^{2} /h p er b e am, 1573 h f or a f u l l 300 mm w a f er, 63 h w i t h 25 b e am s)$

Pre-Charge and Defect Review

Name	Formula	Related Formulae	Variables/Constants
Pre-charge dose	$σ_{Q} = \frac{Q}{A _{p c}}, I_{p c} = \frac{Q}{t _{p c}}$	$A_{p c} \geq 2 A_{ima g e}$	$σ_{Q} : c ha r g e p er a r e a$ $A_{p c} : p r e - c ha r g e a r e a$ $t_{p c} : p r e - c ha r g e t im e; l o w - v o l t a g e p a t e n t : f l oo d b e am c u r r e n t a t l e a s t f o u r t im es t h e ima g in g b e am, b es t se tt in g 250 b y 250 μ m a t 2 \times 1 0^{- 10} C in 60 ms, p r e - c ha r g e a r e a a t l e a s t tw i ce t h e ima g e a r e a (64 t im es in o n e e x am pl e); A ppl i e d M a t er ia l s p a t e n t : d e f oc u se d p r e - c ha r g e s p o t o f a t l e a s t ab o u t 1 μ m, f oc u se d s p o t b e l o w ab o u t 500 nm$ $(co m p u t e d : 3.2 \times 1 0^{- 7} C/c m^{2} an d 3.3 nA)$
Defect relocation window	$F O V_{l o w} \geq 2 Δ_{x y}, F O V = \frac{W _{d i s pl a y}}{M}$	$p = \frac{F O V}{N _{p x}}$	$Δ_{x y} : coor d ina t e er r or f r o m o pt i c a l in s p ec t i o n$ $M : ma g ni f i c a t i o n$ $W_{d i s pl a y} : d i s pl a y e d w i d t h$ $N_{p x} : p i x e l s p er l in e; H i t a c hi p a t e n t : er r or o f ab o u t pl u s or min u s 4 μ m, l o w ma g ni f i c a t i o n ab o u t 15, 000 t im es w i t h ab o u t 9 μ m f i e l d, hi g h ma g ni f i c a t i o n ab o u t 50, 000 t im es (2.5 μ m) in t h e ba c k g r o u n d an d ab o u t 100, 000 t im es in t h e e mb o d im e n t, d e f ec t s i z es o f d oz e n s o f nm n ee d in g se v er a l nm r eso l u t i o n$ $(a ss u m e d : N_{p x} = 512; co m p u t e d : 17.6 nm p i x e l s a t 9 μ m, 2.7 an d 1.35 μ m f i e l d s a t 50, 000 an d 100, 000 t im es)$
Reference image and classification	$D = I_{d e f ec t} - I_{r e f}, r = \frac{cov ( I _{1} , I _{2} )}{σ _{1} σ _{2}}$	$I_{r e f} from adjacent die or synthesized from cell periodicity$	$r : cor r e l a t i o n coe f f i c i e n t$ $I_{r e f} : r e f er e n ce ima g e; H i t a c hi p a t e n t : r e f er e n ce o n e c hi p a w a y in p r i or a r t, r e f er e n ce sy n t h es i z e d f r o m c i r c u i t - p a tt er n p er i o d i c i t y in t h e l o w - ma g ni f i c a t i o n d e f ec t ima g e, cor r e l a t i o n - ba se d s imi l a r i t y, f a l l ba c k t o a r e f er e n ce p os i t i o n i f n o d e f ec t i s f o u n d, A D C a s a r e v i e w - S E M f u n c t i o n; cor r e l a t i o n f or m (m y r e a d in g)$ $(m y r e a d in g : sy n t h es i z in g t h e r e f er e n ce r e m o v es o n e s t a g e m o v e an d o n e ima g e p er d e f ec t, w hi c h d o mina t es r e v i e w t im e)$

Important Questions

Ques: How does voltage contrast reveal a buried electrical defect?

By making connected and floating structures charge to different potentials. The low-voltage patent operates between the two crossover energies, where each primary electron releases more than one secondary, so an isolated conductor charges positive while a grounded one stays near zero. Thomson et al. note that a few volts of positive potential pull most secondaries back to the surface, so a positive conductor appears darker (my reading), so an unlanded via or open contact stands out from its connected neighbours. The Applied Materials patent states the requirement as a charging difference between the defective structure and its surroundings, larger than the secondary-electron energy width if an energy filter separates them. A 0.1 $fF$ floating plug needs only 624 electrons to shift by 1 $V$ , about 10 $ns$ at 10 $nA$ net current (assumed; computed). Reference: ‘Voltage contrast method and apparatus for semiconductor inspection using low voltage particle beam’, US patent 6,566,897 (divisional of US 6,344,750, filed January 1999) (fetch-tool summary); E. T. Bullock, ‘Apparatus and method for enhancing voltage contrast of a wafer’, US patent 7,994,476, Applied Materials Israel (filed November 2007) (fetch-tool summary); C. D. Thomson, V. Zavyalov, J. R. Dennison and J. Corbridge, ‘Electron Emission Properties of Insulator Materials Pertinent to the International Space Station’, Utah State University (NASA NTRS), 2003: SE and BSE yields, unity total yield at the first (below 100 V) and second (above 1 keV) crossover energies, net positive charging between them, a few-volt positive potential pulling most SEs back to the surface (fetch-tool summary).

Ques: Why are landing energies near 1 keV used for voltage contrast?

Because charging polarity depends on the total yield $σ = δ + η$ . Between the crossover energies $E_{1}$ and $E_{2}$ the yield exceeds one, and the surface charges positively (Thomson et al.); an insulator then reaches a steady state where the total yield equals one. The low-voltage patent gives landing energies of 500 $eV$ to 1.5 $keV$ in this window, set partly by wafer bias, and notes that thin silicide needs low landing energy to avoid beam punch-through leaking the charge. With an assumed 10 $keV$ column and a wafer bias of -9.5 $kV$ , the landing energy is 0.5 $keV$ (computed). Above $E_{2}$ the surface charges negatively instead, which is the negative voltage-contrast mode the patent also describes. Reference: C. D. Thomson, V. Zavyalov, J. R. Dennison and J. Corbridge, ‘Electron Emission Properties of Insulator Materials Pertinent to the International Space Station’, Utah State University (NASA NTRS), 2003: SE and BSE yields, unity total yield at the first (below 100 V) and second (above 1 keV) crossover energies, net positive charging between them, a few-volt positive potential pulling most SEs back to the surface (fetch-tool summary); ‘Voltage contrast method and apparatus for semiconductor inspection using low voltage particle beam’, US patent 6,566,897 (divisional of US 6,344,750, filed January 1999) (fetch-tool summary).

Ques: Why does e-beam inspection sample instead of scanning whole wafers?

Because shot noise sets a minimum number of electrons per pixel. The Rose criterion with contrast 0.1, SNR 5 and half of the primaries detected gives 5000 primaries per pixel (assumed; computed). At 100 $nA$ this takes 8.0 $ns$ , a 125 $MHz$ pixel rate, just above the 1 to 100 $MHz$ range of the low-voltage patent (computed). With 10 $nm$ pixels one beam covers 45 $m m^{2} /h$ , so a full 300 $mm$ wafer would take 1573 $h$ , about 66 days (computed). Inspection is therefore restricted to sampled dies, arrays or hot-spot locations, and larger pixels are used for voltage contrast, where the signal is strong (my reading). Higher current enlarges the spot through aberrations and electron interactions. Reference: M. Du and C. Jacobsen, ‘Relative merits and limiting factors for x-ray and electron microscopy of thick, hydrated organic materials’, arXiv:2004.10069 (Ultramicroscopy 184, 2018): Rose criterion SNR = 5, n = SNR^2/Theta^2 quanta per pixel (fetch-tool summary); ‘Voltage contrast method and apparatus for semiconductor inspection using low voltage particle beam’, US patent 6,566,897 (divisional of US 6,344,750, filed January 1999) (fetch-tool summary).

Ques: How do multi-beam systems change e-beam inspection throughput?

By dividing current among many beamlets, each with its own spot and detector. The KLA patent uses 25 beamlets in a 5 by 5 array, with a stated range of 2 to 200, and claims more than 10 and up to 25 times the total current of a single beam at the same spot size, since lens aberrations, source brightness and electron interactions limit one beam. It cites a roadmap need for more than 0.1 wafer per hour at below three times the design rule. At the assumed 10 $nm$ pixel, 25 beams reduce a full wafer from 1573 to 63 $h$ , and about 157 beams would be needed for 10 $h$ (computed), so full-wafer coverage at small pixels still requires sampling (my reading). Reference: ‘Multiple-beam system for high-speed electron-beam inspection’, US patent 8,362,425, KLA-Tencor (filed April 2011) (fetch-tool summary); M. Du and C. Jacobsen, ‘Relative merits and limiting factors for x-ray and electron microscopy of thick, hydrated organic materials’, arXiv:2004.10069 (Ultramicroscopy 184, 2018): Rose criterion SNR = 5, n = SNR^2/Theta^2 quanta per pixel (fetch-tool summary).

Ques: Why is the surface pre-charged before voltage-contrast imaging?

To set a stable potential difference before the imaging scan reads it. The low-voltage patent uses a flood beam with at least four times the imaging current over an area at least twice the image area; its best tabulated setting is 250 by 250 $μ m$ at $2 \times 1 0^{- 10}$ C in 60 $ms$ , which is $3.2 \times 1 0^{- 7}$ $C/c m^{2}$ and 3.3 $nA$ (computed). It also models a micro-retarding field of -0.71 $V$ from returning secondaries charging the surroundings. The Applied Materials patent instead defocuses the main beam to at least about 1 $μ m$ , using scan fly-back for pre-charging, controlled by defocus, duty cycle and scan orientation. Both aim for charging differences large enough to survive leakage during imaging (my reading). Reference: ‘Voltage contrast method and apparatus for semiconductor inspection using low voltage particle beam’, US patent 6,566,897 (divisional of US 6,344,750, filed January 1999) (fetch-tool summary); E. T. Bullock, ‘Apparatus and method for enhancing voltage contrast of a wafer’, US patent 7,994,476, Applied Materials Israel (filed November 2007) (fetch-tool summary).

Ques: How does a review SEM find a defect reported by optical inspection?

By imaging a field larger than the coordinate error, then zooming in. The Hitachi patent states that inspection coordinates carry about plus or minus 4 $μ m$ of error, so the review SEM first images at about 15,000 times with a 9 $μ m$ field, which covers the 8 $μ m$ uncertainty span (computed). The defect is located by comparing with a reference image and then reimaged at high magnification for defects of dozens of nanometres. Prior practice took the reference from a die one chip away; the patent synthesizes it from the periodic pattern in the same low-magnification image, avoiding a stage move. With 512 pixels per line, the 9 $μ m$ field gives 17.6 $nm$ pixels (assumed; computed). Classification of the imaged defect follows. Reference: M. Harada, R. Nakagaki and K. Obara, ‘Method and its apparatus for reviewing defects’, US patent 8,121,397, Hitachi High-Technologies (filed April 2009) (fetch-tool summary).

Ques: What high magnification is used for review: 50,000 or 100,000 times?

The Hitachi patent gives both. Its background describes high-magnification review at about 50,000 times with a roughly 2.5 $μ m$ field, while its embodiment step uses about 100,000 times. Scaling the stated 9 $μ m$ field at 15,000 times gives 2.7 $μ m$ at 50,000 times, consistent with the 2.5 $μ m$ quoted, and 1.35 $μ m$ at 100,000 times (computed). With 512 pixels these give 5.3 and 2.6 $nm$ pixels (assumed; computed). The patent targets defects of dozens of nanometres needing several-nanometre resolution, so 100,000 times is more likely for the advanced-node case it describes, while 50,000 times reflects general prior practice (my reading). Review recipes store magnification with acceleration voltage, probe current and frame count, so either may appear. Reference: M. Harada, R. Nakagaki and K. Obara, ‘Method and its apparatus for reviewing defects’, US patent 8,121,397, Hitachi High-Technologies (filed April 2009) (fetch-tool summary).

References

“Voltage contrast method and apparatus for semiconductor inspection using low voltage particle beam,” US patent 6,566,897 (divisional of US application 09/227,395, filed January 8, 1999, now US 6,344,750). Available: https://image-ppubs.uspto.gov/dirsearch-public/print/downloadPdf/6566897
E. T. Bullock, “Apparatus and method for enhancing voltage contrast of a wafer,” US patent 7,994,476 B2, Applied Materials Israel, filed November 5, 2007. Available: https://patents.google.com/patent/US7994476
C. D. Thomson, V. Zavyalov, J. R. Dennison and J. Corbridge, “Electron emission properties of insulator materials pertinent to the International Space Station,” Utah State University, 2003 (NASA NTRS 20040111072). Available: https://ntrs.nasa.gov/api/citations/20040111072/downloads/20040111072.pdf
M. Du and C. Jacobsen, “Relative merits and limiting factors for x-ray and electron microscopy of thick, hydrated organic materials,” Ultramicroscopy, vol. 184, pp. 293-309, 2018; arXiv:2004.10069. Available: https://arxiv.org/abs/2004.10069
“Multiple-beam system for high-speed electron-beam inspection,” US patent 8,362,425 B2, KLA-Tencor, filed April 27, 2011. Available: https://patents.google.com/patent/US8362425B2/en
M. Harada, R. Nakagaki and K. Obara, “Method and its apparatus for reviewing defects,” US patent 8,121,397 B2, Hitachi High-Technologies, filed April 1, 2009. Available: https://patents.google.com/patent/US8121397

Quartz 5

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E-Beam Inspection and Defect Review