Strain distribution due to ion implantation revealed by extremely asymmetric x-ray diﬀraction

Lattice strain of Si(111) implanted 1.5 MeV Au 2+ ion was investigated by extremely asymmetric x-ray diﬀraction. The measured rocking curves were consisted of a bulk peak and a broad sub peak accompanying with intensity oscillation. Analysis of the strain distribution was done by ﬁtting of the measured curve with curves calculated by a dynamical diﬀraction theory. The resultant strain proﬁle shows introduction of a tensile strain in extent of 500 nm. Comparing the strain proﬁles with the distributions of the projected range and the vacancy calculated by the TRIM code, it was concluded that the lattice strain is contributed by not only the defect due to collision event but also the interstitials of Au ion. In addition, we found that the global shape of the broad sub peak is very sensitive to the strain distribution within the depth of ∼ 80 nm. [DOI: 10.1380/ejssnt.2006.25]


I. INTRODUCTION
Implantation of MeV ion has occupied an important position in field of semiconductor engineering because of its wide applicability; fabrications of buried insulator layer, buried conducting layer [1], and VLSI deep wells [1,2]. Moreover defects due to ion implantation are available for gettering sites of metal impurities [3]. Ion implantation of higher kinetic energy forms an isolated damage layer under a non-damaged layer. At high fluence of ion, buried amorphous layer is formed due to phase transformation from crystalline state to amorphous state. Kamira et al. [4] reported that amorphization occurred at low current ion implantation (5 × 10 13 dose) of 1.5 MeV Au 2+ by Rutherford backscattering spectroscopy/channeling (RBS/C) method. Ghatak et al. [5] observed the lattice spacing around the amorphized region by transmission electron microscopy (TEM).
X-ray diffraction techniques are suitable to observe deformation of lattice in crystalline state of matter. Actually, strain field introduced by doping or ion implantation has been investigated with multi crystal x-ray diffraction and/or x-ray topography [6][7][8][9]. This conventional technique is powerful tool to observe a minute and long-range (higher than micrometer) strain. For example, Kuribayashi et al. [7] reported introduction of a minute tensile strain (in the order of 0.01%) within the depth of 17.5 µm by using multi crystal x-ray diffraction.
Recently new x-ray diffraction technique [10] that is sensitive to lattice deformation near crystal surface was developed. The optics of this technique is extremely asymmetric Bragg-case under grazing incidence condition.
The penetration depth of x-rays in crystal is suppressed within a few nanometers beneath surface because the incident angle of x-rays is set near a critical angle of total reflection. Therefore rocking curve measured in this optics reflects lattice distortion near the surface. They reported strain fields of many systems, SiO 2 /Si(111) interface [11], reconstructed Si surface [12], Ni/Si(111)-H [13], and HfO 2 /Si(001) interface [14].
In this paper, we investigated lattice deformation introduced by MeV ion implantation to Si single crystal by extremely asymmetric x-ray diffraction.

II. EXPERIMENTAL
Mirror polished wafers of Si(111) single crystals were used.
Before implantation of ion, the wafers were cleaned by de-ionized water following rinsing by methanol, trichroloethelene, and de-ionized water. Note that native oxide layer was resided after cleaning.
Implantations of 1.5 MeV Au 2+ ions to Si crystals were done at room temperature with a 3.0 MV pelletron accelerator facility at Institute of Physics, Bhubaneswar, India. Two types of the samples were made with changing an impact angle of ions to the Si wafer. One sample was impinged at 5 • with respect to the surface normal to avoid a channeling effect. Another sample was impinged at 30 • with respect to the surface normal. Here after we call the samples 'normal incidence condition' and '30 •off incidence condition', respectively. The implantation was carried up to a fluence of 5 × 10 13 Au ion/cm 2 while keeping the incident ion current at ∼20 nA.
Strain observations were done at room temperature at atmospheric environment at beam line 15C, Photon Factory, High Energy Accelerator Research Organization, Tsukuba, Japan. Monochromatic x-rays using a double crystal monochromator with Si(111) crystals (which is available in this beam line in front of the experimental hutch) were utilized. We measured rocking curves of Si 113 reflection of samples with x-ray beam of 0.16 nmwavelength under grazing incidence condition. An experimental setting of extremely asymmetric x-ray diffraction was detailed elsewhere [13]. It is noted that atomic plane of (113) makes 29.5 • with respect to that of (111). Therefore variation in lattice spacing of 111 planes is obtained by measuring the variation in the lattice spacing of 113 planes.  Figure 1 shows the cross-sectional images of the sample for the normal incidence condition by transmission electron microscopy (TEM) [5]. In Fig. 1(a), a dark band indicated by symbol (II) is shown at the depth of ∼470 nm with in extent of ∼150 nm. This band represents the distribution of implanted ions where the projected range is ∼470 nm with a straggling of ∼150 nm. This value is comparable with the result from RBS/C analysis of the same system [4]. Fig. 1(b) and Fig. 1(c) show highresolution images of Fig. 1(a). Figure 1(b) corresponds to the surface region indicated by symbol (I) in Fig. 1(a). Figure 1(c) corresponds to the end of range. As clearly shown from Fig. 1(c), Si crystal near the range of ion is partially amorphized. Figure 2 shows the measured rocking curves for the sample for the normal incidence condition. In Fig. 2(a), we can see an intense peak at right side of the curve. This peak corresponds to bulk reflection. On the other hand, a broad peak accompanying with intensity oscillation is corresponding to reflection coming from distorted layer. The intensity of the bulk peak becomes smaller than that of the broad peak as shortening the wavelength of x-rays. The measured curves for the sample for the 30 • -off incidence condition are shown in Fig. 3. It seems that these curves are different from the curves in Fig. 2. But basic structure is similar to the curves shown in Fig. 2. For example, see Fig. 3(b), an intense and doublet peak at right side is corresponding to the bulk reflection. A broad peak coming from a distorted crystal becomes dominant as shortening the wavelength of x-rays. From this result, it is thought that the distorted layer exists on a perfect crystal, because shortening a wavelength means that an extinction depth of x-rays becomes shallower. Moreover, the rocking curves clearly show that a tensile strain, i.e., expanding of 113 planes, is introduced into the Si substrate.

B. Curve-fitting of measured rocking curve
For analysis of strain field introduced in the samples, we used a curve-fitting method with a dynamical diffraction theory. Using of an extended Darwin theory [15] is required for our experimental set up, because a mirror reflection is not negligible with respect to the incident beam and the diffracted beam in our x-ray optics. This theory allows us to calculate rocking curves for structural models including an irregularity, such as lattice distortion and reconstruction of surface structure. We used a strain distribution function consisting of two Fermi-Dirac functions for calculation as follows: where P 1 means a maximum value of the strain for the distorted layer, P 2 a position of a structural transition layer near surface, P 3 a extent of a transition layer near surface, P 4 a position of a structural transition layer in the bulk side, P 5 a extent of a transition layer in the bulk side. This strain model is able to express the extents of structural transition layers and the gradients of strain by few parameters. Note that calculations done in this study did not consider the oxide layer on the crystal. For extremely asymmetric x-ray diffraction under grazing incidence condition, oxide layer acts as an absorber [11]. Therefore the shape of the rocking curve is modified by the absorption effect when the wavelength of x-rays is very short. In this investigation, however, the wavelength of x-rays was relatively long. So the absorption effect by the oxide layer can be neglected. Shape of calculated rocking curve is varied complexly by the parameters of P 1 to P 5 . We would like to explain the influences of the parameters from the viewpoints of (i) global shape of the curve and (ii) intensity oscillation.
Very interesting is an existence of the broad sub peak shown at left side of the bulk peak. The global shape of this sub peak can be extracted by smoothing of the rocking curve. To find most influential parameter for shape of the sub peak, we calculated rocking curve with changing each parameter independently. As shown in Figs  and (e), the parameters of P 4 and P 5 are less effective for the global shape, where P 4 and P 5 are corresponding to a depth of structural transition layer of bulk-side and an extension of the layer, respectively. Note that they hardly affect to the strain distribution near the surface as shown in Figs. 4(i) and (j). From these results, it is thought that strain distribution near the surface decides the global shape of the sub peak of rocking curve. The parameter P 1 also affects to the global shape as shown in Fig. 4(a). Changing this parameter, however, occurs changing of strain distribution near the surface and near the interface. This means that the changing of the global shape of the sub peak shown in Fig. 4(a) includes an influence coming from the change of the strain field near the surface. Fig. 5(a) shows calculated rocking curves for the strain distributions shown in Fig. 5(b). Three profiles of the strain have the same values of P 4 and P 5 and have different values of P 1 . The values of P 2 and P 3 are optimized to take the same global shape of the sub peak (see the arrowed region in Fig. 5(a)). Figure 5(c) is closed up of Fig. 5(b) up to the depth of 120 nm. It is clear that the strain profiles within the depth of 80 nm agree with each other. Therefore the shape change shown in Fig.  4(a) mainly comes from the change of strain-distribution near surface. From this result, it is concluded that the strain-distribution near surface (up to the depth of ∼80 nm) decides the global shape of the sub peak. This sensitivity for lattice strain near surface is a result of our x-ray optics of extremely asymmetric Bragg-case. The parameters of P 4 and P 5 act to detailed structure of the rocking curve rather than the global structure. Figure  6 shows native rocking curve against to change of parameters of P 4 and P 5 . Altering P 4 occurs phase shift of the intensity oscillation. On the other hand, altering P 5 occurs not only phase shift but also changing period and amplitude of the intensity oscillation. In addition, the intensity of the bulk peak becomes intense as sharpening the interface (P 5 ).
For fitting of the measured curve, we firstly decided the parameters P 2 and P 3 using the sensitivity of the global sub peak to surface strain and strain-distribution near surface. Secondly, the period and position of intensity oscillation were decided by controlling the parameters of P 4 and P 5 . Finally, the parameter of P 1 was optimized.
The resultant strain-distributions are shown in Figs. 7(a) and 7(b) for the normal incidence condition and for 30 • -off incidence condition, respectively. The calculated rocking curves are drawn in Fig. 2 and Fig. 3 as thick lines. For the normal incidence condition, the strain at the surface is 0.15% and becomes large up to the depth of 250 nm. The depth of the interface between the distorted layer and the bulk is 520 nm. On the other hand, for the 30 • -off incidence condition, the strain at the surface is 0.03% and becomes large up to the depth of 180 nm. And the depth of the interface is 480 nm.
For introduction of lattice strain due to ion implantation, next two reasons are thought; formation of interstitials by the implanted ion and formation of defect due to elastic collision. We calculated a stopping ion (projected range) distribution and a vacancy distribution by the TRIM code to estimate their contribution to the lattice strain. In Fig. 7, the ion distributions are drawn with the red lines and the vacancy distributions are drawn with the black lines. Note that the maxima of the ion and the vacancy distributions are normalized for comparison. For the normal incidence condition, the projected range and the straggling of the Au ion were estimated 358 nm and 71 nm. On the other hand, for the 30 • -off incidence condition, the projected range and the straggling were estimated 309 nm and 68 nm. The vacancy due to elastic collision between the ion and the target atom is almost created within the depth of 500 nm. The number of the created vacancy is maximum value near the depth of 240-280 nm.
Comparing the strain distribution for both cases, it is clear that the depth of the interface for the normal incidence condition is deeper than that for the 30 • -off incidence condition. It is thought that this difference is based on the difference in the projected range of the ion by the incident angle of the ion as shown in the TRIM result. It is known that the prediction values of the projected range and the straggling by the TRIM code are underestimated by 20% than the experimental values in this energy range [16]. Actually, the projected range and the straggling for the normal incidence condition was estimated 470 nm and 150 nm from RBS/C [4] and TEM [5] observation though they were 358 nm and 71 nm by the TRIM calculation. We draw a realistic ion distribution by the broken red line in Fig. 7(a) as Gaussian with a peak position at the depth of 470 nm and a width of 150 nm. It is noted that the deep side of the Gaussian agrees with the deep side of the strain profile. From this result, it is thought that the strain near the interface between the distorted layer and the bulk comes from the occupation of an interstitial site by the Au ion. In addition, it is clear that the strain distribution cannot explain only with the formation of the interstitials by the ion because the width of the ion distribution is narrower than the width of the resultant strain profile.
From the calculation results by the TRIM code, the formation of the vacancy happens at relatively shallow area as shown in Fig. 7. Comparing the strain profile with the vacancy distribution, it seems that the lattice strain in the shallow area is concerned in the formation of the vacancy. It must be represented that the strain in the shallow area is caused by formation of self-interstitials by recoiled atom rather than by formation of the vacancy because the resultant strain profile shows tensile strain.
Another interesting result is the difference in the strain near the surface for the 30 • -off incidence condition compared to the normal incidence condition. A close look at the vacancy distribution and the projected range distribution by the TRIM simulation (Fig. 7) shows shift in the peak position towards the surface. The vacancy distribution shows, which depicts the number of vacancies per ion per angstroms, a large number of vacancies produced from the surface to a depth of about 200 nm. At surface there are about 2.0 vacancies/ion/angstroms for the case of the normal incidence condition while it is 2.5 vacancies/ion/angstroms for the 30 • -off incidence condition. The TRIM simulations show about 25% more vacancies for the 30 • -off incidence condition compared to the normal incidence up to a depth of 200 nm. Also, the projected ranges are nearly 309 nm and nearly 358 nm for the 30 • -off incidence and the normal incidence conditions, respectively. This shows ∼14% change in the projected range, implying the possibility of more number of interstitials at the surface for the 30 • -off incidence implantation. By comparing Fig. 2 and Fig. 3, it is clear that the broadness of the sub peak depends on damage by ion implantation. As the number of the vacancies and interstitials per ion per angstroms for the 30 • -off incidence condition are ∼25% and ∼14% more compared to the normal incidence condition, the detailed analysis of the sub peak could yield the quantitative information for small change in the damage at the surface and interface.
Note that the strain profiles near the surface shown in Fig. 7 are not intrinsic to the damage by ion irradiation. It was reported that the oxidation of the crystal surface introduces a strain field into the surface [11]. This means that the lattice strain near the surface is contributed by oxidation effect and ion-irradiation damage.
Kuribayashi et al. [7] estimated strain distribution in Si crystal due to 160 MeV Au ion implantation by multi crystal x-ray diffraction. They found that the lattice strain comes from the defect due to elastic collision rather than the Au interstitials. In our case, the kinetic energy of Au ion is much lower than their case, it is concluded that the lattice strain is contributed by not only the defect but also the interstitials by Au ion. For the normal incidence condition, the distribution of the stopping ion (red broken line) observed by RBS/C and TEM is drawn.

IV. CONCLUSION
The lattice strain introduced into Si crystal due to 1.5 MeV Au ion implantation was investigated by extremely asymmetric x-ray diffraction. The measured rocking curves consisted of a bulk peak and a broad sub peak accompanying with intensity oscillation. These curves reveal introduction of tensile strain because the sub peak locates on left side of the bulk peak.
We analyzed strain distribution along to depth by curve-fitting method with a strain model consisting of two Fermi-Dirac fuctions. From the resultant strain distribution, a tensile strain extending for 500 nm was found. It is noted that the distribution of the lattice strain is different in (i) the strain near the surface (up to the depth of 200 nm) and (ii) the depth of the interface between the distorted layer and the bulk for the preparation condition of the sample, i.e., incident angle of the ion.
Comparing the strain profiles with the distributions of the vacancy and the stopping ion calculated by the TRIM code, it is thought that the lattice strain is contributed from not only the defect due to collision event but also the interstitials by the stopping ion in contrast to the case of more energetic ion [7]. For the implantation with 160 MeV Au ion, the strain is dominated by the defect due to collision.
In addition, it was found that a global shape of the sub peak coming from the distorted layer intensely reflects the strain distribution up to the depth of 80 nm from the calculation results.