Comprehensive Characterization of Extended Defects in Semiconductor Materials by a Scanning Electron Microscope

The structural, electrical and optical properties of extended defects in a semiconductor material were studied by different experimental methods in the scanning electron microscope. Generally, it is possible to investigate these properties on the same sample, and with some efforts concerning the sample preparation, even on a distinct single defect like a grain boundary or a localized arrangement of dislocations. However, it should be noted that due to the specific interaction products of the primary electron beam with the semiconductor material used for the inspection of physical defect properties, the spatial resolution which can be achieved by CL, EBIC or ccEBSD investigations differs from each other. In Figure 1, schematic drawings are given for an appropriate set-up of the SEM suited for CL measurements at low temperatures (Figure 1A), the assembly for EBIC investigations (Figure 1B) as well as the layout of the main hardware elements necessary for (cc)EBSD tests (Figure 1C).

All the representative results given here are obtained for silicon as a showcase for a semiconductor material with indirect electronic band structure. This band structure impedes all luminescence measurements due to the low probability of radiative transitions in comparison to semiconductors with direct band gap structures. To realize sufficient luminescence intensity for statistically assured results is challenging. In the following, the experimental procedures are described for the investigation of dislocations induced by plastic deformation as well as by liquid phase re-crystallization in silicon single crystals. Additionally, investigations on a silicon bi-crystal with twin grain boundaries and a low-angle grain boundary are presented.

Figure 2A shows an example of the appropriate positioning of a sample on the indium foil to guarantee a good thermal contact to the cryo-sample holder in which the temperature is measured by the thermocouple. It was proven experimentally that for silicon, a sample thickness of about 200 to 500 µm is well suited for cryo-CL investigations at temperatures down to 5 K. The CL spectra given in Figure 2B were measured for a Si single crystal in the virgin state, after plastic deformation and after an additional annealing. The electron beam in the SEM was run at an electron beam acceleration voltage of 20 kV and a probe current of approximately 45 nA in the defocused scanning mode, which results in a high CL intensity due to electron-hole pair generation in a large volume (about (450 x 250 x 3) µm³) with moderate excitation density. In this scanning mode, the sample surface is actually on WD = 15 mm but electronically a WD = 0 is adjusted. For CL imaging, of course, the electron beam has to be focused which yields a spot diameter of the electron beam on the sample surface of a few nm but with the same penetration depth of some µm for the primary electrons as in the defocused scanning mode. The acquisition time per image with a store resolution of 1,024 x 768 pixels was about 10 min in pixel averaging mode at scan speed 14 of the electron beam. It was calculated and experimentally confirmed that for the defocused scanning mode the temperature of the sample region under investigation is increased no more than some 0.1 K by heat energy transfer due to the electron beam. In the focused mode, the local sample heating strongly depends on the thermal conductivity which in turn depends on the sample doping and the temperature itself²⁰. For the float-zone grown Si sample, p-doped with Boron at a concentration of 10¹⁵ cm^-3, in the focused scanning mode, a local temperature increase ∆T of about 2 K occurred at a cryostat temperature of 5 K, and of ∆T ≈ 0.3 K at 25 K.

To study the optical properties of dislocations, a bulk Si sample was subjected to a plastic deformation at a pressure of 16 MPa at 800 °C followed by a second deformation step at 295 MPa at 420 °C. The slip lines, shown in Figure 2C on the surface of a part of the deformed sample, are caused by dislocation glide processes on two different 111-oriented slip planes. The slip lines can be visualized by backscattered electrons (BSE). The slip lines indicate the traces of the lattices planes on which most of the dislocations are aligned. Monochromatic CL (mono-CL) images (Figures 2D and 2E) were acquired at energetic positions of the D4 and D3 luminescence bands and do not suffer significantly from the surface topography profile caused by slip lines. This was verified by CL investigations after a careful surface polishing which showed the same nearly unaltered luminescence stripe pattern as on the originally wavy sample surface, where the CL intensity stripe patterns are parallel to the slip plane traces. If it is planned to analyze the local distribution of the CL luminescence intensity quantitatively from the image, then the CL image has to be recorded in the linear range of the relation between CL signal and grey value. This relation can be determined experimentally by measuring the correlation between image grey value and absolute signal of the photomultiplier at given contrast and brightness values for the detector. On the contrary, if it is intended to visualize small variations of CL intensity on the sample surface, then for best results, a non-linear signal-to-grey value relation should be applied already during the imaging process in the SEM. The spatial resolution of a CL image on a bulk Si sample at low temperatures is determined by the size of the interaction volume of the primary electrons in the sample, because the size of this interaction volume is only marginally smaller than the volume for the radiative recombination of the electron-hole pairs²¹. The diameter of the interaction volume for a focused and stationary beam is about 3 µm under the given experimental conditions²².

The estimation of the strain field surrounding extended defects by ccEBSD requires the recording of Kikuchi patterns with sufficient quality even on highly strained sample regions. An example is given in Figure 3A. To get these patterns, the sample surface should be free of undesirable surface layers (oxides, carbon contamination, etc.). Good results can be achieved with the following experimental parameters: electron beam at 20 keV and 12 nA, tilt of sample surface normal between 60° and 70° to the incident beam at WD = 15 mm, 2 x 2 EBSD detector pixel binning which yields a resolution of 672 x 512 pixels, amplification gain of the signal set to high, exposure time between 20 and 43 msec per frame on the EBSD detector, averaging over five to ten frames per measuring point and storage of the Kikuchi pattern as images for each measuring point without indexing. The total acquisition time for one Kikuchi pattern can be estimated from the exposure time multiplied by the number of frames plus a few 10 msec due to the time necessary for beam shift, read out and storage. A value of 50 nm turned out experimentally to be a good minimum step size between two sample positions within the EBSD mapping. This is in agreement with recent theoretical considerations²³ concerning the achievable resolution for electron diffraction contrast. To avoid beam drift during the EBSD mapping, it is recommended to wait at least 15 min with the beam scanning in the immediate neighborhood of the region of interest before running the map. It was found that only EBSD line scans parallel to the sample tilt axis provide realistic strain data with a reference pattern on the same line. Otherwise, a very careful determination of the actual sample tilt angle is needed, or alternatively the length of a line scan perpendicular to the tilt axis must be limited to a few µm.

The Kikuchi pattern stored as 8-bit JPEGs were evaluated by Fourier transformation (FT) and cross-correlation with a program "ccEBSD" written by one of the authors (PC). The program is based on the algorithm developed by Wilkinson et.al.⁶, described in detail in ref. 19. In the Kikuchi pattern, several (15 – 19) sub-patterns (128 x 128 pixels) have to be defined with characteristic features as bright band crossings (cf. Figures 3A and 3B). All sub-patterns have to be analyzed by FT. A band pass filter has to be applied to all of the FT images (inner radius 6 pixels for low frequencies, outer radius 40 pixels for higher frequencies) to set all values to zero outside the band pass filter in the Fourier space (cf. Figure 3C). Then the cross-correlation (cc) function (Figure 3D) has to be calculated between the FT of each sub-pattern with the respective FT of the sub-pattern (Figures 3E and 3F) from the reference Kikuchi pattern. From the positions of the peaks in the cc-functions (Figure 3D), the relative displacements of the sub-patterns can be determined. Using these displacements, the normal and shear strain components can be calculated. If the material dependent elastic constants are known, also the stress components can be determined. In the notation by Voigt, these constants are C₁₁ = 165.7 GPa, C₁₂ = 63.9 GPa and C₄₄ = 79.9 GPa for Si with a cubic lattice²⁴. The combination of the results from all sub-patterns of one Kikuchi pattern improves the accuracy of the strain evaluation. The statistical error determined from a ccEBSD line scan on a defect free region in a silicon single crystal is found to be 2 x 10^-4 for all the strain tensor components. Nevertheless, to obtain quantitative results for the case of extended defects, the choice of a Kikuchi pattern as reference pattern is important. If, for example, the sample is completely covered by dislocations as shown in Figure 2, sophisticated procedures that are proposed by Jiang et al.²⁵ could be applied to find out the appropriate reference pattern.

The situation for the use of ccEBSD is easier for a Si wafer ([001]-surface orientation) treated by a high-energy electron beam to induce a liquid phase re-crystallization (see Figure 4). Around the track of re-crystallization, slip lines are visible in the BSE image indicating a dislocation movement on slip planes with traces parallel to the edges of the image (Figure 4A). The CL investigations were performed under the same experimental conditions as for the plastically deformed sample. The mono-CL images, recorded at the energies of the band-to-band transition and of the D4 and D2 dislocation luminescence bands (Figures 4B, 4C and 4D, respectively), show the spatial distribution of the extended defects caused by the re-crystallization procedure. A local anti-correlation between the band-to-band transition and the D line luminescence bands can be inferred from the mono-CL images. This is supported by the CL spectra (Figure 4E) which were measured at sample positions 1, 2 and 3 (cf. Figure 4A) in spot mode of the electron beam. From the ccEBSD investigations performed as a line scan in front of the re-crystallization track (white line in Figure 4A), the local strain tensor components along the line scan could be determined (Figures 4F and 4G). It was proven, that within the statistical error, the values do not depend on which particular Kikuchi pattern was used as the reference pattern if this pattern is situated in a region where the band-to-band transition is dominant. The dislocation related electronic transitions appear when the sum of normal strains Tr(ε) exceeds a value of 5 x 10^-4. Because Tr(ε) is not equal to zero for the scan in a region of about 150 µm length close to the re-crystallization track, there is a mean lattice dilation in a volume near to the sample surface. According to the linear theory of elasticity, the normal stress σ₃₃ is equal to zero as presupposed in the evaluation program "ccEBSD". If there is a crack on the EBSD line scan, then a ccEBSD evaluation cannot be performed over the whole scan with one reference pattern due to abrupt variations of the Kikuchi pattern caused by the geometrical effects of the crack.

What can be achieved in principle by the experimental methods described for the investigation of structural, optical and electrical properties of grain boundaries in Si is shown in Figure 5 for a Si bi-crystal of p-type doping with a Boron concentration of 10¹⁷ cm^-3. The conventional EBSD map yields the full information on the crystal orientation at each point of the map where only the indexing of the Kikuchi pattern is performed immediately after the pattern acquisition by the acquisition software. Additionally, also the type of grain boundaries can be displayed by the conventional EBSD data managing program (Figure 5A). For the detection of a LAGB, a critical angle has to be defined for the misorientation of the crystal lattice at two adjacent measuring points. A minimum value of 1° was proven to be appropriate. For the LAGB indicated in the EBSD map, the misorientation angle is 4.5°. The EBIC-image of the same sample area (Figure 5B) was measured at RT. The incoherent Σ3 grain boundaries and the LAGB appear here as dark lines. This effect is caused by the locally increased carrier recombination. From the contrast profile of the EBIC signal across the LAGB (cf., Figure 5H), a diffusion length of (60 ± 12) µm and a recombination velocity of (4.1 ± 0.4) x 10⁴ cm sec^-1 were determined for the minority charge carriers in the framework of the model by Donolato¹⁴. The single dark points in the EBIC image, spread over the entire sample surface and concentrated especially in the vicinity of the LAGB, indicate the positions of threading dislocations. In CL imaging investigations at 4 K, the LAGB appears dark in the mono-CL image at band-to-band transition energies (Figure 5C), as expected, but surprisingly also in a mono-CL image at the energy of the D4 band (Figure 4D) which is usually assigned to dislocations. However, the LAGB looks bright in a mono-CL image at a wavelength of 1,530 nm corresponding to the D1/D2 luminescence bands (Figure 5E). This luminescence behavior is believed to be induced by point defects in the neighborhood of the dislocations constituting the LAGB. Additionally, the ccEBSD procedure was performed as a line scan across the LAGB to determine its local strain field. The electron beam acceleration voltage was reduced to 10 kV to increase the spatial resolution for the strain determination at the expense of an increased total acquisition time for each Kikuchi pattern. The normal and the shear strain components, shown in Figures 5F and 5G, respectively, cannot be calculated for the center region of the LAGB (over about 50 nm) because double patterns appear that prevent an analysis of the Kikuchi patterns. Moreover, the EBSD patterns on both sides of the LAGB have to be correlated with two different reference patterns because the cross-correlation method can only be applied for small variations of the diffraction pattern. So, two reference patterns were collected on the left hand side and on the right hand side of the LAGB due to the large misorientation angle between the two sub-grains. Nonetheless, it is exciting that the strain components behave symmetrically on both sides of the LAGB. The diagrams for the position dependence of the strain components show that the range of the strain field of the LAGB extends to about 350 nm into both sub-grains. On the contrary, the diagram of the locally varying contrast in the band-to-band transition mono-CL image, and of the EBIC signal contrast in the EBIC image (Figure 5H), indicates that the influence of the LAGB on the luminescence signal and on the EBIC signal ranges up to ± 10 µm and ± 1.5 µm from the center of the LAGB, respectively. This verifies the statement from the beginning that the local resolution for the investigation of different properties of extended defects strongly depends on the experimental method and parameters applied.

Figure 1. Set Up for CL, EBIC and ccEBSD Measurements. (A) SEM with field-emission gun, different apertures for imaging and analysis, the sample on the cryo-sample holder, the CL light-collecting mirror, the monochromator and the IR-PMT for the infrared light, (B) Schottky contact of the sample for EBIC investigations and (C) set-up for the formation and storage of a Kikuchi pattern which can be analyzed numerically to get information on the crystal orientation as well as on crystal lattice distortions by ccEBSD. Please click here to view a larger version of this figure.

Figure 2. CL Spectral and Imaging Investigations on a Plastically Deformed Silicon Single Crystal. (A) Silicon samples on indium foil positioned on the cryo-sample holder. (B) The CL-spectra measured for a high purity Si single crystal (virgin), for a plastically deformed sample, and after additional annealing. The characteristic transitions in the spectra are labeled as usual with B-B for a band-to-band transition, and D1 to D4 for dislocation induced luminescence bands. (C) Slip lines on the surface of the deformed Si crystal (marked by red arrow in Figure 2A) imaged by back-scattered electrons (BSE). These results show plastic deformation for different slip systems. In Figures 2D and 2E, the mono-CL images for the D4 line and D3 line are shown, respectively, with each measured for the same sample region below that shown in the BSE-image (Figure 2C). Please click here to view a larger version of this figure.

Figure 3. Images Visualizing Steps in the Course of ccEBSD Analysis. (A) Full Kikuchi pattern from actual sample position with sub-pattern. (B) One of the sub-patterns and (C) its filtered Fourier transformation. (E) The corresponding sub-pattern from a reference position on the sample and (F) its filtered Fourier transformation. (D) The cross-correlation function (CCF) calculated from the Fourier-transformations of the sub-pattern. The brightness of the CCF was increased by 20% to visualize the details. Please click here to view a larger version of this figure.

Figure 4. CL and ccEBSD Investigations for a Si Wafer After Re-crystallization. (A) BSE image from the surface of a Si wafer with a track of re-crystallized material after treatment by a high-energy electron beam. Positions of spots 1, 2 and 3 for CL spectral investigations are marked as well as the line with direction arrow where the ccEBSD scan was performed. (B-D) Mono-CL images of the sample region shown in (A), taken at the energetic positions of the band-to-band transition (B), D4 (C) and D2 (D) luminescence band. (E) CL spectra measured at the spots 1, 2 and 3. The normal (F) and the shear strain components (G) along the line scan in (A), calculated from ccEBSD investigations. Please click here to view a larger version of this figure.

Figure 5. EBSD, EBIC, CL and ccEBSD Investigations on a Silicon Bi-crystal with HAGBs and LAGB. (A) EBSD orientation map on a Si bi-crystal with twin grain boundaries in yellow and a LAGB in black. The orientation of the normal of the grain surface is indicated. (B) EBIC image at RT of the sample area in (A) where coherent (yellow arrow) and incoherent (blue arrow) twin grain boundaries are indicated. (C-E) The mono-CL images at energies of B-B (C), D4 (D) and D1/D2 (E) belong to the LAGB region which is marked by a red rectangle in the EBIC image (B). The normal (F) and the shear strain components (G) calculated from ccEBSD investigations across the LAGB. (H) Comparison of the contrast found in the B-B mono-CL image at 4K and in the EBIC image at RT across the LAGB. Please note the different scaling on the x-coordinate in the strain component diagrams and in the CL- and EBIC-contrast diagram. Please click here to view a larger version of this figure.