Calculation of Desorption Parameters for Mg/Si(111) System

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1 e-journal of Surfae Siene and Nanotehnology 29 August 2009 e-j. Surf. Si. Nanoteh. Vol. 7 (2009) Conferene - JSSS-8 - Calulation of Desorption Parameters for Mg/Si(111) System S. A. Dotsenko, N. G. Galkin, and K. N. Galkin Department of Surfae Siene, Institute for Automation and Control Proesses, FEB AS, 5 adio Str., Vladivostok , ussia (eeived 29 January 2009; Aepted 30 June 2009; Published 29 August 2009) The method for alulation of desorption parameters developed for differential refletion spetrosopy is presented. It enables to study desorption and to ontrol phase omposition of film simultaneously. Spetra of differential refletane / of the film are initial data for the method. The method was used for Mg/Si(111) system. The desorption parameters for bulk Mg film were alulated and limitations of the method were found. [DOI: /ejssnt ] Keywords: Metalli films; Thermal desorption; Alkaline earth metals; Silion; efletion spetrosopy; Magnesium; Desorption parameters; Si(111) I. INTODUCTION The system of Mg/Si(111) attrats attention of sientists beause of narrow-gap semiondutor siliide (Mg 2 Si) formation. The siliide islands grow epitaxially on Si(111) and speifi thermoeletromotive of this material embedded in Si substrate is high [1]. However low value of the Mg desorption temperature influenes appreiably on Mg adsorption rate. It ompliates exat alulation of deposited film thikness, omparing obtained data with previous ones and building the model of Mg film growth. Therefore alulation of desorption parameters of Mg in the Mg/Si(111) system (v 0 : maximum desorption rate, E des : ativation energy of desorption) is primary task. However phase omposition of deposited Mg film depends on the Mg adsorption rate. Therefore new method for alulation of desorption parameters enabling to study desorption and to ontrol phase transition of Mg film simultaneously should be developed to solve this task. The developing of this method and use it for the Mg/Si(111) system were aims of our paper. desorption inluded 2 stages. At 1st stage Mg deposited on initial sample for 5 minutes at ertain temperature to grow bulk Mg film being desorbed for 5 minutes at the same temperature at 2nd stage. Formation of initial sample and study of Mg desorption were realized at similar growth ondition and at onstant substrate temperature and the rate of Mg atoms deposition. Magnesium was evaporated from tantalum tube. To redue sample heating by evaporation unit the distane between unit and sample was 8 m. The rate of Mg atoms deposition v dep (v dep = 0.6 nm/min) was alibrated by quartz sensor at room temperature (T). EELS spetra were used to study uniformity and omposition of Mg film for initial sample and for bulk Mg film desorbed at ertain temperature. Only samples overed by ontinuous bulk Mg film both before Mg deposition and after Mg desorption were used for study of Mg desorption. DS spetra were reoded in photon energy range ev during Mg deposition on initial sample at onstant temperature. Detailed desription of DS tehnique is presented in ef. [2]. III. ESULTS AND DISCUSSIONS II. EXPEIMENTAL A. Method for alulation of desorption parameters The experiments were arried out in ultrahigh vauum (UHV) hamber Varian with base pressure Pa, whih was equipped with Auger eletron spetrosopy (AES), eletron energy loss spetrosopy (EELS) and differential refletion spetrosopy (DS) tehniques. The samples ( mm) were ut from n-type Si wafer (0.3 Ω m). Surfae phase of lean Si(111) surfae (phase (7 7)) was prepared by several flash heating at 1250 C in UHV hamber. Initial state of sample was ontinuous bulk Mg film grown on ontinuous buffer Mg 2 Si layer overing surfae Si(111). It was grown by Mg deposition on lean surfae Si(111) for 10 minutes at different temperatures ( C). This temperature range was hosen beause the Mg desorption rate in this range is appropriate for it to find by developed method. Study of Mg This paper was presented at the 8th Japan-ussia Seminar on Semiondutor Surfaes (JSSS-8), Tohoku University, Japan, Otober, Corresponding author: doenko@iap.dvo.ru The new method for alulation of desorption parameters will be developed for DS. The value obtained by DS tehnique is differential refletane: = ( h) 0 0, (1) where 0 and ( h) are refletane for initial sample and for the same sample overed by thikness h deposited film of adsorbate, respetively. Thikness of film grown at temperature T is h = (v dep v des (T )) t, where t is deposition time, v dep and v des (T ) are the rates of atoms deposition at T and desorption at temperature T, respetively. To find relation(s) for value / and optial funtions of phases the grown film onsists of, the following is to be arried out: 1) to build a model of the film growth, 2) to use the model for finding /( t, ω) funtion, where ω is light frequeny, 3) to separate variables in /( t, ω) funtion by ombining frequeny dependent variables and onstants in K i (ω) funtion(s) (These funtions ontain optial funtions, whih desribe optial properties of phases the grown film onsists of.), 4) to find ISSN The Surfae Siene Soiety of Japan ( 816

2 e-journal of Surfae Siene and Nanotehnology Volume 7 (2009) relation(s) for funtion(s) K i (ω) and optial funtions of these phases. The used model of film growth and derivation of dependene /( t, ω) for the model is presented in appendies. The theory yields: = 4ωD(ω) os ϕ(v ( ) t = K ad (ω, T ) t. (2) where = metres per seond is fundamental onstant named the rate of light in vauum, ϕ is the inidene angle of light beam, ε B = ε B +iε B is dieletri funtion of substrate (phase B),D(ω) = 1/(1 + 0/) is orretive funtion, ε A = ε A + iε A is dieletri funtion of adsorbate (phase A) and K ad (ω, T ) is slope of linear region of dependene / on deposition time t for deposition stage: K ad (ω, T ) = 4ωD(ω) os ϕ(v ( ). (3) The equation (3) should be solved using Kramers-Kronig s formulas whih are relations for real and imaginary parts of dieletri funtion [5]. If the highest photon energy applied in investigations is lower than energy of photon the first diret transition produes in substrate (phase B), ε B =0 and Eq. (3) is simplified: ε A(ω) = (ε B (ω) 1)K ad(ω, T ) 4ωD(ω) os ϕ(v dep v des (T )). (4) If phase A atoms deposition is stopped (v dep =0), only desorption of phase A atoms from bulk phase A film ours and formula (4) transforms to ε A(ω) = (ε B 1)K des(ω, T ) 4ωD(ω) os ϕv des (T ), (5) where K des (ω, T ) is slope of linear region of dependene / on desorption time t for desorption stage. Diret substitution of expression (5) in (4) yields final formula: v des (T ) = v depk des (T ) K ad (T ) K des (T ). (6) The desorption rate v des does not depend on photon energy E or light frequeny ω. Therefore region of orretness of alulated desorption rate is photon energy region where v des (E) = onst. (7) To alulate the desorption parameters (v 0 : maximum desorption rate, E des : ativation energy of desorption), the following equation should be solved: ln v des (T ) = A B T. (8) When unknowns A and B are found, desorption parameters are alulated: v 0 = exp(a) and E des = kb. (9) The dieletri funtion of film ε desribes optial properties of bulk phase. Spetrum of imaginary part of dieletri funtion of film ε alulated by use of formulas (4) and (5) is used for investigated phase identifiation. Value ε is dereased for metalli phases, and when light frequeny ω is inreased, the dependene of ε versus ω is ε ω a, where a is onstant [5]. Appreiable peaks at spetrum ε are distinguishing harateristi of semiondutor phases. Comparing these peaks positions and values obtained for the potential phases, the investigated phase an be identified exatly. Therefore this method of alulation of desorption parameters enables to study desorption and to ontrol phase transition of film simultaneously. B. Calulation of desorption parameters for Mg in Mg/Si(111) system Curves /( t) obtained for Mg deposition (region 1) and desorption (region 2) in the Mg/Si(111) system at different temperatures are presented in Fig. 1. Dependene / on deposition (desorption) time t is linear and so it orrelates with formula (2). The value of slope of urve /( t) for deposition is positive and that for desorption is negative, as it was predited by formulas (4) and (5). The shape of ε A spetra obtained for deposition and desorption orresponds to bulk Mg film. Formation of bulk Mg film is also onformed by EELS spetra. To find region of orretness of alulated desorption rate v des, dependene of the rate on photon energy at 170 C is presented in Fig. 2. The shape of this dependene is not greatly hanged at different temperatures and so these urves are not shown in Fig. 2. Aording to Fig. 2, photon energy range ev is the region of orretness of alulated desorption rate. For Eq. (8) to formulate, v des (T ) values were used from this region. The alulated desorption parameters for bulk Mg film are: v 0 = (J-Stage: 817

Volume 7 (2009) Dotsenko, et al. The method of alulation of desorption parameters developed in this artile enables to study desorption and to ontrol phase transition of film simultaneously.

3 Volume 7 (2009) Dotsenko, et al. The method of alulation of desorption parameters developed in this artile enables to study desorption and to ontrol phase transition of film simultaneously. It results from involving apability of differential refletion spetrosopy in this method. Growth of ontinuous bulk film and desorption from this film result in linear dependene / on deposition (desorption) time t. To alulate desorption rate at ertain temperature, only deposition rate and values of slope of urves /( t) obtained for deposition and desorption at the same temperature are used. The method of alulation of desorption parameters was used for Mg film in the Mg/Si(111) system. Fine orrelation of theoretial formulas and experimental /( t) urves was observed. The obtained desorption parameters for bulk Mg film enable to alulate the maximum temperature of bulk Mg film formation for v dep =0.6 nm/min (219.8 C). It is lose to the value obtained during experiments (215 C). FIG. 1: Curves of /( t) obtained at different temperatures for Mg film growth (region 1) and desorption (region 2) in Mg/Si(111) system at photon energy 1.13 ev. Solid lines are linear fitting of experimental data. Aknowledgments This study is supported by Program of Physial Siene Department of ussian Aademy of Sienes Fundamental optial spetrosopy and its appliations, Grants for developing new in situ methods of Far Eastern Branh of ussian Aademy of Sienes, Grant of ussian Fund of Basi Investigations (No a) and Grant of ussian Siene Support Foundation. Appendix The used model of film growth meets following requirements (Fig. 3): FIG. 2: (I) Desorption rate of Mg film at 170 C and (II) ativation energy of desorption E des obtained in the range used. nm/min, E des =0.733±0.001 ev. The maximum temperature of bulk Mg film formation obtained during experiments for v dep =0.6 nm/min (215 C) is lose to the value alulated by use desorption parameters (219.8 C). To estimate the variation of E des, if expression (7) is not orret, E des value was alulated in the range used ( ev) and presented in Fig. 2. E des value is seen to be invariable in region of orretness of alulated desorption rate, i.e ev. In this region the values of slope of urve /( t) (K ad and K des ) are high for bulk Mg film. When K ad and K des are low (range ev), expression (7) is not orret and E des value is notieably redued. IV. CONCLUSIONS 1. Initial sample loated in vauum onsists of bulk phase A film, buffer phase A x B y layer, semi-infinite substrate of bulk phase B, interfae layers ib and ia and surfae phase sa (II). Plane XOY oinides with this interfae layer ib. Value z is inreased, when one moves from vauum to substrate. 2. The phase A film and buffer phase A x B y layer are ontinuous during film growth (III). 3. Shape of islands of phase A x B y is retangular parallelepiped. Another shape of islands is also aepted. However the final formula (6) does not depend on island shape, beause this harateristi of island disappears in averaging formula (18). 4. At the interfae phase of A vauum (z = d AxBy d i and z = d AxBy d i d i for i island before atoms A deposition (I) and after t minutes deposition (III), respetively) formation of surfae phase sa ours. 5. Interfaes of phase A x B y phase B (z=0) and phase A phase A x B y (z = d AxBy ) are interfae layers ib and ia, respetively. 6. Thikness of buffer phase A x B y layer is not hanged during film growth, i.e. phase A atoms are not desorbed from phase A x B y, and do not reat with phase B to produe additional moleules of phase A x B y. 7. Boundaries of phases are abrupt (J-Stage:

e-journal of Surfae Siene and Nanotehnology Volume 7 (2009) where =3 10 8 metres per seond is fundamental onstant named the rate of light in vauum, ϕ is angle of light beam inidene, ε B = ε B + iε B

4 e-journal of Surfae Siene and Nanotehnology Volume 7 (2009) where = metres per seond is fundamental onstant named the rate of light in vauum, ϕ is angle of light beam inidene, ε B = ε B + iε B is dieletri funtion of substrate (phase B), ω is light frequeny. Differential refletane alulated in Baghi s approah equals = ( h) sb sb, (11) where sb is refletane for semi-infinite phase B substrate overed by surfae phase sb (I in Fig. 3). It differs from experimental value of differential refletane / alulated by use of formula (1). Therefore to apply formula (10) for our experimental ondition, interrelation of experimental value / and theoretial one / should be found. Having divided numerator and denominator of fration presented in formula (1) by sb and having substituted formula (11) in it, we obtained this dependene: ( h) = = D(ω) ( ( h) ) 0, (12) where D(ω) = 1/(1 + 0/) is orretive funtion, 0/ and ( h) / are differential refletane alulated in Baghi s approah for initial sample and for the same sample overed by thikness h deposited film of adsorbate, respetively. The appearane of orretive funtion D(ω) in formula (12) means that formula (10) should be multiplied by D(ω) to onform to our experimental ondition. Spetrum of variation of response funtion δλ(ω) presented in formula (10) onsists of other strutures ontribution to optial properties of film, namely ontribution of bulk phases A and A x B y, surfae phase sa and interfae layers ib and ia. Within the framework of Baghi s approah [3] we derived relation for optial funtion of these strutures and spetrum δλ(ω): FIG. 3: Model of film growth, where I is semi-infinite substrate, II is initial sample, and III is initial sample subjeted deposition of thikness h film of adsorbate A. sb and sa are surfae phases of substrate medium (phase B) and adsorbate (phase A), respetively. ib and ia are interfae layers. S i and d i are area and height of i island of phase A, respetively. 8. Thikness of surfae phases and interfae layer is zero. However a value of optial funtions of these 2D strutures is finite. 9. Deposited film of adsorbate is thin. The 3rd, 7th and 8th items of this model enable to use Baghi s approah [3] for deriving basi formula for ontinuous film: 4ω os ϕ = ( ) δλ(ω), (10) δλ = 1 S 0 N S i ( ε (a) i (z) ε i (z) )dz, (13) where S 0 is area of light beam used for sample investigation, S i is area of top surfae of i island of phase A, N is number of islands of phase A, ε i (z) and ε (a) i (z) are value of dieletri funtion of system at point z alulated for either ase (I) and (II) or ase (I) and (III) in Fig. 3, respetively. Point z is loated within infinite height olumn, the base of olumn is i island of phase A. Aording to Fig. 3, these dieletri funtions equal: 1, ( ; 0) ε i (z) = δλ sb δ(z), 0 (J-Stage: 819

5 Volume 7 (2009) Dotsenko, et al. or 1, ( ; d AxBy d i ) δλ saxby δ(z + d AxBy + d i ), d AxBy d i ε A, ( d AxBy d i ; d AxBy ) ε (a) i (z) = δλ ia δ(z + d AxBy ), d AxBy ε AxBy, ( d AxBy ; 0) δλ ib δ(z), 0 1, ( ; d AxBy d i d i ) δλ saxby δ(z + d AxBy + d i + d i ), d AxBy d i d i ε A, ( d AxBy d i d i ; d AxBy ) ε (a) i (z) = δλ ia δ(z + d AxBy), d AxBy ε AxBy, ( d AxBy ; 0) δλ ib δ(z), 0 To satisfy the item 8 of model, optial funtions of 2D strutures were multiplied by delta-funtion δ(z). Substituting the values of dieletri funtions in the formula (13) produes: δλ 0 = 1 N S i [d i (ε A 1) + d AxBy (ε AxBy 1) + δλ sa + δλ ia + δλ ib δλ sb ], (14) S 0 δλ( h) = 1 N S i [(d i + d i )(ε A 1) + d AxBy (ε AxBy 1) + δλ sa + δλ ia + δλ ib δλ sb ], (15) S 0 where δλ 0 and δλ( h) are variation of response funtion for initial sample and for the same sample overed by thikness h deposited film of adsorbate, respetively. Having substituted in the formula (10), the formulas (14) and (15) produe 0/ and ( h) /, respetively. Diret substitution of 0/ and ( h) / in the formula (12) yields the relation for / and optial funtions of phases the film onsists of: 4ωD(ω) os ϕ = S 0 ( ) εa (ω) 1 N S i d i. (16) Sine the film is ontinuous, we ould use Aspnes s approah [4]: all islands of phase A light beam overs are replaed by effetive island. Beause the film is ontinuous, area of effetive island S = S 0. This island onsists of only adsorbate atoms and so its effetive height d = h = (v dep v des (T )) t, (17) where v dep and v des (T ) are the rates of phase A atoms deposition at T and desorption at temperature T, respetively. Effetive height of this island is related to the values S i and d i for islands of phase A: h = N S i d i /S 0. (18) Diret substitution of the expressions (17) and (18) in the formula (16) yields: = 4ωD(ω) os ϕ(v ( ) t. (19) [1] N. G. Galkin, K. N. Galkin, and S. V. Vavanova, e-j. Surf. Si. Nanoteh. 4, 319 (2006). [2] S. A. Dotsenko, N. G. Galkin, A. S. Gouralnik, and L. V. Koval, e-j. Surf. Si. Nanoteh. 3, 113 (2005). [3] A. Baghi,. G. Barrera, and A. K. ajagopal, Phys. ev. B 20, 4824 (1979). [4] J. D. E. MIntyre and D. E. Aspnes, Surf. Si. 24, 417 (1971). [5] P. Y. Yu and M. Cardona, Fundamentals of Semiondutors (Springer, Berlin, 1996) (J-Stage:

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