Due to its unique capability of providing near-quantitative compositional and layer structure information during depth profiling analysis, in favourable cases, with sub-nanometre resolution,medium energy ion scattering (MEIS) is becoming increasingly important to the characterisation of microelectronic device structures in which scaling laws have demanded the growth and doping of layers of nanometre thickness. Here we assess the quantitative accuracy in terms of both depth and concentration, that can be achieved in MEIS depth profiling

Bailey, P.

Reading, M. A.

Rossall, A. K.

Van den Berg, J. A.

Zalm, P. C.

University of Huddersfield Repository

University of Huddersfield RepositoryVan den Berg, J. A., Zalm, P. C., Bailey, P., Rossall, A. K. and Reading, M. A.Quantitative considerations in Medium Energy Ion ScatteringOriginal CitationVan den Berg, J. A., Zalm, P. C., Bailey, P., Rossall, A. K. and Reading, M. A. (2016) Quantitative considerations in Medium Energy Ion Scattering. In: High Resolution Depth Profiling Conference (HRDP08), 7th­11th August 2016, Western University, London, Ontario, Canada. (Unpublished) This version is available at http://eprints.hud.ac.uk/id/eprint/29643/The University Repository is a digital collection of the research output of theUniversity, available on Open Access. Copyright and Moral Rights for the itemson this site are retained by the individual author and/or other copyright owners.Users may access full items free of charge; copies of full text items generallycan be reproduced, displayed or performed and given to third parties in anyformat or medium for personal research or study, educational or not­for­profitpurposes without prior permission or charge, provided:• The authors, title and full bibliographic details is credited in any copy;• A hyperlink and/or URL is included for the original metadata page; and• The content is not changed in any way.For more information, including our policy and submission procedure, pleasecontact the Repository Team at: E.mailbox@hud.ac.uk.http://eprints.hud.ac.uk/Quantitative considerations in medium energy ion scatteringP.C. Zalma, P. Baileya, M. A. Readingb, A. K. Rossalla, and J. A. van den Berga*. a International Institute for Accelerator Applications, School of Computing and Engineering, University of Huddersfield, Huddersfield, HD1 3DH, UK.b Physics and Materials Research Centre, University of Salford, Salford, M5 4WT, UK.*Contact: j.vandenberg@hud.ac.ukIntroductionDue to its unique capability of providing near-quantitative compositional and layerstructure information during depth profiling analysis, in favourable cases, with sub-nanometre resolution,medium energy ion scattering (MEIS) is becoming increasinglyimportant to the characterisation of microelectronic device structures in whichscaling laws have demanded the growth and doping of layers of nanometrethickness. Here we assess the quantitative accuracy in terms of both depth andconcentration, that can be achieved in MEIS depth profiling.Contact:   j.vandenberg@hud.ac.ukSpectrum	simulation	&	Experimental	confirmationMore	complex	layer	systems	can	only	be	effectively	interpreted	using	computer	sim-ulation of	spectra.	The	simulation	model	used	at	IIAA, based	on	the		IGOR	graphing	software	incorporates	the	corrections	considered	above.	Its	outputs	are	the	fitted	spectra	and	best	fit	depth	profiles	of	species	in	a	layer.	In	all	cases	depth	scales	have	been	used	which	require	assumptions	re	the	correct	densities	of	atom	species.	Layer	thickness	and	composition	compare	well	with	reference	data,	as	shown					↩Combined	Screening	&	Neutralisation	correctionCorrection	curves	for	50,	100	and	200keV H+ &	He+	ions	scattered through	90o	(at	surface)	off	target	atom	number	ZtFor	H:	correction			≲10%For	He:	correction	≲20%Overall	correction	is	mass	and	energy	dependent	and	needs	to	be	included	to	yield	quantitative	data.Combining	the	screening	and	neutralisation corrections	gives	correction	curves	for	the	Rutherford	X-section	as	a	function	of	target	atom	number,	normalised to	1	for	SiThe	absolute	backscattering	yield	of	target	atoms	at	a	depth	x		in	a	homogeneous	target	is	according		to	Chu	et	al.	(Backscattering	Spectrometry,	1978)𝐻 𝑬𝒐𝒖𝒕 = 𝜎 𝑬 Ω Φ	 𝑫𝛆 𝑬 𝒄𝒐𝒔 𝜽𝒊𝒏 𝛆 𝑲𝑬𝛆 𝑬𝒐𝒖𝒕 																																(3)where	Eout is	the	energy	at	the	detector	after	scattering	off	a	target	atom	at	depth	x,	E is	the	energy	immediately	before	scattering	at	that	depth,	σ(E)	the	energy-dependent	Rutherford	scattering	cross	section,	Ω	the	detector	acceptance	angle,	Φ the	total	number	of	incident	particles,	D the	detector	energy	bin	or	channel	width,	e the	stopping	cross	section,	and	K the	kinematic	factor	for	the	scattering	geometry	adopted.	[ε(E)]	is	called	the	stopping	cross-section	factor	(Chu	et	al.):𝜺 𝑬 = 	 𝑲𝒄𝒐𝒔𝜽𝒊𝒏 	 𝟏𝑵 𝒅𝑬𝒅𝒙7𝑬 + 𝟏𝒄𝒐𝒔𝜽𝒐𝒖𝒕 	 𝟏𝑵 𝒅𝑬𝒅𝒙7𝒌𝑬 (4)The	term	D is	given as: 𝑫 = 𝜺(𝑬) 𝑵𝝉																																																						 (5)N is	the	atom	density	and t the	thickness	of	the	surface	layer	across	which	an	ion	will	lose	the	energy	equivalent	to	the	width	of	a	single	bin	within	the	detection	system.For	scattering	at	the	top	surface	E	=	E0 and	Eout =	KE0 so	that	the	final	term	in	eq.	(3)	disappears;	the	yield	off	the	surface	is	then:𝑯 𝑲𝑬𝟎 = 𝝈 𝑬𝟎 	𝛀	𝚽 𝑫[𝜺 𝑬𝟎 ]	𝒄𝒐𝒔𝜽𝒊𝒏 (6)The	change	in	yield	due	to	scattering	off	atoms	at	depth	x as	a	ratio	to	scattering	off	atoms	at	the	surface	follows	directly	as:𝑯(𝑬𝒐𝒖𝒕)(𝑯(𝑲𝑬𝟎)) = 	 𝝈(𝑬)𝝈(𝑬𝟎)	 . [𝜺 𝑬𝟎 ][𝜺 𝑬 ] 	 . 𝜺 𝑲𝑬𝜺 𝑬𝒐𝒖𝒕 		 (7)as	long	as		the	detector	channel	width	D	is	independent	of	energy (as	in	RBS	- surface	barrier	detectors).	Factors	like	Ω,	Φ and	cosθin have	cancelled	in	eq.	(7).	The	Rutherford	cross	section	is		σ∝ E-2.	The	scattering	geometry	dependent	stopping	cross	section	factors	[ε],	are	defined	in	eq.	(4);	again	constants	such	as	the	atomic	density	are	ignored	in	this	analysis	which	is	permissible	since	only	ratios	of	either	ε’s	or	[ε]’s	are	considered	here.	The	benefit	of	the	power	law	eq.(1)	is	now	clear	since:[𝜺 𝑬𝟎 ][𝜺 𝑬 ] = 𝑬𝟎𝑬 𝑩				and 𝜺 𝑲𝑬𝜺 𝑬𝒐𝒖𝒕 	= 𝑲𝑬𝑬𝒐𝒖𝒕 𝑩		so	that	eq.	(7)	reduces	to: 𝑯(𝑬𝒐𝒖𝒕)𝑯(𝑲𝑬𝟎) = 		 𝑬𝟎𝑬 𝟐 . 	 𝑲𝑬𝟎𝑬𝒐𝒖𝒕 	𝑩	 (8)I.e.	deviations	from	the	energy	dependence	of	the	yield	according	to	the	Rutherford	prediction	(1st term	eq.	(8))	scale	with	the	inverse	ratio	of	the	energies	at	the	detector(Eout)	to	a	power	B » ½	(2nd term	eq.	(8)).	B	depends	mainly	on	energy,	little	on	material	type.	Acquisition	software	makes	D	independent	of	E	in	our	MEIS	instrument.	Using	eq.2	for	the	previous	example	we	get: H(x)/H(0)	=	1	+	0.0055x	i.e <	1%	/nmSlope	varies	with	geometry	but	is	almost	independent	of	atom	type.	Peakheights ratiosThe	energy	lossInelastic	energy	loss	to	depth	scale	conversion		Depth	scales	in	MEIS	are	derived	from	the	inelastic	energy	loss	of	the	scattered	projectiles	on	the	way	in	and	out.	NB.• The	near-linear relationship	between	KEin-Eout &	depth (for	depths	≤40	nm)• Substantial	differences	between	slopes	for	Si	,	As	and	O	by	up	to	15%Approach	is	also	valid	for	compounds.	For	multilayered	samples,	A	will	be	different	for	each	layer	but	B	changes	little;		but	now	computer	simulations	are	required.The	energy	loss	rate	dE/dx	is	dependent	on	the	energy	of	the	projectile	and	can	be	obtained	from	SRIM	calculations,	shown	for	for	H+&	He+.For	the	energies	used	in	MEIS	the	electronic	loss	rates	can	be	well	approximated	by	a	power	law:−𝒅𝑬𝒅𝒙 = 𝑨𝑬𝑩																							(1)e.g.	low	E	approx.	(40-100	keV)A=	0.043,	B	=	0.58	(	1%)or:	high	E	approx.	(80-200	keV)A=	0.0248,	B=	0.46	(	1%)NB.	dE/dx in	keV/nm,	E in	keV.Eq.(1)	enables	a	fully	analytical	conversion	of	inelastic	energy	loss	to	pathlength:𝒑𝒂𝒕𝒉𝒍𝒆𝒏𝒈𝒕𝒉 = 	∫ 𝟏Q𝒅𝑬 𝒅𝒙R𝑬𝒇𝒊𝒏𝒊𝒔𝒉𝑬𝒔𝒕𝒂𝒓𝒕 	𝒅𝑬 = 𝟏𝟏U𝑩 𝑨 𝑬𝒔𝒕𝒂𝒓𝒕𝟏U𝑩 − 𝑬𝒇𝒊𝒏𝒊𝒔𝒉𝟏U𝑩 (2)Example:	100	&	200	keV He+ ions	incident	on	a	28Si	(100)	surface,	containing	O	and	As;	Θ =	90o;	Θ1 =	35.26o &	Θ2=	54.74o.	Apply i)	eq.(2)	on	the	way	in,	then	ii)	the	kinematic	factor	K	(Θ =	90o)K=(Mtarget-Mion)/(Mtarget+Mion)and	finally	iii)	eq.	(2)	on	the	way	out,	This	gives	 kEin–Eout vs	depth	to	40nm(using	a	Si	density	of	5	x	1022 at/cm3)0 5 10 15 20 25 30 35 40051015202530100 keV He kEin- Eout (keV)Depth (nm) DE  As DE  Si DE  O DE  As DE  Si DE  O200 keV He50 100 150 200100150200250300  dE/dx (eV/nm) Energy (keV) dE/dx SRIM LE approx  HE approxHe+         Si10 100 10000510152025303540  dE/dx (eV/Ang)Energy (keV) (dE/dx) inelHe          SiH         Si      MEIS  Energy range50 60 70 80 90 1000200400600800100012001400  Scattering yield (cts)Energy (keV) MEIS data SimulationN O SiTiSr(a)STO(Sr rich)/TiN/SiExperimental	validationTiN layer:	2.6	nm;	Ti:N =	1:1	away	from	top	oxideSTO	layer:	2.3	nm;	TiN layer:	2.9	nmSr/(Sr+Ti)	=	0.6				cf.	RBS:	0.62HfO2 layer:	1.6	nm	- 1.75	nm	Hf:O =	1:2	stoichiometric	(≤ 2%) HfSiO2 layer:	1.4	nm	- 1.6	nmHf:Si =	0.6/0.4	(≤ 2%)0 1 2 3 4 5 6 7 8 9 100.00.20.40.60.81.0  Atomic fractionDepth (nm)  Sr N Ti  O SiNominal structureSTO TiN SiSTO (Sr rich)          TiN                 Si(100)   3 nm                       3 nm (b)0 1 2 3 4 5 6 7 8 9 100.00.20.40.60.81.0  Atomic fractionDepth (nm) Ti N O SiTiN SiTiO2Nominal structureTiN                   SiO2    Si(100)3 nm                1 nm (b)50 60 70 80 90 10005001000150020002500  Scattering Yield (cts)Energy (keV) MEIS data SimulationNO SiTi (a)TiN/SiO2/Si70 75 80 85 90 95 10005000100001500020000 (a)  Scattering yield (cts)Energy (keV) MEIS data SimulationHfx10HfO2/SiO2/ Si OSi0 1 2 3 4 5 6 7 80.00.20.40.60.81.0  Atomic fractionDepth (nm) Hf Si OHfO2 SiO2 Si(b)HfO2           SiO2       Si(100)    2 nm          1 nm    Nominal layer structure:65 70 75 80 85 90 95 10005000100001500020000  Scattering yield (counts)Energy (keV) MEIS data SimulationHfx10Hf0.6Si0.4O2/SiO2/SiOSi(a)0 1 2 3 4 5 6 7 80.00.20.40.60.81.0Nominal layer structure:  Atomic fractionDepth (nm) Hf Si OHfSiOx SiO2 Si(b)HfSiO2          SiO2     Si(100)2 nm            1 nm    0 10 20 30 40 50 60 70 80 900.70.80.91.01.11.2HfLaAuRuAsCoNaOCSi  Normalised screening * ionisation factorAtomic number Zt 50 keV H 100 keV H 200 keV H 50 keV He 100 keV He 200 keV He He  and H scattering through 90oIn	MEIS	the	velocities	of	the	H+ or	He+	ions	are	moderate	and	a	fraction	of	the	scattered	projectiles	leave	the	surface	neutralised.	When	using	electrostatic	analysers	(unlike	for	TOF	ones)	these	particles	are	not	counted,	but	cannot	be	ignored	in	quantitative	analysis.	Fractions	of	particles	leaving	ionised	are	not	generally	accurately	known.	Shown	beloware	data	measured	by	various	groups	for	H	and	He	projectiles	as	as	a	function	of	energy.Neutralisation	correctionFOM	group	data	library	of	50	sets	at	5	different	energies	(collated	by	Bailey)(no	clear	dependence	on	target	atom)Kido	group	(Kitsudo et	al.	NIMB	267,	(2009)	566	)	(some	dependence	on	target	atom	and	exit	angle)Rutgers	group	(Busch,	Doctor	thesis)Also	Marion	&	Young,	calculationsGeneral	form	for	effective	ion	survival	probability	as	function	of	energy	Ebased	on	available	data	(lines,	Bailey):𝑷𝒊𝒐𝒏 = 𝟏 − 𝒆U𝜶𝑬          (13)For	H: 	𝛼 = 0.019 /keV	For	He		𝛼 = 0.0064 /keVP ion	for	for	H+ &	He+	ion	scattering	through	90o	(at	the	surface)	as	function	of target	atom	number	ZtAlso	100	keV He	from	depth	40nm0 20 40 60 800.40.50.60.70.80.91.0 Normalised ionisation factorAtomic number Zt H 50 keV H 100 keV H 200 keV He 50 keV He 100 keV He 200 keV 40 nm surf40 60 80 100 120 140 160 180 2000.00.20.40.60.81.0   Ion fractionEnergy (keV) H FOM H eq. (13) H Kitsudo H Rutgers  He FOM He eq. (13) He Si  Kitsudo He SiO2 Kitsudo He HOPG Kitsudo He Ni Kitsudo He Au Kitsudo H Marion & Young He Marion & YoungvbvScreening	correctionIn	the	MEIS	energy	regime	the	nuclei	are	partially	screened	during	the	interaction.	The	Rutherford	scattering	cross	section	is	not	exactly	valid	and	need	a	correction.	Following	Andersen	[Phys	Rev	A21	(1980)1891]	for	a	screened	Coulomb	potential:𝑉 𝒓 = 𝒁𝒊𝒁𝒕𝒆𝟐𝒓 𝛗 𝒓𝒂 (9)Zi and	Zt are	the	atomic	numbers,	𝜑	(r/a)	is	the	so-called	screening	function	and	a	is	 the	screening	length,	that	depends	on Zi and Zt .	At	r	=0,	𝜑	=1	(Coulomb	pot.).	Expanding	𝜑 near	r	=0	to	first	order	in	a	Taylor	series	yields:𝝋 𝒓𝒂 ≈ 𝟏 + 𝒓𝒂	?̇?(𝟎) (10)with	?̇? 0 	the	gradient	of	the	screening	function	r	=	0.	Inserting	eq.	(10)	into	eq.	(9)	gives: 𝑉 𝒓 = 𝒁𝒊𝒁𝒕𝒆𝟐𝒓 	+𝒁𝒊𝒁𝒕𝒆𝟐𝒂 =	𝑽𝒄𝒐𝒖𝒍𝒐𝒎𝒃+ 	𝑽𝒄𝒐𝒏𝒔𝒕																								 (11)	?̇? 0 is	negative;	screening	decreases the	Coulomb	potential	by	a	constant	amount.	Andersen	et	al.	incorporated	this	by	increasing the	kinetic	energy	of	the	projectile	in	the	CoM system	by	exactly	the	same	amount.	E is	now	replaced	by	 E+Vconst in	the	Rutherford	cross	section.		The	net	effect	is	to	decrease	the	scattering	cross	section	progressively	with	increasing	Zt.	In	the	CoM system	the	screening	correction	factor Pscr can	now	written	as:𝑷𝒔𝒄𝒓 ≡ 𝝈(𝑬𝟎q𝑽𝒄𝒐𝒏𝒔𝒕)𝝈(𝑬𝟎) = (𝟏 + 𝑽𝒄𝒐𝒏𝒔𝒕𝑬𝟎 )U𝟐≈ 𝟏 − 𝒇 𝒁𝒊𝒁𝒕𝑬𝟎 (12)Example:• 100	keV He+	ions	scattered	off	surface	C	to	Bi	(Zt=	6-83) @	60.5o,	90o and	125.26o.• 100	keV He+	ions	@	90o off	depth	40	nm• 50	keV H+ ions	@	90ousing	the	Biersack-Ziegler	universal	potential	(5x)	and	Lens-Jensen	(L	J)	1x.NB:	• Pscr depend	almost	linearly	on	Zt• Pscr is	similar	for Zt/E0 =	constant	(cf.	50	keV H+ similar	to	100	keV He+).• 𝒇	is	almost	constant and	depends	mainly	on	choice	of	potential	(e.g.	L	J)• 𝒇 depends	weakly	on	scattering	angle	and	depth.• 𝒇	=	0.16	±	0.04	(max	intrinsic	error)0 10 20 30 40 50 60 70 800.750.800.850.900.951.00  Screening correction factorAtomic number Z 90 deg 60.5 deg 125.26 deg 40 nm LJ H 50 keVConclusions• the	MEIS	yield	ratio	of	particles	scattered	off	surface	atoms	to	those	at	depth	x	is	given	by	the	Rutherford	E-2 prediction	*	the	inverse	ratio	of	the	particle	exit	energies	to	a	power	B.• The	impact	of	screening	of	the	potential	on	the	backscattering	yield	in	MEIS	has	been	evaluated	for	H+ and	He+ ions	at	different	energies	using	the	Andersen	approach.	For	a	fixed	beam	energy	the	screening	correction	depends	mainly	and	almost	linearly	on	Zt• Using	experimental	neutralisation	data	convolved	with	the	screening	correction	leads	to	a	correction	factor	to	the	Rutherford	backscattering	cross	section	ratio.	Its	dependence	on	both	projectile	energy	and	the	atomic	number	of	the	scattering	atom	is	presented.• This	approach	has	been	validated	for	a	number	of	representative	examples	that	yield	quantitative	depth	profiles	derived	from	MEIS	spectra	of	nanolayers.	• Although	absolute	quantification	especially	when	using	He	ions,	may	not	always	be	achievable,	relative	quantification	in	which	all	species	in	a	layer	add	up	to	100%,	is.• Elastic	energy	lossyields	the	mass of	the	atom	scattered	off• Inelastic	energy	loss within	the	sample	enables	depth	analysisMEIS	basicsBackscattering	of	50	- 200	keV H+ or	He+ ions	off	shallow	implants,	nanometre thin	overlayers and	thin	films	on	top	of	a	Si	(100)	surface.Detectorx

Quantitative considerations in Medium Energy Ion Scattering

Abstract

Similar works

Full text

Available Versions

University of Huddersfield Repository