1. Theory

Definition: An X-ray photoelectron spectrometer irradiates a surface with soft X-rays and measures the kinetic energy of emitted core-level electrons, giving elemental composition and chemical state of the top few nanometres (Smart et al.; EAG).
Energy balance: $K E = h ν - (E_{B} + ϕ_{s p})$ , so each element shows core peaks at characteristic binding energies (Smart et al.).
Chemical shift: Binding energy rises when valence charge is withdrawn, distinguishing, for example, Si from SiO2 (Smart et al.; background knowledge, Briggs and Seah).
Surface sensitivity: Photoelectrons lose energy within a few inelastic mean free paths, so 95 per cent of the signal comes from within $3 λ$ (Smart et al.; Physical Electronics).

2. Working Principle

Source: Monochromated Al K-alpha, or Mg K-alpha, and hard X-ray Cr K-alpha for deeper analysis (Smart et al.; Physical Electronics).
Analyser: A hemispherical analyser at fixed pass energy disperses electrons by energy (Smart et al.).
Charge control: Low-energy electron flood guns neutralize insulating samples (Smart et al.).
Depth information: Angle-resolved measurements, harder X-rays or ion sputtering extend depth analysis (EAG; Physical Electronics).

3. Applications

Gate dielectrics: SiO2, oxynitride and high-k thickness and bonding (Physical Electronics; EAG).
Contamination and failure analysis: Stains, residues and cleaning checks (EAG).
Interface chemistry: Suboxides, silicides and metal oxidation states (background knowledge, Briggs and Seah).
Thin-film stacks: Depth profiling of compositions (EAG).

Photoemission and Chemical State

Name	Formula	Related Formulae	Variables/Constants
Photoelectric energy balance	$K E = h ν - (E_{B} + ϕ_{s p})$	$h ν = 1486.6 eV (Al K α), 1253.6 eV (Mg K α)$	$K E : m e a s u r e d k in e t i c e n er g y$ $h ν : p h o t o n e n er g y$ $E_{B} : bin d in g e n er g y r e l a t i v e t o t h e F er mi l e v e l$ $ϕ_{s p} : s p ec t r o m e t er w or k f u n c t i o n; S ma r t e t a l . : r e l a t i o n, M g K α 1253.6 eV, A l K α so u r ce; A l K α e n er g y an d C r K α 5414.7 eV f or ha r d X - r a y X P S (ba c k g r o u n d k n o w l e d g e, B r i g g s an d S e ah)$ $(a ss u m e d : ϕ_{s p} = 4.5 eV; co m p u t e d : S i 2 p a t 99.3 eV l e a v es w i t h 1382.8 eV u n d er A l K α)$
Chemical shift	$Δ E_{B} = E_{B} (compound) - E_{B} (element)$	$charge withdrawn \Rightarrow Δ E_{B} > 0$	$Δ E_{B} : c h e mi c a l s hi f t; S ma r t e t a l . : w i t h d r a w in g v a l e n ce c ha r g e r ai ses an d a dd in g c ha r g e l o w er s bin d in g e n er g y, s p in - or bi t s pl i tt in g an d a r e a r a t i os n e a r l y co n s t an t; E A G : c h e mi c a l s t a t e an d o x i d a t i o n s t a t e f r o m p e ak p os i t i o n an d s ha p e; S i 2 p n e a r 99.3 eV in S i an d 103.3 eV in S i O 2 (ba c k g r o u n d k n o w l e d g e, B r i g g s an d S e ah)$ $(co m p u t e d : t h e S i t o S i O 2 s hi f t i s 4.0 eV, ab o u t 1 eV p er o x y g e n n e i g hb o u r a cr oss t h e f o u r s u b o x i d es)$
Analyser energy resolution	$Δ E \approx 0.63 w \frac{E _{0}}{R _{0}}$	$Δ E_{t o t a l}^{2} \approx Δ E_{so u r ce}^{2} + Δ E_{ana l y ser}^{2} + Γ^{2}$	$Δ E : ana l y ser r eso l u t i o n$ $w : s l i t w i d t h$ $E_{0} : p a ss e n er g y$ $R_{0} : m e an ana l y ser r a d i u s$ $Γ : na t u r a l l in e w i d t h; S ma r t e t a l . : ana l y ser r e l a t i o n, m o n oc h r o ma t e d A l K α na r r o w er t han M g K α, c ha r g e n e u t r a l i z er a t ab o u t 2 t o 20 eV f or in s u l a t or s; q u a d r a t u r e co mbina t i o n (ba c k g r o u n d k n o w l e d g e, B r i g g s an d S e ah)$ $(a ss u m e d : w = 1 mm, R_{0} = 165 mm, E_{0} = 20 eV; co m p u t e d : Δ E = 0.076 eV)$

Depth Sensitivity and Thickness

Name	Formula	Related Formulae	Variables/Constants
Signal attenuation with depth	$I_{s} = I_{0} exp (- \frac{d}{λ s i n θ})$	$d_{in f o} = 3 λ sin θ$	$I_{s} : s i g na l f r o m b e l o w d e pt h d$ $λ : in e l a s t i c m e an f r ee p a t h$ $θ : t ak e - o f f an g l e f r o m t h e s u r f a ce$ $d_{in f o} : in f or ma t i o n d e pt h; S ma r t e t a l . : I_{s} = I_{0} e^{- d / λ}, 3 λ f or 95 p er ce n t, λ o f 1 t o 3.5 nm an d 3 t o 10 nm d e pt h f or A l K α; E A G : d = 3 λ sin θ, 1 t o 10 nm; P h y s i c a l E l ec t r o ni cs : 3 λ f or ab o u t 95 p er ce n t (see t h e Q / A)$ $(co m p u t e d : 1 - e^{- 3} = 95.0 p er ce n t; λ = 3.1 nm g i v es 9.3 nm a t n or ma l e mi ss i o n an d 4.65 nm a t 30^{\circ} t ak e - o f f)$
Inelastic mean free path	$λ_{S i 2 p}^{S i} \approx 3.1 nm (Al K α), 9.3 nm (Cr K α)$	$λ \propto K E^{0.75} (approximate, high energy)$	$λ : T P P - 2 M in e l a s t i c m e an f r ee p a t h; P h y s i c a l E l ec t r o ni cs : 3.1 nm (A l K α) an d 9.3 nm (C r K α) f or S i 2 p in S i, S i 1 s t h r o ug h S i O 2 6.7 nm, in f or ma t i o n d e pt h s 9.3 an d 27.9 nm, t y p i c a l 5 t o 10 an d 15 t o 30 nm; e n er g y sc a l in g (ba c k g r o u n d k n o w l e d g e, T an u ma, P o w e l l an d P e nn)$ $(co m p u t e d : K E r a t i o 5310/1383 = 3.84 r ai se d t o 0.75 i s 2.74, c l ose t o t h e 3.0 r a t i o o f t h e T P P - 2 M v a l u es)$
Oxide overlayer thickness	$d_{o x} = λ_{o x} sin θ ln (1 + \frac{I _{o x} / I _{S i}}{R _{0}})$	$R_{0} = \frac{I _{o x}^{\infty}}{I _{S i}^{\infty}} \approx 0.9 (Si 2p)$	$d_{o x} : S i O 2 t hi c k n ess$ $λ_{o x} : a tt e n u a t i o n l e n g t h in t h e o x i d e$ $I_{o x}, I_{S i} : S i 2 p o x i d e an d s u b s t r a t e p e ak a r e a s$ $R_{0} : b u l k in t e n s i t y r a t i o; S t r o hm e i er - t y p e r e l a t i o n (ba c k g r o u n d k n o w l e d g e, S t r o hm e i er); P h y s i c a l E l ec t r o ni cs : o v er l a y er t hi c k n ess f r o m t ak e - o f f an g l e, I M F P an d minim u m s u b s t r a t e s i g na l, H f O 2/ S i O 2 ma x im u m ab o u t 19 nm a t 75^{\circ}; E A G : o x i d e - t hi c k n ess co m p a r i so n b e tw ee n s am pl es$ $(a ss u m e d : λ_{o x} = 3.5 nm, R_{0} = 0.9, n or ma l e mi ss i o n, e q u a l a r e a s; co m p u t e d : d_{o x} = 2.6 nm)$

Quantification and Profiling

Name	Formula	Related Formulae	Variables/Constants
Quantification	$N_{i} = \frac{I _{i} / ( σ _{i} λ _{i} )}{\sum _{j} I _{j} / ( σ _{j} λ _{j} )}$	$C_{i} = \frac{I _{i} / S _{i}}{\sum _{j} I _{j} / S _{j}} (sensitivity factors)$	$N_{i}, C_{i} : a t o mi c f r a c t i o n$ $I : p e ak a r e a$ $σ : S co f i e l d cr oss sec t i o n$ $S : a t o mi c se n s i t i v i t y f a c t or; S ma r t e t a l . : cr oss - sec t i o n f or m, a cc u r a cy ab o u t 10 p er ce n t, b e tt er t han 15 p er ce n t w i t h A S F s an d 5 p er ce n t w i t h s t an d a r d s, p r ec i s i o n b e tt er t han 2 p er ce n t; W a g n er A S F s O 1 s 0.66 an d S i 2 p 0.27 (ba c k g r o u n d k n o w l e d g e, W a g n er e t a l .)$ $(a ss u m e d : r a w O 1 s t o S i 2 p a r e a r a t i o 4.9; co m p u t e d : (4.9/0.66) / (1/0.27) = 2.0, s t o i c hi o m e t r i c S i O 2)$
Detection limit and analysis area	$C_{min} \sim 0.1 at. per cent$	$spot ≳ 30 μ m$	$C_{min} : d e t ec t i o n l imi t; E A G : ab o u t 0.1 a t o mi c p er ce n t, s ma l l es t a r e a ab o u t 30 μ m, a l l e l e m e n t s e x ce pt H an d H e, d e pt h p r o f i l in g f or maj or s ab o v e 1 a t o mi c p er ce n t an d d o w n t o l o w p er ce n t in s t a c k s$ $(co m p u t e d : 0.1 p er ce n t o f a 9.3 nm S i in f or ma t i o n d e pt h (5 \times 1 0^{22} c m^{- 3}) i s ab o u t 4.6 \times 1 0^{13} a t o m s p er s q u a r e ce n t im e t r e)$
Sputter depth profiling	$z = \overset{z}{˙} t_{s p}$	$Δ z \approx (2 λ)^{2} + Δ z_{mi x}^{2} + Δ z_{r o ug h}^{2}$	$z : d e pt h$ $\overset{z}{˙} : s p u tt er r a t e$ $t_{s p} : s p u tt er t im e$ $Δ z : d e pt h r eso l u t i o n; E A G : d e pt h p r o f i l in g o f maj or s an d t hin s t a c k s; r eso l u t i o n t er m s (ba c k g r o u n d k n o w l e d g e, B r i g g s an d S e ah)$ $(a ss u m e d : λ = 3.1 nm, mi x in g 2 nm; co m p u t e d : Δ z i s ab o u t 6.5 nm)$

Important Questions

Ques: How does XPS turn electron energies into chemistry?

Through the photoelectric balance and chemical shifts. Smart et al. give $K E = h ν - (E_{B} + ϕ)$ , so a measured kinetic energy gives the binding energy of the core level. With Al K-alpha at 1486.6 $eV$ and an assumed 4.5 $eV$ spectrometer work function, Si 2p at 99.3 $eV$ appears at 1382.8 $eV$ kinetic energy (background knowledge, Briggs and Seah; computed). Withdrawing valence charge raises binding energy (Smart et al.), so SiO2 Si 2p sits near 103.3 $eV$ , a 4.0 $eV$ shift, about 1 $eV$ per oxygen neighbour (computed). Spin-orbit doublets with nearly constant splitting and area ratios help assign peaks (Smart et al.). EAG adds that XPS sees all elements except H and He. Reference: R. Smart, S. McIntyre, M. Bancroft, I. Bello and others, ‘X-ray Photoelectron Spectroscopy’ slides, City University of Hong Kong and Surface Science Western, hosted by National Taiwan University (fetch-tool summary); D. Briggs and M. P. Seah, Practical Surface Analysis, Vol. 1, 2nd ed., Wiley 1990; B. R. Strohmeier, Surf. Interface Anal. 15, 51 (1990); C. D. Wagner et al., Surf. Interface Anal. 3, 211 (1981); S. Tanuma, C. J. Powell and D. R. Penn, TPP-2M IMFP formula (background knowledge; not opened); EAG Laboratories, ‘X-ray Photoelectron Spectroscopy (XPS)’ technique note M-067322 (fetch-tool summary).

Ques: Is the information depth 3 lambda, 3 lambda sin theta or 3 lambda cos theta?

They are the same once the angle convention is fixed. Smart et al. give $3 λ$ for 95 per cent of the signal, the normal-emission value, while EAG writes $d = 3 λ sin θ$ with $θ$ measured from the surface; texts measuring the angle from the surface normal write $cos θ$ instead (background knowledge, Briggs and Seah). Physical Electronics uses take-off angles such as 75 $^{\circ}$ in the surface-referenced sense. With $λ$ = 3.1 $nm$ , $1 - e^{- 3}$ = 95.0 per cent of signal arises within 9.3 $nm$ at normal emission and 4.65 $nm$ at 30 $^{\circ}$ take-off (computed). The sine form with surface-referenced angles is more likely what a given instrument reports, so the convention must be checked before comparing data (my reading). Reference: R. Smart, S. McIntyre, M. Bancroft, I. Bello and others, ‘X-ray Photoelectron Spectroscopy’ slides, City University of Hong Kong and Surface Science Western, hosted by National Taiwan University (fetch-tool summary); EAG Laboratories, ‘X-ray Photoelectron Spectroscopy (XPS)’ technique note M-067322 (fetch-tool summary); Physical Electronics, ‘StrataPHI part 3’ application article (fetch-tool summary; equations shown only as images); D. Briggs and M. P. Seah, Practical Surface Analysis, Vol. 1, 2nd ed., Wiley 1990; B. R. Strohmeier, Surf. Interface Anal. 15, 51 (1990); C. D. Wagner et al., Surf. Interface Anal. 3, 211 (1981); S. Tanuma, C. J. Powell and D. R. Penn, TPP-2M IMFP formula (background knowledge; not opened).

Ques: How is oxide thickness measured by XPS?

From the ratio of oxide and substrate Si 2p peaks. A Strohmeier-type relation gives $d = λ_{o x} sin θ ln [1 + (I_{o x} / I_{S i}) / R_{0}]$ with $R_{0} \approx 0.9$ for Si 2p (background knowledge, Strohmeier). For equal peak areas, an assumed 3.5 $nm$ oxide attenuation length and normal emission, the oxide is 2.6 $nm$ thick (computed). Because the substrate signal falls as $e^{- d / λ}$ (Smart et al.), the method works only while enough substrate signal remains; Physical Electronics estimates a maximum of about 19 $nm$ for an HfO2/SiO2 overlayer with hard X-rays at 75 $^{\circ}$ . EAG lists oxide-thickness comparison between samples as a routine application. Elastic scattering and the choice of $λ$ limit accuracy to roughly 10 per cent (background knowledge). Reference: D. Briggs and M. P. Seah, Practical Surface Analysis, Vol. 1, 2nd ed., Wiley 1990; B. R. Strohmeier, Surf. Interface Anal. 15, 51 (1990); C. D. Wagner et al., Surf. Interface Anal. 3, 211 (1981); S. Tanuma, C. J. Powell and D. R. Penn, TPP-2M IMFP formula (background knowledge; not opened); R. Smart, S. McIntyre, M. Bancroft, I. Bello and others, ‘X-ray Photoelectron Spectroscopy’ slides, City University of Hong Kong and Surface Science Western, hosted by National Taiwan University (fetch-tool summary); Physical Electronics, ‘StrataPHI part 3’ application article (fetch-tool summary; equations shown only as images); EAG Laboratories, ‘X-ray Photoelectron Spectroscopy (XPS)’ technique note M-067322 (fetch-tool summary).

Ques: Why does hard X-ray XPS see deeper?

Because faster photoelectrons travel farther before losing energy. Physical Electronics gives TPP-2M mean free paths for Si 2p in silicon of 3.1 $nm$ with Al K-alpha and 9.3 $nm$ with Cr K-alpha, and information depths of 9.3 and 27.9 $nm$ . The Si 2p kinetic energy rises from about 1383 to 5310 $eV$ with Cr K-alpha at 5414.7 $eV$ (background knowledge; computed), a factor of 3.84; the approximate scaling $λ \propto K E^{0.75}$ predicts 2.74 times longer paths, close to the factor 3.0 of the TPP-2M values (computed). Physical Electronics notes typical ranges of 5 to 10 and 15 to 30 $nm$ because of IMFP dispersion. Buried interfaces under high-k and metal gates thus become accessible without sputtering, which would alter the chemistry. Reference: Physical Electronics, ‘StrataPHI part 3’ application article (fetch-tool summary; equations shown only as images); D. Briggs and M. P. Seah, Practical Surface Analysis, Vol. 1, 2nd ed., Wiley 1990; B. R. Strohmeier, Surf. Interface Anal. 15, 51 (1990); C. D. Wagner et al., Surf. Interface Anal. 3, 211 (1981); S. Tanuma, C. J. Powell and D. R. Penn, TPP-2M IMFP formula (background knowledge; not opened).

Ques: How accurate is XPS quantification?

About 10 per cent routinely, better with standards. Smart et al. normalize intensities by Scofield cross sections and mean free paths, $N_{i} = (I_{i} / σ_{i} λ_{i}) / \sum_{j} (I_{j} / σ_{j} λ_{j})$ , and quote accuracy better than 15 per cent with sensitivity factors, better than 5 per cent with standards, and precision better than 2 per cent. With Wagner sensitivity factors of 0.66 for O 1s and 0.27 for Si 2p, a raw area ratio of 4.9 gives O to Si of 2.0, stoichiometric SiO2 (background knowledge, Wagner et al.; computed). EAG gives detection limits near 0.1 atomic per cent, about $4.6 \times 1 0^{13}$ atoms per square centimetre within a 9.3 $nm$ silicon depth (computed), far worse than TXRF for metals. Reference: R. Smart, S. McIntyre, M. Bancroft, I. Bello and others, ‘X-ray Photoelectron Spectroscopy’ slides, City University of Hong Kong and Surface Science Western, hosted by National Taiwan University (fetch-tool summary); D. Briggs and M. P. Seah, Practical Surface Analysis, Vol. 1, 2nd ed., Wiley 1990; B. R. Strohmeier, Surf. Interface Anal. 15, 51 (1990); C. D. Wagner et al., Surf. Interface Anal. 3, 211 (1981); S. Tanuma, C. J. Powell and D. R. Penn, TPP-2M IMFP formula (background knowledge; not opened); EAG Laboratories, ‘X-ray Photoelectron Spectroscopy (XPS)’ technique note M-067322 (fetch-tool summary).

Ques: What limits XPS energy and depth resolution?

Source width, analyser settings, charging and sputter damage. Smart et al. give the analyser resolution $Δ E \approx 0.63 w E_{0} / R_{0}$ ; an assumed 1 $mm$ slit, 165 $mm$ radius and 20 $eV$ pass energy give 0.076 $eV$ (computed), small compared with the natural width of many core lines, so monochromated Al K-alpha, narrower than Mg K-alpha, dominates the total. Insulators charge positively and shift peaks, which flood guns at about 2 to 20 $eV$ correct (Smart et al.). In sputter profiles, depth resolution combines the escape depth with ion mixing and roughness; with $λ$ = 3.1 $nm$ and an assumed 2 $nm$ mixing it is about 6.5 $nm$ (background knowledge, Briggs and Seah; computed). EAG uses profiling mainly for majors above 1 atomic per cent. Reference: R. Smart, S. McIntyre, M. Bancroft, I. Bello and others, ‘X-ray Photoelectron Spectroscopy’ slides, City University of Hong Kong and Surface Science Western, hosted by National Taiwan University (fetch-tool summary); D. Briggs and M. P. Seah, Practical Surface Analysis, Vol. 1, 2nd ed., Wiley 1990; B. R. Strohmeier, Surf. Interface Anal. 15, 51 (1990); C. D. Wagner et al., Surf. Interface Anal. 3, 211 (1981); S. Tanuma, C. J. Powell and D. R. Penn, TPP-2M IMFP formula (background knowledge; not opened); EAG Laboratories, ‘X-ray Photoelectron Spectroscopy (XPS)’ technique note M-067322 (fetch-tool summary).

References

R. Smart, S. McIntyre, M. Bancroft, I. Bello and others, “X-ray Photoelectron Spectroscopy,” lecture slides, City University of Hong Kong and Surface Science Western. Available: https://www.hic.ch.ntu.edu.tw/PES/file/%E5%8F%83%E8%80%83%E8%B3%87%E6%96%99/XPS_Slides.pdf
D. Briggs and M. P. Seah, Practical Surface Analysis, Vol. 1, 2nd ed., Wiley, 1990; B. R. Strohmeier, Surface and Interface Analysis, vol. 15, p. 51, 1990; C. D. Wagner et al., Surface and Interface Analysis, vol. 3, p. 211, 1981; S. Tanuma, C. J. Powell and D. R. Penn, TPP-2M inelastic mean free path formula (cited from background knowledge).
EAG Laboratories, “X-ray Photoelectron Spectroscopy (XPS),” technique note M-067322. Available: https://www.eag.com/wp-content/uploads/2022/12/M-067322-XPS_w.pdf
Physical Electronics, “StrataPHI part 3.” Available: https://phi.com/news-and-articles/strataphi-part-3.html

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X-Ray Photoelectron Spectrometer (XPS)