Detector open

Figure 2.9: Scattered intensity versus time after nuclear excitation in an NRIXS experiment (schematically). At time zero, a synchrotron radiation pulse excites a material containing a nuclear resonant isotope. The scattering from electrons is prompt, i.e., almost immediately after the pulse arrived. The response of the resonant nuclei is delayed. Time discrimination permits to distinguish nuclear and electronic scattering.
The quantitative analysis gives the probability for the excitation of the nuclear resonance when the energy is tuned away by an amount needed for creation or anni-
hilation of phonons. The arrival of a very short (<100 ps) synchrotron radiation ash triggers the emission process of an inelastically scattered photon and of a conversion electron and subsequent uorescence radiation. The discrimination of the delayed events, which then signal the creation or annihilation of phonons from all other non-nuclear scattering contributions, that are prompt in time, is achieved by conventional electronic timing methods. If only the delayed photons are counted, one can expect to measure a function that is proportional to S(E). S(E) is obtained from the measured data after normalization, and the partial phonon or vibrational density of states (VDOS) can be extracted by a mathematical procedure mentioned in 7.3.4. Setup and components NRIXS experiments require synchrotron radiation of high brightness and high spectral density, being feasible mainly at third-generation synchrotrons like the European Synchrotron Radiation Facility (ESRF) in Grenoble, the Advanced Photon Source (APS) in Argonne (USA), and SPRING8 in Japan. A typical experimental setup of a nuclear resonance beamline is shown in gure 2.10.
Detector #2 Resonant Sample Ionization chamber Premonochromator Detector #1 Undulator
Figure 2.10: Experimental set-up for measurements of inelastic nuclear resonant scattering (schematical).
High-resolution monochromator Storage ring e
The X-ray source are electrons that are orbiting in the storage ring and periodically (once per turn) pass through an undulator. The X-rays are monochromatized in two steps (premonochromator and high-resolution monochromator) to an energy bandwidth that is much narrower than the phonon spectrum of our samples. The monochromatic X-rays excite nuclear resonances in the sample, and the re-emitted X-radiation is observed with the detector. An electronic timing circuit measures the elapsed time between excitation and re-emission and removes prompt eects. A control unit permits us to remotely interact with the devices that are inside the radiation area and thus are not directly accessible during the measurement. The rst component of the experimental setup is an undulator, which creates a broad energy band of X-rays (white beam) that ranges from about 6 keV up to several 100 keV. A water-cooled diamond double-crystal monochromator is used as premonochromator (or high-heat monochromator) to lter an energy band of about 1 eV from the white

The magnetic hf eld, Bhf , measured, at low T (near saturation) is roughly proportional to the local Fe atomic moment. Therefore, a measurement of Bhf provides information about possible high or low Fe magnetic moments in Fe lms. Fig. 4.2 exhibits a plot of the saturation hf eld versus the Wigner-Seitz radius rws [59] (in atomic units) for dierent fcc-like Fe systems [39]. (Note that rws =2.67 a.u. for Cu at 300 K). Bhf was o measured by 57 Fe Mssbauer spectroscopy. Fig. 4.2 demonstrates unambiguously that there is a transition from a low-moment fcc-Fe state to a high-moment fcc-like Fe state. The transition seems to occur around rws 2.69 a.u., which is in good agreement with theoretical predictions for bulk fcc Fe [3638]. A word of caution is justied in view of the rws values associated with the data points in Fig. 4.2. The only experimentally determined rws values are those of 5-10 ML thick low-moment fcc-Fe/Cu(001) (rws = 2.653 a.u., full square) and 2-4 ML thick high-moment fct-Fe/Cu(001) (rws = 2.705 a.u., full circle), reported in Refs. [45, 48, 60] on the basis of quantitative LEED results, as well as the value of rws = 2.643 a.u. (open triangle) reported for AFM low-moment -Fe precipitates in a Cu matrix [43]. The other rws data in Fig. 4.2 are nominal values that were obtained under the following assumptions: (i) the lattice
parameter of AFM low-moment fcc-Fe precipitates in a Cu1x Alx matrix (open triangles) is expanded with increasing x in proportion to the lattice parameter increase of the matrix [61, 62]; (ii) the FM high-moment fct-Fe lms in Fe/Cu1x Aux (001) multilayers (open circles [63]) and on ordered Cu3 Au(001) (full triangle [62]) expand their atomic volume proportional to that of the substrate. As compared to Cu, atomically ordered A Cu3 Au has an expanded lattice parameter of 3.75. Whether assumption (ii) is justied will be studied later. Many of the unique physical and magnetic properties of bulk iron-based alloys are related to the martensitic transformation (MT), i.e. the fcc-bcc phase transformation of iron. This is a rst-order discontinuous non-diusive transition that involves a sudden lattice deformation via a correlated motion of groups of atoms, and large lattice strain. The MT has been investigated in bulk iron-base materials for decades [37, 6466]. More recently, the MT in pure ultrathin epitaxial Fe lms on single-crystal Cu(001) substrates has become the subject of considerable interest: scanning tunneling microscopy (STM) [6770] and other techniques [40, 71, 72] including computer simulations [73] revealed a discontinuous transformation from the metastable fcc to the stable bcc phase at a critical lm thickness of usually 10 monolayers (ML) Fe upon increasing the thickness. In theoretical work, the energetics of the fcc-bcc MT may be described by a continuous transition known as the Bain transformation from fcc to bcc structures [74]. Already in 1924 Bain [74] suggested that an fcc phase can transform spontaneously into a bcc phase by a contraction of the interlayer spacing along the c-axis and biaxial expansion of the in-plane lattice along < 110 > directions in the fcc(001) plane (see Fig. 4.3). According to Fig. 4.3, the lattice parameter, a0 , of the fcc lattice denes the in-plane being twice the interlayer atomic distance a=a0 / 2 and the lattice parameter c=a0 , distance along the c axis. The path of tetragonal states with 2 c/a 1 between the fcc and bcc phases is called the Bain path. It has been used to calculate the ground-state energetics of the MT [37,65,75,76]. However, one has to keep in mind that this continuous Bain path is a convenient theoretical tool only, to the best of my knowledge it has never been observed experimentally. Searching for a Bain-transformation, pseudomorphic metal lms grown on (001) surfaces of fcc substrates are attractive systems [77]. A sharp strain-driven fcc-bct phase transition of pseudomorphic Cu lms on Pd(001) with increasing lm thickness shows features of a Bain transition [77]. Based on a low energy electron diraction (LEED) and scanning tunneling microscopy (STM) study, recently M.-T. Lin et al. [50] suggested that the observed structural transformation from fcc(001) to bcc(001) of pseudomorphic Fe lms on Cu3 Au(001) is driven by lattice mismatch induced strain through a Bain path; however, a continuous fcc-to-bcc lattice deformation was not reported by these authors [50], and only the initial (fcc(001)-oriented) and nal (bcc(001)-oriented) Fe phases of the presumed Bain transition were observed [50]. This work reports on the experimental observation of the continuous fcc-to-bcc Bain transformation in ultrathin epitaxial Fe lms on Cu3 Au(001) with increasing Fe coverage, contrary to the usual discontinuous MT of Fe. The out-of-plane interlayer distance (c=a0 , Fig. 4.3) and the in-plane atomic distance (a=a0 / 2, Fig. 4.3) of the growing Fe lm

4.2 Experimental

Figure 4.3: Lattice distortion during the fcc-bcc transition according to Bain [74]. ao is the lattice parameter of the fcc unit cell.
were precisely determined by combining X-ray photoelectron diraction (XPD) [78] and reection high-energy electron diraction (RHEED) results. The XPD investigation was performed in the group of Prof. R. Courths (Duisburg). Lattice parameters c and a both were observed to behave monotonically as a function of lm thickness from the fct to the bcc region. The atomic volume of tetragonal states that are produced by epitaxial strain was found to follow closely fct (face-centered tetragonal) or bct (body-centered tetragonal) epitaxial lines according to strain-energy calculations [79], with a critical value of a for crossover from the fct to the bct epitaxial line. The fct and bct states were found to be distinguishable by 57 Fe conversion electron Mssbauer spectroscopy (CEMS), and a Fe spin reorientation transition was directly o observed by CEMS.
The samples were prepared by molecular beam epitaxy (MBE) in an ultrahigh vacuum (UHV) system with a base pressure of 6 x 1011 mbar. In order to obtain a clean Cu3 Au(001) surface the single crystal surface was mechanically polished rst, followed by Ar+ sputter cleaning in the UHV system (1 kV, 5 x 105 mbar Ar pressure) at 200 C for 2-3 h, until no impurities could be detected by Auger electron spectroscopy (AES). Subsequent Ar+ sputter smoothing of the surface (0.5 kV, and 5.5 x 105 mbar Ar pres-
sure) was achieved at 200 C for 40 min. The atomically ordered Cu3 Au(001) surface was obtained after subsequent sequential annealing at 447 C for 1 h, at 417 C for 1 h, and at 327 C for 15 h, i.e. below the chemical order-disorder transition temperature of 390 C for Cu3 Au [34]. Several cycles of sputter smoothing and annealing were performed until sharp half-integer streaks of the ordered c(2x2) superstructure appeared in the RHEED pattern (Figs. 4.4(a),(e) and Fig. 4.5), in addition to the fundamental streaks, revealing the well ordered atomically at Cu3 Au(001) surface. RHEED was used to select the azimuthal orientation of the Cu3 Au(001) surface with an accuracy of 1. The iron lms were deposited from shielded water-cooled Knudsen cells with alumina crucibles. Natural Fe (99.9985 at. % purity) or 57 Fe metal (95.5 % isotopic enrichment) were used as starting materials. The evaporation sources were outgassed and stabilized carefully prior to sample deposition. The lm thickness and deposition rate (1.8 /min) were measured A by quartz-crystal microbalances that were calibrated previously by RHEED intensity oscillations observed during fcc-Fe deposition onto a clean Cu(001) substrate. The lm thicknesses are estimated to be accurate within 10 %. During deposition, the substrate temperature, though nominally RT, increased continuously up to 40 C for the thickest lms, as measured by the thermocouple of the sample holder. RHEED patterns were recorded during growth by a CCD camera connected to a computerized data storage and processing system. I/V-curves of the specular (0,0) LEED spot were measured by the same CCD camera/computer data storage system. 57 Fe CEMS spectra were measured in-situ in UHV, with the sample transferred to the UHV cold-nger of a liquid He-cooled ow cryostat. Electrons emitted from the sample surface after the o nuclear resonant absorption were detected by a channeltron [80]. A 57 Co-in-Rh Mssbauer source of 100 mCi activity was used. The incoming 14.4 keV -ray entered the UHV chamber through a Be window in normal incidence to the lm plane.

Figure 4.12: Relative Fe atomic volume V, (full squares) versus the lattice parameter ratio c/a, experimentally obtained combining present RHEED results and XPD results (Courths et al. [78]). Also plotted are results from ab-initio calculations of the total energy of iron as a function of c/a (along the Bain-path) and of the atomic volume within the GGA (generalized gradient) approximation perA formed by Friak et al. [86]. The experimental atomic volume of FM bcc Fe (Vexp =11.) was used for normalization. Only states with minimum energy are shown. Thick black lines show the FM/AFMD and AFMD/AFM1 phase boundaries. The dark blue straight lines correspond to constant lateral lattice parameters of various (001) substrates. The crosses composed by the vertical and horizontal error bars centered at the straight lines, represent structures of Fe lms on the corresponding substrates found experimentally. The green circle, shifted from the straight line, stands for Fe/Cu3 Au [58]. The other two circles show experimental structures where no error bars were given. Yellow asterisks represent the theoretical results found by Friak et al. [86].
Thick black lines show the FM/AFMD (ferrromagnetic/double-layer antiferromagnetic) and AFMD/AFM1 (double-layer antiferromagnetic/single-layer antiferromagnetic) phase boundaries. The included straight lines correspond to constant lateral lattice parameters of various (001) substrates, assuming that the pseudomorphic Fe overlayers adopt the lateral lattice dimensions of the substrate in the (001) plane and relax only the interlayer distance (characterized by c/a). The large crosses composed of the vertical and horizontal error bars centered at those straight lines and the full circles represent experimental data of Fe lms on the corresponding substrates reported in the literature. Yellow asterisks

4.5 Conclusions

represent theoretical results by Friak et al. [86]. The theoretical calculations for the Fe Cu3 Au(001) case are within error bars in accordance with the experimental Fe-atomic volume obtained by Feldmann et al. [57] (light blue cross) that lies on the straight line for the Cu3 Au substrate. However, the atomic volume determined by Schirmer et al. (green circle) [58] is shifted from the Cu3 Au line, but can be found in the FM area of the plot. Almost all experimental volumes of the present thesis (full squares) can be also found in the ferromagnetic region predicted in the calculations [86], although the two volumes corresponding to 1.39 c/a 1.40 are close to the calculated FM/AFMD phase boundary. One can notice that most of the present experimental values (full squares) do not follow the calculated straight line behavior for the Cu3 Au substrate.
The structure of epitaxial Fe lms on Cu3 Au(001) was precisely determined by the present RHEED measurements and XPD results by Courths et al. [78]. With increasing lm thickness a nearly linear continuous compression of the perpendicular lattice parameter, c, and a simultaneous continuous expansion of the in-plane atomic distance, a, was observed. Films with thicknesses between 1-12 ML do not grow pseudomorphous , but appear to form twisted crystallographic domains including some kind of atomic disorder. Apparently, the strain energy induced by the compressed perpendicular interlayer spacing is lowered by rotating the planar Fe unit mesh array from the surface mesh of the substrate. Films thinner than 2 ML are fct and show reduced in-plane spacings as compared to the substrate surface due to island growth and lattice relaxation. Up to 3.5 ML the lm structure is fct. There is an intermediate region between 3.5 ML - 6.5 ML, where the in-plane atomic spacing of 2.68 remains nearly independent of thickness, while the A perpendicular spacing c changes continuously. Above 6.5 ML thickness the lms have bct structure, and a as well as c approach bulk bcc-Fe values at 13.5 ML. The observed continuous compression of c and the simultaneous continuous expansion of a implies that a continuous fcc-bcc Bain transformation takes place in the Fe/Cu3 Au(001) system with increasing lm thickness, contrary to the Fe/Cu(001) system, where a discontinuous martensitic transformation is known to exist. One can speculate that Au atoms observed to be present at the Fe lm surface in the case of Fe/Cu3 Au(001) [78] act as surfactants and prevent the martensitic transformation. The atomic volume of the tetragonal states was found to be close to fct or bct epitaxial lines [79]. A crossover from ferromagnetic high-moment high-volume fct to bct Fe was found to occur in the intermediate thickness range between 3.5 ML - 6.5 ML where the in-plane atomic distance a is nearly constant. Conversion electron Mssbauer spectroscopy (CEMS) was used to prove that o a fct-plus-bct two-phase structure does not exist. Fct-Fe lms are in a high moment FM state. The Mssbauer results also prove that the structural changes observed by RHEED o and XPD (which are surface sensitive techniques) do not occur only in the surface region, but seize the lm as a whole.

5.3.1.2

Fe/GaAs(001)-HEMT
Since the last layer of the GaAs-HEMT substrate is a 30 nm thick GaAs(001) lm (doped with Si), it is not expected to nd remarkable dierences between the epitaxial growth of Fe on GaAs-HEMT(001) (Fig. 5.7) or on GaAs(001) (Fig. 5.5). Nevertheless, the RHEED streaks of the clean GaAs(001)-HEMT surface obtained after annealing up to 500 C (Fig.5.7(a)) were not as sharp as those of the corresponding clean GaAs(001) surface

100 (a) 40 20

GaAs substrate

Intensity (a.u.)

<5 ML >5 ML

Intensity

kFe// ( 1,0) ( 0,0) ( 1,0)
In-plane atomic distance relative to GaAs
1.07 1.06 1.05 1.04 1.03 1.02 1.01 1.00 0.10

Position (pixels)

bulk Fe GaAs
Figure 5.6: (a)(left) Specular RHEED intensity versus Fe thickness (the insert shows a magnied section); (right) schematics of the growth morphology. (b) Thickness dependence of the relative Fe inplane atomic distance (relative to that of GaAs(001)) measured along the [110] azimuthal direction. Insert: intensity prole obtained for 30 ML Fe thickness from the horizontal scan indicated in Fig. 5.5(a) and least-squares tted with three Lorentzian lines and a parabolic background.
(Fig.5.5(a)), and the HEMT surface did not show a clear surface reconstruction (Fig. 5.7(a)).

GaAs-HEMT(001)

Fe(4 ML)/GaAs-HEMT(001)

Fe(40 ML)/GaAs-HEMT(001)

Figure 5.7: RHEED patterns measured along the [110] azimuthal direction of (a) clean GaAs(001)HEMT substrate, covered by (b) 4 ML Fe and (c) 40 ML Fe. (Beam energy 9 keV, 35A).
Analogous to the epitaxial growth of Fe on GaAs(001) (sample A), the epitaxial growth of Fe/GaAs(001)-HEMT (sample D) also exhibits 3D-type RHEED patterns after 5 ML (Fig. 5.7(b)) and 55 ML (Fig. 5.7(c)) Fe coverage. The only dierence observed by RHEED between the growth of bcc-Fe on both types of substrates is a very weak 2-fold
surface reconstruction that appears after the deposition of 5 ML Fe on the GaAs-HEMT surface (hardly visible in Fig. 5.7(b)) and that disappears at thicker Fe thicknesses (Fig. 5.7(c)). 5.3.2 5.3.2.1

Fe CEMS Fe/GaAs(001)

o Fig. 5.8 shows the 57 Fe Mssbauer spectrum (CEMS) of sample A measured ex-situ at RT. This spectrum can be decomposed in terms of three subspectra: a sextet due to bulk-like bcc-Fe, a distribution of hyperne magnetic elds assigned to the intermixed magnetic Fe/GaAs interface, and a central quadrupole-split doublet caused by a non-magnetic Fe-Sn alloy formed at the interface between Fe and the Sn coating layer. From the intensity ratio of lines No.2 (5) and No.3 (4) in the sextet (see I2,5 /I3,4 in table 5.2) one can calculate the angle () between the Fe magnetic moment and the incident -ray (perpendicular to the sample surface), averaged over the sample: sin2 = 2I2,5 /I3,+ I2,5 /I3,4 (5.1)

CHAPTER 6. Epitaxial growth and interfacial structure of Sn on Si(111)
layers that undergo the transition to -Sn. The purpose of the present work was to clarify this question. LEED and RHEED performed during the growth of Sn on the Si(111)-(7x7) surface will show that ultrathin -Sn layers are formed. It will be demonstrated by 119 Sn conversion electron Mssbauer spectroscopy (CEMS) that these layers remain stabilized o as buried -Sn at the interface up to 3.5 ML after further coverage by thick -Sn layers. Moreover, the epitaxial relationship between thick -Sn layers on Si(111) is reported.
Thin epitaxial Sn layers of natural isotopic composition (of 99.995 at. % purity) and 119 Sn enriched epitaxial Sn layers were grown in UHV on the (7x7) reconstructed clean Si(111) surface at room temperature (RT). The isotopic enrichment of 119 Sn was 82.9 %. Before being loaded into the UHV system (base pressure 8x1011 mbar), the Si substrates were rinsed in acetone and ethanol. The (7x7) substrate surface was obtained after in-situ annealing in UHV at 1100 C for 15 minutes to eliminate the top SiO2 layers. Auger electron spectroscopy (AES) measurements after the in-situ cleaning showed a Si surface free of oxygen and carbon contaminants. A Sn layers with thicknesses (tSn ) between 2 and 1000 were evaporated from KnudsenA cells (Al2 O3 crucible) with low deposition rates (0.02-0.025 /s). The deposition rates were controlled by a quartz-balance monitor. The pressure during the evaporation was always lower than 5x1010 mbar. To avoid the oxidation of the Sn layers during the exsitu measurements, all samples were covered with a 50-60 thick amorphous Si layer A deposited from an e-gun. For the structural characterization, RHEED measurements were carried out during deposition. The RHEED patterns were recorded by a CCD camera connected to a computerized data storage and processing system. The thickness dependent - to -Sn phase transition was also studied ex-situ by 119 Sn conversion electron Mssbauer spectroscopy (CEMS) at room temperature. For the 23.88 o keV Mssbauer -radiation, 119 Sn in a CaSnO3 matrix was used as source. For electron o detection a He-4% CH4 gas proportional counter was used, with the sample mounted inside of the counter. An electromechanical Mssbauer drive and conventional electronics o were employed, the source being moved in constant acceleration mode. All isomer shift o () values are given relative to a CaSnO3 absorber at RT. The Mssbauer spectra were least-squares tted with the program NORMOS [120] with a Lorentzian line shape.

Results

Figure 6.1 displays RHEED patterns recorded during growth along the [112] azimutal direction of the clean Si(111)(7x7) surface (a), and the Sn covered Si(111)(7x7) surface (b)-(d). All images are taken with a low electron beam voltage (6 keV) and a low beam

6.3 Results

current (25 A) to avoid heating of the sample surface by the electron beam. The sharpness of the superstructure streaks (six vertical streaks between the central (0,0) and the fundamental (1,1) or (1,1) reection) observed in Fig. 6.1(a), and the presence of superstructure reections along several Laue circles, together with the appearance of Kikuchi lines, indicate atomically smooth and well-ordered surfaces. In the same way, sharp fundamental (0,0), (1,1) and (1,1) reections were found after the deposition of 6.8 ML Sn (Fig. 6.1(d)) demonstrating the atness of the epitaxial layers. The growth was observed to be pseudomorphic up to a thickness of 3 to 3.5 ML (Figs. 6.1(b-c)). The intensity of the fundamental RHEED reections initially decreases with increasing lm thickness (Fig. 6.1(c)), reaching a minimum at around 3.5 ML. Above this critical thickness, lattice relaxation starts, and the RHEED pattern becomes brighter again. Finally, after depositing 6.8 ML Sn (Fig.6.1(d)), a clear increase in the separation of the (1,1) and (1,1) RHEED reections as compared to the Si substrate was observed, implying a contraction of the in-plane atomic distance in real space (see Fig. 6.4(b) below). This fact can be understood if one considers that for thick Sn layers the more stable phase would be the bulk -Sn phase, which has a smaller lattice parameter than -Sn. Therefore, the higher lattice mismatch between substrate and deposited material observed above 3.5 ML appears to be related to the -Sn transition. A change in the structure of the lm from diamond (-Sn) to body-centered tetragonal (-Sn) can explain the end of the pseudomorphic growth of Sn on the silicon substrate with diamond structure above 3.5 ML. After deposition of 30 Sn, a (1x1) RHEED pattern was observed (Fig. 6.2) characA terized by sharp (1,1) and (1, 1) fundamental streaks, together with weak (2,2) and (2, 2) reections indicating good epitaxial quality and surface atness of the -Sn islands grown on the interfacial -Sn layer. Thicker Sn lms between 100 (Fig. 6.3(a)) and 200 (Fig. A A 6.3(b)) still showed relatively long and sharp RHEED streaks, and a weak 2-fold surface reconstruction appeared. The absence of a spotty pattern in RHEED (characteristic of 3D-islands growth) observed after the deposition of thick Sn layers indicates the growth of Sn islands with a very at surface. The evolution of the RHEED intensity during growth was measured on the (0,0) specular spot near the shadow-edge (in the region of diuse scattering). Fig. 6.4(a) shows that immediately after opening the shutter, the intensity rst increases to a maximum and then reaches a minimum at 1 ML thickness as expected under diuse scattering conditions and layer-by-layer growth. Such intensity oscillations are observed up to 3 ML coverage. The observation of intensity oscillations by RHEED provides evidence for quasi layer-by-layer growth for the rst 3 monolayers. Above this thickness, the intensity changes only weakly, and no more oscillations are found. The periodicity of the RHEED oscillations corresponds to the thickness of 1 ML -Sn that experienced a 9 % expansion in the out of plane atomic distance along the [111]--Sn direction, as measured with a quartz microbalance during the evaporation. This eect is correlated with the contraction of the in-plane spacing that the interfacial -Sn experiences to match the in-plane atomic distance of the silicon substrate. The intensity proles obtained for dierent thicknesses from the horizontal scan (as

Above 115 eV and up to 200 eV, the LEED patterns observed show only reections from the Si(111) substrate. The spots observed were not elongated or rotated, but rather sharp, showing a three-fold symmetry for certain energies which is characteristic of the Si(111) surface. Scanning electron microscopy images performed ex-situ on Sn(200 )/Si(111) (see section 6.3.4) will conrm the hypothesis of the formation of Sn islands A that do not coalesce even after the deposition of a large amount of Sn, leaving regions on the substrate between -Sn islands which are almost uncovered. 6.3.3 Auger Electron Spectroscopy (AES)
The Sn-thickness dependence of Auger electron spectra has been measured as an additional check of the origin of the substrate-like spots observed by LEED on Sn-covered Si(111). Fig. 6.8 displays AES spectra measured after the deposition of (a) 10 A Sn, (b) 20 Sn, (c) 40 A Sn, (d) 60 Sn, (e) 100 A Sn, and (f) 200 Sn. In addition to A A A the double peak of Sn at 430-437 eV, the weak peak of Si at 91 eV can be observed in all spectra. The intensity of the AES Si signal relative to the Sn signal decreases with increasing thickness from 10 to 200 Sn, but does not approach zero (Fig. 6.9). This A demonstrates that there are substrate regions covered only by a small amount of Sn (very likely -Sn) even after the deposition of relatively thick Sn lms, and these open regions provide a non-negligible substrate signal to the LEED patterns. 6.3.4 Scanning Electron Microscopy (SEM)
In collaboration with the group of Prof. E.F. Wassermann and Dr. G. Dumpich (Duisburg) scanning electron microscopy measurements were performed ex-situ on a 200 thick A Sn lm epitaxially grown on Si(111). Figures 6.10(a) and (b) show large Sn islands of diameters between 100-500 nm. The islands do not coalesce even after depositing 200 A Sn, and regions of the Si substrate almost uncovered by Sn can be observed. This eect must be due to a large surface energy of the -Sn clusters formed compared to the Sn/Si interfacial energy, resulting in agglomeration rather than wetting of the substrate. The rather sharp RHEED streaks (Fig. 6.3(b)) measured on such samples show that the top of the Sn islands must be relatively at on an atomic scale. 6.3.5

Sn CEMS

It is well known [124, 125], that measurements of the isomer shift in thin Sn layers and multilayers enable one to distinguish - from -Sn [121, 126], taking into account the 0.5 mm/s dierence in the isomer shifts of bulk -Sn ( = + 2.03 0.02 mm/s at RT) and bulk -Sn ( = + 2.56 0.01 mm/s at R.T.), both values relative to the BaSnO3 (or CaSn03 ) standard absorber [124126]. Fig. 6.11 displays the thickness dependence of 119 Sn CEM spectra of epitaxial Sn layers grown on Si(111)-(7x7) at RT. Below 4 ML coverage (Fig. 6.11(a)-(c)), pure Sn was found. -Sn appears above this critical thickness when the coverage is further increased (Fig. 6.11(d),(e)). Fig. 6.11(f) shows a typical -Sn spectrum corresponding

The epitaxial growth of Sn layers on Si(111)(7x7) surfaces at room temperature was investigated by RHEED, LEED and 119 Sn CEMS. The formation of up to 3.5 ML of metastable -Sn at the Sn/Si(111) interface was observed. The interfacial -Sn layer remains stabilized even after further deposition of thick Sn layers that undergo the -Sn -Sn transformation. Layer-by-layer-like growth is observed up to 3 ML coverage, i.e. in the -Sn region. Only a small decrease (relative to bulk -Sn) by 1.5 a3 of the 0 total s-electron density at the 119 Sn nucleus was measured for submonolayers of 119 Sn at the Sn/Si interface, indicating only weak electronic charge transfer at the interface. The present RHEED and LEED results demonstrate that for Sn coverages larger than 3.5-4 ML at epitaxial -Sn islands grow, with the epitaxial relationship Sn(200)//Si(111) and -Sn[011]//Si[110]. The observed six-fold LEED pattern is compatible with three crystallographic domains with this epitaxial relationship, but rotated
by 60 and 120. These rotational angles show a small angular distribution in the lm plane with a width of 10 -15. The measured in-plane atomic distance of epitaxial -Sn is expanded by 2-7 % relative to that of bulk--Sn. AES signals and SEM images demonstrate that the at -Sn islands do not uniformly cover the substrate surface even after the deposition of up to 200 Sn. Thus, wetting of the Si substrate by Sn is inhibited, A probably due to the high surface energy of Sn. For several incident electron energies (85-110 eV) and rather thick Sn lms, an additional six-fold (1x1) LEED pattern similar to that of the Si(111) substrate, but rotated by 30 , was observed. This pattern might originate from uncoated -Sn regions, located in the space between -Sn islands.
Structure and vibrational dynamics of interfacial Sn layers in Sn/Si multilayers
Elemental semiconductors with diamond structure, e.g. Si or Ge, are known to exist in amorphous form when prepared either as bulk glasses or as thin lms [128, 129]. An exception is gray tin (-Sn) which in the crystalline state is a non-polar semiconductor with diamond structure and a band-gap nearly equal to zero (0.08 eV at 300 K) [130]. Only one literature report is known to exist on the observation of the amorphous phase of -Sn, in this case produced by ion implantation [131]. The amorphous structure of group IV semiconductors (Ge,Si) has been shown [132] to deviate from the ideal tetrahedral coordination of the diamond structure by bending of the four nearest neighbor covalent bonds, with a spread in bond angles of about 10 degrees around the ideal value of 109. Deviations by bond lengthening are not observed to be more than 1% [132]. At ambient pressure -Sn is the stable low-temperature phase of bulk tin, which transforms into the metallic body-centered tetragonal -Sn phase (with lattice parameters a=5.83 , c= 3.18 A ) when the temperature is raised above Tc =13.2 C. The phase transition of bulk A Sn is an entropy driven structural transformation which is determined by the dierence in vibrational entropy of the two phases [133]. It has been shown that crystalline -Sn (a=6.489 A) can be stabilized as a metastable phase above Tc (and in particular at room temperature, RT) in the form of a lm of considerable thickness ( 1000 ) by A heteroepitaxy on an appropriate substrate. For instance, epitaxial RT growth of -Sn lms is feasible on InSb(001) substrates (a=6.4798 ) because of close lattice matching A [110, 126, 130, 134137]. On the other hand, RT growth of epitaxial -Sn type overlayers on Si(111) substrates has been shown in chapter 6 to be limited to only 3 atomic layers, because the larger lattice mist (Si: a=5.4309 ) favors the transition to -Sn above such A low Sn coverages. In the present work Sn(tSn )/Si(tSi ) multilayers of dierent Sn and Si thicknesses (tSn and tSi , respectively) are investigated. Contrary to the crystallographically well-ordered epitaxial systems described in chapter 6, the Sn layers in the present multilayers are embedded between amorphous Si (a-Si) layers. This poses the interesting question for the type of crystallographic structure of the Sn layers under this condition, in particular in the Sn/Si interfacial region. In general, knowledge of the interfacial structure is important for the detailed understanding of Schottky barriers in metal/semiconductor systems [138]. Sn/Si multilayers form an interesting system, where atomic interdiusion at the Sn/Si interfaces may be excluded, because Sn and Si do not form any solid solutions or compounds, even after melting, according to the thermodynamic phase diagram [139]. The principle aim of this study was to gain insight on the structure and lattice dynamics of the Sn layers, in particular, the Sn/Si interfacial region. Phonons in superlattices are of general interest, because phenomena like Brillouin zone folding, interface modes and conned phonon modes that do no exist in bulk materials may be observed [140, 141].

CHAPTER 7. Structure and vibrational dynamics of interfacial Sn layers in.
Since the maximum phonon energy of bulk Sn (-Sn in this case) is near 200 cm1 (or 24.8 meV) and thus rather low [133], while the vibrational excitations of a-Si extend up to much higher energies ( 600 cm1 or 74.4 meV) [128,129,132], connement may be expected for a considerable part of high energy excitations in a-Si, but not in the Sn layers. However, phonons in the Sn layers might be inuenced by evanescent modes of conned excitations in the a-Si layers [140, 141]. Several techniques have been employed, including X-ray diraction (XRD), Raman o scattering, 119 Sn conversion-electron Mssbauer spectroscopy (CEMS), and 119 Sn nuclear resonant inelastic X-ray scattering (NRIXS) of synchrotron radiation. NRIXS is an efcient and unique method for the direct measurement of the vibrational (or phonon) density of states (VDOS) of thin lms and buried interfaces that contain Mssbauer isoo topes, independent of whether the structure is crystalline or amorphous [12, 142145]. CEMS and NRIXS are local methods providing information on an atomic scale.
Sn/Si multilayers of composition [Sn(tSn )/Si(tSi )]n were grown on Si(111) wafers in an A A ultrahigh vacuum (UHV) system, with Sn thicknesses (tSn ) between 0.4 and 100 , A A and Si thicknesses (tSi ) between 20 and 80. The number of bilayers, n, varies between 1 and 50. The enrichment of 119 Sn was 82.9 %. The Si substrates were rinsed in acetone and ethanol just before being loaded into the UHV chamber. The Si(111) substrates were cleaned in situ by annealing for 15 minutes at 300 C. The multilayers were grown at two dierent deposition temperatures, Ts , i.e. -50 C and RT, to investigate the eect of temperature on the phase transition. Highpurity (undoped) Si was evaporated by an electron gun with a deposition rate of 0.1-0.2 /s, and a deposition pressure of 3-5109 mbar. At rst, a Si layer was deposited on the A Si(111) substrates, and all multilayers were coated with Si on the top to avoid oxidation. It is known that UHV deposition of Si lms under such conditions results in amorphous (a-)Si layers. Metallic 119 Sn was evaporated from a Knudsen cell (Al2 O3 crucible) at a A deposition pressure of 1-2109 mbar and a deposition rate between 0.02-0.025 /s. The real substrate temperature during deposition was somewhat higher than the previously indicated values, since up to 40 C was measured by a thermocouple at the sample holder for the RT case. The evaporation rates and lm thicknesses were monitored with a calibrated quartzcrystal microbalance and were determined from the bulk density of -Sn. Additionally, X-ray (-2) reectometry studies under grazing incidence geometry were performed to check the quality and thickness periodicity of the multilayers. For comparison, also epitaxial 200-Sn(001) lms (crystalline -Sn) on A InSb(001)substrates were grown, as described in Ref. [126].

Table 7.4: Mssbauer parameters of [Sn(10 )/Si(77 )]4 multilayer deposited and measured at RT o A A before and after annealing at 350 C.

Raman spectroscopy

The rst-order Raman scattering by phonons (or vibrational excitations) was measured in Sn/Si multilayers at RT. Fig. 7.8 displays intensity versus Raman shifts of four dierent samples: (a) A Si(70 )/Sn(1000 )/Si(111), (b) [Sn(15 )/Si(50 )]6 /Si(111), (c) [Sn(10 )/Si(50 A A A A )]50 /Si(111), and (d) Pt(20 )/-Sn(60 )/InSb(001), all grown at RT. A A A The spectrum in Fig. 7.8(a) shows a sharp peak at 523 cm1 that originates from transverse optical (TO) phonons of the crystalline Si substrate [151, 152]. The 1000 A
Figure 7.8: Raman spectra measured at RT in He atmosphere of (a) Si(70 A)/Sn(1000 )/Si(111); A )/Si(50 )]6 /Si(111); (c) [Sn(10 )/Si(50 )]50 /Si(111); and (d) Pt(20 )/Sn(60 A A A (b)[Sn(15 A A A)/InSb(001).
Sn layer in this sample exists in the crystalline (metallic) -Sn phase (see section 7.3.1) with bct structure which cannot be detected by means of Raman spectroscopy. The broad peaks observed in Fig. 7.8(a)-(c) at around 476 and 144 cm1 are those of the TO-like and transverse acoustical (TA) like excitations, respectively, of amorphous (a-)Si, indicating the amorphous structure of the deposited Si layers [152]. Since the total amount of Si in samples (b) and (c) is much larger than that of Sn, it is very dicult to detect any contribution of -Sn (if present at all) in these spectra. Furthermore the Raman peak of the TO phonons in -Sn grown on InSb is found at 180 cm1 (Fig. 7.8(d)), in agreement with Ref. [153]. Since the broad 144-cm1 peak of a-Si is in the same Raman shift region, it is not possible to distinguish -Sn from a-Si because of considerable overlap of the spectra. One should note that if the -Sn layers were in a highly disordered or amorphous -Sn-like structure, they are expected to show a broadened TO-like peak with reduced intensity, making its detection even more dicult. 7.3.4 Nuclear resonant inelastic X-ray scattering (NRIXS)
A NRIXS spectra were measured at RT on the following samples: 119 Sn(500 )/InSb(001), [119 Sn(10 )/Si(20 )]50 , [119 Sn(10 )/Si(50 )]46 and [119 Sn(20 )/Si(50 )]25. The A A A A A A

S1 (E) =

and the subsequent terms in the harmonic approximation may be found through the recursive relation:
Figure 7.9: (a) NRIXS spectrum (raw data) of 500 thick epitaxial - 119 Sn on InSb(001) (red line) A measured at RT. The dotted line shows the instrumental resolution function; (b) decomposition of the NRIXS spectrum (after normalization and removal of the elastic peak) in a one-phonon (1), two-phonon (2) and a higher-order phonon (3) contribution.

Sn (E) =

S1 (E )Sn1 (E E )dE
Here =(kB T)1 with kB the Boltzmann constant, T is the temperature, ER = 2 k 2 /2M the recoil energy of the free nucleus, k the wave vector of the photon, and M the mass of
the atom. The function g(E) is the normalized phonon (or vibrational) density of states (VDOS). The relative contribution Sn (E)dE of the n-phonon term is given by (-ln f)n /n!.
Figure 7.10: (a) The sum of NRIXS spectra (raw data) of [119 Sn(10 )/Si(50 )]50 and [119 Sn(10 A A )/Si(20 )]46 measured at RT; (b) decomposition of the NRIXS spectrum (after normalization and A A removal of the elastic peak) in a one-phonon (1), a two-phonon (2), and a higher-order-phonon (3) contribution.
In order to extract the phonon excitation probabilities, the program PHOENIX [154] was used. The contributions of the one-, two- and higher order phonon excitation probabilities are displayed in Fig.7.9(b), 7.10(b) and 7.11(b), respectively. The clear distinction of the multi-phonon contributions is no longer possible, if the Lamb-Mssbauer factor is o
small, like in -Sn [13,122]. In this case, the expansion in eq.(7.2) converges slowly, and a large number of terms has to be taken into account. With an f factor of 0.16 [13], -Sn has signicant multiphonon contributions, but not to the degree of preventing the separation of S1 (E), S2 (E), S3 (E).
Figure 7.11: (a) INRS spectrum (raw data) of [119 Sn(20 )/Si(50 )]25 measured at RT; (b) decompoA A sition of the INRS spectrum (after normalization and removal of the elastic peak) in a one-phonon (1), a two-phonon (2), and a higher-order phonon (3) contribution.
The phonon (or vibrational) density of states g(E) in eq.(7.3) is proportional to the one-phonon term in the expansion of eq.(7.2). The measured spectra of Figs.7.9(b), 7.10(b) and 7.11(b) were deconvoluted with the resolution function and eq.(7.3) was ap-

1600 1400

a -Sn (scaling) TO Theory

VDOS (at.vol.-1 eV-1)

exp LO

350 300

a-Sn (scaling) (b)

VDOS (at.vol.-1eV -1 )

400 350
a-Sn (scaling) (c) a -Sn (exp.)

VDOS (at. vol.-1 eV-1)

Energy (meV)
Figure 7.12: Vibrational density of states (VDOS): (a) for -119 Sn(500 )/InSb(001), derived from A Fig.7.9(b) (full circles); the theoretical phonon DOS convoluted with the the experimental resolution A A function of 0.8 meV is shown for comparison (pink solid line) [133]. (b) for [119 Sn(10 )/a-Si(50 )]46 and [119 Sn(10 )/a-Si(20 )]50 multilayers, derived from Fig.7.10(b) (full circles). (c) for [119 Sn(20 )/aA A A Si(50 )]25 multilayer, derived from Fig.7.11(b) (full circles); the bar diagram (-Sn (exp)) indicates the A A measured peak and shoulder positions for -119 Sn (500 ) in (a); the theoretical VDOS for bulk -Sn (in arbitrary units) is also shown for comparison (blue solid line) [133]. The other bar diagrams indicate the energies of the prominent peak or shoulder of the various phonon-like bands predicted for amorphous -like Sn (a-Sn) by scaling (use of eq.(7.5), see also Fig.7.14(b)).
Probability Density (eV-1)
[Sn(20 )/Si(50 )]-[Sn(10 )/Si(50 )]50

E-E0 (meV)

Figure 7.13: Phonon excitation probability density (after normalization and removal of the elastic peak) of a -Sn foil [13] (full line) plotted together with the dierence of the spectra shown in Figs. 7.11(b) and 7.10(b)(full squares).
the lower-energy peak in Fig. 7.12(c) near 10 meV appears to be larger than that of the corresponding peak in Fig. 7.12(b). One reason for this broadening is the additional contribution of -Sn in the VDOS of Fig. 7.12(c), which is known to extend only up to 17 meV ( 140 cm1 ) [122, 133] (see solid blue curve in Fig. 7.12(c)), and thus essentially overlaps with the 10 meV VDOS peak of amorphous -like-Sn. Similar to the case of Fig. 7.12(b), the strong TO peak of crystalline -Sn near 23 meV appears to be largely suppressed, also in the VDOS of -Sn covered interfacial amorphous -like-Sn (Fig. 7.12(c)). The peak near 20 meV (which coincides with the position of the LO peak of crystalline -Sn) is more pronounced in Fig. 7.12(c) than in Fig. 7.12(b). Denitive evidence of the presence of -Sn in the multilayer with 20 A Sn is shown in Fig. 7.13. Here, the phonon excitation probability density of a -Sn foil [13] (full line) is plotted together with the phonon probability density obtained after the subtraction of the spectra shown in Fig. 7.10(b) and Fig. 7.11(b)(full squares). These spectra correspond to multilayers with 10 and 20 Sn, respectively. The dierence spectrum obtained A A (Fig. 7.13, data points) is in excellent agreement with the phonon excitation probability

References [109] J.H. Becker, J. Appl. Phys.29 (1958) 1110
[110] R.F.C. Farrow, D.S. Robertson, G.M. Williams. A. G. Cullis, G. R. Jones, I.M. Young, and P.N.J. Dennis, J. Crystal Growth 54 (1981) 507 [111] T. Osaka, H. Omi, K. Yamamoto, and A. Ohtake, Phys. Rev. B50 (1994) 7567 [112] D.T. Wang, N. Esser, M. Cardona, and J. Zegenhagen, Surf. Sci. 343 (1995) 31 [113] T. Ichikawa, Surf. Sci.140 (1984) 37 [114] R.F. Schmitsdorf, T.U. Kampen, and W. Mnch, J. Vac. Sci. Tech. B 15 (1997) o 1221 [115] D.R. Heslinga, H.H. Weitering, D.P. van der Werf, and T.M. Klapwijk, Phys. Rev. Lett. 64 (1990) 1589 [116] P.J. Estrup and J. Morrison, Surf. Sci.2, 465 (1964) [117] C. Trnevik, M. Hammar, N.G. Nilsson, and S.A. Flodstrm, Phys. Rev. B 44 o o (1991) 13144 [118] M.S. Worthington, J.L. Stevens, C.S. Chang, and I.S.T. Tsong, Nuclear Instr. and Methods in Phys. Research B 64 (1992) 566 [119] A.H. Levermann, P.B. Howes, K.A. Edwards, H.T. Anyele, C.C. Matthai, J.E. Macdonald, R. Feidenhansl, L. Lottermoser, L. Seehofer, G. Falkenberg, and R.L. Johnson, Applied Surface Science 104-105 (1996) 124 [120] R.A. Brand, Nucl. Instr. Meth. B 28 (1987) 417 [121] B. Roldan Cuenya, W. Keune, W. Sturhahn, M.Y. Hu, and T.S. Toellner, Phys. Rev. B (submitted) u [122] A. Barla, R. Rer, A.I. Chumakov, J. Metge, J. Plessel, M. M. Abd-Elmeguid, Phys. Rev. B 61 (2000) R14881 [123] T. Ichikawa, and S. Ino, Surface Science 105 (1981) 395 [124] A. Svane, N.E. Christensen, C.O. Rodriguez, and M. Methfessel, Phys. Rev. B 55 (1997) 12572 [125] Mssbauer Eect Data Index covering the 1974 literature, J.G. Stevens and V.E. o Stevens (Eds.), (IFI/Plenum, New York, 1975), p.153 [126] B. Roldan Cuenya, M. Doi, O. Marks, W. Keune, and K. Mibu, in Structure and Dynamics of Heterogeneous Systems, P. Entel and D.E. Wolf (Eds.), (World Scientic, Singapore, 2000), p.251.
[127] M. Grodzicki, V. Mnning, A.X. Trautwein, and J.M. Friedt, J. Phys. B: At. Mol. a Phys. 20 (1987) 5595 [128] D.L. Weaire, in Amorphous Solids-Low Temperature Properties, Topics in Current Physics vol. 24, W.A. Phillips (Ed.), (Springer, Berlin, Heidelberg, New York 1981), p.13, and references cited therein. [129] M. Cardona, in : Phonon Physics, J. Kollr, N. Kro, N. Menyhrd and T. Sikls a o a o (Eds.), (World Scientic, Singapore, 1985) p.2, and references cited therein. [130] H. Omi, H. Saito, and T. Osaka, Phys. Rev. Lett. 72 (1994) 2596 [131] L.K. Nanver, G. Weyer, and B.I. Deutch, Z. Phys. B-Condensed Matter 47 (1982) 103 [132] R. Alben, D. Weaire, J.E. Smith, Jr., and M.H. Brodsky, Phys. Rev. B 11, 2271 (1975); Phys. Rev. Lett. 29 (1972) 1505 [133] P. Pavone, S. Baroni, and S. Gironcoli, Phys. Rev. B 57 (1998) 10421 [134] W.T. Yuen, W.K.Liu, S.N. Holmes, and R.A. Stradling, Semicond. Sci. Technol. 4 (1989) 819 [135] W.T. Yuen, W.K.Liu, B.A. Joyce, and R.A. Stradling, Semicond. Sci. Technol.5 (1990) 373 [136] W.T. Yuen, W.K.Liu, R.A. Stradling, and B.A. Joyce, J. Crystal Growth 111 (1991) 943 [137] B.F. Mason, and B.R. Williams, Surf. Sci. 262 (1992) 169 o [138] see, for instance, W. Mnch, Semiconductor surfaces and interfaces, Springer Series in Surface Science vol. XV, (Springer, Berlin, New York 1995) [139] M. Hansen and K. Anderko, Constitution of binary alloys, (McGraw-Hill, New York 1958), p.1193 [140] J.M. Worlock, in: Phonon Physics, J. Kollr, N. Kro, N. Menyhrd, and T. Sikls a o a o (Eds.), (World Scientic, Singapore, 1985), p.506 [141] T. Ruf, Phonon Raman Scattering in Semiconductors, Quantum Wells and Superlattices-Basic Results and Applications, Springer Tracts in Modern Physics vol. 142 (Springer, Berlin, Heidelberg, 1998), p.9 [142] M. Seto, Y. Yoda, S. Kikuta, X.W. Zhang, and A. Ando, Phys. Rev. Lett. 74 (1995) 3828 [143] W. Keune and W. Sturhahn, Hyperne Int. 123/124 (1999) 847