200 مجلة إبن الهيثم للعلوم الصرفة و التطبيقية 2012 السنة 25 المجلد 2 العدد Ibn Al-Haitham Journal for Pure and Applied S cience No. 2 Vol. 25 Year 2012 Study to the Main Effects on the Auger de-excitation Transition F.H. Al-Asadi Department of Physics, College of Science, University of Thi-Qar Received in: 20 September 2011, Accepted in: 7 December 2011 Abstract An Eigen-state expansion method is applied to the transition of the Auger de-excitation charge transfer (AD) process in the interaction between clean Cu,Al and Na surfaces and excited incident gases H and He .We use this method to describe the effective surfaces electronic structure. It's shown that the AD efficiency is deeply influenced by the presence of the energy band for the surfaces and the potential energy stored within the excited incident atom, thus for long interaction time we use a slowly atom's about 1KeV to scatter from metals surfaces where the electron couldn't probe the metal band structure and Za the surface - projectile distance. Also we drive a new formula for AD interaction Matrix element. Keywords: Auger De-excitation (AD), Scattering, Ion Surface interaction. Introduction Charge exchange phenomena of ions (atoms) in front of a metal surface are of considerable interest in fundamental research as well as in technological applications. The basic processes for electron transfer in the scattering of thermal and hyperthermal beams were established some decades ago[1-3] and comprise resonant one- electron tunneling and two-electron Auger processes .when a slowly moving projectile incident on a metal surface of sufficiently small work function Φ the possible processes for Auger charge transition are shown in fig.(1)[4]. Neutralization of scattered ions is well-known to be an important effect which enhances the surface sensitivity of the technique but leads to low scattered ion yields. The main mechanism of charge exchange with the target material (usually metallic) has been generally agreed to be Auger neutralization (AN) fig.1 (b), involving direct transfer of a surface valance electron into He+ ion core hold ground state. With the excess energy being given, as kinetic energy, to other valence electron of the surface. An alternative process of charge exchange is resonance neutralization (RN) fig.1 (a) in which a metal surface valance electron tunnels across into an unoccupied state of the ion at essentially the same binding energy in a one-electron process. This mechanism is believed to be important, for example, in charge exchange with incident alkali metal ions whose ground state empty levels lie energetically close to the Fermi level [5-7]. Some important resurgence of interest in the theory of surface charge exchange processes , the one-electron resonant mechanism, demonstrate a special case of "quasi-resonant" charge exchange with a deeper lying occupied state of the solid as in fig.1(d)[8,9]. Auger De-excitation Background The Auger de-excitation process[10] is shown in fig.1(c). Where, an excited atom is de- excited with simultaneous ejection of an electron from the system. The ejected electron that originated from the metal is shown clearly in fig. (2) (direct capture). Whereas, the other one in which the ejected electron originated from the atom is shown in the same figure (indirect capture).In either case, one of the two electrons must originate in a specific level, namely, the atomic excited level. The excited electron may appear outside the solid if it poses a sufficient 201 مجلة إبن الهيثم للعلوم الصرفة و التطبيقية 2012 السنة 25 المجلد 2 العدد Ibn Al-Haitham Journal for Pure and Applied S cience No. 2 Vol. 25 Year 2012 momentum component (normal to the surface) to surmount the surface potential barrier [11, 12]. As clear from fig. (2) Auger de excitation, it is two-electron process, but in fact, it is quasi one-electron in character .This property causes Auger de-excitation to have fundamentally different energetic character resulting in a quite different kinetic energy distribution of the excited electron from that of the auger neutralization. The potential energy stored within the excited atom and the work function of the metal surface are the driving parameters for the electronic transitions which are studied by detecting and measuring both the yield and kinetic energy distribution of the emitted electrons during these processes which are Auger character . X*(e1) + n em X(e1) + (n-1) em + e 2 direct capture X*(e1) + n em X(e2) + (n-1) em + e 1 indirect capture X* incident excited atoms; n em denoted n electrons in the metal surface, e1 , e 2 free electrons[13] . Theoretical model We use Eigen-state expansion method to describe the scattering of excited atom from the metal surface, where the Auger level described by the wave function qf with kinetic energy εq outside the metal. For incident excited atom εm , εa are excitation and ground energies near the metal respectively, also εo , εf are the energies of vacuum, Fermi levels above the bottom of the conduction band in the metal respectively , Φ is the metal work function . The kinetic energy for the emitted electron is given as: εq= εa(za) - εm(za)- εj The maximum εq is when εj = Φ and the minimum is when εj = εo . Starting from the broadening coefficient for the final level bqa(t) taken from Ref [14]: 12 )( 0 ),( ),()()( 0 - ¢ ¢ ¢- ˙ ˙ ˚ ˘ Í Í Î È - --=  j jj ajj j ttiE ajj j jmqa EE zM EezMtbtb j e e ........ (1) qaaamjj zzE eeee --+= )()( For the case that the projectile is fixed (i.e. incident velocity equals zero) then: …………….(2) ),(),(),()( 22 ajj j ajjaqa zBTfzMzb eeep Â= Where ),( aj zB e represent the energy broadening function for AD spectrum, and it’s defined as: ............. (3) [ ] [ ]{ } 122 ),(),(1),( -D+L-= ajajjaj zzEzB eepe Where, 202 مجلة إبن الهيثم للعلوم الصرفة و التطبيقية 2012 السنة 25 المجلد 2 العدد Ibn Al-Haitham Journal for Pure and Applied S cience No. 2 Vol. 25 Year 2012 ............... (4) 2 ),()(),( ajjjsdaj zMz eeprge =D γd is normalization constant, ρs (εj) is the surface density of state, 2Δ(ε) is Auger de- excitation transition rate , Mj(εj,za) represents the matrix element for AD transition .............. (5) Ú ¢- D =L jj aj aj z Pz ee e p e ),(1 ),( The effective density of state for the metal surface is given by: ..................... (6) Â= q aqjajeff z ),,()( eerer Where ........................... (7) [ ] [ ]22 ),(),( ),(1 ),( ajajqamj aj aja ZZ Z Z eeeeee e p er D+L---+ D = Matrix element For the above equation we drive a new formula to find AD matrix element where M' is the matrix element for indirect capture, M" for the direct capture. The general form for matrix element is [3]: ................. (8) )()2,1()( tVtM if yy= )(tiy , )(tfy represent initial, final wave function for AD interaction respectively V(1,2) represents colomb interaction potential between the two electrons. Substituting in eq (8) we get: .............. (9-a) )2()1()2,1()2()1( mjqa VM ffff=¢ ............. (9-b) )1()2()2,1()2()1( mjqa VM ffff=¢¢ Where amj fff ,, represent the wave functions for the electron in metal, excited and ground levels for the incident atom respectively. MMM ¢¢+¢=a For singlet case MMM ¢¢-¢=b For triplet case By sitting  + += g gk rgkij gj zueA L r )( 1 )( // //// ).( 2 f ................ (10) 203 مجلة إبن الهيثم للعلوم الصرفة و التطبيقية 2012 السنة 25 المجلد 2 العدد Ibn Al-Haitham Journal for Pure and Applied S cience No. 2 Vol. 25 Year 2012 L is the normalize area, g is the reciprocal lattice Ajg is factor depends on the surface density of state . So we interest with g=0. .................... (11) Z gk jezu q- + =)( // This is the solution for Schrödinger equation for one demotion. ........................ (12) ra a aer b p b f -= 3 )( .......................... (13) r m m m merr bb p b f --= )1()( 3 )( mab (Effective core charge) ................. (14) riq q eL .2 3- =f ............. (15) )( 2 02 ee -= q m q h By substituing the above wave functions in equations (9-a) & (9-b) and simplify we get the final form for the matrix element as: Í Í Î È - - -- - ÔÓ Ô Ì Ï ˙ ˙ ˚ ˘ Í Í Î È + + + -=¢ -- 222 33 2 )( 2 )( 1 )( 21 )( )2( ajajaaja Z ajaaja Z ma ajaj ee M bqbqbbqbbqbbqbp bb p qq Ǫ̂ Ô ˝ ¸ ˙ ˙ ˚ ˘ - + - - ˙ ˙ ˚ ˘ Í Í Î È - --+-+ -- 2 2))(( )( 2 )( 1 )( 21 )()( ajajaaja aa Z ZZe aaj bqbqbbqb gggbq (16)......... ÚÚ • ¢+¢-- •- ¢+ ¢¢¢¢ 0 2 322 )'( 22 wr rrww wrbg ma e dd Z ˙ ˚ ˘ Í Î È -+-+-+ Ó Ì Ï +-=¢¢ --- 32 2 2 )( 542 33 2 21)( 3 )(24 6 )2( bb g b g bb b bqp bb p gbgq aa Z m j ma ZZ ee M aj ……. (17) ( ) 3 2 2 2 3 5 12 12 ( ) ( ) ( )aZm a a ae Z Z Z b gb g g g b b b b - - ¸È ˘+ - + - + - + ˝Í ˙ Î ˚˛ Where 204 مجلة إبن الهيثم للعلوم الصرفة و التطبيقية 2012 السنة 25 المجلد 2 العدد Ibn Al-Haitham Journal for Pure and Applied S cience No. 2 Vol. 25 Year 2012 am bbb += Results and Discussion We apply the theoretical model on real systems such as He/Cu , He/Al , He/Na ,(as shown in Fig.3) to investigate the effects of the energy band on the AD transition , then we campier the results of He/Cu , H/Cu ,(as shown in Fig.4) to investigate also the effects of the stored potential energy in the incident projectile. We show in fig.5 that the direct capture transition is the most effective in (AD) process, where this transition describes the effective density of state ρeff for the metal surface as shown in fig. 6 , where ρeff is effected by the elliptic shape for ρs that used. Fig.7 shows that the transition rate Δ increases as the metal energy band width increases (See table.1 also).Fig.9 shows that Δpik decries exponentially as za increase, and that’s means that AD interaction increase as the projectile becomes closer to the surface. Fig.8 also shows that Λ increase as the surface energy band width increases. From Fig.10 we see that Δ for He/Cu system is larger than H/Cu system because the excited energy for He atom is larger than H atom which means that as the stored potential energy in the excited incident atom increases then AD transition decreases. Acknowledgment This work was partially supported by the head of program of the Future Nano- Techniques in Nitride Semiconductor Material, Dr. Amin H. AL-Khursan, College of Science, Thi-Qar University, Nassiriya, Iraq. References 1. Cobas ,A. and Lamb, W. E. (1944) ,On the Extraction of Electrons from a Metal Surface by Ions and Metastable Atoms, J. Phys. Rev. 65, 327 . 2. Shekhter,S. S. (1937) J. Expl. Theoret. Phys. (U.S.S.R.) 7 ,750. 3. Hagstrum, H. D. (1954) ,Theory of Auger Ejection of Electrons from Metals by Ions, Phys. Rev. 96, 336 . 4. Woodruff , D.P. (1983),Auger vs resonance neutralization in low energy He+ ion scattering, Vacuum 33 :651-3. 5. Behringer, E. R. ; Andersson, D. R. ;Cooper, B. H. and Marston, J. B. (1996) ,Charge transfer in hyperthermal energy collisions of Li+ with alkali-metal-covered Cu(001). I. Dynamics of charge state formation", Phys. Rev.,B 54, 14765 . 6. Borisov,A. G.; Teillet-Billy, D.;Gauyacq, J. P. Winter, H. and Dierkes, G. (1996) Resonant charge transfer in grazing scattering of alkali-metal ions from an Al(111) surface, Phys. Rev. B 54, 17166 . 7. Borisov, A. G. ; Kazansky, A. K. and Gauyacq, J. P. (1999). Resonant charge transfer in ion–metal surface collisions: Effect of a projected band gap in the H--Cu(111) system, Phys. Rev. B 59, 10935 8 Burgdorfer , J. (1993)in Review of Fundemental Processes and Aplications of atoms and Ions , edited dy C.D. Lin (World Scientific , Singapore, 517. 9. Shao , H., D. C. Langreth , and P. Nordlander , (1994) in Law Energy Ion-Surface Interactions, edited by J.W. Rabalais (Wiley , New York ,)118. 10. Cazalilla, M. A.; Lorente, N.; Díez Muiño, R. J.-P.; Gauyacq, D. ;Teillet-Billy, and P. M. Echenique, (1998) , Theory of Auger neutralization and deexcitation of slow ions at metal surfaces, Phys. 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Mol. Phys. 14 2995. 13. Homer, D. Hagstrum, (1979), Excited-Atom Deexcitation Spectroscopy using Incident Ions, Phys. Rev. Lett. 43, 1050. 14. Selman ,T. A. and Easa , S.I. (2001). In Auger,s De-excitation Processes: Matrix Element, Basrah J. Science 7, (4) : 120-126. 15.Zimnya, R. ; Miškovićb,Z.L. ; Nedeljkovićc, N.N. and Nedeljković, Lj.D. (1991),Interplay of resonant and Auger processes in proton neutralization after grazing surface scattering, J. Surface Science, Volume 255, Issues 1–2, 1 September, Pages 135–156. 16. Easa, S. I. (1986)In, Charge Exchange Processes in atom–surface scattering, PhD. Thesis, Univ. of Salford.,. Table (1): The transition rate Δ increase as the metal energy band width mε - a ε mε aε 0ε - F ε Fε 0ε - - - 11.65 -4.26 -15.91 Al - - - 6.96 -4.65 -11.61 Cu - - - 5.45 -2.75 -8.2 Na 19.85 -4.75 -24.6 - - - He 10.16 -3.4 -13.56 - - - H * All energies in eV http://www.sciencedirect.com/science/article/pii/0168583X93957935 http://iopscience.iop.org/search?searchType=fullText&fieldedquery=N+N+Nedelikovic&f=author&time=all&issn= http://iopscience.iop.org/0022-3700/14/16/027?fromSearchPage=true http://iopscience.iop.org/0022-3700/14/16/027?fromSearchPage=true 206 مجلة إبن الهيثم للعلوم الصرفة و التطبيقية 2012 السنة 25 المجلد 2 العدد Ibn Al-Haitham Journal for Pure and Applied S cience No. 2 Vol. 25 Year 2012 Fig.(1):Types of Auger charge transition Fig.(2): The ejected electron that originated from the metal 207 مجلة إبن الهيثم للعلوم الصرفة و التطبيقية 2012 السنة 25 المجلد 2 العدد Ibn Al-Haitham Journal for Pure and Applied S cience No. 2 Vol. 25 Year 2012 Fig.3: The theoretical model on real systems such as He/Cu , He/Al , He/Na , to investigate the effects of the energy band on the AD transition Fig.(4): The effects of the stored potential energy in the incident projectile 208 مجلة إبن الهيثم للعلوم الصرفة و التطبيقية 2012 السنة 25 المجلد 2 العدد Ibn Al-Haitham Journal for Pure and Applied S cience No. 2 Vol. 25 Year 2012 Fig.(5): The direct capture transition is the most effective in (AD) process Fig.(6): The transition describe the effective density of state ρeff for the metal surface 209 مجلة إبن الهيثم للعلوم الصرفة و التطبيقية 2012 السنة 25 المجلد 2 العدد Ibn Al-Haitham Journal for Pure and Applied S cience No. 2 Vol. 25 Year 2012 Fig.(7): The transition rate Δ increase as the metal energy band width increase Fig.(8): The Λ increase as the surface energy band width increase 210 مجلة إبن الهيثم للعلوم الصرفة و التطبيقية 2012 السنة 25 المجلد 2 العدد Ibn Al-Haitham Journal for Pure and Applied S cience No. 2 Vol. 25 Year 2012 Fig.(9): Tthe Δpi k decries exponentially as za increase Fig.(10): Comparison between Δ for He/Cu and H/Cu systems 211 مجلة إبن الهيثم للعلوم الصرفة و التطبيقية 2012 السنة 25 المجلد 2 العدد Ibn Al-Haitham Journal for Pure and Applied S cience No. 2 Vol. 25 Year 2012 غير المثار هدراسة التأثيرات االساسية في انتقال اوجي فالح حسن االسدي قسم الفيزياء ،كلية العلوم ، جامعة ذي قار 2011كانون االول 7، قبل البحث في : 2011ايلول 20استلم البحث في الخالصة Na, Cu, Al استخدم في هذه الدراسة طريقة مفكوك الحالة الذاتية لعملية انتقال اوجبه للشحنة بين سطوح عملية انتقال استخدمنا هذه الطريقة لوصف تاثيرات التركيب االلكتروني للسطوح في He ,H وغازي ان طاقـة الجهـد تخـزن داخـل الـذرات المتهيجـة æ ثير كثيـرا بحـزم الطاقـة للسـطوح ،اتتـالشحنة . وقد تبين ان كفايـة عمليـة االنتقـال لالسـتطارة مــن السـطح المعـدني وجــد ان االلكتـرون اليتحســس KeV1اي ذرات بطاقـة اعـل كبيــر السـاقطة وعليـة ففــي زمـن تف القـذائف والسـطوح . كمـا قمنـا باشـتقاق صـيغة جديـدة لعناصـر المصـفوفة بـين Zaتركيب الحزمة للمعـدن ويعتمـد علـى المسـافة .لتفاعل اوجيه غير المتهيج .رة، تفاعل ايون سطح: اوجيه الالمثار ، استطا الكلمات المفتاحية