High-esolution XD
Wht is thin film/lyer? Mteril so thin tht its chrcteristics re dominted primrily by two dimensionl effects nd re mostly different thn its bulk properties Source: semiconductorglossry.com Mteril which dimension in the out-of-plne direction is much smller thn in the in-plne direction. A thin lyer of something on surfce Source: encrt.msn.com
Epitxil yer A single crystl lyer tht hs been deposited or grown on crystlline substrte hving the sme structurl rrngement. Source: photonics.com A crystlline lyer of prticulr orienttion on top of nother crystl, where the orienttion is determined by the underlying crystl. Homoepitxil lyer the lyer nd substrte re the sme mteril nd possess the sme lttice prmeters. Heteroepitxil lyer the lyer mteril is different thn the substrte nd usully hs different lttice prmeters.
Accessible Informtion to X-ry Diffrction Definition for structurl types Structure Type Definition Perfect epitxil Nerly perfect epitxil Textured epitxil Textured polycrystlline Perfect polycrystlline Amorphous Single crystl in perfect registry with the substrte tht is lso perfect. Single crystl in nerly perfect registry with the substrte tht is lso nerly perfect. yer orienttion is close to registry with the substrte in both inplne nd out-of-plne directions. yer consists of mosic blocks. Crystlline grins re preferentilly oriented out-of-plne but rndom in-plne. Grin size distribution. ndomly oriented crystllites similr in size nd shpe. Strong intertomic bonds but no long rnge order. P.F. Fewster X-ry Scttering from Semiconductors
Accessible Informtion to X-ry Diffrction Defects tht re common in epilyer structures
Wht we wnt to know bout thin films? Crystlline stte of the lyers: Epitxil (coherent with the substrte, relxed) Polycrystlline (rndom orienttion, preferred orienttion) Amorphous Crystlline qulity Strin stte (fully or prtilly strined, fully relxed) Defect structure Chemicl composition Thickness Surfce nd/or interfce roughness
Accessible Informtion to X-ry Diffrction Structurl prmeters tht chrcterize vrious mteril types Thickness Composition elxtion Distortion Crystlline size Orienttion Perfect epitxy Defects Nerly perfect epitxy Textured epitxy Textured polycrystlline Perfect polycrystlline Amorphous prmeters tht hve mening prmeters tht could hve mening
Accessible Informtion to X-ry Diffrction
Mismtch Consider two mterils with the sme spce group, sme tomic rrngements, but slightly different lttice prmeters nd elstic prmeters. c S S = S S S Before deposition After deposition
Mismtch The pek seprtion between substrte nd lyer is relted to the chnge of interplnr spcing norml to the substrte. If it is 00 reflection then the experimentl x-ry mismtch : S S d d d d d m* True lttice mismtch is: s s m eltionship: 1 1 m* m Poisson rtio 2 * 3 1 m m ll = S S S
elxtion The problems occur when the elstic prmeters re incpble of ccommodting the distortions necessry for perfect epitxy. Fully or prtilly relxed Fully or prtilly relxed nd tilted c c S S S S
Tetrgonl Distortion ttice mismtch between cubic lttice prmeters: S S Strined, coherent, pseudomorphic c S 0 S S Prtilly relxed S S elxed Before deposition 0 ttice mismtch induces lttice strin: zz d d d After deposition S S
elxed yer (00l) (10l) (20l) (000) (100) (200) Cubic: > S Cubic
Strined yer (00l) (10l) (20l) (000) (100) (200) Tetrgonl: II = S, > S Tetrgonl distortion Cubic
Perfect yers: elxed nd Strined (00l) (00l) eciprocl Spce (hkl) (hkl) (000) (000) Cubic > S Tetrgonl Cubic Cubic
Strin zz d z d d z z SiGe(004) Si(004) xx d x d d x x yy d y d d y y zz zz 1 2 1 xx ve yy F. C. Frnk nd J. H. vn der Merwe, Proc.. Soc. ondon, Ser. A 198, 216 (1949).
Composition Vegrd's lw Vegrd s lw sttes tht the lttice prmeter of substitutionl solid solution vries linerly between the lttice prmeter vlues for the components. The composition is expressed in tomic percentge. A B xa (1 x) x 1 x B
Composition B A B B A B A B A x x x x x x x 1 1 ) (1 For Si 1 x Ge x : Gex Si 1 x = x Ge + 1 x Si + 0.007 2x 1 2 1 Si(004) SiGe(004) S S S z S z S z S S S S d d d m m m sin sin sin * 1 1 *
Brgg s lw: Si(004) 2dsinθ = λ SiGe(004) For out-of-plne lttice prmeter: c = ld hkl d hkl = λ 2sinθ θ = θ S + Δθ θ S cn be clculted from Brgg s lw knowing s = 5.431 A
yer Tilt If the lyer is tilted reltive to the substrte then this will result in shift of the lyer pek reltive to tht of the substrte. This is not connected with the composition. The resulting lyer pek splitting will depend on: mismtch pek splitting δθ tilt ngle rottion ngle If specimen is rotted by ngle bout its norml the lyer pek will be displced by: αcosφ cos 0 180 0 cos 180 Then true splitting mismtch: 0 180 2
yer elxtion Our lyer is completely coherent. In this cse it is enough to mesure misfit only long (00l ) direction. Prtilly or fully relxed lyers. We need to mesure misfit prllel to the interfce s well s perpendiculr. For this we need n symmetric reflection (e.g. 224, 113).
yer elxtion The effect of tilt on the pek splitting is reversed if the specimen is rotted by 180 o bout its surfce norml. The splitting due to mismtch will not be ffected by such rottion. We cn mke grzing incidence or grzing exit mesurements to seprte the tilt from the true splitting.
elxtion The resulting mesured splittings re now different between these two geometries: gi ge grzing incidence grzing exit We need to know the lttice prmeter of the lyer prllel nd perpendiculr to the substrte:, b, nd c. From these we my clculte the relxtion nd the fully relxed lttice prmeter S. Consider = b (tetrgonl distortion). S S ngle between reflecting plne nd the surfce
elxtion sin 2 1 2 2 2 2 2 2 d c l k h d hkl Using interplnr spcing eqution nd Brgg lw: we obtin cell constnts for the lyer (001 oriented): 2 2 2 sin 2sin cos 2sin l k h l l c
elxtion The relxtion is defined s: 100 x x x x S S x the fully relxed in-plne lttice prmeter of the epilyer. 1 2 1 x x x x z x is the vlue tht is used in Vegrd s lw to find the composition of the epilyer. yy xx zz 1 1 2 1 1 2 x z x For cubic lttice: yy xx x zz z nd Then:
Substrte misorienttion Substrtes re often specified t some ngle from (001) or (111). This my need to be verified. 1 2 ottion of the surfce plne through 180 o between mesurements 1 2 2 If we do mesurements t 0 o nd 180 o to get 0 nd t 90 o nd 270 o to get 90, then mximum mx is given by: mx rctn tn 2 0 tn 2 90 mx rctn tn90 tn 0
Determintion of Thickness Interference fringes observed in the scttering pttern, due to different opticl pths of the x-rys, re relted to the thickness of the lyers. t 1 n1 n2 n1 n2 ~ 2 sin sin 2 cos 2 1
Determintion of Thickness Interference fringes observed in the scttering pttern, due to different opticl pths of the x-rys, re relted to the thickness of the lyers. t 1 n1 n2 2 sin sin 2 Substrte yer Seprtion S-pek: -pek: Seprtion: Omeg( ) 34.5649 Omeg( ) 33.9748 Omeg( ) 0.59017 2Thet( ) 69.1298 2Thet( ) 67.9495 2Thet( ) 1.18034 yer Thickness Men fringe period ( ): 0.09368 Men thickness (um): 0.113 ± 0.003 2Thet/Omeg ( ) Fringe Period ( ) Thickness (um) 66.22698-66.32140 0.09442 0.111637 66.32140-66.41430 0.09290 0.113528 66.41430-66.50568 0.09138 0.115481 66.50568-66.59858 0.09290 0.113648 66.59858-66.69300 0.09442 0.111878 66.69300-66.78327 0.09027 0.117079
Are Homogeneity Whtever the crystl growers clim, epitxil lyers re not uniform cross their re. 1% consistency is good. 33 grid 99 grid Surfce mesh plot showing the vrition of In content in n InAlAs lyer on GAs
Mterils eserch Diffrctometer Triple xis pth Hybrid monochromtor Open detector pth
Mterils eserch Diffrctometer Six Motorized Movements of MD Crdle
High-esolution Diffrctometry Schemtic of high resolution double-xis instrument
High-esolution Diffrctometry Brtels
High esolution Geometry Incident Bem: X-ry Hybrid Monochromtor Prbol F = 0.5 o < 19 rcsec Mirror Ge(220) Crystl Smple
Scn Directions eciprocl ttice Point s s0 2 sin * dhkl d sin 2 hkl 1 d hkl Diffrcted bem s λ Scttering vector s s 0 λ s 0 λ Incident bem (00l) (00l) scn (00l) (00l) scn (hkl) (-hkl) (h00) scn (hkl) Symmetricl Scn Asymmetricl Scn (000) elxed yer (h00) (000) Strined yer
Scn Directions (00l) (hkl) Symmetricl Scn - 2 scn Asymmetricl Scn - 2 scn Smple Surfce 2 2
Scn Directions (00l) (hkl) Smple Surfce
Scn directions (00l) (hkl) scn scn 2 scn Symmetricl - 2 scn Asymmetricl - 2 scn Smple Surfce
eciprocl Spce for Si(001) Along Si[100] Along Si[110]
eciprocl Spce -scn is in the direction of n rc centered on the origin 2-scn is n rc long Ewld sphere circumference -2 scn is lwys strit line pointing wy from the origin of the reciprocl spce
elxed SiGe on Si(001) Shpe of the P might provide much more informtion
-2 direction (00l) Defined by receiving optics (e.g. slits) direction Mosicity (000)
Symmetricl Scn nlyzer crystl -2 direction (00l) nlyzer crystl direction receiving slit receiving slit d-spcing vrition (000) mosicity
(002) SrTiO 3 With receiving slit With chnnel nlyzer (220) SruO 3
el P shpes Finite thickness effect c < S S Heteroepitxy Compressive stress Heteroepitxy Tensile stress Homoepitxy d-spcing vrition Heteroepitxy Mosicity
(00l) (00l) (hkl) (hkl) (000) Prtilly elxed (000) Prtilly elxed + Mosicity
Mosic Spred nd terl Correltion ength The Mosic Spred nd terl Correltion ength functionlity derives informtion from the shpe of lyer pek in diffrction spce mp recorded using n symmetricl reflection 2 q 3 x q 2 z q z q x x q x q z 2 1 2 2 3 1 cos x cos x 3 sin cos x nd 1 q x tn qz 1 x qx tn qz (000) terl correltion length Microscopic tilt 1 1 2 2 2 q x q z