Stress State Determination in Nanoelectronic Silicon Devices Coupling COMSOL Multiphysics and a Recursive Dynamical CBED Pattern Simulation

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1 Excerpt from the Proceedngs of the COMSO Conference 2008 Hannover Stress State Determnaton n Nanoelectronc Slcon Devces Couplng COMSO Multphyscs and a Recursve Dynamcal CBED Pattern Smulaton A. Spessot* 1,2, S. Frabbon 1, A. Armglato 3 and R. Balbon 3 1 Numonyx, Advanced R&D, NVMTD-FTM, Va Olvett 2, Agrate Branza (Italy) 2 Natonal Research Center S3, CNR-INFM and Department of Physcs, Unversty of Modena e Reggo Emla, Va G. Camp 213/A, Modena, (Italy) 3 CNR-IMM Secton of Bologna, Va P. Gobett 101, Bologna, (Italy) *Correspondng author: alesso.spessot@numonyx.com Abstract: Straned technology s beng promoted as the best way to extend the performance of semconductor transstors. An nhomogeneous layer deposted on top of a slcon devce can nduce a strong modfcaton n the real slcon stran state, and consequently n ts electronc performance. Couplng the fnte elements analyss done by COMSO wth a recursve CBED and ACBED dynamcal smulaton, we are able to explan the observed dffracton pattern modfcaton, reconstructng the stran feld n the devce. Keywords: Straned slcon technology, devce, CBED, ACBED, TEM 1. Introducton Straned technology s beng promoted as the best way to extend the performance of semconductor transstors, and the downscalng of the slcon technology contnues the shrnkng of the devce geometry. hen the devces are straned by a non unform stressor source, the usual process devce smulators are no more able to descrbe the stran dstrbuton, and a more accurate descrpton of the resultng stran dstrbuton s requred. Ths s the case of almost all the recent mcroelectronc devces, where the actual dmensons are reduced down to 45 nm and even below for both memory cell elements and transstor devce [1]. To mprove ther performance, the straned slcon technology s currently used by the electronc ndustres [2]. The most used stressor sources are ether the lateral stran elements (.e.: SC or SGe source and dran contact) or the deposted-on-top stressor layer (.e.: tensle or compressve ntrde layer). An example of stressed devce s gven n Fg. 1, whch shows a sketch of the slcon substrate and the stressor source. The acronym CBED and ACBED refer to two TEM methods of electron dffracton and wll explaned n the followng. The correspondng electronc devce s vsble n Fg. 2 and. In ths knd of problem, a mere process devce smulaton s not Stressor sources Gate ACBED data drecton Slcon substrate CBED data drecton STI Source Slcon substrate Dran STI Fg. 1 A sketch of the analyzed sample, wth the stressor sources on top of the slcon substrate Fg. 2 A lateral and a top vew of the electronc devce; the man electronc elements are evdenced, as the geometrcal dmensons (wdth, length )

2 accurate enough to reproduce the stran feld, and an expermental method should be employed. 2. Expermental problems It has been recently proved that quanttatve stran mappng can be expermental obtaned by the Convergent Beam Electron Dffracton (CBED) technque of the Transmsson Electron Mcroscopy (TEM). Ths technque [3] s based on the analyss of dffracton lnes, called HOZ (Hgh Order aue Zone), whch are very senstve to the varaton n the crystal lattce parameters: a spatal resoluton n the nanometre range s feasble, [4], even n the case of hghly straned samples [5], lke the one presented n Fg. 1. Furthermore, n ths case the lnes are splt n two components, whch must be ftted to a computer smulated pattern. To perform the smulatons, a model of the nduced deformaton s needed. e set up a recursve approach, based on the refnement of some parameters nvolved n the dsplacement smulaton, untl the reconstructon of the observed sample s reached. An expermental vew of the stressng layer deposted on top of the substrate s gven by Fg. 3: four gran boundary nterfaces, generatng the dsplacement feld n the underlyng slcon, are vsble. In Fg. 4a) s presented an example of expermental pattern, wth the correspondng smulaton n Fg. 4b). An addtonal dffculty s gven by the requrement for the TEM/CBED analyss of a thnned sample, that should be transparent to the electron beam. After the thnnng, the stran state of the sample can be modfed by the elastc relaxaton wth respect to the orgnal bulk-lke case (whch s our real nterest). Therefore, to reconstruct the real sample confguraton before the thnnng, we need also addtonal nformaton from a lateral vew, coupled wth a recursve smulaton of ths case. The expermental pattern should be acqured wth a bgger feld of nvestgaton, whle a smaller resoluton s allowed. 3. Governng Equatons 3.1 Thn sample stran state The modelng of the thnned sample starts from the reproducton of the stressor source n the expermental slce. e modeled the dfferent stran state of the stressor layer onto the slcon substrate usng the Structural Mechancs Module. The deformaton nduced n the slcon substrate by the gran boundares (shown n Fg. 3) are well descrbed by a lattce msmatch [6]. e reproduced the morphology of the expermental sample observed n the TEM mage, then we used a statc analyss of a thermal relaxaton. e recursvely adjusted some selected parameters (thermal expanson coeffcents, geometrcal parameters) for the varous elements nvolved, n order to reproduce the stran state of the devces. By ths way, we obtan the nput for the Fg. 3 A strpe of gran boundary, whch are the nduced deformaton sources. The bamboo-lke dstrbuton s clearly vsble; four nterfaces between adjacent grans are shown by the arrows. Fg. 4 a) A detal of an expermental CBED pattern, ncludng splt dffracton lnes, and b) the correspondng smulaton, resultng from the recursve stran feld reconstructon.

3 calculaton of the recursve dynamcal CBED smulatons, n order to reproduce the expermental patterns n the 3D sample. e started assumng for the stressor source a purely radal shape (and consequently a radal deformaton). Then we ntroduced a more complex ellpsodal deformaton, adjustng the rato between the sem-axes. The resultng dsplacement feld, obtaned by COMSO, s shown n Fg Entre sample stran state reconstructon After the reproducton of the stran state n the thnned sample, we can ntate the reconstructon of the deformaton observed n the thck case. For these case, we should use the expermental nformaton taken from a dfferent vew of the sample, acqured wth the ACBED (arge Angle CBED) technque [7]. By ths method, we can obtan nformaton about the stran state from a larger area wth respect to the CBED technque. Startng from the reconstructed deformaton model n the thn sample, we use the expermental data acqured by ACBED n the lateral vew to extend the deformaton model n the 3D space, agan usng a recursve method. 4. Theory The deformaton nduced nto the substrate by the stressor source can be computed by usng a pseudo thermal expanson, assumng a lattce msmatch between the gran boundary and the substrate. The nduced stran s computed by the followng relaton: ε = α T where α s the thermal expanson coeffcent and T s the temperature varaton. In our case, we use a value of T=1K, and then we recursvely modfed the value of the parameter α. The relaton between the resultng stran components ε j and the dsplacement s calculated accountng for the large deformaton by the Green-agrange stran equaton: ε = j 1 ( 2 R R j R Rk (1) + + ) j k where the R represents the dsplacement components along the x drectons, and the thrd term takes nto account the non-lnearty. After the stran calculaton, we compute the stress n the materal usng the consttutve relaton: σ = Dε (2) where D s the 6x6 elastcty matrx and σ represents the stress tensor. 5. Numercal Model j Ry +1.5A 200-5A nm Fg. 5 Dsplacement feld reconstructed n the thnned sample. The vertcal component s shown. Exp. Sm. Fg. 6 a) Expermental, lateral vew of the sample. Two bendng of the Bragg contour (connected to the deformaton nduced n the crstallographc plane by the stressor sources) are evdenced by the red arrows. b) Correspondng smulaton, obtaned by the ACBED smulaton after the recursve reconstructon n the thck sample.

4 Channel Ry 4A Stress_ 0 Channel 1500 nm Bulk -9A Fg. 7 The resultng dsplacement feld obtaned by the presented method, dsplayed n the drecton. The green arrows ndcate the stressor source on top of the slcon substrate. The current flow occurs on top of the selected regon. 500 nm -1GPa Fg. 8 The resultng dsplacement feld obtaned by the presented method, dsplayed n the drecton, representng the startng pont for the calculaton of the moblty varaton. The green arrows ndcate the stressor source on top of the slcon substrate. A peak of compressve stress up to 1GPa s reached. The dsplacement deformaton nduced nto the thn sample are calculated by a 3D geometry, usng two dfferent elements: the stressor source and the substrate. The substrate was smulated usng the standard slcon propertes, wth the assumpton of the correct ansotropy of the elastc stffness n the dfferent used drectons. The stressor source was modeled wth an ellpsodal shape, nserted on the hghest part of the substrate, as presented n the sketch of Fg. 1. Dfferent confguratons of the stran source were used, untl the observed deformaton nduced nto the substrate are ftted. e analyzed dfferent thnned samples, wth thckness n the range between 400 and 500 nm (calculated n the drecton, see Fg. 1). Then we are able to reconstruct the thck sample also n the drecton (Fg. 1). The bulk-lke was smulated wth a 3D model, usng the same thckness of the thn sample and a lateral dmenson n the mcrometer range. 6. Results and Dscusson e found that the problem of the stran feld generated by a non homogeneous stressor layer n a slcon devce can be descrbed by an approprate seres of stressors, wth dfferent thermal relaxaton parameters. Frst, we reconstruct the straned confguraton of the thn sample, by usng an approprate recursve smulaton code for the HOZ pattern smulaton [8]. The good agreement between the expermental data of Fg. 4 and the correspondng smulaton of Fg. 4 s evdent. The resultng dsplacement feld s gven n Fg. 5. Then, we can reconstruct the complete real sample stran state, usng the nformaton of the lateral vew to recursvely reconstruct the expermental ACBED pattern of the thck sample. The results of the teratve procedure s vsble n Fg. 6, whch shows the expermental data (Fg. 6a) and the correspondng smulaton (Fg. 6b). The resultng dsplacement feld, obtaned by the COMSO smulaton, s gven n Fg. 7. From these results, the stress confguraton close to the nterface can be calculated, for both the and drectons (ndcated n the sketch of Fg. 1). By the stress feld computaton n the regon of the channel, the carrer moblty can be evaluated, gvng fundamental nformaton about the electronc performance of the devces. [9]. 8. Conclusons The varous components of the stran feld n the actve area of a straned slcon devce can be obtaned, couplng the fnte elements analyss by COMSO wth a recursve CBED pattern dynamcal smulaton. Startng from ths stress state results, the carrer moblty varatons can be calculated.

5 8. References 1. ITRS Roadmap 2007, 2. S.E.Thompson, G. Sun, Y.S. Cho, T. Nshda Unaxal process nduced straned S: extendng the CMOS roadmap, IEEE Trans. El. Dev., 53,1010 (2006) 3. J.C.H. Spence, J.M. Zuo, Electron Mcrodffracton Plenum Press, New York (1992). 4. A. Armglato, R. Balbon, S. Frabbon, Improvng spatal resoluton of convergent beam electron dffracton stran mappng n slcon mcrostructures Appl. Phys. ett., 86, (2005) 5. A. Armglato, A. Spessot, R. Balbon, A. Benedett, G.P. Carnevale, S. Frabbon, G. Mastraccho and G. Pava, TEM/CBED nvestgaton of stran nduced by T-salcdes n shallow trench S solaton structures, J. of Appled Physcs, 99, (2006) 6. D. Jackob, Y. Androuss, T. Benabbas, P. Francos, A. efebvre, Surface relaxaton of straned semconductor heterostructures revealed by fnte element calculatons and transmsson electron mcroscopy, Phl Mag A, Vol. 78, 879 (1998) 7. J. P. Mornrol, arge-angle Convergent- Beam electron dffracton, SF, Pars. (2002) 8. A. Spessot, S. Frabbon, R. Balbon, A. Armglato, Method for determnaton of the dsplacement feld n patterned nanostructures by TEM/CBED analyss of splt hgh-order aue zone lne profles, J. of Mcroscopy, 223, 249 (2007) 9. P.Y. Yu and M. Cardona, Fundamentals of Semconductors, Sprnger, Berln(1996) 9. Acknowledgements One of the authors (A.S.) would lke to thank Paolo Fantn and Andrea Marmrol (of Numonyx Technology and Devce Modellng Group) for frutful dscussons.