Birefringence Microscopy of Unit Dislocations in Diamond - Crystal

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Birefringence microscopy of unit dislocations in diamond Hoa Thi Mai LE, Thierry Ouisse, Didier Chaussende, Mehdi Naamoun, Alexandre Tallaire, and Jocelyn Achard Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/cg5010193 • Publication Date (Web): 24 Sep 2014 Downloaded from http://pubs.acs.org on September 29, 2014

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Crystal Growth & Design

Birefringence microscopy of unit dislocations in diamond

Le Thi Mai Hoa 1*, T. Ouisse 1, D. Chaussende 1, M. Naamoun 2, A. Tallaire 2 and J. Achard 2

1

Univ. Grenoble Alpes, LMGP, F-38000 Grenoble, France

CNRS, LMGP, F-38000 Grenoble, France

2

LSPM, CNRS (UPR 3407), Université Paris 13, Sorbonne Paris Cité, Laboratoire des Sciences

des Procédés et des Matériaux, 99 avenue JB Clément, 93430 Villetaneuse, France

Email: [email protected]

Abstract We use the rotating polarizer birefringence technique to investigate the properties of dislocations in single crystalline diamond produced by a High Pressure High Temperature (HPHT) process or by Microwave Plasma Assisted Chemical Vapor Deposition (MPACVD). The birefringence pattern of individual dislocations is measured and modeled. Although the combination of experiment and simulation does not permit to identify the Burgers vector with absolute certainty, the sensitivity is sufficient to show that the detected defects are unit dislocations. In most cases, the patterns are compatible with straight, threading edge or mixed dislocations with Burgers vectors a/2[110] or a/2[011]. Birefringence microscopy can also be used to probe newly formed defects during the growth of a homo-epitaxial layer.

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Introduction

Due to its excellent physical, mechanical and optical properties, diamond is a potentially interesting material for many applications such as high frequency, high temperature, high power and hostile environment electron device operation [1]. However, and despite an active research, some limitations still prevent its use in the field of power electronic devices. More specifically, linear defects are well known for degrading the performance of power devices [2]. Several research groups have studied the influence of crystal defects on device properties. They suggested that a low defect density is essential for ensuring a stable performance [3-5]. Therefore, probing and identifying dislocations in diamond is a highly relevant topic.

Extended defects such as dislocations and stacking faults are common in both natural and synthetic diamond. Umezawa et al. reported that possible dislocations in type-Ib diamond are edge and mixed 60° dislocations [6]. Y. Kato et al. studied (001) diamond epitaxially grown by CVD on a type-Ib HPHT substrate using X-ray topography. They focused on the analysis of threading dislocations, which they assumed to be responsible for the generation of localized current leakage paths in vertical Schottky diodes. According to them, the Burgers vectors of threading edge dislocations and threading mixed dislocations were a/2[110] and a/2[011], respectively [7]. As reported in [8], Gaukroger et al. also studied dislocations in (001) homoepitaxial CVD diamond grown on type-Ib HPHT substrates and CVD synthetic diamond substrates. The Burgers vector analysis indicated that mixed dislocations dominate and that the majority of these have a Burgers vector a/2[011]. They also demonstrated that many dislocations are observed as bundles emanating from isolated points located at the interface between the substrate and the CVD layer grown onto it. Such bundles are formed of dislocations which finally propagate in a direction close to the 〈001〉 growth direction. Those bundles exhibit a specific birefringence pattern consisting of four or eight approximately equally bright petals. Several research groups have observed similar defect signatures [9-11]. N. Tsubouchi et al. suggested that many mixed dislocations are generated at the interface between the homoepitaxial layer and the substrate [9].


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X-ray topography is a technique of choice for studying extended defects [6-9]. It is nondestructive and, among its variants, synchrotron white beam X-ray topography (SWBXT) is fast and provides useful information on dislocations in diamond. Using a conventional X-ray source, this technique becomes much slower but still provides quantitative and essential information. Birefringence microscopy is an alternative non-destructive technique which can be straightforwardly used in any laboratory, for it only requires an optical microscope. It is based on the observation of strain-induced birefringence. A crystal defect generates a strain field distributed around it. Detection of the strain-induced birefringence allows one to probe the properties of the crystal defects indirectly. Several research groups have applied cross-polarized birefringence microscopy to diamond (see, e.g., [9-11]). A. Crisci et al. investigated single crystal diamond grown by CVD using cross-polarized microscopy. The birefringence patterns exhibit four or eight bright petals, depending on the observation conditions [10]. Y. Kato et al. analyzed the dislocations in the epitaxial CVD single crystal (001) grown on HP-HT type Ib by combining birefringence and cathodoluminescence images. In their study, birefringence microscopy was used to determine the position of the defects [12].

In some materials, the observation of the birefringence pattern of unit dislocations has already been demonstrated (see, e.g., [13] for a recent reference). To the best of our knowledge, and in spite of the many published studies on extended defects in diamond, there exists no published report on the detection of isolated, unit dislocations in diamond by birefringence microscopy. Using the rotating polarizer method developed by Wood and Glaser [14] and a setup already described in [13], our present work aims at identifying unit dislocations in diamond by combining experimental and simulated patterns of dislocation-induced birefringence. We characterize the birefringence of HPHT substrates as well as that of CVD layers. The observation of unit dislocations in diamond is demonstrated by showing that the simulated patterns, which involve no other fitting parameter than the Burgers vector, and otherwise use the fundamental elastic and piezo-optical constants of diamond, are in good agreement with experiment only when the input Burgers vector correspond to unit dislocations.

Experimental details



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1. Samples

The investigated samples have thicknesses of several hundreds of micrometers and a (001) surface plane. The transmitted light has a 〈001〉 direction. Homoepitaxial diamond layers were grown by MPACVD at LSPM on (001) Ib HPHT substrates purchased from Sumitomo. Before the growth procedure, the HPHT substrates were first exposed to a high-power H2/O2 (98/2) plasma at 850°C for an hour in order to treat the substrate surface (typically 200 mbar pressure/ 3kW microwave power). The growth was performed at 850°C by using typically a 3kW injected microwave power, a pressure of 200mbar and a methane concentration of 4%. Details of the growth conditions have been extensively reported elsewhere [15-17].

2. Birefringence measurement

In this study, we use the rotating polarizer method which was initially proposed by Wood and Glazer [14]. We use a green light source of wavelength λ = 546nm and Zeiss Neofluar objectives with magnifications ranging from 2.5 to 100. The description of the experimental apparatus has already been discussed in [13], and the reader is referred to previous publications [13, 18-20] for more detailed information. Due to the combination of a circular analyzer and a rotating polarizer, it is not necessary to discuss the orientation of the sample with respect to that of the analyzer and polarizer. All the birefringence images are plots of the absolute value of sinδ, where δ is the phase shift which would be obtained at a given position between two plane waves crossing the sample and polarized along the two principal axes of the optical indicatrix, respectively.

3. Birefringence modeling

Modeling of the dislocation-induced birefringence is briefly summarized as follows: a given Burgers vector is selected, and the dislocation is assumed to be straight and infinite. The stress field of the dislocation is first calculated in a coordinate system x1,x2,x3 whose third axis is parallel to the dislocation line. Due to the particular symmetry of diamond, in general the stress field cannot be analytically calculated, therefore it is numerically computed. This implies first to 4 ACS Paragon Plus Environment

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express the matrix of elastic constants in this coordinate system, and then to obtain the displacement field under the form ui=ΣAinf(x1+pnx2), where the pn’s are roots of a sextic equation [21] (we refer the reader to the exhaustive treatment expounded in [21] for more details). The values of the elastic constants were taken from [22]. Having retrieved the stress field induced by the dislocation, we add to it a residual, uniaxial in-plane stress whose coordinates must be transformed by an appropriate rotation before being added in the x1,x2,x3 system. It is well known that this residual stress component also determines the shape of the birefringence pattern, and its value can be precisely extracted from the background value of sinδ [13, 18]. Then, the stress field is calculated in the crystal system x,y,z by an appropriate rotation. The stress field is connected to the optical retardance by piezo-optic coefficients which are fully known in the case of diamond [23]. Besides, an approximation detailed in [18] allows us not to restrict ourselves to vertical dislocation lines, but also to estimate the birefringence of tilted dislocations; the optical retardance δ is then calculated for each pixel by numerically integrating over the optical path.

It is worth noticing that the magnitude of the in-plane residual stress can be precisely extracted from the background birefringence, and is therefore not a fitting parameter. Besides, the elastic and piezo-optic constants of diamond were taken from the literature and not adjusted. As a consequence, for a vertical dislocation, the only fitting parameters are the Burgers vector components and the angle between the in-plane projection of the Burgers vector and the in-plane direction of the residual stress. For a given fit, all possible Burgers vectors can be chosen using a linear combination of the elementary vectors defined by Thompson’s tetrahedron [24].

The identification procedure of a dislocation is carried out as follows: First, the background stress was accurately extracted by adjusting the background value of the birefringence. Then, the birefringence pattern was fitted by choosing a Burgers vector from Thompson’s tetrahedron and rotating the direction of the in-plane background stress until the shape of the simulated and experimental patterns become similar. Then, we adjusted the modulus of the Burgers vector by multiplying the initial input vector by the integer n which gave the best quantitative agreement with the experiment. This can be easily achieved since only a slight variation of the modulus has a large impact on the image intensity. Such a procedure was repeated for all Burgers vectors given by Thompson’s tetrahedron. 5 ACS Paragon Plus Environment


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Results and discussion

1. Identification of the dislocations.

Due to its cubic symmetry, unstressed diamond is not birefringent. However, as often observed, the presence of extended defects induces birefringence. Although the experimental birefringence images exhibit patterns of different shapes and size, they do not immediately permit to specify the Burgers vector unambiguously. In order to analyze the type of the observed dislocations and in an attempt to determine the Burgers vector, we have to combine the experiment with simulation. It is highly desirable to assess if the birefringence technique permits to detect unit dislocations in diamond, as has been proven in the case of Silicon Carbide (SiC) [13]. Although it is somewhat difficult to estimate the ultimate sensitivity of the technique, a rough estimation can be made by calculating the variation of the intensity of the birefringence pattern when the Burgers vector is varied from one to a few units, everything otherwise fixed, and to compare those patterns with experiment.

Fig.1a shows the experimental birefringent pattern of an almost isolated dislocation in a CVD diamond layer. Its shape (two aligned lobes with a different contrast) is characteristic of almost parallel in-plane components of the residual stress and of the Burgers vector [18]. The simulated images 1b, 1c and 1d show the patterns expected for Burgers vectors b1=a/2[110], b2=2b1 and b3=4b1, respectively. The unit dislocation pattern (b1) is clearly closer to the experiment than the other ones. Besides, it is worth noticing that an increase by only one lattice unit of the smallest in-plane Burgers vector component induces a large discrepancy between simulation and experiment. Since there is no other fitting parameter but the orientation and the size of the Burgers vector, and since the final input orientation is indeed required to recover the shape of the pattern, we conclude that the experimental birefringent pattern of Fig.1a is that of a unit dislocation. To confirm this, we note that a vast majority of observed patterns follow this conclusion. Since most articles referring to other characterization techniques and isolated dislocations only report the observation of unit dislocations, and since the best agreement that we most often obtain between the experimental and observed birefringent patterns also correspond 6 ACS Paragon Plus Environment

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to unit dislocations, we can reasonably assume that the dislocation-induced birefringence allows us to state whether the dislocation strength is equal to unity or higher. Birefringence can therefore be used to assess the density of dislocations in a given area, pure screw dislocations omitted (since in the latter case, the vertical orientation of the induced shear stress and cubic symmetry prohibit in-plane stress-induced birefringence [18]). Then, the drawback of this technique is that in order to detect the patterns unambiguously, the birefringence intensity scale must be finely tuned around the background stress value. A residual stress varying across the diamond crystal thus prohibits automatic counting, because the scale has to be adjusted differently, depending on the observed area [13]. In addition, if a reasonable assessment of the Burgers vector modulus seems to be achievable, a precise determination of the Burgers vector coordinates is indeed much more hazardous, for reasons which are detailed below.

In Fig.1 the simulated patterns exhibit small lobes which are not visible in the experiment. It is worth noting that the equivalent patterns of SiC dislocations exhibit all predicted lobes [18]. The absence of the smallest lobes in the case of diamond might be ascribed to the particular structure of vertical [001] dislocations [25]. In contrast with the case of SiC, these vertical dislocations do not lie in a glide plane, and this imposes a specific core structure. Some proposals have been made, e.g., by Fujita et al. [25] to describe the atomic displacements at the dislocation core. For instance, the core might exhibit a zig-zag structure at the atomic scale. Although this point has never been studied in detail, it is clear that such a structure could also modify the short-range and medium-range stress field associated to the dislocation. In particular, a zigzag line with a large zigzag amplitude, with an in-plane projection of the zigzags directed perpendicularly to the Burgers vector, might favor the cancellation of the birefringence close to the core in a way quite similar to that described for some specific tilted dislocation lines [18]: there would be a succession of regions where the sign of the birefringence experienced by a light beam transmitted close to the dislocation core alternates between a zig and a zag, so that the overall birefringence in that location cancels. That this may happen if the zigzags extend only over a few atomic distances is difficult to ascertain, but cannot be excluded. This point is difficult to appreciate as long as an analytical formulation of the long range stress field is not available.



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Figure 2 (a) shows the experimental pattern of a dislocation from a single crystal CVD diamond layer with a thickness of 310µm. The simulated birefringence images are presented in Figure 2b, c and d. They are obtained by varying the Burgers vector coordinates. The observed pattern is characteristic of an almost vertical dislocation for which the in-plane background strain and the in-plane component of the Burgers vector b form an angle close to π/4 [18]. In such a case, and as can be seen in Figure 2, the birefringence patterns exhibit four lobes. In these figures, we did not show the simulations that we carried out with Burgers vectors bigger than unit ones, but as for Fig.1, the discrepancy between such simulations and the experiment was obvious. In Fig.2 are reproduced simulations with either unit Burgers vectors, or with smaller Burgers vectors corresponding to partial dislocations. In contrast to the conclusion drawn in the previous paragraph, it is now clearly more difficult to attribute the experimental pattern to one of the simulated patterns unambiguously, even if the simulation with b=a/2[110] seems to be closer to the experiment. The same applies to Fig.3 (same experimental pattern as that of Fig.1): it is clearly not possible to discriminate between the various sets of b coordinates corresponding to pure edge or mixed unit dislocations, or edge partial dislocations which are used for the simulations. Figs.2 and 3 are not specific cases, and in general, even if it is possible to discriminate between unit and non-unit dislocations, it is practically impossible to attribute a given experimental birefringence pattern to a precise set of Burgers vector coordinates. From this point of view, the birefringence technique cannot be as efficient as more involved techniques, such as Transmission Electron Microscopy (TEM) or X-ray topography.

2. Interpretation of atypical birefringence patterns.

According to most recorded data, the simulated patterns best agreeing with experiment correspond to straight dislocations threading throughout the whole substrate thickness. However, we sometimes observed very faint patterns. Their shape was similar to conventional patterns, but their intensity was not amenable to simulation by assuming the existence of a straight, unit dislocation. A reasonable interpretation is that some conversion of the dislocation line occurs in the crystal, or that it originates in a bundle of dislocations issued from a point defect and moving away from one another before adopting a vertical direction during the growth. In [13], where we 8 ACS Paragon Plus Environment

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reported SiC birefringence data, a comparison of the experimental birefringence patterns and simulated ones demonstrated that dislocations could exhibit a vertically oriented line over less than the full substrate thickness.

Fig.4 shows a faint dislocation pattern measured from single crystal CVD diamond, presumably not always vertical. In this case, it is difficult to observe the pattern without adjusting the color scale carefully (see Figure 4(b)). Such a dislocation is impossible to simulate using the full substrate thickness. In order to explain the experimental observation, we have assumed a Burgers vector a/2[110]. Then the simulation process is performed using different dislocation lengths (l) along the growth axis. The simulated patterns are presented in Fig.4 (c-g). From a direct comparison between these patterns to the experiment, an acceptable fit required to use an effective thickness l=100µm (see Figure 4(g)), which is much smaller than the substrate thickness L=310µm. Although the simulation roughly agrees with experiment, in such a case it becomes clearly impossible to assess the Burgers vector value, since different Burgers vectors and reducing or increasing the dislocation length may lead to equally good fits. Finding such patterns can therefore only be used as an indication that the observed dislocations are not straight, which is already important information, but which must rather be confirmed by, e.g., the use of cathodoluminescence in order to follow the full dislocation line [16].

4. Dislocation-induced birefringence before and after CVD growth.

The quality of single crystal CVD diamond can be improved by using HPHT substrates combining a low surface damage and low defect density [5, 7, 8, 26, 27]. In this section, we describe the observation of birefringence patterns before and after CVD growth. Figs.5a and b show experimental birefringence images of a synthetic HPHT type Ib(001) diamond substrate before and after CVD growth, respectively. They are obtained from the same sample region. Comparing Figs.5a and b show that there is a one-to-one correspondence between the dislocations mapped before and after CVD growth.

In Fig.5, it is already visible that the CVD growth modifies the background stress. This may lead in turn to a modification of individual dislocation patterns, as exemplified by the 9 ACS Paragon Plus Environment


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isolated patterns shown in Fig.6a and b, corresponding to the same dislocation but measured before and after CVD growth. In this case, the background stress has not only changed in intensity, but also in orientation (for a detailed account of the dependence of the pattern shape on the residual stress orientation, see, e.g., [18]).

After CVD growth, new defects are also observed, which were not initially present in the HPHT substrate (Fig.7). Many of them correspond to birefringent patterns of a high intensity, not compatible with unit dislocations. We attribute those newly formed patterns either to dislocations bundles as described by Pinto et al. [11], or to microscopic inclusions.

Conclusion

We have combined experimental and simulated birefringence patterns to identify dislocation types in single crystal CVD diamond and HPHT diamond substrates. In most cases, the patterns are compatible with straight, unit dislocations with Burgers vector a/2[110] or a/2[011]. Sometimes, we suspect that the dislocations change their orientation, particularly when they are observed in a CVD layer. We have provided good evidence in favor of the fact that the birefringence technique permits to detect individual, presumably unit dislocations in diamond. Although the exact coordinates of the Burgers vector are not amenable to an unambiguous determination, the non-destructive character and the rapidity of the technique make it a useful one, even if the full characterization of an individual dislocation clearly requires more involved techniques, such as TEM or X-ray topography. We have also shown that birefringence microscopy can be used to distinguish newly formed defects in a homo-epitaxial layer from those already present in the diamond substrate.

Acknowledgements This work has been supported by the French National Research Agency (ANR) within the frame of the CROISADD project, contract ANR-11-ASTR-020.


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Figure captions Fig.1: (a) Experimental birefringence pattern of an individual dislocation from a CVD diamond layer. (b, c, d) Simulated birefringence patterns, starting from a unit dislocation (Fig. 1b) to a few units. Simulation parameters: the Burgers vectors are indicated in the figure, the colour scale for sinδ is from 0.02 to 0.11, the substrate thickness is 310 µm, the image size is 95µm x 95 µm, the residual strain is ε = 8.6 x10-6. Fig.2: Experimental (a) and simulated (b, c, d) birefringence images of a dislocation from a CVD diamond layer. Simulation parameters: the Burgers vectors are indicated in the figure, the colour scale for sinδ is from 0.16 to 0.22, the substrate thickness is 310 µm, the image size is 95µm x 95 µm, the residual strain is ε = 17.4 x10-6. Fig.3: Experimental (a) and simulated (b, c, d) birefringence images of a dislocation from a CVD diamond layer. Simulation parameters: the Burgers vectors are indicated in the figure, the colour scale for sinδ is from 0.02 to 0.11, the substrate thickness is 310 µm, the image size is 95µm x 95 µm, the residual strain is ε = 8.6 x10-6. Fig.4: (a, b) Experimental birefringence pattern of a dislocation which is presumably not always vertical and (c-f) simulated patterns. Simulation parameters: the effective dislocation length is varied from 100 µm to 310 µm, the colour range for sinδ is from 0.147 to 0.166, input Burgers vector is b = a/2[110]. Fig.5: Experimental birefringence images of synthetic high-pressure, high-temperature (HPHT) type Ib (001) diamond: (a) before and (b) after CVD growth. There is a one-to-one correspondence between the dislocations mapped before and after CVD growth.

Fig.6: Experimental birefringence images of synthetic high-pressure, high-temperature (HPHT) type Ib (001) diamond: (a) before and (b) after CVD growth. The dislocations are located at the same location but exhibit different birefringence patterns. Fig.7: Experimental birefringence images of the sample consisting of the CVD layer on its HPHT substrate: (a) HPHT substrate, (b) HPHT substrate+CVD layer. The two images are obtained from the same sample region. D6 and D7 are defects generated in the CVD layer. 13 ACS Paragon Plus Environment


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Birefringence microscopy of unit dislocations in diamond

Le Thi Mai Hoa 1*, T. Ouisse 1, D. Chaussende 1, M. Naamoun 2, A. Tallaire 2 and J. Achard 2

1

Univ. Grenoble Alpes, LMGP, F-38000 Grenoble, France

CNRS, LMGP, F-38000 Grenoble, France 2

LSPM, CNRS (UPR 3407), Université Paris 13, Sorbonne Paris Cité, Laboratoire des Sciences des Procédés et des Matériaux, 99 avenue JB Clément, 93430 Villetaneuse, France

Table of Contents Graphic

Experimental birefringence pattern of an individual dislocation (A) and the simulated birefringence patterns (B).

Brief summary An individual dislocation is measured from a single crystal CVD diamond layer with a thickness of 310m. The type of the individual dislocation is determined by combining experiment and simulation. The result indicates that the observed dislocation corresponds to unit ones.

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Birefringence Microscopy of Unit Dislocations in Diamond - Crystal

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