Contributions of different generations of recoils to sputtering by backscattered light ions

Summary Neumann's expansion of the integral form of the Boltzmann transport equation is used to estimate the contribution of different generations of recoils to sputtering. By considering the flux generated by backscattered ions it is shown that primary recoils are, in the region of low energy (few keV), the main contribution to sputtering.     

Energy distribution of reflected ions at normal incidence on the target surface

Summary The energy distribution of reflected ions at normal incidence of the primary beam on the target surface is obtained as a result of approximate solution of the Boltzmann equation by the method of discrete streams. This method gives the opportunity to avoid the problem of negative distribution function, arising in the generally applied method of spherical harmonics, and to present the final result in analytical form. The analysis is performed for a power scattering cross-section and the theoretical energy distribution demonstrates one maximum when the ion mass is equal to the mass of a target atom, and two maxima when the ion mass is much less than the mass of a target atom.     

Nonadiabatic effects in auger-induced ionic desorption

Summary The Knotek-Feibelman mechanism of desorption is analysed in the context of a microscopic dynamical theory that has been proposed recently for closed-band systems. To understand the physical contents of the general equations, the probabilityP of ionic desorption is derived analytically in several selected model situations as a function of the characteristic desorption timet _o. Although typicallyt _o is quite long compared to the inverse level widthW _B ⁻¹, the results show very significant deviations from the limit of small velocities. This is due to the fact thatP is not primarly determined by the level width, but by the structures, like peaks and singularities, that are contained in the two-hole continuum. Such features, that are completely missed in the traditional approach that represents the continuum by a Lorentzian, are naturally enbodied in the present theory. They may originate from the position of the adatom energy level ɛ relative to the substrate band and/or by hole-hole correlation. When split-off localized states arise,P may become comparable with unity even in the limit of small velocities, giving raise to the Knoteck-Feibelman reneutralization bottleneck; however, this is not the case when the localized states are readsorbed by the continuum in the course of desorption. An explicit example of this behaviour is given. On the other hand, when ions desorb from ionic crystals with a large Madelung energy, the bond-breaking process may approach the sudden limit. A strongly nonadiabatic behaviour is then predicted, including a correlation-induced enhancement ofP by several orders of magnitude, even in bandlike situations. This rapid variation leads to suggestions for a new experiment that should enable us to see the effects of a fine tuning of the electronic parameters.

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Riassunto Il meccanismo di Knotek e Feibelman di desorbimento è studiato nel contesto di una teoria quantistica dinamica che è stata recentemente proposta ed è applicabile al caso di sistemi con bande chiuse. Al fine di mettere in luce il contenuto fisico delle equazioni generali, si sono scelte alcune situazioni modello per le quali si è ottenuta analiticamente la dipendenza della probabilitàP di desorbimento ionico dal tempo caratteristico di desorbimentot _o. Benchè tipicamentet _o risulti molto piú lungo della larghezza inversaW _B ⁻¹ del livello, i risultati dimostrano cheP può deviare in modo molto significativo dal limite di velocità basse. Infatti,P è determinato principalmente non dalla larghezza del livello, ma dalle strutture (picchi e singolarità) che sono contenute nel continuo. Questi aspetti sono ignorati completamente nell'approccio consueto, che rappresenta il continuo con una lorentziana, ma sono inclusi in questa teoria in modo naturale. Una possibile origine di strutture nel continuo è rappresentata da una posizione del livello eccentrica rispetto alla banda del substrato; un'altra, dalla correlazione buca-buca. Se ne risultano stati disereti isolati dal continuo,P può essere dell'ordine dell'unità anche nel limite di velocità basse, e questo è appunto il ≪collo di bottiglia≫ che impedisce la rineutralizzazione secondo Knotek e Feibelman; questo non avviene, però, se lo stato discreto è riassorbito dal continuo nel corso del desorbimento. Di tale fenomeno è fornito un esempio esplicito. D'altra parte, quando gli ioni desorbono da cristalli ionici con un'elevata energia di Madelung, il processo di rottura del legame può avvicinarsi al limite repentino. La teoria allora predice un comportamento fortemente non adiabatico, in cuiP è accresciuta di ordini di grandezza dagli effetti di correlazione, anche in situazioni in cui lo spettro è di tipo banda. Questa rapida variabilità diP porta a suggerimenti utili per verificare, con un nuovo esperimento, gli effetti di piccoli aggiustamenti dei parametri elettronici.

     

On the observation of anomalous electron emission from a thin film under the influence of an outside electric field

Summary It is established that accelerated secondary electrons with very low energies emitted from a thin surface layer where M?ssbauer absorption and normal photoeffect are taking place show two distinctly separated energy lines. The maximum of the first line corresponds to the applied accelerating voltage while that of the second one corresponds to about 30% higher energy. The investigations are performed with a magnetic beta-spectrometer and with an electrostatic analyser. It is found that the intensity of the second, ?anomalous? line depends on the nature of the emitting layer. A number of experiments confirming the reality of the observed effects are reported. This authors of this paper have agreed to not receive the proofs for correction.     

Many-body effects in the electron spectroscopies of incompletely filled bands

Summary Photoemission and Auger line shapes from almost completely filled bands have been widely discussed in recent years within a simplified model based on an Anderson Hamiltonian in which the virtual level shift due to the interactions is suitably compensated for. Up to now, the theory has been much more successful with XPS than with AES, and the reason for this was obscured by the lack of an exact solution and by the difficulty to assess the degree of validity of various approximate treatments that have been proposed. Here we present a Green’s function formalism that allows us to extend the closed band solution to the partially occupied case and lends itself to the exact numerical treatment of finite systems. By applying the theory to 27 and 125 atom clusters, we analyse the dependence of the spectra on hole-hole repulsionU with a degree of unfillingn _h≤0.25. We also consider the case when one of the spin subbands is full as a rough model for ferromagnetic metals. Correlation effects on the one-hole density of states produce a narrowing of the band region, while a split-off structure develops below the band forU comparable to the band width. The low-density approximation is good agreement with the exact results forn _h=0.1 and also forn _h=0.25 for small and moderateU. Our results on the Auger line shapes justify somewhat the suggestion by Haak and Bennetet al. that split-off states observed in photoemission must be discarded before computing the two-hole spectrum. Indeed self-energy corrections must be excluded also in bandlike cases, when the simple procedure of cutting off the unwanted structure is not applicable. This arises because, in a wide range of physical situations, the Auger line shape reflects the mutual scattering of undressed final-state holes.

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Riassunto Il modello teorico piú usato negli ultimi anni per le forme di riga di fotoemissione ed Auger di bande quasi completamente occupate si basa su un hamiltoniano di Anderson in cui lo spostamento del livello virtuale dovuto alle interazioni è opportunamente compensato. Finora la teoria ha dato risultati molto migliori per la fotoemissione che per lo spettro Auger. Le ragioni di ciò non sono chiare poiché non si dispone di una soluzione esatta ed è difficile valutare l’attendibilità delle varie approssimazioni note. Pertanto noi proponiamo un formalismo basato sulle funzioni di Green che permette, nel caso di aggregati finiti di atomi, di estendere la soluzione esatta, nota nel caso di bande chiuse, al caso di bande parzialmente occupate. Applicando il metodo a sistemi di 27 e 125 atomi, analizziamo la dipendenza degli spettri dalla repulsioneU tra lacune, per una concentrazione di lacunen _h≤0.25. Abbiamo considerato anche il caso in cui una delle sottobande di spin è completamente occupata come una prima approssimazione al problema di metalli ferromagnetici. Gli effetti di correlazione restringono il continuo nella densità di stati ad una particella e producono una struttura discreta sotto la banda seU è confrontabile con la larghezza della stessa. L’approssimazione di bassa densità è in buon accordo coi risultati esatti pern _h=0.1 ed anche pern _h=0.25 seU è piccolo o moderato. I nostri risultati sulla forma di riga Auger legittimano in qualche modo quanto suggerito da Haak e Bennetet al., e cioè che il picco satellite di fotoemissione deve essere soppresso nel calcolo della forma di riga Auger. Anzi, tutte le correzioni al propagatore ad un corpo, dovute agli effetti di correlazione, debbono essere escluse anche nel caso di spettri di tipo banda, dove, per l’assenza della struttura satellite in fotoemissione, il procedimento di Bennettet al. non è piú applicabile: infatti nella maggior parte dei casi d’interesse fisico, la forma di riga Auger riflette la dinamica di lacune non rinormalizzate.

     

The integral approach to the sputtering

Summary The emission-oriented integral form of Boltzmann transport equation is applied to the sputtering phenomenon. It is shown that the central quantity in the formulation, namely the characteristic mean free path of the phenomenon, can be the low-energy transport mean free path. The same mean free path gives a measure of the mean escape depth as derived in experiments and computer simulation studies. Finally, the sputtering yields, calculated by using the same mean free path, when compared with the experimental results, show an evident improvement with respect to the Sigmund theory.     

Inelastic ion interaction in solid hydrocarbons

Summary Erosion and decomposition of solid hydrocarbons under bombardment with proton, helium and argon ions is studied as a function of ion energy in the keV÷MeV range. Methane (10K), benzene (77K) and polystyrene (300 K) show a strong molecular hydrogen emission with a complex behaviour as a function of ion fluence (10¹²÷10¹⁷ions/cm²). Dimer formation is observed in the irradiated volume and high yield is measured (200 dimers/ion) for all the samples. At high fluence a three-dimensional carbon-hydrogen network is formed whose thickness is proportional to the ion range.

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Riassunto L'erosione e la decomposizione di idrocarburi solidi indotte da irraggiamento con fasci ionici quali protoni, elio e argo sono state studiate in funzione dell'energia dello ione incidente nel range keV÷MeV. Metano (10 K), benzene (77 K) e polistirene (300 K) mostrano una forte emissione molecolare con un comportamento complesso in funzione della fluenza nel range (10¹²÷10¹⁷) ioni/cm². Dal volume irradiato è osservata una alta emissione di dimeri (200 dimeri/ione). Ad alta fluenza si ha formazione di un composto carbone-idrogeno il cui spessore è proporzionale al range dello ione incidente.

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Реэюме ИсследуУтся эроэия и распад углеводородов при бомбардировке протонами и ионами гелия и аргона в эависимости от энергии ионов в кэВ-МэВной области. Метан (10 K), бенэол (77 K) и полистирол (300 K) обнаруживают сильную эмиссию молекулярного водорода, которая слоьной функцией флуенса ионов ((10¹²÷10¹⁷)ион/см²). Наблюдается образование димеров в облученном объеме и для всех образцов измеряется большой выход (200 димеров/ион). При высоком флуенсе образуется трехмерная углеводородная структура, толщина которой пропорциональна пробегу ионов.

     

On the existence of an universal energy function for sputtering yields by low-energy light-ion bombardment

Summary The mechanism wherenism whereby heavy solids are sputtered by lowenergy light ions can be explained by a linear-transport theory, by assuming only primary recoils as candidate for sputtering. It is shown that, from a theoretical point of view, scaling properties of the sputtering yield can be introduced if the appropriate dimensionless energy variable is assumed. In fact, the yield expression can be reduced to a formulation in which an energy function common to all the target-ion combinations is multiplied by a constant factor different for each combination. This expression, free from any kind of fitting parameter, gives a good approximation to the experimental data. Further developments are discussed in relation to the spreading of experimental points which do not exibit strict scaling properties.

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Riassunto Il meccanismo di erosione di solidi durante il bombardamento di ioni leggeri di bassa energia può essere spiegato nell'ambito della teoria del transporto assumendo che solo i rinculanti primari contribuiscono all'erosione. L'approccio teorico mostra che il coefficiente di erosione può esprimersi in termini di una funzione universale assumendo un'opportuna variabile energetica adimensionale. Infatti il coefficiente di erosione può essere ricondotto ad un' espressione in cui una funzione della sola energia, comune a tutte le combinazioni ione-bersaglio, è moltiplicata per una fattore costante differente per ogni combinazione. Questa espressione, priva di parametri aggiustabili, fornisco una buona approssimazione per i dati sperimentali. Ulteriori sviluppi sono discussi in relazione al fatto ai dati sperimentali non sono strettamente riconducibili ad una fuzione universale.

     

Crystal-glass transition in ion-bombarded alloys

Summary A model for glass formation and crystal structure retainment in binary alloys undergoing irradiation by energetic ion beams is presented. The major physical features provided by experimental conditions, namely spike formation and evolution of bombardment-induced surface compositional variations, are taken into account. At spike-lattice interface interatomic interactions with charge transfer occur, which induce formation of amorphization, or crystallization nuclei. Qualitative differences are found between glass forming and crystalline systems. To speed up publication, the author of this paper has agreed to not receive the proofs for correction.     

Influence of the deposited-energy function on the sputtering yield

Summary An explicit spatial dependence (a Gaussian) of the depositedenergy function has been considered in order to compare the sputtering yield obtained by taking into account all the energy deposited inside the target with that obtained by assuming the deposited-energy function throughout constant, namely equal to its value at the surface. The results indicate that the two yields differ sensibly for high incident-ion atomic number and/or for small target/ion mass ratio. To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

Heavy ion induced cluster formation and fragmentation phenomena in amorphous graphite

A study has been conducted into the mechanisms of evolution of clusters and their subsequent fragmentation under energetic heavy ion bombardment of amorphous graphite. The evolving clusters and their subsequent fragmentation under continuing ion bombardment are revealed by detecting various clusters in the energy spectra of the Direct Recoils (DRs) emitted as a result of collisions between ions and surface constituents. The successive DR spectra reveal that the energetics of bond formation as well as any subsequent fragmentation can be related to the processes of energy dissipation in a cylindrical volume of a few ? surrounding the ion path. The dependence of formation or fragmentation is seen to be a function of the ionic stopping powers in this cylindrical volume. Received: 2 January 1998 / Accepted: 5 March 1998     

Vibrations at 3C-SiC(001)-(32) surfaces

Si-terminated 3C-SiC(001) surfaces with () and ()reconstructions were investigated by high-resolution electron energy-loss spectroscopy (HREELS), low-energy electron diffraction (LEED) and Auger electron spectroscopy. The surfaces were prepared by subsequent annealing steps after cleaning by heating in a Si flux. At ()-reconstructed surfaces, the HREELS intensity increases while the widths of the loss lines decrease with proceeding preparation. Eventually, weak loss structures at 380 and 700 cm^-1 are detected besides the strong Fuchs-Kliewer phonon loss peaks. They are attributed to surface-localized vibrations, i.e., to stretching modes of on-top Si dimers and of C-Si-C groups, respectively. The weak features vanish after exposure to atomic deuterium, but reappear after subsequent annealing. At () reconstructed surfaces the HREELS lines are broadened and no surface-localized modes were resolved. Received 18 January 1999     

HREELS investigation of hydrogenated and deuterated GaN{0001} surfaces

The vibrational properties of clean, H- and D-covered GaN{0001} surfaces were investigated by high-resolution electron energy-loss spectroscopy. Auger electron spectroscopy and low-energy electron diffraction were utilized to monitor the surface cleanliness and structure, respectively. At the clean surface the Fuchs-Kliewer surface phonon frequency was determined to 700 cm^-1 (86.8 meV). For the adsorbate-covered surfaces current structure models predict only Ga-H vibrations for surfaces of either polarity. Despite of this, the HREEL-spectra of the hydrogenated sample show a new loss structure at 3255 cm^-1 (403.6 meV) and a shoulder at 1900 cm^-1 (235.6 meV) which are attributed to N-H and Ga-H stretching vibrations, respectively. After deuterium exposure an isotope shift occurs. Again, a N-adsorbate vibration is clearly resolved. A Ga-D bending mode is observed at 390 cm^-1 (48.4 meV), indicating that vibrations of both species are present. Received 1 February 2000     

Transmission spectra of thin CdS and CdSe crystals near higher-order isotropic points

Summary For photon energies below the absorption edge in CdS, CdSe and other II–VI crystals the polariton dispersion curves forE⊥c andE‖c (c-axis in a wurtzite crystal) corss at some points called isotropic points (IP). The occurrence of isotropic points provides the possibility of mode coupling between ordinary and extraordinary waves. Since the consequences of mode coupling on the optical properties for photon energies near the lowest IP lying much below the first excitonic state were widely discussed in recent years, more attention is now paid to isotropic points lying near the band gap and related to then=2,3, … excitonic states (?higher isotropic points?). Making use of Stahl's real density matrix approach we derive the polariton dispersion relationsk _⊥ (ω), andk _‖ (ω), for CdS and CdSe bulk crystals and determine the positions of IP's due to the crossing of theB-polariton with higherA-excitonic resonances. By the method of multiple internal reflection we calculate the transmission spectra for various crystal thicknesses (between 3 μm and 0.5 mm) and coupling mechanisms. The calculated transmission shows sharply peaked structures centred at the isotropic points.     

Heavy- and light-hole excitons in anisotropic semiconductors

Summary We show how to compute the eigenvalues of an anisotropic Schroedinger equation for light-and heavy-hole excitons using a simplified deltalike interaction potential. Performing the calculation with a potential appropriate to bulk GaAs crystal, we obtain the excitonic binding energies for the heavy- and light-hole excitons, with the heavy-hole binding energy greater than that for the light hole. Inversion of this order for the case of a quantum well is discussed and expalined     

Resonant and surface polaritons in quantum wells

Summary We show how the breaking of the translational invariance in a quantum well modifies the concept of polariton with respect to that defined for bulk material. Polaritons in quantum wells result from the combination of the exciton states with the radiation field. They are here obtained as the solutions of Maxwell equations with retardation, provided an appropriate nonlocal response function is used for the electric susceptibility, and Maxwell boundary conditions are imposed. We find two types of polaritons depending on the values of the in-plane wavevectork _II: those atk _II<ω/v (wherev=c/n is the velocity of light in the sample) are resonant with the radiation field in the barrier and those atk _II>ω/v cannot be coupled to waves in the barrier. In both cases explicit expressions are given for radiative shifts and radiative broadenings as functions ofk _II. Numerical results are obtained for GaAs-Ga_1−x Al _x As and for CuCl quantum wells and new experiments are suggested. The existence of resonant and surface polaritons justifies an interpretation of the temperature dependence of the radiative lifetime suggested by the same authors. It also decreases the radiative efficiency in the direction perpendicular to the planes and increases the radiative efficiency parallel to the planes with increasing temperature. Due to the relevance of its scientific content, this paper has been given priority by the Journal Direction.     

Longitudinal-transverse splitting in Wannier excitons and polariton states

Summary In the theory of Wannier excitons, the long-range nonanalytical part of the exchange interaction is usually expressed in terms of the dipole matrix element between Wannier functions. We show that it can be expressed in terms of the dipole matrix element between zone-centre Bloch functions, without any assumption on the localization of Wannier functions. We obtain an expression for the longitudinal-transverse splitting in terms of the dipole matrix element between the crystal ground state and the excition state. This is required in order to prove that the transverse upper polariton is degenerate with the longitudinal exciton in the limitk _ex→0. A new expression for the short-range part of the exchange interaction is also obtained, which is more suitable for microscopic calculations and which is evaluated for the case of CuCl. The resulting exchange parameter isΔ _ex = 12.6 meV, which compares well with the experimental value.

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Riassunto Nella teoria degli eccitoni di Wannier, la parte a lungo raggio e non analitica dell’interazione di scambio è generalmente espressa in termini dell’elemento di matrice di dipolo fra funzioni di Wannier. Noi mostriamo che può invece essere espressa in termini dell’elemento di matrice di dipolo fra funzioni di Bloch al centro della zona di Brillouin, senza assumere che le funzioni di Wannier siano localizzate. Otteniamo quindi un’espressione per lo splitting longitudinale-trasverso in termini dell’elemento di matrice di dipolo fra stato fondamentale del cristallo e stato eccitonico. Ciò è necessario per dimostrare che il polaritone trasverso del ramo superiore è degenere con l’eccitone longitudinale nel limitek _ex→0. Otteniamo inoltre una nuova espressione per la parte a corto raggio dell’interazione di scambio, che è più appropriata per un calcolo microscopico e che calcoliamo nel caso del CuCl. Otteniamo un parametro di scambioΔ _ex = 12.6 meV, in buon accordo col valore sperimentale.

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Резюме В теории экситонов Ваннье дальнодействуйщая неаналитическая часть обменного взаимодействия обычно выражается через дипольный матричный элемент между функциями Ваннье. Мы показываем, что эта часть обменного взаимодействия может быть выражена через дипольный матричный элемент между функциями Б=qlоха без каких-либо предположений о локализации функций Ваннье. Мы получаем выражение для продольно-поперечного расщепления в терминах дипольного матричного элемента между основным состоянием кристалла и экситонным состоянием. Это выражение требуется, чтобы доказать, что поперечный поляритон является вырожденным с продольным экситоном в пределеk _ex→0. Получается новое выражение для короткодействующей части обменного взаимодействия, которое более удобно для микроскопических вычислений и которое оценивается для случая CuCl. Вычисляется обменный параметрΔ _ex = 12.6 мэВ, который хорошо согласуется с экспериментальной величиной.

     

Magnetoexciton ground state for heavy- and light-hole excitons in anisotropic semiconductors

Summary We show how to compute the eigenvalues of an anisotropic Schr?dinger equation for light- and heavy-hole excitons in the presence of a magnetic field using a perturbational approach and a simplified deltalike interaction potential. Performing the calculation with a potential approapriate to bulk GaAs crystal we obtain a simple relation between the binding energy at zero field and the diamagnetic shift at low fields.     

Evidence of the exciton-plasma transition in the emission spectra of GaSe

Summary We present luminescence spectra of gallium selenide at 2 K in which a slow and continuous evolution from excitonic recombination to an electron-hole plasma emission is observed when the excitation intensity is increased. We find a small red-shift and a broadening of the direct exciton emission line which is followed by its disappearing. We explain these results with a model which takes into account the electron-hole correlation. Part of this work was carried out during a stage at the Institut de Physique Appliquée of the Ecole Polytechnique Fédérale de Lausanne (Switzerland).