QNN 02 9-11 Septemer 2002 Tsuku, Jpn TUP-40 Formtion mechnisms of quntum dots in the Sn/Si system Peter Möck*, Yunyun Lei, Tey Topuri, nd Nigel D. Browning Deprtment of Physics, University of Illinois t Chicgo, 845 W. Tylor Street, Chicgo, Illinois 60607-7059, * now t: Portlnd Stte University, Deprtment of Physics, P.O. Box 751, Portlnd, OR 97207-0751; tel.: 312 497 4424, e-mil: peter_moeck@hotmil.com, pmoeck@uic.edu Regin Rgn**, Kyu S. Min***, nd Hrry A. Atwter Thoms J. Wtson Lortory of Applied Physics, Cliforni Institute of Technology, MS 128-95, Psden, CA 91125, ** now t Hewlett-Pckrd Lortories M/S 1123, 1501 Pge Mill Rd, Plo Alto, CA 94304, *** now t Intel Corportion, Cliforni Technology nd Mnufcturing, MS RNB- 2-35, 2200 Mission College Blvd, Snt Clr, CA 95052-8119 Trnsmission electron microcopy in oth the prllel illumintion nd scnning proe mode reveled the existence of two mechnisms for the formtion of quntum dots in the Sn/Si system. Both mechnisms re elieved to operte simultneously during temperture nd growth rte modulted moleculr em epitxy comined with ex situ therml tretments. One of the mechnisms involves the cretion of voids in Si, which re susequently filled y endotxilly grown Sn, resulting in QD tht consist of pure -Sn. The other mechnism involves phse seprtion nd proly leds to sustitutionl solid solutions with much higher Sn content thn the predecessor quntum well structure possesses. In oth cses, the quntum dots possess the dimond structure, the typicl shpe of tetrkidechedron, nd n excess Gis free energy of pproximtely 1.5 ev per tom due to compressive lttice mismtch strins. 1. Introduction Self-ssemled semiconductor quntum dots (QDs) re expected to led to prdigm chnges in semiconductor physics [1]. For semiconductor opto-electronic devices, the QDs must e sized on the order of the exciton Bohr rdius for quntum confinement of crriers with n energy ndgp smller thn the surrounding semiconductor mtrix. No structurl defects (such s disloctions) which led to non-rditive recomintions of the ound sttes of electrons nd holes re llowed to exist in the QDs [2]. As α-sn is direct, ~ 0.08 ev, nd gp semiconductor nd sustitutionl solution Sn x Si 1-x re predicted to possess direct nd gps for 0.9 < x < 1 [3], QDs in Si mtrix consisting of pure -Sn or Sn x Si 1-x with sufficiently high Sn content hve potentil pplictions s direct nd-gp mteril for chep nd effective optoelectronics nd thermo-photovoltic devices. There re, however, 19.5 % lttice mismtch etween α-sn nd Si nd n equilirium solid soluility of Sn in Si of only 0.12 % t room temperture, tht restrict growth of pseudomorph Sn x Si 1-x lyers on Si y moleculr em epitxy (MBE) [4-7] to Sn content of out 10 % nd thickness of the order of mgnitude of 10 nm. At growth tempertures in the rnge 220 to 295 ºC, pseudomorph Sn x Si 1-x lyers with up to 5 % Sn content hve een grown with film thicknesses up to 170 nm. Therml tretments of these lyers t tempertures ove 500 ºC for 1 hour led to the formtion of -Sn precipittes, ß-Sn precipittes, precipittes tht consisted of oth -Sn nd ß-Sn, nd misfit disloctions [5-7]. While these -Sn precipittes my e considered to constitute QDs in this system (ccording to the requirements given ove), the simultneously present misfit disloctions re clerly undesirle for device pplictions. Alterntively, temperture nd growth rte modulted MBE [8,9] produces Sn x Si 1-x /Si superlttices with essentilly pseudomorph Sn x Si 1-x sustitutionl solutions hving Sn composition in the rnge of x = 0.02 to 0.05 nd film thickness rnging from 1 to 2 nm. The growth tempertures of the Sn x Si 1-x lyers rnged from 140 to 170 ºC nd the growth rte ws 0.02 nm per second. To prevent segregtion of Sn to the surfce during growth, the Sn x Si 1-x lyers were overgrown with 4 to 6 nm of Si t the Sn x Si 1-x growth temperture nd t growth rtes rnging from 0.01 to 0.03 nm per second. The temperture ws then rised to 550 ºC nd Si cpping lyer with thickness of the order of mgnitude 100 nm ws grown t rte of 0.0 per second. By the time this growth sequence hs
een completed, the Sn x Si 1-x lyer hs experienced n in situ therml tretment t 550 ºC for time of the order of mgnitude 30 minutes. For the growth of Sn x Si 1-x /Si multilyer structures, the whole growth sequence ws repeted severl times, effectively resulting in n in situ therml tretment for the first Sn x Si 1-x lyer t 550 ºC for time on the order of mgnitude few hours [8,9]. In ddition to this in situ therml tretment, ex situ nnels t tempertures etween 550 nd 900 ºC were performed for 30 minutes. There re some uncertinties s to the formtion mechnisms nd crystllogrphic phses of the QDs tht result from temperture nd growth rte modulted MBE. Employing trnsmission electron microscopy in oth the prllel nd scnning proe mode, we will ddress these two issues in the min prt of this pper. Thermodynmiclly driven structurl trnsformtions my occur over time in such QDs s one cn esily estimte [10] tht there is n essentilly hydrosttic pressure in the GP rnge [11] on these entities with corresponding excess Gis free energy of pproximtely 1.5 ev per tom. This excess Gis free energy my e reduced or eliminted y structurl trnsformtions from α-sn to β-sn or from Sn x Si 1-x lloys into ordered Sn-Si compounds over long enough time, even t room temperture. Here we would like to mention only tht we ctully oserved in the ove mentioned smples ß-Sn precipittes nd other yet unidentified precipittes tht my hve come into eing y mens of such structurl trnsformtions [12]. 2. Experimentl detils Three sets of pirs of multilyer smples (one with nd one without n dditionl ex-situ nnel for 30 minutes t 800 ºC) with four Sn x Si 1-x /Si lyers nd sustitutionl Sn contents of nominlly 2 %, 5 %, nd 10 % in ech of the Sn x Si 1-x lyers were grown y temperture nd growth rte modulted MBE [8,9], stored t room temperture for few yers, nd eventully selected for our TEM investigtions. Our structurl nlyses employed TEM in oth the prllel illumintion nd scnning proe mode using JEOL JEM-2010F Schottky field emission STEM/TEM nd JEOL JEM-3010 TEM. Prllel illumintion TEM utilized conventionl diffrction contrst (CTEM) nd high-resolution phse contrst (HRTEM) imging. Atomic resolution Z-contrst imging in the scnning proe mode (STEM) proved to e especilly useful for our investigtions s the effects of strin fields in nd round QDs nd interference effects such s the formtion of moiré fringe due to doule diffrction re negligile. TEM specimen preprtion followed stndrd procedures involving mechnicl grinding nd ion milling to electron trnsprency. 3. Results nd Discussions Fig. 1 shows Sn 0.1 Si 0.9 multilyer structure in CTEM overview nd Fig. 1 shows the structure in Z-contrst STEM overview. While the Sn 0.1 Si 0.9 lyers pper drk in the CTEM imges (due to strin field influences nd comintion of diffrction nd sorption contrst), the Z-contrst imge shows these lyers righter thn the surrounding Si mtrix since the verge tomic numer in these lyers is much lrger tht of Si. Most of the Sn QDs formed t or in close proximity to the Sn 0.1 Si 0.9 lyers, ut there re lso mny Sn QDs tht grew within the Si spcer lyers. Figs. 2 nd show HRTEM imges of structurlly defective nd perfectly pseudomorph Sn x Si 1-x lyers in Si, respectively. The defect density ws oserved to decrese with the nominl Sn content in the Sn x Si 1-x lyers. Smples with nominl Sn content equl to or less thn 5 % in the Sn x Si 1-x lyers were found to e essentilly free of defects. Erlier pln-view TEM investigtions of essentilly defect free Sn x Si 1-x lyers nneled t 650 ºC reveled n initilly rpid increse of the verge Sn QD volume (<r> 3 ) with time (t) for the first 2.2 hours of the nnel, Fig. 3 [9]. After this time, the function <r> 3 (t) showed the typicl liner ehvior tht is expected for precipitte corsening y volume diffusion [13]. Textook knowledge [13] ttriutes non-linerities of <r> 3 with t to diffusion shortcuts such s disloctions, stcking fults, grin oundries, nd other common lttice defects.
Z-contrst STEM imging in tomic resolution, Figs. 4, nd 5, however, reveled tht within the Si mtrix quite fr wy from the sptil positions of the Sn x Si 1-x lyers (see lso Figs. 1,), there re mny voids in the Si mtrix which re prtly filled y Sn in oth ex situ nneled nd s grown smples (tht hd only hd in situ therml tretments). Fig. 5 is especilly instructive s one cn see tht Sn lines the interfce etween the void nd the Si mtrix. Additionl evidence for the existence of voids in Si tht re prtly filled with Sn hs een gthered y quntittive electron energy loss spectroscopy nd will e presented elsewhere [14]. We consider such voids s preferentil sinks for diffusing Sn toms, i.e. s very likely cndidtes for the ove mentioned diffusion shortcuts. 100 nm 50 nm Figure 1: Sn 0.1 Si 0.9 /Si multilyer structures in [110] cross sections, dditionl exsitu nnel; the rrows points towrds QDs tht grew within the Si lyer; () CTEM overview; () Z-contrst STEM overview. Figure 2: [110] cross section HRTEM imges with power spectr inserts; () Sn 0.1 Si 0.9 lyer (rrow) with lttice defects on {111} nd {111} plnes, s deposited (i.e. only in-situ therml tretments); () Sn 0.02 Si 0.98 lyer s deposited. Figure 3: Results of erlier ex situ nneling experiments t 650 ºC, fter ref. [9]. The plot of the verge QD size (<r> 3 ) over the nneling time (t) shows tht within the first 2.2 hours, the volume of the QDs increses very rpidly. Lter on, the <r> 3 (t) function shows the typicl liner reltionship tht is expected when the precipitte corsening is governed y volume diffusion. We ttriute the initil rpid increse of the verge QD size to diffusion shortcuts such s voids in the Si mtrix. It is now importnt to relize tht the equilirium shpe of void in Si hs een determined experimentlly [15] to e tetrkidechedron, Fig. 6. The pplictions of Neumnn s symmetry principle [16,17] to the determintion of the shpe of -Sn precipittes in Si mtrix shows tht this cn e tetrkidechedron s well. Filling void in Si with Sn y mens of diffusion (into diffusion shortcut) s result of n dditionl therml tretment t moderte prmeters (300 ºC for pproximtely three hours) directly in the electron microscope resulted in n -Sn QD, Fig. 4, s -Sn nd Si oth possess the dimond structure. We consider this oservtion s direct proof of the void-filling hypothesis presented ove.
This mechnism lso provides strightforwrd explntion for the initilly rpid increse of the verge Sn QD volume with nneling time in Fig. 3. The cretion of voids in Si nd susequent filling with Sn emerges, therefore, s the first of the two mechnisms y which quntum dots in the Sn/Si system form. = 2 nm [001] Figure 4: [110] cross section Z-contrst STEM imges of voids in Si, x = 0.05, ex-situ nnel; () prtilly filled with -Sn; () filled with more -Sn nd grown in size s result of moderte dditionl therml tretment inside the microscope (300 ºC for pproximtely 3 hours). Figure 5: [110] cross section Z-contrst STEM imges, x = 0.1, ex-situ nneled; () void in Si, lined on its interfce with the Si mtrix y Sn; () prtilly formed SnxSi 1-x precipitte in Si with x > 0.1, grown y phse seprtion from Sn0.1Si 0.9 lyer. The rrows represent the respective growth directions. Figure 6: Sketch of tetrkidechedron fter ref. 16. This shpe is determined y {111}, i.e. octhedron, nd {100}, i.e. cue, plnes. A = t/ is shpe prmeter; for A = 0 the shpe is n octhedron nd A = 2/3 corresponds to cue. Clculting the point group of the interfce energy density y mens of Neumnn s symmetry principle results in the possile precipittes shpes: tetrkidechedron, octhedron, cue, nd sphere. While the shpes of smll precipittes re likely to e determined y the nisotropy of the interfce energy, the shpes of lrger precipittes re likely to e determined y the nisotropy of the lttice mismtch strin energy [16]. [010] [100] 2 Figure 7: Shpe trnsition of Sn QDs in Si () tetrkidechedron s dominted y the nisotropy of the interfce energy density; () essentilly octhedron s dominted y the nisotropy of the elstic mismtch strin energy. The rrows represent the respective growth directions.
An interesting question is how these voids my hve risen in the first plce. The possile nswer to this question my e found in mechnism nlogously to tht descried in ref. 18, which sttes tht when freshly prepred Si surfce is exposed to ir, voids of out 10 nm dimeter nd numer density of out 10 10 cm -2 form spontneously pproximtely 10 nm elow the surfce due to compressive strin tht rises from the formtion of Si0 2 on the surfce. Deposited Sn x Si 1-x lyers my lso cuse the formtion of voids during the growth process since they lso compress freshly grown Si surfce. Finlly, the therml cycling during temperture nd growth rte modulted MBE [8,9] of multilyer structures ensures tht there is no shortge of vcncies in the structure nd this could llow preformed voids of ny shpe to grow nd rech their equilirium shpe. Phse seprtion of Sn from pseudomorph Sn x Si 1-x predecessor lyer, result in QDs s well since the dimond structurl prototype cn e conserved. Fig. 5 shows n erly stge of the formtion of such QD t the sptil position of pseudomorph Sn 0.1 Si 0.9 lyer. The chemicl composition nd compositions rnge of such QDs re, however, uncler. When fully formed, these QDs my e sustitutionl solid solutions of Sn in Si with much higher Sn content thn the pseudomorph Sn x Si 1-x predecessor lyers. This mechnism is considered the second formtion mechnism for QDs in the Sn/Si system. Note tht only for very high Sn content, lrger thn 90 %, is direct nd gp predicted for Sn x Si 1-x lloys [3]. A shpe trnsition with size of Sn rich precipittes tht is proly due to n incresing contriution of the elstic mismtch strin energy to the totl energy of the QDs hs een oserved, Fig. 7. While smller Sn rich precipittes possess the typicl tetrkidechedron shpe, Figs. 5, 6, nd 7 (which proly results from the nisotropy of the interfce energy density), much lrger Sn (rich) precipitte hd shpe tht resemles more closely n octhedron, Fig. 7. The shpe of this lrge precipitte proly results from the nisotropy of the elstic mismtch strin energy. Intermeditely sized Sn rich precipittes possessed tetrkidechedron shpes with smller {001} fcets, i.e. smller shpe prmeters A, see cption of Fig. 6, indicting grdul trnsition to the shpe of n octhedron (A = 0) with incresing size. As this lrge precipitte ws prtly oserved t the predecessor sustitutionl Sn 0.1 Si 0.9 solution lyer nd prtly within the Si spcer lyer, it my hve formed y the simultneous opertion of oth mechnisms. The upper prt of the QD my, therefore, consist of -Sn nd the lower prt of sustitutionl solution with high Sn content. This hypothesis is consistent with the Z-contrst imge seen in Fig. 7. Finlly, we would like to suggest tht the employment of the void cretion nd susequent filling mechnism (y with -Sn QDs form in Si) my offer n opportunity to mke progress in other (less severely strined) QD systems such s InAs QDs in Si. 4. Conclusions Two mechnisms for the formtion of quntum dots in the Sn/Si system hve een proposed. The first of these mechnisms involves the cretion of voids in the Si mtrix nd their susequent filling with Sn toms y diffusion. The second mechnisms results from phse seprtion. While the QDs tht result from the first mechnism consist of pure -Sn, the quntum dots tht result from the second mechnism re proly sustitutionl Sn x Si 1-x lloys with high Sn content. Both of these mechnisms result in QDs which possess the dimond structure nd the typicl shpe of tetrkidechedron. As the chemicl compositions nd composition distriutions of the QDs re not known t present, further experiments re to e undertken in order to clrify this issue. Acknowledgments Aln Nicholls (Electron Microscopy Service, University of Illinois t Chicgo, UIC) is thnked for experimentl support. This reserch ws supported y oth grnt to NDB y the Ntionl Science Foundtion (DMR-9733895) nd grnt to PM y the Cmpus Reserch Bord of UIC. References [1] D. Bimerg, Quntum dots: Prdigm chnges in semiconductor physics, Semiconductors 33, 951-955 (1999). [2] N.N. Ledentsov, V.M. Ustinov, V.A. Shchukin, P.S. Kop ev, Zh.I. Alferov, nd D. Bimerg,
Quntum dot heterostructures: friction, properties, lsers (Review), Semiconductors 32, 343-365 (1998). [3] R.A. Soref nd C.H. Perry, Predicted nd gp of the new semiconductor SiGeSn, J. Appl. Phys. 69, 539-541 (1991). [4] S.Y. Shiryev, J. Lundsgrd Hnsen, P. Kringhøj, nd A.N. Lrsen, Pseudomorphic Si 1-x Sn x lloy films grown y moleculr em epitxy on Si, Appl. Phys. Lett. 67, 2287-2289 (1995). [5] M.F. Flyn, J. Chevllier, J. Lundsgrd Hnsen, nd A. Nylndsted Lrsen, Relxtion of strined, epitxil Si 1-x Sn x, J. Vc. Sci. Technol. B 16, 1777-1785 (1998). [6] M.F. Flyn, J. Chevllier, A.Nylndsted Lrsen, R. Feidenhns l, nd M. Seit, -Sn nd ß-Sn precipitted in nneled Si 0.95 Sn 0.05, Phys. Rev. B 60, 5770-5777 (1999). [7] C. Ridder, M. Fnciulli, A. Nylndsted Lrsen, nd G. Weyer, Precipittion of Sn in metstle, pseudomorphic Si 0.95 Sn 0.05 films grown y moleculr em epitxy, Mter. Sci. Semicond. Processing 3, 251-255 (2000). [8] K.S. Min nd H.A. Atwter, Ultrthin pseudomorphic Sn/Si nd Sn x S 1-x /Si heterostructures, Appl. Phys. Lett. 72, 1884-1886 (1998). [9] R. Rgn, K.S. Min, nd H.A. Atwter, Direct energy gp group IV semiconductor lloys nd quntum dot rrys in Sn x Ge 1-x /Ge nd Sn x Si 1-x /Si lloy systems, Mter. Sci. Engin. B 87, 204-213 (2001). [10] For hydrosttic pressure, the product of the ulk modulus (42.6 GP for -Sn nd 70.2 GP for Sn 0.5 Si 0.5 ssuming Vegrd s lw pplicle) nd the reltive elstic volume chnge is equl to the product of pressure nd volume, which is lso the excess Gis free energy due to lttice mismtch strins. Strting with n unstrined -Sn sphere of 10 nm dimeter (with lttice constnt 0.6489 nm) tht contins 15329 toms, one otins for reltive elstic volume chnge of 19.5 % pressure of 8.3 GP nd n excess Gis free energy of 1.77 ev per tom. For sme dimeter Sn 0.5 Si 0.5 sphere (with lttice constnt 0.596 nm, ssuming Vegrd s lw pplicle) tht contins 19785 toms, one otins for 9.75 % reltive elstic volume chnge pressure of 6.84 GP nd n excess Gis free energy of 1.13 ev per tom. The usge of this simple formul is justified y studies of the size dependency of elstic properties of nnometer sized prticles, e.g. S.P. Bker, R.P. Vinci, nd T. Aris, Elstic nd Anelstic Behvior of Mterils in Smll Dimensions, MRS Bulletin 27, No. 1, 26-29 (2002) nd R.E. Miller nd V.B. Shenoy, Sizedependent elstic properties of nnosized structurl elements, Nnotechnology 11, 139-147 (2000). [11] This hydrosttic pressure rnge is known to led to structurl trnsformtions in elementl (group IV) nd inry III-V compound semiconductors; see, e.g., G.J. Acklnd, High-pressure phses of group IV nd III-V semiconductors, Rep. Prog. Phys. 64, 483-516 (2001). [12] P. Möck, Y. Lei, T. Topuri, N.D. Browning, R. Rgn, K.S. Min, nd H.A. Atwter, Structurl Trnsformtions in self-ssemled Semiconductor Quntum Dots s inferred y Trnsmission Electron Microscopy, Proc. of 47 th Annul Meeting of The Interntionl Society for Opticl Engineering (SPIE), Symposium Physicl Chemistry of Interfces nd Nnomterils, 7-11 July, 2002, Settle, WA. [13] D.A. Porter nd K.E. Esterling, Phse Trnsformtions in Metls nd Alloys, Chpmn & Hll, London, New York, 1992. [14] Y. Lei, P. Möck, T. Topuri, N.D. Browning, R. Rgn, K.S. Min, nd H.A. Atwter, in preprtion. [15] D.J. Egleshm, A.E. White, L.C. Feldmn, N. Moriy, nd D.C. Jcoson, Equilirium Shpe of Si, Phys. Rev. Lett. 70, 1643-1646 (1993). [16] W.C. Johnson, Influence of Elstic Stress on Phse Trnsformtions, in: Lectures on the Theory of Phse Trnsformtions, 2nd Edition, Ed. H.I. Aronson, The Minerls, Metls & Mterils Society, Wrrendle, 2001. [17] As the pressure on the precipittes is in first pproximtion hydrosttic, i.e. isotropic, Curie s symmetry principle, e.g. ref. 16, yields no influence of the misfit stress field on the nisotropy of the interfce energy density. [18] S. Lin, I. Mck, N. Pongkrpn, nd P. Frundorf, Ten-nnometer surfce intrusions in room temperture silicon, Electrochem. Solid-Stte Sci. Lett. in press (2002), con-mt/0110393.