Triple-axis diffraction: strain relaxation in Si_1­xGe_x structures

= (a ­ a

a

Good substrates have been achieved by careful control of the growth of a series of Si_1­xGe_x layers of increasing Ge concentration on Si(001) wafers using ultrahigh-vacuum chemical-vapor deposition [16]. For lattice mismatch strain <0.02, the strain is relieved by the introduction of 60° misfit dislocations. These defects have misfit segments running parallel to the growth interface that relieve the strain and terminate with threading arms running up to the surface. When a Si_1­xGe_x layer exceeds a “critical thickness” [17], relaxation occurs through two different mechanisms. If a Si_1­xGe_x layer is grown on Si(001) at higher temperatures and has a higher mismatch strain, it relaxes by roughening and subsequent formation of 60° misfit dislocations in regions of high strain [16, 18]. In this case, the misfit segments lie at the Si_1­xGe_x/Si interface, and there is a high density of threading arms (threading dislocations) terminating at the surface. If the layer is grown at a lower temperature and has a lower mismatch strain, the surface remains smooth, and the 60° misfit dislocations are formed primarily by a Frank­Read multiplication mechanism [16, 19]. This mechanism results in pile-ups of dislocations on the <111> glide planes extending several microns below the Si_1­xGe_x/Si interface and also in a relatively defect-free surface [19]. Grading the alloy composition continuously or stepwise from pure Si up to Si_0.7Ge_0.3 results in a high-quality relaxed buffer layer having defect densities in the range of 5 × 10⁵­ 5 × 10⁷ defects/cm², depending on the grading rate [16]. Triple-axis diffraction has verified that strain relaxation occurs continuously during growth of the step-graded buffer layer and thus that dislocation nucleation always occurs at low mismatch strain in these structures, as is necessary for Frank­Read multiplication [20].

When a crystal has a significant mosaic structure, for example due to the distortion or bending of the lattice planes by the strain field of the dislocations, many diffracted rays may enter through the detector slit during an or ­2 scan and broaden the diffraction peaks. For a sample consisting of several layers that have only slightly different unit cell dimensions, the mosaic broadening makes the individual diffraction peaks indistinguishable. In such a case, the addition of a third diffraction “axis,” in the form of an analyzing crystal that greatly reduces the angular and energy acceptance of the detector, can greatly enhance the resolution of these peaks [21]. (The first axis is the monochromator, and the second is the sample.) The highest resolution in terms of q, the scattering vector having a magnitude of (4sin)/, is obtained in a nondispersive configuration where each diffraction “bounce” off an axis changes the vertical direction sign of the beam (i.e., the incident beam is reflected down, then up, then down). P. M. Mooney and collaborators have used a Ge(111) monochromator and Si(111) analyzer on beamline A to measure small d-spacing shifts due to strain relaxation in compositionally graded Si_1­xGe_x structures [16, 20, 22, 23]. Figure 6 shows the advantage of using triple-axis diffraction to resolve peaks from the various layers in a SiGe/Si structure step-graded up to Si_0.66Ge_0.34. The use of a synchrotron source improves both the signal-to-noise and data collection times by orders of magnitude.

Figure 6

Figure 7(a) shows the Ge mole fraction growth profile observed for a series of step-graded structures grown on Si(001), each sample having an additional layer (i.e., sample 3 had layers 1, 2, and 3; sample 4 had layers 1, 2, 3, and 4; etc.) [20]. Figure 7(b) shows the (004) radial (­2) scans for samples 3 through 7. Distinct peaks can be seen not only for the Si substrate, but also for the ~0.25-µm-thick step-graded layers. Increasing the Bragg angle, _B, corresponds to decreasing the lattice spacing in the growth (z or [001]) direction. In order to calculate the layer composition (Ge mole fraction) and strain, one must determine the lattice parameters both in the growth direction and parallel to it (a_z and a_y). This is achieved by measuring diffraction peaks from two sets of lattice planes that are not equivalent or parallel. A commercial simulation program⁴ was used to determine the alloy composition and strain for each layer from its (004) and (044) reflections. Reciprocal space maps of the (044) region were made by taking a mesh of radial scans (­2 scans) at intervals of . Figure 8 shows the log-scale intensity maps (displayed in q-vector notation for clarity) obtained for samples 3, 4, and 5. The component q_z is normal to the sample surface (parallel to the growth direction), and q_y is parallel to the surface. The peak position for a fully relaxed layer would lie upon the 45° dashed line (q_z = q_y). A fully strained layer peak would have the same q_y value as that of the layer directly below it. Figure 8(a) shows that layer 3 was fully strained; the mismatch strain was 0.0052. Figure 8(b) shows that both layer 3 and layer 4 were fully strained; however, the increased broadening of peaks 3 and 4 indicated that the layers had a significant amount of mosaicity, even though only a few misfit dislocations had formed. As the fifth layer is deposited, the critical thickness is exceeded, and the layers start to relax. Figure 8(c) shows that layers 3, 4, and 5 were all partially relaxed. The mismatch strains at the start of the growth of layers 4 and 5 were found to be 0.0069 and 0.0083, respectively. Subsequent layers show mismatch strains at the start of their growth averaging around 0.006. Thus, once the layers start to relax, the mismatch strain always remains low and essentially constant. These strains are well within the range for the dislocation multiplication mechanism.

Figure 7 Figure 8

A number of other studies have been published using triple-axis diffraction at Port X20 on Si_1­xGe_x structures. The nucleation activation energy for the introduction of misfit dislocations was determined from the tilt angles between various SiGe layers and a miscut Si(001) substrate [24]. A unique signature for the long misfit dislocations in very thin (360 Å) multiplication-relaxed films has been discovered using grazing-incidence reciprocal-space mapping [25]. The quality of Si_1­xGe_x/Si heterostructures on sapphire substrates for application as p-channel FETs has been assessed [26]. Measurements also have been performed to evaluate several SiGe buffer- layer growth profiles for high-mobility FET devices [27].

Grazing-incidence diffraction: Near-surface ordering in polymers for flat-panel displays

Figure 9

GIXS has been used by M. F. Toney, T. P. Russell, and collaborators to obtain direct information on the near-surface structure of the polyimide films used to control the alignment of liquid crystals in flat-panel displays [14]. Buffing the polymer substrate films with a cloth produces liquid crystal alignment in the rubbing direction. Several possible explanations for this template effect have been postulated, including the generation of microgrooves or scratches and/or alignment of the polymer chains near the surface. Figure 10 shows three diffraction scans for a rubbed 200-nm-thick BPDA­PDA film spun onto a Si(001) wafer and imidized at 300°C. The top scan was taken at an incident angle > _c, where X-rays penetrate the entire film. Scans taken with the scattering vector q both parallel and perpendicular to the rubbing direction were identical, and matched scans taken of unrubbed films. Thus, it was concluded that the bulk of the polyimide film was isotropic. The two lower scans were taken at grazing incidence ( = 0.25_c), so that just the top ~5 nm of the sample was being probed. The scans for q vs. q were distinctly different. The sharp Bragg peaks arising from the periodicity along the BPDA­PDA molecular axes [labeled (004), (0010), (0014), and (0016)] were significantly more intense for q than for q. The broad reflections at q 13 and 30 nm^­1 were much stronger for q than for q. These arise primarily from intermolecular packing normal to the polymer chain axis. By comparing the (004) peak intensities, GIXS indicated that approximately twice as many chains in the surface region ( top 50 Å) are aligned parallel to the rubbing direction than are aligned perpendicular to it. These results show that the oriented polyimide chains act as a molecular template for liquid crystal alignment in flat-panel displays.

Figure 10

Scans taken of a 6-nm-thick rubbed film showed essentially complete alignment of chains along the rubbing direction. The angular spread of the aligned chains in the surface plane was determined by rotating the sample about an axis normal to the surface (-scan) while measuring the (004) peak intensity (Figure 11). Nearly all of the intensity occurred within ±10° of the buffing direction. The difference in amount of surface-region alignment between the 200-nm and 6-nm films indicated that either T_g or the yield stress of the thinner film is lower than that of the near-surface region of the thicker film. This may be due to a lower “entanglement density,” which would make the thin-film polymer chains more mobile.

Figure 11

Time-resolved diffraction: Phase transformations in titanium silicide contacts

E/E

The second important component of a time-resolved diffraction instrument is the ability to collect the diffracted intensities on the appropriately rapid time scale. Two detectors are in current use: a linear diode array which is an inch in length and intercepts ~10° 2 over 1024 pixels,⁵ and a CCD area detector which is 1 × 1 inch and has 1152 × 1242 pixels.⁶ The maximum speed of the linear detector is limited by the digitization rate; a 1024-point scattering pattern can be taken every 17 ms and a grouped-pixel 64-point pattern requires 3 ms. This instrumentation was first developed to study the kinetics of phase separation and ordering in binary alloys such as the Al­Zn system and Cu₃Au [13, 29]. It also has proven to be extremely valuable for studying a number of materials systems important to the CMOS and DRAM processes used by IBM. Knowledge and control of the behavior of materials as they undergo processing steps in the manufacture of chips is vital to the success of each new generation of device. On beamline C, phase transformations, intermixing of materials, and texture evolution can be studied in situ and in real time during rapid thermal annealing (RTA).

The third vital component for these time-resolved studies is precise control of sample temperature over the time resolution desired. A unique chamber and “furnace” have been designed that can ramp small samples up in temperature to 1200°C at a rate of 35°C/s in vacuum or an inert atmosphere [30]. Samples can be quickly quenched to room temperature in order to freeze in an interesting phase for more detailed ex situ analysis. In addition to X-ray diffraction, the chamber also is equipped to provide, in real time, four-point resistance measurements of a sample and optical-wavelength elastic light scattering from the surface of the sample [31]. A HeNe laser provides light which passes through fiber optic cables into the chamber and strikes the sample at = 25°. Light scattered at ­21° and 52° with respect to the surface normal is collected by a fiber optics system and sent to photodiodes. Scattered light from the two angles is sensitive to surface morphologies on lateral length scales of ~0.5 µm and ~5.0 µm, respectively. A schematic of beamline C configured for three-probe time-resolved studies is shown in Figure 12.

Figure 12

Metal silicides are used as contacts on sources, gates, and drains of MOSFETs and for interconnections in logic and memory devices. TiSi₂ has been the material of choice for past and current generations of CMOS circuits because of its low resistivity and good thermal stability [32]. Unfortunately, it exhibits a bimodal contact resistance when formed on small features, behavior that wreaks havoc on the timing structure of signals in a circuit [33]. In the SAlicide (Self-Aligned salicidation) process (Figure 13), Ti is deposited onto a wafer and reacts with exposed silicon on gates, sources, and drains during a formation anneal at ~700°C for 20 s. A base-centered orthorhombic phase of TiSi₂ is formed (C49) that has a high resistivity of ~60­90 µ-cm. After unreacted Ti is etched away from SiO₂ and Si₃N₄ spacer regions, a transformation anneal above 800°C converts the C49 TiSi₂ to a face-centered polymorph called C54, which has a resistivity of ~12­20 µ-cm. It is untransformed C49 that causes the bimodal behavior, and the transformation from C49 to C54 TiSi₂ requires more heat as the widths of narrow silicide lines decrease [34]. This requirement for higher temperatures or longer heating times is detrimental to the narrow processing window required for ULSI.

Figure 13

The behavior of TiSi₂ formation as a function of RTA ramp rates, endpoint temperatures, substrate type and doping, contact area, and aspect ratio has been studied extensively at beamline C by members of J. M. E. Harper's group and their collaborators. There are several advantages to using time-resolved, in situ diffraction for these studies, rather than the more conventional electrical testing or postannealing X-ray diffraction [30]. It is extremely efficient. A sample can be mounted and measured, and data collected and processed for the entire temperature range in about 15 minutes. Hundreds of samples can be measured during an experimental run. Thus, the effect of variations in many parameters can be studied exhaustively. In ex situ electrical testing only one feature is measured at a time, and the large contact probes have been shown to affect the results of the measurement [35]. However, the diffraction measurements are statistically meaningful and free from this and other artifacts because the X-ray beam probes a sample containing hundreds of thousands of isolated, identical features. The transformation can be followed continuously in real time, so that the exact temperature of transformation is always obtained, and interesting phases can be noted and “frozen in” by thermal quenching for subsequent ex situ analysis [30]. Samples consist of either blanket films or test sites that simulate gates, or sources, drains, and interconnects. Figure 14 shows a schematic of these test sites and two types of experimental structures. Each sample was ~4 mm × 7 mm in area and contained an array of identical line or segmented line structures. The linewidths varied from 0.1 µm to 1.0 µm and the areas varied from 1 µm² to 25 µm².

Figure 14

For the study of TiSi₂ phase transformations, an X-ray energy of 6.9 keV was used, and the center pixel of the linear diode array was set at 2 = 45°. Over an angular spread of 10° 2, diffracted intensity from the Ti(002), C49­TiSi₂(131), C54­TiSi₂(311), and C54­TiSi₂(040) reflections was collected. Series of 2 traces were taken every 0.5 s for samples ramped from 600°C to 1020°C at a rate of 3°C/s under a nitrogen atmosphere. Two series are shown in Figure 15 as contour maps of diffracted X-ray intensity. Red and blue represent high and low intensity, respectively. The top sample consisted of arrays of 0.50-µm-wide gate contact structures, 2 µm² in area, formed by deposition of a 32-nm Ti film on a polysilicon substrate doped with a boron dose of 4 × 10¹⁵/cm² at 40 keV. The patterned samples were typically annealed to form the C49­TiSi₂ and etched before the time-resolved analysis. The maximum increase in slope for the integrated intensity over the C54­TiSi₂(040) region of interest yields the transformation temperature. The lower sample was an array of narrower, 0.35-µm-wide structures, 2 µm² in area, and doped with 3 × 10¹⁵/cm² As at 35 keV. It is clear that the narrower-linewidth structures do not fully transform to C54 TiSi₂, even up to 1020°C. The fraction of C49 transformed into C54 at a given temperature is [I_C54(040) + I_C54(311)]/[I_C49(131) + I_C54(040) + I_C54(311)], where I is the integrated area under the designated diffraction peak at that temperature. Transformation temperatures and fractions transformed were measured for a series of samples of constant area (2 µm²), ranging in linewidth from 0.1 to 0.35 µm (see footnote 7). Each sample had about half a million identical gate structures probed by the X-ray beam. For arsenic-doped (3 × 10¹⁵/cm² at 35 keV) structures, the transformation temperature increased from 855°C to 904°C with decreasing linewidth. For boron-doped (4 × 10¹⁵/cm² at 40 keV) structures, the transformation temperature increased from 879°C to 949°C. For both types of dopant, the fraction transformed by 1025°C ranged from 50% down to 38% with decreasing linewidth. None of these small-area structure samples underwent complete transformation to the C54 polymorph. Another set of samples having constant linewidth (0.2 µm) and areas varying from 25 µm² down to 1 µm² was also measured.⁷ Arsenic-doped samples displayed transformation temperatures that increased from 822°C to 1010°C with decreasing area. Boron-doped sample temperatures increased from 820°C to 960°C. The fraction transformed to C54 was strongly dependent upon area, independent of dopant. Areas of 12 µm² and higher underwent complete transformation. Below 12 µm², the fraction transformed decreased rapidly, down to ~25% for 0.1-µm² structures.

Figure 15

Kinetic studies have been carried out by maintaining samples at an elevated temperature and recording the evolution of C54 peaks over time.⁸ The resultant sigmoidal curves showed typical incubation, rapid growth, and saturation, and were fit using Johnson­Mehl­Avrami analysis [36]. Three of these “isothermal” curves are shown in Figure 16. As can be seen, the blanket film transformed much more rapidly than the 2-µm- or 0.7-µm-wide lines; the narrower lines must be elevated to higher temperatures to obtain complete transformation. From the analysis, the Avrami exponent and activation energy were obtained [36] for the C54 nucleation, which usually occurs at C49 triple-grain boundaries [37]. From the Avrami exponent one can derive information about nucleation and growth, as well as about the dimensionality of the transformation. For blanket films and lines (independent of width), the activation energy for the nucleation of C54 has been found to be ~4 eV (see footnote 8).

Figure 16

The behavior of these structures can be explained qualitatively by a model in which, for small-area features, the nucleation site density is small enough that not all features contain a site. Those features then would not undergo transformation.⁷ In narrow lines, the growth is one-dimensional because of the boundary constraints of the sides of the lines. A crossover from 1D to 2D growth occurs at a critical linewidth, which depends upon C54 nucleation site density [30]. For samples studied, the nucleation density was <0.3/µm² (see footnote 8), and the crossover width was below 1 µm.

The ion implantation of a small dose of Mo into the silicon before deposition of Ti lowers the transformation temperature by 100­150°C and makes the complete transformation less dependent upon structure geometry [38]. The addition of an intermediate Mo layer between the Ti and Si has the same effect [39]. A series of experiments were performed by C. Cabral, Jr., and coworkers to test the transformation behavior and contact quality of a series of Ti alloys of varying concentration [40]. The lowest resistivities and transformation temperatures down to 715°C were obtained for blanket films with less than 10 at.% Ta or Nb. For isolated submicron Ti(Ta) alloy structures on Si(001) and polysilicon, the temperature at which the C49­C54 phase transformation takes place was reduced to less than 900°C. Figure 17 shows the effect of Ti(Ta) alloys on the transformation temperatures and fraction transformed for submicron gate structures (polysilicon) as a function of linewidth. This improvement allows for C54 formation before the onset of thermal degradation. It has been postulated that all of these improvements arise because of an increase in the nucleation-site density through the formation of smaller C49 grains [38]. Cabral et al. also discovered the appearance of a Ti(alloy)Si₂ C40 phase (in agreement with other Mo interlayer studies [41]). MoSi₂, TaSi₂, and NbSi₂ all have C40 “CrSi₂”-type structures which are similar enough to C54 to possibly provide a template effect for the nucleation of C54 grains [40].

Figure 17

Some of these improvements have been incorporated into device-processing technology at IBM. The time-resolved instrumentation at X20C has been used for a number of other applications, including CoSi₂ formation [42], NiSi formation, intermetallic mixing and phase formation, and diffusion barrier studies.

Microdiffraction: Strain fields in Ni/Si structures

The microdiffraction apparatus used consists of a microfocusing tapered glass capillary and 0.5-µm-resolution x, y, and z sample-scanning stages mounted on a standard two-circle Huber diffractometer with partial and arcs. The capillary accepts the incident X-ray beam and condenses it into a spot several microns in diameter just in front of the sample. A photograph of the capillary (thin glass tube at the center of the photograph) and sample stage is shown in Figure 18. The and arcs are mounted on translators so that all of the diffractometer circles can be adjusted carefully to bring them into concentricity. Despite this, the “sphere of confusion” of the diffractometer cannot be reduced mechanically to less than tens of microns. Accordingly, a protocol for measuring and compensating for the , , and radii of confusion has been developed [49]. This is essential in cases where several diffraction peaks are to be measured at a specific location on the sample.

Figure 18

The capillaries used are fabricated in-house⁹ and have inner surfaces tapered to approximate a parabola so that X-rays undergo several total external reflections off the inside walls and converge at a critical angle of ~0.3°. Precise alignment is crucial, and the capillary used is mounted in a gimbal having two rotational and three translational degrees of freedom. The focus of the X-ray beam is extremely close to the tip of the capillary. The divergence and spot size have been measured by knife-edge scans to be ~0.35° and from 2 to 20 µm in diameter, respectively. The FWHM of the X-ray beam from our “best” capillary, at a typical sample distance of 1.4 mm from the tip, is ~3 µm, and the flux at 8.5 keV is ~1.5 × 10⁸ cts/s. The actual footprint of the beam on the sample increases as sin , where usually = 2/2 for the diffraction peak being measured.

The instrument has three modes of operation. One is diffraction imaging (microtopography), in which the detector is moved to a reflection of interest, and the diffracted intensity is collected as the sample is rastered in the beam. This mode is used for grain mapping, defect imaging, strain contrast mapping, etc. Once a “mesh” has been made across a submillimeter-sized area, one can return easily to regions of high intensity and “tweak” them up, in preparation for more detailed measurement of lattice tilt, mosaic broadening, or lattice spacing. This is the second mode: standard diffraction analysis. For a silicon wafer at the Si(004) reflection angle of 32° (at 8.5 keV) the measured d-spacing repeatability is d/d = 0.0003 [50]. The third mode of operation is fluorescence mapping, for which the sample again is translated in the beam and the fluorescence signal of interest is collected by a Si(Li) energy-dispersive detector. This is useful for mapping fluorescence markers or other features for alignment of the sample in the X-ray beam, for measuring the sphere of confusion of the diffractometer, and for measuring the electromigration material along a line.

A recent illustration of the capabilities of this instrument (one that yielded unexpected results) was the study of interfacial strain caused by residual stresses in small Ni metallization features deposited on Si(111) [48]. In discrete thin-film features, the feature edges cause significant shear stresses/strains, unlike blanket films, in which the stresses are biaxial and isotropic. The sample in this study consisted of an array of 190-µm-diameter Ni pads, 1 µm thick, separated by 220 µm, deposited by vacuum evaporation onto a Si(111) substrate maintained at room temperature. To characterize the strain distribution, the Si(333) integrated diffraction intensity was mapped by step-scanning over an area containing several pads. Simultaneously, the Ni K fluorescence signal at 7.478 keV was recorded using a Si(Li) detector. The X-ray spot on the sample was an ellipse 14 µm in the direction parallel to the diffraction plane and 10 µm normal to it. Figure 19 shows contoured area maps of the Si(333) diffraction intensity and Ni fluorescence intensity. Part (a) is essentially a strain map of the Si substrate. When unperturbed, diffraction from a silicon substrate is dynamical and is limited by extinction effects [51]. When the silicon lattice is strained, it becomes imperfect, extinction effects are eliminated, and the diffracted intensity increases. The smooth blue regions correspond to relatively strain-free Si under or close to the Ni pads. The lack of intensity fluctuations under the pad demonstrated that the adhesion was uniform and good. The contours outside the pads correspond to the far-field strains induced in bare Si by the Ni, which appeared to be circularly symmetric. Comparison with part (b) indicates that the strain field was much larger than the pad diameter. Figure 20 shows a close-up profile scan across one pad. The blue circles corresponding to the diffraction intensity reached a maximum outside the edge of the fluorescence intensity (red circles). This surprising result showed that the position of maximum strain contrast is ~20 µm outside the edge of the Ni pad, contrary to results from analytical solutions and finite-element models of interfacial strain. Work is in progress on comparing the stress/strain transfer between a variety of metal film structures and silicon substrates, including Al [43­45], W, and Cu.

Figure 19 Figure 20

Summary

Acknowledgments

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**Trademark or registered trademark of The Open Group or X/Open Company Ltd.

References and notes

Footnotes

Received April 14, 1999; accepted for publication September 21, 1999