Internal friction of amorphous and nanocrystalline silicon at low temperatures

Materials Science and Engineering A 442 (2006) 307–313

Internal friction of amorphous and nanocrystalline silicon at low temperatures Xiao Liu a,∗ , C.L. Spiel b , R.D. Merithew b , R.O. Pohl b , B.P. Nelson c , Qi Wang c , R.S. Crandall c a Naval Research Laboratory, Washington, DC 20375, USA Department of Physics, Cornell University, Ithaca, NY 14853-2501, USA c National Renewable Energy Laboratory, Golden, CO 80401-3393, USA

b

Received 16 August 2005; received in revised form 10 January 2006; accepted 27 January 2006

Abstract We measured the low temperature internal friction of a variety of hydrogenated amorphous, nanocrystalline, polycrystalline, and epitaxial silicon thin films. Most of the films studied are prepared either by hot-wire chemical-vapor deposition (HWCVD) or by plasma-enhanced chemical-vapor deposition (PECVD). We show that structural changes with varying modes of deposition can be monitored by the internal friction measurements, which are a sensitive probe to structural disorder resulted from atomic tunneling states below 10 K. For hydrogenated amorphous silicon films, the measurements are also sensitive to the content of atomic hydrogen and bulk molecular hydrogen trapped in the films. With H2 dilution of the silane during deposition, a transition from amorphous to nanocrystalline phase takes place as H2 dilution increases. We show that with increasing volume of nanocrystallinity, the internal friction increases in contrast to our common expectation. The results suggest a large structural disorder in the nanocrystalline phase that is at least comparable to that of amorphous phase exists. The observation of internal friction peaks in amorphous HWCVD films and in nanocrystalline PECVD films indicates that the microstructures of the HWCVD and PECVD films are different. © 2006 Elsevier B.V. All rights reserved. Keywords: Internal friction; Hydrogenated amorphous silicon; Double-paddle oscillator; Tunneling states

1. Introduction Synthesis of nanocrystalline silicon thin films by chemicalvapor deposition (CVD) has attracted much attention due to the improved device quality of the films in solar cell applications [1]. Superior film properties could be obtained by using a dilute mixture of silane in hydrogen. As H2 dilution increases, a transition from amorphous to nanocrystalline phase takes place. Studies show that H2 dilution improves the structural ordering in the amorphous phase and the best amorphous silicon (a-Si) is grown just below the edge of amorphous to nanocrystalline transition [2]. Such films also show a reduced light-induced degradation [3,4]. We have shown previously that low temperature internal friction measurements of a-Si films deposited on silicon oscillators are useful for the study of their disorder [5,6], and in particular

∗

Corresponding author. Tel.: +1 202 404 8065; fax: +1 202 404 1721. E-mail address: [email protected] (X. Liu).

0921-5093/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2006.01.146

for the detection of H inclusions in these films [7,8] and lightinduced structural changes [9]. We found that properly prepared hydrogenated amorphous silicon (a-Si:H) films with H content at about 1 at.% show an internal friction below 10 K that is three orders of magnitude smaller than any other amorphous solids [5]. This was the first amorphous solid without any significant two-level tunneling states. With the same film deposition and measurement techniques, we will study the internal friction of silicon films as the nanocrystalline grain structure starts to grow inside the a-Si matrix until a nanocrystalline film is fully developed with an increase of H2 dilution of the silane gas during deposition. One would expect a decrease of atomic tunneling states, and hence a decrease of the low temperature internal friction with an increase of nanocrystallinity. What we find is, however, that these nanocrystalline films are at least as disordered as in the amorphous form, and in some instance, the disorder may even increase as the nanocrystalline fraction increases, although such films show no significant light-induced increase in internal friction. In contrast, we find that the internal friction of a polycrystalline silicon film and

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an epitaxial silicon film prepared by similar CVD technique, but without H2 dilution, are much smaller. 2. Experimental The amorphous and nanocrystalline silicon films studied here were deposited at the US National Renewable Energy Laboratory either by hot-wire chemical-vapor deposition (HWCVD) or by plasma-enhanced chemical-vapor deposition (PECVD). The HWCVD films grown in H2 diluted silane were deposited at a substrate temperature of 250 ◦ C with a deposition rate of about 0.7 nm/s, similar to those described by Han et al. [10] and by Yue et al. [11]. The film thicknesses were between 1.0 and 1.2 ␮m. The important parameter in this case is the molar ratio of H2 gas flow rate to SiH4 gas flow rate R, which was varied from 0, i.e. pure silane, up to 8. On the basis of the H2 dilution used by Yue et al. [11], the H contents are estimated to be 4.5 at.% H for H822, 4 at.% H for H969 and H820, 11 at.% H for H819, 14 at.% H for H818, and H1060 should have an even higher H content. According to Yue et al. [11], the transition from amorphicity to nanocrystallinity is expected to occur for R ≈ 3. Therefore, H822, H969, and H820 are 90%, 80%, and 70% crystalline, respectively, while H819, H818, and H1060 are amorphous. For the PECVD films, two series of samples were used. The samples L313–L315 came from a different deposition chamber than the samples H755–H758 and H390. All depositions were made at a substrate temperature of 200 and 160 ◦ C for L and H series, respectively. The deposition rate varied between 0.14 and 0.5 nm/s from sample to sample. The film thicknesses were between 0.6 and 1.9 ␮m. R varied from 0 to 60. For R < 28, the PECVD films have been found to be amorphous. For 28 < R < 36, the transition to nanocrystallinity is observed by X-ray diffraction on films grown under similar conditions on stainless steel substrates [12]. For R > 36, nanocrystalline film is developed. For comparison, we also show a PECVD aSi:H film (T485) (published in Refs. [8,9,13]) which was de-

posited at a substrate temperature of 230 ◦ C, at a deposition rate of 0.13 nm/s, conditions which have been found to lead to optimal solar cell devices. This film was 0.92 ␮m thick, its H content was 9 at.%. The H contents in the other films are estimated to be of the same magnitude, although it will be highly nonuniform as the films crystallize. Film H390, having the same R as L314 (R = 25), was used for light-soaking study. For details of light-soaking experiments, see Ref. [9]. The deposition parameters of the HWCVD and PECVD samples described above are summarized in Table 1. To compare with the nanocrystalline silicon films deposited with H2 dilution, we also examined a few different types of crystalline silicon (c-Si) films. A polycrystalline silicon film was deposited by low-pressure chemical-vapor deposition (LPCVD) with a substrate temperature of 620 ◦ C and a deposition rate of 0.14 nm/s on both sides of an oscillator at Cornell Nanofabrication Facility. The thickness on each side was 0.45 ␮m. Because of the high deposition temperature, no hydrogen would be expected in the film. Using HWCVD, an epitaxial silicon film was deposited with a substrate temperature of 255 ◦ C and a deposition rate of 0.5 nm/s at the US National Renewable Energy Laboratory. The thickness was 0.41 ␮m. The H content should be less than 0.01 at.% according to structure analysis. Measurements of internal friction were performed using the double-paddle oscillator technique [14]. The oscillators were fabricated out of high purity undoped silicon wafers, with resistivity >5000  cm. The overall dimension of the oscillators was 28 mm high, 20 mm wide, and 0.3 mm thick. See Fig. 1 for its geometry. Thin films were deposited on the front side through a stainless steel mask, except for the LPCVD polycrystalline Si film which was deposited all over an oscillator. On the back side of the oscillator a metal film (3 nm Cr and 50 nm Au) was deposited from the foot up to the wings. The oscillator was attached with Stycast 2850 FT epoxy to an invar block before mounting in a 3 He cryostat. Two electrodes were coupled to the wings from the back side so that the oscillator could be driven and detected capacitively. The so-called second antisymmetric mode

Table 1 Deposition parameters of the silicon samples prepared by hot-wire chemical-vapor deposition (HWCVD) and plasma-enhanced chemical-vapor deposition (PECVD) shown in Figs. 5–7 Sample

Type

Deposition rate (nm/s)

Thickness (␮m)

Tsub (◦ C)

R (H2 :SiH4 )

Figure

H822 H969 H820 H819 H818 H1060 L313 L314 L315 H756 H755 H757 H758 H390 H485

HWCVD HWCVD HWCVD HWCVD HWCVD HWCVD PECVD PECVD PECVD PECVD PECVD PECVD PECVD PECVD PECVD

0.70 0.70 0.70 0.80 0.70 0.70 0.50 0.40 0.17 0.50 0.40 0.28 0.14 0.40 0.13

1.21 1.08 1.07 1.20 1.08 1.0 0.9 1.17 0.94 1.88 1.03 1.80 1.89 0.58 0.92

250 250 250 250 250 250 200 200 200 160 160 160 160 170 230

8 4 3 2 1 0 50 25 0 60 40 11 0 25 0

Fig. 5 Fig. 5 Fig. 5 Fig. 5 Fig. 5 Fig. 5 Fig. 6 Fig. 6 Fig. 6 Fig. 6 Fig. 6 Fig. 6 Fig. 6 Fig. 7 Figs. 6 and 7

Tsub is the substrate temperature during deposition, and R is the molar ratio of H2 gas flow rate to SiH4 gas flow rate during deposition. In the last column are listed the figure numbers to indicate where the results are shown in the paper. The parameters for sample T485 is taken from Ref. [13] for comparison.

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Fig. 1. Outline of the double-paddle oscillator. The left side shows the front view, and the right side shows the back view. The hatched area in the front view is where silicon thin films were deposited through a stainless steel mask, except for the polycrystalline Si film prepared by low-pressure chemical-vapor deposition (LPCVD) (see text for details). On the back side of the oscillator a thin Cr and Au film is covered in the gray area. The dashed circles indicate the position of electrodes for capacitive drive and detection.

had an exceptionally small internal friction Q−1 ≈ 2 × 10−8 at low temperatures (T < 10 K), which was reproducible within ±10% for different oscillators. Therefore, they are extremely sensitive to disorder in films applied to their surface. The small Q−1 was attributed to its unique design. In one of the resonance modes, the head and wings vibrate against each other, which lead to the torsional oscillation of the neck while leaving the leg and foot with little vibration to minimize the external loss. This mode was excited capacitively at a frequency of 5500 Hz. The internal friction results presented in this work were obtained exclusively using this mode for maximum detection sensitivity. Deposition of a thin film onto the oscillator changes its internal friction, Q−1 osc . From the increase above the bare oscillator (substrate) internal friction, Q−1 sub , the internal friction of the thin film itself, Q−1 , can be calculated through [15]: film Q−1 film =

Gsub tsub −1 (Q−1 − Q−1 sub ) + Qosc , 3Gfilm tfilm osc

(1)

where t and G are thicknesses and shear moduli of substrate and film, respectively. Gsub = 6.2 × 1010 Pa is the shear modulus of silicon along 1 1 0 orientation as for the neck of the doublepaddle oscillator. We assume Gfilm to be the same as the corresponding amorphous films estimated via Gfilm = ρv2 based on mass density and sound velocity measurements [16], which are 80% and 74% that of polycrystalline silicon for HWCVD and PECVD a-Si:H films, respectively. When H2 dilution increases during deposition, Gfilm may approach that of polycrystalline silicon. That may lead to an error of about 20% in our internal friction calculations. 3. Results Fig. 2 shows the internal friction of a double-paddle oscillator (Q−1 osc ) carrying a 2.1 ␮m thick HWCVD a-Si:H film with 8 at.% H, taken from Ref. [13], in comparison with those of oscillators

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Fig. 2. Internal friction of double-paddle oscillators Q−1 osc . Solid curve shows the internal friction of a bare paddle oscillator (background), in comparison with oscillators carrying a 2.1 ␮m thick a-Si:H film with 8 at.% H prepared by hot-wire chemical-vapor deposition (HWCVD), a double-sided 0.45 ␮m thick polycrystalline Si film prepared by low-pressure chemical-vapor deposition (LPCVD), a 0.4 ␮m thick MBE Si film, and a 0.41 ␮m thick epitaxial Si film prepared by HWCVD.

carrying several types of c-Si films: LPCVD polycrystalline silicon, HWCVD epitaxial silicon, and a 0.4 ␮m thick molecular beam epitaxial (MBE) silicon. The MBE Si result is taken from Ref. [17]. For both epitaxial films, although they differ in the ways being deposited, they are a simple extension of the silicon lattice underneath. It is not surprising that they show negligible increase of internal friction from the background shown as a solid curve. Even for the polycrystalline Si film which may contain some disorder in their grain boundaries, the internal friction increase is insignificant and much smaller than that of the HWCVD a-Si:H films with 8 at.% H. Using Eq. (1), one can calculate the internal friction of the film itself, Q−1 film . Fig. 3, which is taken from Ref. [13], summarizes Q−1 film of some HWCVD a-Si:H films deposited with varying H content, including the one shown in Fig. 2. For the discussion of the films grown with diluted silane, it will be useful to review briefly these results on HWCVD films grown in pure silane, which are, therefore, completely amorphous. In Fig. 3, the double arrow shows the range of the universal internal friction plateau, in which virtually all other amorphous solids lie [16]. It is often called the “glassy range”. Also shown in Fig. 3 are the internal friction results of the prototypical glass, amorphous SiO2 (a-SiO2 ) measured at 4500 Hz [18] and of an electron-beam (e-beam) deposited hydrogen-free a-Si [5]. The film with the smallest hydrogen concentration, 1 at.% H, differs from all other amorphous solids in that its low temperature internal friction, ∼3×10−7 , is more than two orders of magnitude smaller than that of all other amorphous solids (1000 times smaller than that of a-SiO2 ). The data show, however, an anomaly occurring at 13.8 K, the triple point of bulk molecular hydrogen. With increasing hydrogen

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Fig. 4. Internal friction of an a-Si:H film (2 at.% H, 4.5 ␮m thick), compared to that of an a-Si:D film (deuterium concentration not known, 1.8 ␮m thick), both prepared by hot-wire chemical-vapor deposition (HWCVD). The dotted lines mark the respective triple points. Data are taken from Ref. [8].

Fig. 3. Internal friction of a-Si:H films prepared by hot-wire chemical-vapor deposition (HWCVD) with different hydrogen contents. The internal friction of bulk a-SiO2 [18] and e-beam a-Si [5] are shown for comparison. The double arrow denotes the “glassy range” explained in the text. The vertical dotted line labeled “13.8 K” is the triple point of H2 .

concentration, the internal friction increases over the entire temperature range. Together with the 13.8 K anomaly, a broad peak arises around 5 K in the 3 at.% H and 4 at.% H films. It becomes a shallow plateau in the 8 at.% H film due to the appearance of a peak at ∼30 K, although the 13.8 K anomaly is still visible. In the 20 at.% H film, no structure is seen, and the value of the internal friction is close to that of e-beam a-Si. The peak at 13.8 K and the anomaly at ∼5 K have been identified as caused by bulk molecular hydrogen collected in voids of the films. These features can be enhanced or eliminated by heat treatments [8,13]. Convincing evidence for their nature has been provided by the observation that a similar film deposited using deuterated silane (SiD4 ) showed the narrow anomaly peak shifted to 18.7 K, the triple point of bulk molecular deuterium, as shown in Fig. 4, taken from Ref. [8]. We believe that the freezing of the H2 liquid at the triple point produces the large internal friction. Below the triple point, plastic deformation causes the internal friction. Golter and Roshchupkin [19,20] have observed a similar internal friction peak in heavily cold-worked iron containing voids, which had been loaded electrolytically with hydrogen. These authors attributed the peak to plastic deformation of the solid hydrogen: close to the freezing point by self-diffusion of H2 , as expected for grain boundary motion, and near 5 K by dislocation motion. We mention in passing that the

first observation of a similar peak in the internal friction has been reported at 273 K for copper containing water [21]. The damping above the triple point has been explained as being caused by the viscosity of the H2 liquid [22]. The broad peak observed in the 8 at.% H film around 30 K, however, can hardly be explained that way, nor do we understand the complete lack of structure seen in the 20 at.% H film. We now turn to the measurements of the HWCVD films deposited with H2 dilution shown in Fig. 5. Below 10 K, all films, except for H1060, which is the only film deposited without H2 dilution, have nearly the same temperature independent internal friction. The values of the internal friction are between those of the HWCVD a-Si:H films with 8 and 20 at.% H shown in Fig. 3, indicating the range of their H contents in agreement with the literature [10,11]. Around 40 K, the three amorphous films have a pronounced peak, which decreases with increasing H2 dilution. This is, however, absent in the nanocrystalline films. The peak at round 40 K is similar to that of the HWCVD film with 8 at.% H shown in Fig. 3 and they probably have the same unknown structural origin that exists only in the amorphous phase. The important point here is that with increase of nanocrystallinity, the internal friction below 10 K stays the same. The internal friction of eight PECVD films is shown in Fig. 6. The optimal device quality a-Si:H film (T485) has the lowest internal friction, approaching those of the HWCVD a-Si:H films with a small internal friction in Fig. 3. Two other PECVD amorphous films deposited without H2 dilution (L315 and H758), although of nominally similar quality, have a distinctly larger, fairly temperature independent internal friction. Note that their deposition conditions are different from that of T485 (see Table 1). A film deposited with an H2 dilution small enough so as not to cause crystallization (H757) also shows a similar internal

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Fig. 5. Internal friction of six Si films prepared by hot-wire chemical-vapor deposition (HWCVD) with H2 diluted silane, as indicated. Note the relaxation peaks at ∼40 K, which occur only in the three amorphous films.

friction. However, with an increase of nanocrystallinity, a relaxation peak arises around 60 K as a new feature and the internal friction below 10 K increases. Here we point out two major differences between the H2 diluted HWCVD and PECVD films. (1) For the HWCVD films, the low temperature internal friction below 10 K keeps at about the same value when the films become crystallized, while for the PECVD films the internal friction increases. (2) The peak at around 60 K that appears after

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Fig. 7. The light-soaking effect on internal friction. The internal friction results of an Si film (H390) prepared by plasma-enhanced chemical-vapor deposition (PECVD) in H2 diluted silane, as indicated, and of a device quality PECVD a-Si:H film (T485) deposited without H2 dilution, both in as-deposited and light-soaked states are shown. Data for T485 are taken from Ref. [9].

the film crystallizes in the PECVD films is the opposite of what has been seen in the HWCVD films, in which the 40 K peak disappears as the films become crystalline. This finding reveals a striking difference between the HWCVD and PECVD films as to their microstructure and the ways that they crystallize during deposition. The results of light-soaking are shown in Fig. 7 for a PECVD film (H390) with H2 dilution just at the edge of nanocrystallinity. It is compared with that of a device quality PECVD a-Si:H film (T485) taken from Ref. [9], to which details of light-soaking should be referred. Note that because the internal friction in H390 before light-soaking is already about one order of magnitude larger than in T485, any possible light-induced relative change in internal friction in H390 would appear smaller than in T485. Despite of that, we see no internal friction change in H390 after 7 days of light-soaking in contrast to the over a factor of two increase of the internal friction in T485. This is in agreement with the reports that PECVD films on the edge of nanocrystallinity have a much reduced light-soaking effect on electronic properties [3,4]. 4. Discussions

Fig. 6. Internal friction of seven Si films prepared by plasma-enhanced chemical-vapor deposition (PECVD) with H2 diluted silane, as indicated. They are compared with the internal friction of a device quality PECVD a-Si:H film (T485), see Refs. [8,9,13].

Contrary to what one might expect, the nanocrystalline silicon films do not have a small internal friction as do, for example, the LPCVD polycrystalline, HWCVD epitaxial, and the MBE Si films (Fig. 2), or also the e-beam a-Si film which had been annealed at 700 ◦ C for 1 h, which is ∼90% crystallized [17]. Rather, the most highly crystallized PECVD films have an internal friction below 10 K which is close to that observed on fully amorphous samples (the “glassy range”, see Fig. 3). If one considers that the internal friction might be caused by disorder in the amorphous tissue connecting the crystallites, one would

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need an extraordinarily high internal friction in this tissue to explain the large (average) internal friction of the films, which is close to that of a fully amorphous e-beam Si, given the small volume fraction of this tissue in the most highly crystallized films (∼10%). This does not seem to be a possibility. However, this is not the first time a large internal friction in a crystalline silicon film is reported. We have found evidence of such unusually large internal friction in laser-flash recrystallized films of e-beam a-Si and of ion-implantation amorphized Si [23]. In fact, such a large temperature independent internal friction is also known for chemically highly disordered crystalline solids, in which large internal random stresses may be expected [24]. We have found that internal stress is responsible for the high internal friction in ion-implanted silicon films [25] and in amorphous carbon films [15]. Kroll et al. [26] found that the compressive stress in a series of PECVD Si films increases with increasing H2 dilution, and then, decreases slightly as the films fully crystallized, in qualitative agreement with what we have observed here in internal friction, see Fig. 6. A recent study by Pantchev et al. demonstrated that the origin of the internal compressive stress in PECVD a-Si:H films prepared with H2 dilution with R = 10 has to do with the distribution of hydrogen in the films. The high temperature relaxation peaks are also puzzling. In the HWCVD films, the 40 K peak is seen only in the amorphous films, and it seems to weaken progressively with H2 dilution. In the nanocrystalline films this peak is absent. In the PECVD films, the opposite is observed, in which no peak occurs in the amorphous films. A 60 K peak arises only when most of the film is crystallized. All we can conclude is that it is unlikely they have the same origin. Upon closer inspection, one could notice that the internal friction of nanocrystalline films deposited with H2 dilution from the L series (L313 and L314) exhibit a more complicated temperature dependence at above 10 K than those from the H series. This is remarkable as they ought to be comparable according to their deposition parameters, and suggests a possible influence of the deposition chamber used. Both samples show two peaks, a sharper one at 20 K that seems independent of R, and an additional broad peak that depends on R. The broad peak appears with a smaller magnitude at 40 K for L314 (R = 25), and shifts to higher temperature and becomes more prominent for L313 (R = 50). In fact for L313, this peak appears at ∼60 K, as in the H series. More work is needed to understand the 40 K peak in amorphous HWCVD films and the 60 K peak in nanocrystalline PECVD films. A variety of structural investigations [2,27,28] have been performed to understand the microstructure, and in particular, the origin of the improved stability of its device quality of the Si films deposited with H2 dilution. Neither X-ray diffraction [27] nor fluctuation electron microscopy [28] observes structural difference in amorphous matrix of H2 diluted and undiluted films. The quality improvements have been, therefore, attributed to the existence of nanocrystallites inside the matrix. Our unique internal friction study reveals a different aspect of the structural disorder in this technically important material; in particular, even the nanocrystallites are different in HWCVD and PECVD films.

5. Conclusion The nanocrystalline HWCVD and PECVD Si films show a remarkable amount of disorder of the kind common in amorphous solids, leading to a large, temperature independent internal friction below 10 K, in contrast to other crystalline Si films. The unexpectedly large internal friction may have their origin of large internal stress. The films studied here show no evidence for an accumulation of bulk molecular hydrogen as previously observed in HWCVD a-Si:H films. The peaks observed in amorphous HWCVD films and nanocrystalline PECVD films are puzzling, indicating at least the microstructure of these two types of films is quite different in both amorphous and nanocrystalline forms. Acknowledgments This work was supported by the Office of Naval Research. We thank E. Iwaniczko, Wei Gao, and Yueqin Xu for film preparation at the US National Renewable Energy Laboratory. References [1] S. Guha, Solar Energy 77 (2004) 887–892. [2] D.V. Tsu, B.S. Chao, S.R. Ovshinsky, S. Guha, J. Yang, Appl. Phys. Lett. 71 (1997) 1317–1319. [3] S. Guha, K.L. Narasimhan, S.M. Pietruszko, J. Appl. Phys. 52 (1981) 859– 860. [4] J. Yang, A. Banerjee, S. Guha, Appl. Phys. Lett. 70 (1997) 2975– 2977. [5] X. Liu, B.E. White Jr., R.O. Pohl, E. Iwanizcko, K.M. Jones, A.H. Mahan, B.N. Nelson, R.S. Crandall, S. Veprek, Phys. Rev. Lett. 78 (1997) 4418– 4421. [6] X. Liu, R.O. Pohl, Phys. Rev. B 58 (1998) 9067–9081. [7] X. Liu, E. Iwanizcko, R.O. Pohl, R.S. Crandall, Mater. Res. Soc. Symp. Proc. 507 (1998) 595–600. [8] X. Liu, R.O. Pohl, R.S. Crandall, Mater. Res. Soc. Symp. Proc. 557 (1999) 323–328. [9] X. Liu, C.L. Spiel, R.O. Pohl, E. Iwanizcko, R.S. Crandall, J. Non-Cryst. Solids 266 (2000) 501–505. [10] D. Han, G. Yue, J.D. Lorentzen, J. Lin, H. Habuchi, Q. Wang, J. Appl. Phys. 87 (2000) 1882–1888. [11] G. Yue, J. Lin, Q. Wang, D. Han, Mater. Res. Soc. Symp. Proc. 557 (1999) 525–530. [12] D.L. Williamson, Mater. Res. Soc. Symp. Proc. 557 (1999) 251–256. [13] X. Liu, D.M. Photiadis, H.D. Wu, D.B. Chrisey, R.O. Pohl, R.S. Crandall, Philos. Mag. B 82 (2002) 185–195. [14] B.E. White Jr., R.O. Pohl, Mater. Res. Soc. Symp. Proc. 356 (1995) 567– 572. [15] X. Liu, T.H. Metcalf, P. Mosaner, A. Miotello, Phys. Rev. B. 71 (2005) 155419-9. [16] R.O. Pohl, X. Liu, E. Thompson, Rev. Mod. Phys. 74 (2002) 991–1013. [17] P.D. Vu, X. Liu, R.O. Pohl, Phys. Rev. B 63 (2001) 125421-10. [18] J.E. Van Cleve, Ph.D Thesis, Cornell University, 1991. [19] A.E. Golter, A.M. Roshchupkin, Sov. J. Low Temp. Phys. 8 (1982) 622– 623. [20] A.E. Golter, A.M. Roshchupkin, Sov. J. Low Temp. Phys. 13 (1987) 105– 106. [21] S. Imoto, G. Mina, Technol. Rep. Osaka Univ. 6 (1956) 141–142. [22] H. Wada, K. Sakamoto, Mater. Sci. Eng. 50 (1981) 263–270. [23] X. Liu, R.O. Pohl, R.S. Crandall, K.M. Jones, Mater. Res. Soc. Symp. Proc. 469 (1997) 419–424. [24] S.K. Watson, Phys. Rev. Lett. 75 (1995) 1965–1968.

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