1. Introduction

Indium nitride (InN) has the narrowest bandgap of 0.63 eV and the smallest electron effective mass among III–nitrides semiconductor materials. The latter characteristic leads to a much higher electron mobility than that of gallium nitride (GaN) and makes InN potentially applicable in high-speed electronic devices [1–3]. All these devices require high-quality InN or its alloys. However, the epitaxy of those materials have so many defects due to the low maximum epitaxial temperature (500~600 °C) [4, 5] and the large lattice mismatch of InN with common buffer layers or substrates [6, 7]. The commonly used defects-testing methods consist of high resolution x-ray diffraction (XRD), transmission electron microscopy (TEM), photoluminescence (PL) and the cathodoluminescence spectroscopy (CL) [6, 8–10]. The XRD has big measurement error and can only obtain a statistical average information from macroscopic material. The TEM of a very high resolution can demonstrate the crystal dislocations, stacking faults, grain boundaries, etc. more directly, but the sample preparation for this measurement method is very difficult. The PL and CL only characterize material microstructural defects in an indirect manner, particularly the nature of point defects [6, 8–10]. However, μ-RDS obtains the information of microstructural defects by testing optical anisotropy caused by the strain around these defects. Furthermore, the μ-RDS system has advantages over others including its simplicity, high accuracy and high sensitivity.

The reflectance difference spectroscopy (RDS) has been demonstrated as an effective measurement tool to investigate the in-plane optical anisotropy on semiconductor surfaces and interfaces [11–13]. The microscopic reflection difference spectroscopy (μ-RDS) with sub-micron spatial resolution was firstly introduced by Koopmans who adopted a microscopic objective lens in the RDS optical path in order to study microscopic structure materials in-depth. They applied this technique to studying the various layers from the side of the cleaved GaAs/AlGaAs multiple quantum well (MQW) structures and the anisotropy in the reflection coefficients around the laser-crystallized seeds [14, 15]. In 2005, Zhiyu Yang’s group improved the μ-RDS based on Koopmans and acquired RDS microscope that can detect shallow surface and interface topographic features with nanometer step height resolution [16]. After that, Dr. Chunhua Wang added Kerr microscopy to the μ-RDS system to detect the off-plane magnetization in polar configuration and the in-plane magnetization with high sensitivity [17]. Yonghai Chen’s group has confirmed that the µ-RDS system can test optical anisotropy caused by strain field through research on strain field information around the nanoindentation [18] and identify the layer number of graphene [19]. Compared to the macro-RDS (RDS), the μ-RDS system also has the advantages of high-resolution besides high sensitivity and non-destruction. So this system has the potential to be applied for studying the microscopic surface and interface properties of semiconductors.

In this work, we present the research background and progress of µ-RDS system, and we also discuss the potential research value of the system in introduction. In Section 2, we present in details the experimental schematics and test principles of the µ-RDS system that our laboratory has improved, and further analyze the origin of anisotropy signal. In Section 3, we use the scanning electron microscopy (SEM), atom force microscopy (AFM), micro-Raman and µ-RDS system to study the specific defects from the InN films grown on GaN grown by molecular beam epitaxy (MBE), then we obtain the real normal reflectivity images and reflectance difference (RD) images by the data processing methods of the plus or minus averaging algorithm. Finally, we compare the µ-RDS results with those of SEM, AFM, Raman mapping and theoretical simulation, which can help us to understand the physical meaning of the real normal reflectivity image and RD image from µ-RDS more directly. We present our conclusions and outlook in Section 4.

2. Material and methods

2.1 Material

InN films in our study were grown on GaN grown by MBE at the 370 °C growth temperature. More specifically, about 4 μm thick GaN layers grown by metal organic chemical vapor deposition (MOCVD) were used as template. After the regrowth of a 200 nm thick GaN layer on the GaN template, 800 nm thick Mg-doped InN films were directly grown. The InN growth was performed under slightly In-rich condition, leading to a flat surface and efficient Mg incorporation. However, there were a lot of In droplets on InN films under In-rich growth condition which would affect the quality of InN films, and the circular defects still existed at the position of In droplets even after we used hydrochloric acid to etch these In droplets [20–22]. These mentioned details can be clearly seen from AFM image and SEM image. Besides this information on the surface topography, the µ-RDS system can also provide some other information about strain distribution introduced by the circular defects. The research on the working principle and the physical meaning of the reflectivity and RD images can be taken as an example for developing a new method to characterize surface microstructural defects.

2.2 The schematics of our μ-RDS

A schematic of our µ-RDS setup, is shown in Fig. 1. After the laser beam from the source (wavelength 532 nm from a 300 mW solid state laser, 2% output power stability) is spatially filtered, it passes through a polarizer (set at 0^◦) and photoelastic modulator (PEM, set at 45^◦). Then the beam, 1μm in estimated diameter, is splitted by a polarization preserved 50/50 beam splitter down into a long working distance objective lens (Mitutoyo 100X, NA = 0.95), and is focused on the sample taken on a piezoelectric ceramic electric translation (PCET) stage which can move in two dimensions in plane. The reflected beam, after passing through the objective lens and the beam splitter, is directed to an analyzer (set at 45^◦) and then confocally focused onto a silicon detector.

 

Fig. 1 Schematics of the optical components of the μ-RDS setup.

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In addition to the main optical path, a LED auxiliary optical path illuminates the sample surface, and the reflected light is accepted by the CCD camera. Then we obtain the surface topography and the accurate scan area of the sample to identify the focal distance of the scanning laser spot. The auxiliary optical path can be placed out of the main optical path, so it does not affect the measurements when the system starts working. The optical signals are converted into electrical signals by silicon detector. The normal reflectivity signals are detected by a lock-in amplifier referenced by the 220 Hz of mechanically chopper and the reflectance difference (RD) signals by 100 kHz of PEM, whose modulation frequency is 50 kHz. Then we change the light spot positions on the sample and record the signal values at different positions. Finally we obtain the scanning normal reflectivity image and RD image by moving the sample and recording signals at every point on it.

Our µ-RDS system is essentially the same as that in [14, 16], but we absorbed the advantages of μ-RDS system made by Koopmans and Zhiyu Yang and also achieved some improvements on their basis. The µ-RDS could readily be converted from a conventional scanning laser microscope by adding the RDS components outside the microscope. Therefore, the core of this system is that the polarization modulation components of the essential RDS components are placed outside the microscope. This arrangement has two main advantages. First, the beam passes the PEM only once, avoiding the case that the reflected beam is modulated by PEM in [14]. Second, this arrangement still maintains the RDS functions of the setup so that the µ-RDS system also has diffraction limit of lateral resolution while maintaining the same optical anisotropy sensitivity as that of conventional macro-RDS. Another major improvement is that we add the optical lens and pinhole in front of the detector in the confocal microscopy system. This confocal system can filter the reflected stray light from different depth of the sample, except the reflected light from the layer which is focused at the position of the pinhole.

2.3 Test principle and origin of signal

The normal reflectivity image is associated with the intensity of reflected beam, and the RD image of μ-RDS represents the change of the reflectance anisotropy signals with the spatial position. Briefly stating, precisely measure the in-plane optical anisotropy by the relative reflection coefficient difference between x and y directions, which is defined as [11, 23],

Where the r_x and r_y are the reflection coefficient in the x and y directions, respectively. It is well known that the strain field is an important origin of in-plane optical anisotropy, which can be easily detected by macro-RDS system. On this basis, its distribution can be detected by a scanning image through μ-RDS system. In our previous work, RD image caused by strain around the nanoindentation has been obtained and it was well simulated with quantum-wire (QWR) structure model [18]. Although microstructural defects of the semiconductor material surface is small, it produces a relatively larger strain field around it than itself based on the theories of photoelasticity and crystal defects. This strain field changes the polarization of the optical axis, so r_x and r_y are not equal, resulting in the in-plane optical anisotropy signal (∆r/r≠0). Quite complex is the theoretical model of anisotropy signals featuring the interaction of strain field and nonuniformity, so we can build an ideal model where only one of the two factors is considered and simulate the corresponding RD image. The relationship between anisotropy signal Δr/r and the strain tensor ε is given by,

The $f$ in Eq. (2) is a complex function related to strain field, and it can be obtained the following relationship through further simplification [18]:

Δr/r is the relative difference of reflection coefficient at two perpendicular directions in plane for each test point, and the RD image can be obtained by changing positions. $\theta$ is the rotation angle of optical anisotropy principal axis caused by strain field. ε_xx, ε_yy and ε_xy are the components of strain tensor. If we know the specific function of strain field, we can get the simulation result of RD image.

The studies have found that the boundary between two materials, the nanometer height steps and lineal defects along the surface of samples within the light spot can induce anisotropy signals [14, 16, 24, 25]. For example, at a step edge, the slight extra optical path of the light reflected from the lower region of the step edge introduces a phase difference between the two halves of the light spot, and this feature gives rise to an anisotropy signal. The anisotropy signals (∆r/r) result from nonuniformity of the surface, if the result of the sample within the spot region is not symmetric, such as in the case where the reflectance of one half of the spot region is different from the other, a finite anisotropy signal will then be introduced (∆r/r≠0). However, there is no anisotropy signal (∆r/r = 0) that will be introduced when a beam with perfect cylindrical symmetry is precisely introduced along the optical axis of the objective and reflected from a uniform surface. What should be noted is that, unlike the signal caused by the strain field, the signal generated by nonuniformity is localized in the vicinity of the edge, the size of which is determined by the light spot diameter. The generation mechanism of the nonuniformity signal will be discussed in detail in the following.

3. Results and discussions

3.1 The results of our μ-RDS

A series of metal markers have been done on InN surface by the process of photolithography and vapor deposition which help us find the same test area after the translation or rotation of the sample.

We tested many specific circular defects on the sample surface in an area of 10 × 10 μm² around these defects. We only took one of the defects as an example to explain the new solution that we adopted for data processing and selected typical representatives to show the results of the μ-RDS. A normal reflectivity image and RD image are shown in Figs. 2(a1) and 2(b1). The results of a 90° clockwise rotation are presented for comparison in Figs. 2(a2) and 2(b2). The black circles in the images are the guide line of the circular defect boundary representing the position of circular defect, as shown in the following figures.

 

Fig. 2 The scanning normal reflectivity images ((a1) and (a2)) and RD images ((b1) and (b2)) of the circular defect (D1).The signal unit in (a1) and (a2) is arbitrary, and that in (b1) and (b2) is 10⁻³.

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According to Eq. (1), a 90° rotation of the sample exchanges the direction of x and y axis. As a result, the signature of the RD image is converted, just as shown in Figs. 2(b1) and 2(b2). The signature of the RD signal is converted as a whole, from which the reliability of our μ-RDS system is verified just as our previous work did [18]. For the existing background signal and system error which are unchanged with rotation of the sample, the RD image after a 90° rotation deviates from the ideal result regarding some details. Theoretically, the effect of the background signal and system error can be eliminated by a plus or minus averaging algorithm. We adopt a plus averaging algorithm to reduce the error of the normal reflectivity images, while the real RD images are obtained by a minus averaging algorithm. The specific data processing formulas are the Eq. (5).

Figures 3(a) and 3(b) respectively show the real scanning normal reflectivity image and RD image of the circular defect D1 obtained by Eq. (5), and Figs. 3(c) and 3(d) respectively show the real scanning normal reflectivity image and RD image of another circular defect D2 by the same averaging algorithm. We find that the reflectivity images are basically the same in which the red zone has an uneven shades of blue outer ring. The red represents the strong reflectivity signal and the blue represents the weak one. However, the RD signals of different circular defects are around the defect boundaries and the two RD images are quite different. In fact, we have got the reflectivity images and the RD images of different circular defects through this algorithm. In terms of the RD images, the circular defects can be classified into two categories, and we select two different typical RD images (just as Fig. 3) of the circular defects in an effort to explore the root cause to the difference of RD images in this work.

 

Fig. 3 (a) and (c) are the real scanning normal reflectivity images, and (b) and (d) are RD images of the circular defect D1 and D2 through the plus or minus averaging algorithm, respectively. The signal unit in (a) and (c) is arbitrary, and that in (b) and (d) is 10⁻³.

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3.2 Discussions

The components and the principles of μ-RDS system are presented in details at the beginning of the paper. This system was also applied in our experiment to obtaining the reflectivity image and RD image of the specific circular defects on InN films. However, the research on μ-RDS system is not mature enough. For making better use of this system, we should understand the physical meaning of the reflectivity image and the RD image correctly on the basis of its operating characteristics and principles. In this work, we use the mature surface defects characterization techniques including SEM, AFM and micro-Raman to assist discussing and analyzing the physical meaning of the experimental results of μ-RDS. Therefore, we confirmed the operability and reliability of our optical microscopy system.

3.2.1 Discussion of reflectivity image

Since the real scanning normal reflectivity images [Figs. 3(a) and 3(c)] are almost the same, we select the reflectivity images of circular defect D1 and D2 to study as representatives. Figures 4(a) and 4(d) show the AFM images of D1 and D2, respectively. Through the AFM images, we know that there are many circular defects with a diameter of about several microns and a height of approximately 50 nm on the surface of InN film. Figures 4(b) and 4(c) show that the line scan profiles of μ-RDS and AFM on the black short dash line in Figs. 3(a) and 4(a) of the D1, and Figs. 4(e) and 4(f) present the line scan profiles of μ-RDS and AFM on the black short dash line in Figs. 3(c) and 4(d) of the D2. As shown in Fig. 4(a) [or Fig. 4(d)] and its cross-sectional diagram of Fig. 4(c) [or Fig. 4(f)], the inside has much smaller fluctuations than the outside circle, so there is no more difficult to understand that the more smooth the surface is, the weaker the scattering effect of the light spots is, causing the reflectivity signal stronger. Therefore, the position of the circular defect at the reflectivity image is covered by a red round spot meaning that reflected signal is stronger.

 

Fig. 4 (a) and (d) are the AFM images of the circular defect D1 and D2, respectively. (b) and (c) are the line scan profiles of μ-RDS and AFM on the same position (black short dash line) of D1. (e) and (f) are the line scan profiles of μ-RDS and AFM on the same position (black short dash line) of D2.

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We can draw two preliminary conclusions from the results of AFM and μ-RDS (the real normal reflectivity image) on the circular defects D1 and D2. First, the red round spots’ positions in the reflectivity images correspond exactly to the actual position of circular defects, and the sizes of these red round spots are slightly smaller than the actual sizes of the circular defects. This difference is caused by the light spot size effect which can be clearly seen through comparing the line scan results of the AFM with the reflectivity image along the diameter direction (as shown in Figs. 4(b) and 4(c) of D1, the same as Figs. 4(e) and 4(f) of D2). When the light passes the boundary of the circular defect, it results in a normal reflectivity signal experiencing various processes from the minimum to the maximum (see the red round spot in the reflectivity image) instead of an abrupt variation that happens in the AFM images. The diameter of the circular defect is the distance between the two minimum which is almost the same as that in the AFM images. Second, the circular defect boundary is uniform except for a deep blue region in the upper left area of Fig. 3(a) of D1. In the same region, more potholes and more rough can be clearly noted from the AFM image [Fig. 4(a)], and the deep blue area in the reflectivity image is attributed to the attenuation of light scattering in the upper left area larger than the lower right area. In the Fig. 4(f), the right side is much higher than the left side, which may result in the deep blue region in the left area of Fig. 3(c) of D2.

3.2.2 Discussion of RD image

We can find that the two types of RD images [Figs. 3(b) and 3(d)] obviously differ from each other in different representatives of the circular defects. Based on the analysis of Section 2, the RD signals of the circular defects may result from the common contribution of nonuniformity surface or strain field. Whereas the RD signals of every circular defects certainly contain the contribution of boundary height fluctuations as we know that the boundary of every circular defects exists about 50 nm step height from the AFM images. To better understand that the RD image feature is only generated by the boundaries of circular defects, we establish an ideal circular defect model in that the RD signals only result from boundary fluctuations in Fig. 5(a), where the R and R' represent the radius of an ideal circular defect and the light spot, respectively. Since the light spot is affected by the boundary of circular defect, the reflection coefficient nuances will appear at two mutually perpendicular directions in plane when light spot perpendicularly incident to the position “A”. This process illustrates that the anisotropy signal produced by the boundary will undergo a process of change during which it firstly increases and then decreases when the light spot moves from left to right at the position “B” of Fig. 5(a). So we introduce an attenuation factor α of RD signal while the light spot moves away from the boundary of the circular defect. Based on the study of the laser-crystallized seed detected by μ-RDS (our PEM set at oblique 45° relative to the PEM their μ-RDS,then $\varphi =\theta +45°$ [15] and the theoretical justification of isolated step-induced change $\Delta \tilde{r}/\tilde{r}$ [26], the optical reflectance anisotropy signal of the position O' around circular defects is:

 

Fig. 5 (a) The ideal circular defect model. (b) The top view of schematic diagram (a). (c) The simulation result of RD image base on ideal model.

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We know that L represents the repeat distance of the ridges and H is the step height from the references.

Figure 5(b) is the top view of Fig. 5(a) in the Cartesian coordinate system when the light spot center at the point O' (θ, d), $\theta \left(0\le \theta \le 2\pi \right)$ and $d$ are the polar angle and polar radius of point O' in the XOY plane, so we define the attenuation factor α,

$\Delta d$ is the induced distance generated by circular defect boundary and $l_{CD}$ is the arc length of circular defect boundary contacted with light spot. We consider this variable as a key determinant of RD signal, so we should get the numerical expression of $l_{CD}$. According to the Helen formula, the area of triangle OO'C is,

Since$S_{△}=\frac{1}{2}dh$ and$\text{ sin}\phi =\frac{h}{R}$, we can obtain the central angle$\phi$,

Given the central angle$\phi$, we can get arc length $l_{CD}=R\cdot 2\phi$,

When the spot center locates at the point O' on the sample, we bring Eq. (7) and Eq. (10) into Eq. (6). So the optical reflectance anisotropy signal is,

At the same time, we obtain the coordinate of incident light spot point O' by the conversion rule between polar coordinates and Cartesian coordinates in Fig. 5(b),

Figure 5(c) shows the simulation result of RD image based on an ideal circular defect model under the conditions of $R=2.25\mu m,R^{\prime }=0.5\mu m$. Therefore, we know that the RD images, produced only by boundaries height fluctuations, present the standard four polar symmetrical distribution.

The RD image of the circular defect D2 is a typical four polar pattern as shown in Fig. 3 and the deviation from an ideal four polar pattern is caused by the imperfect boundary of the circular defects, which is clearly presented in the AFM and SEM image of D2. We think that the RD signals of D2 mainly result from boundary height fluctuations and the contribution of strain field may be negligible. However, during the experiments we found another RD images without a typical four polar pattern. The characteristic of these kinds RD images, as mentioned above, were illustrated as an example by the selected Fig. 3(b) of the D1. Figures 6(a) and 6(c) show the SEM images of the circular defect D1 and D2, respectively. By comparing the AFM images [Figs. 4(a) and 4(d)] and the SEM images [Figs. 6(a) and 6(c)] of D1 and D2, we find the boundary of D1 is more regular and closer to an ideal circular boundary of the theoretical model. To exclude the effect of the uniform surface, we avoid the left up region of D1 and focus on the region with a smooth plane and a regular boundary. But for the ideal boundary of D1 at the lower right area, the four polar pattern is still lost. Considering the difference of the components at the boundary, we conclude that there exists a strain field induced by the lattice mismatch between the InN film and the substrate around the boundary which modifies the four polar pattern of the RD image.

 

Fig. 6 (a) and (c) are the SEM images of the circular defect D1 and D2 under the same azimuth angle, and (b) and (d) are the Raman peak-shift mapping of D1 and D2, respectively.

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To verify the presence of strain field around the defects, we adopt the micro-Raman to study the region around the circular defects. Technically, the strain value can be measured by the E₂ phonon frequency shifts for hexagonal phase InN films [27–29]. Figures 6(b) and 6(d) provide the peak position mapping of E₂(H) around the circular defect D1 and D2, and the peak of E₂(H) about 488~490 cm⁻¹ which is basically consistent with the references [28, 30, 31]. Raman mapping is measured in back-scattering at room temperature by using a Jobin-Yvon HR800 micro-Raman system equipped with a liquid-nitrogen-cooled CCD and a × 100 objective lens (NA = 0.90). The excitation wavelength is 532 nm from a diode-pumped solid-state laser, and the area and step-size of scan are 10 × 10 μm² and 1 μm, respectively. The InN films grown on GaN are in compression due to the lattice mismatch. Comparing the red with the blue in the Raman mapping, the Raman frequency of red is much bigger than that of blue, so the Raman frequencies of circular defects are lower than that of the InN film, showing that the circular defects where the strain is released are less compressively strained than the thin film [28]. For circular defect D1, the low Raman frequencies are mainly around the boundary of the D1 where the peak positions are not entirely consistent, indicating that the very existence of the uneven residual strain around the boundary of D1. Therefore, this results show that both the strain field and the height fluctuations are the reasons for the RD image of D1 presenting a new non-four polar distribution [Fig. 3(b)]. However, the low Raman frequencies of circular defect D2 are only located in circular defect, indicating that strain relaxation around the boundaries of D2 are basically the same, thus the difference of the strain caused by the inhomogeneous distribution of dislocations or the residual strain around the boundaries is negligible. Hence the RD image of D2 [Fig. 3(d)] is close to four polar distribution.

4. Conclusions and outlook

In conclusion, we have developed a RDS microscope (μ-RDS) system. This system in our research was tested through its application to detect the circular defects on InN films. During the data processing, we obtained the real scanning normal reflectivity images associated with the morphology of defects, the different RD images caused by nanoscale height fluctuations and weak strain field in the circular defect. Besides, we divided the circular defects into two categories in accordance with the characteristics of RD images. One type of the RD images shows four polar distribution (such as D2), and the analysis shows that the RD signal of this circular defect mainly result from boundary height fluctuations. The other type is the RD images with non-four polar distribution (such as D1), and the RD signals of this type circular defect mainly result from boundary height fluctuations and strain field. These results show that we can try to adopt the µ-RDS system based on the theories of photoelasticity and crystal defects to obtain a distribution of strain field, in order to characterize the smaller microstructural defects and provide guidance for the growth of high-quality crystal as well.

The μ-RDS is a promising method for solving the issues existing in other characterization methods, including the big measurement errors, destructive effect, complicated testing process, high cost, etc. So this system is a non-destructive, convenient, and effective method to study the microstructural defects on semiconductor material surface. For some sub-micron and even nanoscale microstructural defects that are not yet possible to be directly characterized, such as the dislocations, we get a large range of RD image around defect through μ-RDS when the dislocation density is appropriate. We can also make efforts to identify the dislocation type and density, the size and direction of the burgers vector, the strain distribution and other information of dislocations through experiments and theoretical simulation. What’s more, this method may also be used to measure other microstructural defects in different semiconductor material surface even in other crystal material. Given that μ-RDS has such many advantages over other testing methods, it is a promising material surface microstructural defect characterization method.