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X-ray topographic study of defect in p− diamond layer of Schottky barrier diode
DIAMAT-06395; No of Pages 6 Diamond & Related Materials xxx (2015) xxx–xxx
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X-ray topographic study of defect in p− diamond layer of Schottky barrier diode Yukako Kato ⁎, Hitoshi Umezawa, Shin-ichi Shikata Advanced Industrial Science and Technology (AIST), Ikeda, Osaka 563-8577, Japan
a r t i c l e
i n f o
Article history: Received 30 November 2014 Received in revised form 25 March 2015 Accepted 25 March 2015 Available online xxxx
a b s t r a c t Semiconducting diamond has received significant attention as a material for use in power devices owing to its high breakdown characteristics and high carrier mobility in high-temperature, high-voltage environments. Several research groups have postulated that the density of defects is a critical issue for the development of high-performance devices. In addition, they have suggested that a high-quality crystal with a flat surface and a low defect density is required for achieving high and stable performance. In this study, we investigated the reverse leakage current of some Schottky barrier diodes and the defect distribution in the area of each Schottky electrode by using X-ray topography. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Semiconducting diamond has attracted considerable attention as a more advanced-generation material for power devices owing to its ability to perform with high breakdown characteristics and high carrier mobility in a high-temperature, high-voltage environment. The latest progress of development of diamond power devices is remarkable [1]. For example, the reported diamond Schottky barrier diode (SBD) worked stable at temperatures above 200 °C [2]. On the other hand, high switching performance under high temperature was shown [3]. Such stable behavior is essential for power device applications [4]. The relationship between defects and device properties has been discussed by several research groups [5–10]. It is assumed that defects degrade the performance of power devices. When considering a vertical power device structure, one of the issues is leakage current at threading dislocations. In the case of type-Ib diamond, screw dislocations are observed on the (111) surface by using an etch-pit figure [11,12]. Umezawa et al. suggested that the possible dislocations in type-Ib diamond are edge dislocations and 60° dislocations [13]; these are threading dislocations. Type-IIa diamond too has threading dislocations [14]. When chemical-vapor-deposited (CVD) diamond is grown on a diamond substrate, dislocations in the substrate are extended to CVD diamond [15]. It is assumed that if a SBD is fabricated with a bilayer structure as shown in Fig. 1, these extended dislocations degrade the electrical performance of each layer. In a previous study, high leakage current was measured in a SBD when the etch-pit density was high after plasma treatment [16]. This etch-pit was made on a non-epitaxial crystallite in CVD diamond. In another study, it was suggested that threading dislocations and other
⁎ Corresponding author. E-mail address: [email protected] (Y. Kato).
defects are etched preferentially, thus leaving typical etch-pits [17]. Because the chemical stability of diamond is high, an etch-pit is made by the plasma treatment method. According to several studies involving etch-pits on diamond, it is assumed that the origin of an etch-pit depends on plasma conditions such as gas, etching rate, and sample temperature. However, the etch-pit formation mechanism has not been explained yet. If the device performance depends on the defect distribution, a method for characterizing defects in the device is necessary for the fabrication of high-performance devices. By using the etch-pit method, the defect points in a device can be identified. However, a destructive inspection method is not acceptable for device fabrication. X-ray topography (XRT) is a defect analysis method [18]. From the standpoint of device fabrication, this method has two major merits. First, it is a nondestructive method. Second, identification of the Burgers vector is possible using this method. This means that the dislocation type can be estimated using XRT. In the case of diamond, XRT has been used in many previous studies [19–21]. However, the correlation between defects and device performance has not been reported yet. In this study, we investigated the reverse leakage current of some SBDs and the distribution of dislocations in the area of each Schottky electrode. 2. Experimental We analyzed a diamond SBD with a pseudo-vertical structure as shown in Fig. 1. The substrate was a type-Ib single-crystal diamond (001) plate provided by Sumitomo Electric Industries, Ltd, Japan. The substrate size and thickness were 3 mm × 3 mm and 0.5 mm, respectively. The samples were prepared as follows. The substrate was polished using a scaife [22]. To produce a flat surface for the epitaxial layer, the normal to the substrate surface was misoriented from the [001] direction by approximately 3° by using step-flow homoepitaxial growth of the substrate surface [23,24].
http://dx.doi.org/10.1016/j.diamond.2015.03.021 0925-9635/© 2015 Elsevier B.V. All rights reserved.
Please cite this article as: Y. Kato, et al., X-ray topographic study of defect in p− diamond layer of Schottky barrier diode, Diamond Relat. Mater. (2015), http://dx.doi.org/10.1016/j.diamond.2015.03.021
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Fig. 1. A cross-sectional view of schematic sample image. The figure shows a layered structure with p− layer, p+ layer, and type-Ib diamond (substrate) with electrodes. Sample size is 3 mm × 3 mm. Ohmic electrodes (Ti/Pt/Au) are drawn as gray circles, and Schottky electrodes (Pt/Au) are drawn as white circles.
Two types of homoepitaxial single-crystal diamond layers, namely, lightly boron-doped layer (p− layer) and p + layer, were grown using the chemical vapor deposition (CVD) method. The thickness of these layers was about 17.8 and 1 μm, respectively. A schematic crosssectional image is shown in Fig. 1. A p− layer, with a boron concentration of about 8 × 1014 cm−3, has been used as a semiconducting layer in diamond devices [25,26]. The boron concentration of a p + layer is about 1 × 1020 cm−3. Because the critical doping level of the metal-to-insulator transition is over 1020 cm−3 [27], the p+ layer acts as an electrical conduction layer in SBD. Ti (30 nm)/Pt (30 nm)/Au (100 nm) Ohmic electrodes were formed on the four corners on the p− layer via electron beam evaporation by using a shield mask. The satisfactory Ohmic contacts to semiconducting diamond by an annealing process conducted [28]. The diameter of Ohmic electrodes was 400 μm. Pt (30 nm)/Au (100 nm) Schottky electrodes were also formed on the p− layer by using lithography, electron beam deposition and lift-off techniques. The diameter of Schottky electrodes was 200 μm. We fabricated a total of 25 Schottky electrodes. Each electrode was characterized by I–V measurements and defect analysis. Fig. 2 are the I–V curve of diodes. The forward performance is not varied, but reverse performance is varied. For an easy discussion on correlations between device characteristics and defect distribution
in Schottky electrodes, we defined a parameter, VR (1 mA). It means the reverse voltage when the leakage current is 1 mA/cm2. Because the maximum measurement voltage is limited as 1100 V due to depend the I–V measurement system limit, the maximum VR (1 mA) was 1100 V. The average VR (1 mA) value and standard deviation were 735.9 V and 220 V, respectively. All electrodes were removed after the I–V measurements for the defect analysis of the p− layer. Dislocations in the sample were analyzed using XRT. XRT is a two-dimensional image of X-ray diffraction intensities, and acts as a defect distribution map for a single crystal. The Burgers vector b can be determined by this method because the dislocation image disappears when b is perpendicular to the diffraction vector g. The bright area in the image is virtually free of any defects. Moreover, the dislocation vector t is suggested by the dislocation figure in the projection image of the dislocation. XRT measurements were carried out at BL14B and BL20B of the Photon Factory in Japan. The used wavelength range of monochromatic X-rays from a double-bounced Si (111) crystal was 0.7–1.0 Å. Diffraction plans g were set to {404}, {113} and (220). Because the X-ray wave length is 0.9 Å and incident angle is set to 0.5° in the case of {404}, the extinction distance of X-ray ξ is about 7 μm [18]. This surface sensitivity is enough for discussion about p− layer (17.8 μm). In the case of {113}, a stainless steel put in front of the sample as x-ray shield for surface sensitive measurement. Because XRT of (220) is measured with the transmission geometry (Laue case), this XRT image is bulk sensitive.
3. Results and discussion Fig. 3 shows an XRT image (g = 0–44). Fig. 3a shows the overall view of the sample. A lot of black/white contrast can be observed; this is caused by defects, mainly dislocations. For discussing the effect of defects on device characteristics, this figure is trimmed to the size of a Schottky electrode, as shown in Fig. 2b. From these figures, we were able to observe the defects in each Schottky electrode. The average number of defects in a Schottky electrode was 8.5. The defect distribution varied between the electrodes. The minimum and maximum defect densities were about 3 × 103 and about 9 × 104/cm2, respectively. Because this defect density was almost consistent with dislocation density in the Ib substrate [6] and epitaxial layer (p− layer) [15] as per previous papers, the crystal quality of our sample was similar to commonly used samples. By using XRT, we were estimated five types of defects: edge dislocation (ED), threading mixed dislocation (TMD), mixed dislocation on {111} (MD), large unknown defect (LUD), and small unknown defect (SUD). The “small”
Fig. 2. I–V curves of diamond Schottky barrier diode (SBD). (a) Forward and (b) reverse characteristics of diamond SBD with electrode sizes of 200 μm.
Please cite this article as: Y. Kato, et al., X-ray topographic study of defect in p− diamond layer of Schottky barrier diode, Diamond Relat. Mater. (2015), http://dx.doi.org/10.1016/j.diamond.2015.03.021
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Fig. 3. X-ray topographic (XRT) image of p− layer. g vector is set to [0−44]. (a) XRT image of the p− layer of a sample. The sample size is 3 mm × 3 mm. (b) Trimmed XRT images. There are 25 Schottky electrodes with several defects. The average number of defects in a Schottky electrode is 8.5. It means that the average defect density is about 2.7 × 104/cm2.
in SUD implies that the XRT contrast size was similar to the dislocation size. Fig. 4 and Table 1 show the one example of dislocation analysis. Analyzed device (group 2) is shown in Fig. 3b. The vertical axis on left in Fig. 5 represents the defect density of each Schottky electrode, the vertical axis on right in Fig. 5 represents the defect number of each Schottky electrode and the horizontal axis represents VR (1 mA). As shown by the red dotted line, there was one group whose defect density agreed but VR (1 mA) varied. On the other hand, there was another group whose defect density varied but VR (1 mA) agreed, as shown by the blue dotted line.
These observations suggest that there was a correlation between the defect density and VR (1 mA). For quantitative analysis, we used a correlation coefficient, C, given by the following equation. X ðx−xÞðy−yÞ ffi C ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X X 2 2 ðx−xÞ ðy−yÞ
In the case of discussion on defect density and VR (1 mA), x is VR (1 mA), x is the average of VR (1 mA), y is defect density, and y is the average of VR (1 mA). A C value exceeding implies high VR (1 mA); thus, a good device can be fabricated using diamond with high defect density. A C value below zero implies high VR (1 mA); thus, a good device can be fabricated using diamond with low defect density. Because the correlation coefficient between defect density and VR (1 mA) was −0.09, it means that there was no correlation between the two parameters. Next, we discuss about the correlation between each type of defect (ED, TMD, MD, LUD, and SUD) and VR (1 mA). The vertical axis of Fig. 6 represents the defect density of the Schottky electrodes, and the horizontal axis represents VR (1 mA). In the cases of ED and TMD, correlation coefficients CED and CTMD were −0.21 and −0.14, respectively. Fig. 6a and b shows this weak correlation. In the case of MD, it was assumed that there was a correlation because CMD was 0.57. However, the CMD value and Fig. 6c for high VR (1 mA) samples contradict each other. For example, in the case of samples that showed high VR (1 mA), one of them had a defect density of 6 × 103/cm2, but another
Table 1 Burgers vector, dislocation vector, and dislocation type of each dislocation shown in Fig. 3. The analysis data of dislocation type in device shown in Fig. 3. In device shown in Figs. 3, there are five dislocations. One of dislocations is mixed dislocation on {111} and others are edge dislocations.
Fig. 4. X-ray topographic (XRT) image of one device (group 2) which is marked by red line in Fig. 3b. (a) This is XRT image (g = 0−44) of one of device. Because of the reflection geometry (Bragg case), this is surface sensitive image. (b) This figure is same as Fig. 2a, but g = − 404. (c) This figure is same as Fig. 2a, but g = 113. (d) This figure is same as Fig. 2a, but g = 404. (e) This figure is same as Fig. 2a, but g = −113. (f) This figure is same as Fig. 2a, but g = 220. Because of the transmission geometry (Laue case), this is bulk sensitive image. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
0−44 −404 404 113 −113 220 b t Type of dislocation
a
b
○ ○ N.D. ○ ○ ○ [10−1] or [−101] 1−12 Mixed on {111}
○ ○ ○ ○ ○ ○ ○ ○ ○ ○ N.D. N.D. [1−10] or [−110] 001 001 Edge Edge
c
d
e
○ ○ ○ ○ ○ N.D.
○ ○ ○ ○ ○ N.D.
001 Edge
001 Edge
Please cite this article as: Y. Kato, et al., X-ray topographic study of defect in p− diamond layer of Schottky barrier diode, Diamond Relat. Mater. (2015), http://dx.doi.org/10.1016/j.diamond.2015.03.021
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Fig. 5. Dislocation density and reverse voltage at 1 mA/cm2 (VR (1 mA)). This figure is for the discussion about the correlation between the dislocation density of a Schottky electrode and the reverse voltage at 1 mA/cm2. (a) The vertical axis shows the defect density of each Schottky electrode, and the horizontal axis shows VR (1 mA). As shown by the red dotted line, there is one group whose defect density agrees but VR (1 mA) varies. On the other hand, there is one group whose defect density varies but VR (1 mA) agrees, as shown by the blue dotted line. We could not able find a correlation from this figure. (b) A schematic image for explaining VR (1 mA). VR (1 mA) is the reverse voltage when the leakage current density is 1 mA/cm2. We defined this parameter for an easy discussion about correlations between device characteristics and defect distribution in Schottky electrodes. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
had a defect density of 2 × 104/cm2. Fig. 6d shows about the correlation for LUD and SUD. Because CLUD was −0.05, there was no correlation between LUD and VR (1 mA). In the case of SUD, we cannot discuss about
anything with correlation coefficient because CSUD is −0.29. However, in Fig. 6d, there are not any SUDs in high withstand-voltage devices having VR (1 mA) is 800 V or higher. These trends indicate that SUDs will cause current leakage at low voltage. Thus, we could find a clear correlation between dislocation and the withstand-voltage performance via the analysis of individual defect types. Finally, we show a correlation between the dislocation type and device performance by using the following assumption. If each defect acts as a different type of resistance, the SBD circuit includes various conductance depend on the distribution of dislocation. Because the conductance measurement for each defect in the p− layer is difficult in the case of our sample, we defined that one factor includes conductance factor. This factor named “contribution factor” (mdefect). The conductance of one SBD circuit is denoted as G and can be calculated using mdefect G ¼ nED mED þ nTMD mTMD þ nMDonf111g mMDonf111g þ nLUD mLUD þ nSUD mSUD
Fig. 6. Each type of dislocation density and reverse voltage at 1 mA/cm2 (VR (1 mA)). (a) The vertical axis shows the defect density and the number of ED, and the horizontal axis shows VR (1 mA). There is a weak correlation between ED density and VR (1 mA). (b) This is similar to Fig. 4a, but the vertical axis shows the defect density and the number of TMD. There is also a weak correlation between the TMD density and VR (1 mA). (c) This is similar to Fig. 4a but the vertical axis shows the defect density and the number of MD. CMD is 0.57; however, the MD density varies widely at high VR (1 mA). (d) This is similar to Fig. 4a, but the vertical axis shows the defect density and the number of LUD and SUD. Two squares mean LUD data and cross-marks mean SUD data. SUDs will cause current leakage at low voltage because we could not observe SUD in the Schottky electrode whose VR (1 mA) was higher than 800 V.
where ndefect is the number of defects. mdefect is estimated by parameter for evaluating the discrepancy between the experimental data and the estimation model, residual sum of squares (RSS). When RSS is minimum value, it means that mismatch between experimental data and estimation model is small. Table 2 is the contribution factors mdefect with normalized mdefect by mED. Fig. 7 is for comparison between VR (1 mA) and calculated reverse voltage. The vertical and horizontal axes of Fig. 7 represent VR (culc) and VR (1 mA), respectively. Because the correlation coefficient in this figure is 0.57, it is assumed that VR (culc) is in good agreement with VR (1 mA). For evaluation that this result is threshold-independent, other thresholds' results are shown in Fig. 7 and Table 2. For 0.5 mA/cm2 and 1 mA/cm2, we found the same results as shown Fig. 7. In the case of 1 μA/cm2, the absolute value of each m is different from other high leak current region, but the magnitude relation is same as others. In the future work, we will discuss this difference of absolute value in detail. 4. Conclusions In this paper, we reported the correlation between defect density and device performance for various SBDs. We couldn't find any type of dislocation which is worked as device performance killer, but it was
Please cite this article as: Y. Kato, et al., X-ray topographic study of defect in p− diamond layer of Schottky barrier diode, Diamond Relat. Mater. (2015), http://dx.doi.org/10.1016/j.diamond.2015.03.021
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Table 2 Contribution factors mdefect normalized by mED with different threshold current densities, 1 μA, 0.5 mA, 1 mA and 2 mA. For showing an influence of conclusion degree of the threshold of current density, contribution factors under other condition are shown. When threshold is 0.5 mA/cm2 or 2 mA/cm2, each contribution factors are similar to mdefect at 1 mA/cm2. In the case of 1 μA/cm2, the absolute value of each m is different from other high leak current region, but the magnitude relation is same as others. In the future work, we will discuss this difference of absolute value in detail. Thresholds
1 μA
0.5 mA
1 mA
2 mA
Edge Threading Mixed Mixed on {111} Large unknown Small unknown Correlation coefficient
2.64E+6 (1.00) 3.20E+6 (0.83) 3.30E+6 (0.80) 1.00E+7 (0.26) 2.50E+5 (10.56) 0.79
1.79E+6 (1.00) 8.70E+6 (0.21) 6.30E+6 (0.28) 4.00E+8 (0.01) 7.60E+5 (2.36) 0.55
1.77E+6 (1.00) 9.35E+6 (0.19) 6.20E+6 (0.29) 3.00E+8 (0.01) 7.90E+5 (2.24) 0.57
1.90E+6 (1.00) 9.65E+6 (0.20) 6.30E+6 (0.30) 1.00E+8 (0.02) 7.75E+5 (2.45) 0.58
assumed that the device performance depends on several types of defects, each having its own contribution factor, mdefect. This correlation doesn't depend on the threshold, 1 mA. In future work, we will fabricate a vertical SBD. When the current route is clearly vertical to the p− layer, the discussion about a killer defect will be simple. In addition, we will design new electrode pattern for the simple description of electric circuit. For example, we will make the guard ring for leakage current and field plate for electrode edge effects. The guard rings play a major role in reducing the leakage of extraneous charge to the collecting electrode. A field plate will act as a suppressor of leak occurrence due to local electric field concentration. In other words, it would block the occurrence of extra current routes.
Prime novelty statement The suggestion of correlation between the types of defect dislocation density of Schottky electrode for the fabrication of high performance diode is new in this manuscript.
Fig. 7. Calculated reverse voltage at various threshold from 1 μA/cm2 to 2 mA/cm2 (VR(threshold)) and reverse voltage at various threshold (VR(threshold)). This figure was drawn under the assumption that each defect has a various contribution factor. X-axis shows experimental data and Y-axis shows calculated data. Blue square shows the Calculated reveres voltage at 1 mA/cm2 (VR (1 mA)) and reverse voltage at 1 mA/cm2 (VR (1 mA)). Black triangle, red cross and green circle mean the case of VR (1 μA), VR (0.5 mA) and VR (2 mA), respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Acknowledgments This work has been performed under the approval of the Photon Factory (Proposal No. 2014G036). This work was supported in part by grants from JSPS KAKENHI(25820128).
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Diamond & Related Materials journal homepage: www.elsevier.com/locate/diamond
X-ray topographic study of defect in p− diamond layer of Schottky barrier diode Yukako Kato ⁎, Hitoshi Umezawa, Shin-ichi Shikata Advanced Industrial Science and Technology (AIST), Ikeda, Osaka 563-8577, Japan
a r t i c l e
i n f o
Article history: Received 30 November 2014 Received in revised form 25 March 2015 Accepted 25 March 2015 Available online xxxx
a b s t r a c t Semiconducting diamond has received significant attention as a material for use in power devices owing to its high breakdown characteristics and high carrier mobility in high-temperature, high-voltage environments. Several research groups have postulated that the density of defects is a critical issue for the development of high-performance devices. In addition, they have suggested that a high-quality crystal with a flat surface and a low defect density is required for achieving high and stable performance. In this study, we investigated the reverse leakage current of some Schottky barrier diodes and the defect distribution in the area of each Schottky electrode by using X-ray topography. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Semiconducting diamond has attracted considerable attention as a more advanced-generation material for power devices owing to its ability to perform with high breakdown characteristics and high carrier mobility in a high-temperature, high-voltage environment. The latest progress of development of diamond power devices is remarkable [1]. For example, the reported diamond Schottky barrier diode (SBD) worked stable at temperatures above 200 °C [2]. On the other hand, high switching performance under high temperature was shown [3]. Such stable behavior is essential for power device applications [4]. The relationship between defects and device properties has been discussed by several research groups [5–10]. It is assumed that defects degrade the performance of power devices. When considering a vertical power device structure, one of the issues is leakage current at threading dislocations. In the case of type-Ib diamond, screw dislocations are observed on the (111) surface by using an etch-pit figure [11,12]. Umezawa et al. suggested that the possible dislocations in type-Ib diamond are edge dislocations and 60° dislocations [13]; these are threading dislocations. Type-IIa diamond too has threading dislocations [14]. When chemical-vapor-deposited (CVD) diamond is grown on a diamond substrate, dislocations in the substrate are extended to CVD diamond [15]. It is assumed that if a SBD is fabricated with a bilayer structure as shown in Fig. 1, these extended dislocations degrade the electrical performance of each layer. In a previous study, high leakage current was measured in a SBD when the etch-pit density was high after plasma treatment [16]. This etch-pit was made on a non-epitaxial crystallite in CVD diamond. In another study, it was suggested that threading dislocations and other
⁎ Corresponding author. E-mail address: [email protected] (Y. Kato).
defects are etched preferentially, thus leaving typical etch-pits [17]. Because the chemical stability of diamond is high, an etch-pit is made by the plasma treatment method. According to several studies involving etch-pits on diamond, it is assumed that the origin of an etch-pit depends on plasma conditions such as gas, etching rate, and sample temperature. However, the etch-pit formation mechanism has not been explained yet. If the device performance depends on the defect distribution, a method for characterizing defects in the device is necessary for the fabrication of high-performance devices. By using the etch-pit method, the defect points in a device can be identified. However, a destructive inspection method is not acceptable for device fabrication. X-ray topography (XRT) is a defect analysis method [18]. From the standpoint of device fabrication, this method has two major merits. First, it is a nondestructive method. Second, identification of the Burgers vector is possible using this method. This means that the dislocation type can be estimated using XRT. In the case of diamond, XRT has been used in many previous studies [19–21]. However, the correlation between defects and device performance has not been reported yet. In this study, we investigated the reverse leakage current of some SBDs and the distribution of dislocations in the area of each Schottky electrode. 2. Experimental We analyzed a diamond SBD with a pseudo-vertical structure as shown in Fig. 1. The substrate was a type-Ib single-crystal diamond (001) plate provided by Sumitomo Electric Industries, Ltd, Japan. The substrate size and thickness were 3 mm × 3 mm and 0.5 mm, respectively. The samples were prepared as follows. The substrate was polished using a scaife [22]. To produce a flat surface for the epitaxial layer, the normal to the substrate surface was misoriented from the [001] direction by approximately 3° by using step-flow homoepitaxial growth of the substrate surface [23,24].
http://dx.doi.org/10.1016/j.diamond.2015.03.021 0925-9635/© 2015 Elsevier B.V. All rights reserved.
Please cite this article as: Y. Kato, et al., X-ray topographic study of defect in p− diamond layer of Schottky barrier diode, Diamond Relat. Mater. (2015), http://dx.doi.org/10.1016/j.diamond.2015.03.021
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Fig. 1. A cross-sectional view of schematic sample image. The figure shows a layered structure with p− layer, p+ layer, and type-Ib diamond (substrate) with electrodes. Sample size is 3 mm × 3 mm. Ohmic electrodes (Ti/Pt/Au) are drawn as gray circles, and Schottky electrodes (Pt/Au) are drawn as white circles.
Two types of homoepitaxial single-crystal diamond layers, namely, lightly boron-doped layer (p− layer) and p + layer, were grown using the chemical vapor deposition (CVD) method. The thickness of these layers was about 17.8 and 1 μm, respectively. A schematic crosssectional image is shown in Fig. 1. A p− layer, with a boron concentration of about 8 × 1014 cm−3, has been used as a semiconducting layer in diamond devices [25,26]. The boron concentration of a p + layer is about 1 × 1020 cm−3. Because the critical doping level of the metal-to-insulator transition is over 1020 cm−3 [27], the p+ layer acts as an electrical conduction layer in SBD. Ti (30 nm)/Pt (30 nm)/Au (100 nm) Ohmic electrodes were formed on the four corners on the p− layer via electron beam evaporation by using a shield mask. The satisfactory Ohmic contacts to semiconducting diamond by an annealing process conducted [28]. The diameter of Ohmic electrodes was 400 μm. Pt (30 nm)/Au (100 nm) Schottky electrodes were also formed on the p− layer by using lithography, electron beam deposition and lift-off techniques. The diameter of Schottky electrodes was 200 μm. We fabricated a total of 25 Schottky electrodes. Each electrode was characterized by I–V measurements and defect analysis. Fig. 2 are the I–V curve of diodes. The forward performance is not varied, but reverse performance is varied. For an easy discussion on correlations between device characteristics and defect distribution
in Schottky electrodes, we defined a parameter, VR (1 mA). It means the reverse voltage when the leakage current is 1 mA/cm2. Because the maximum measurement voltage is limited as 1100 V due to depend the I–V measurement system limit, the maximum VR (1 mA) was 1100 V. The average VR (1 mA) value and standard deviation were 735.9 V and 220 V, respectively. All electrodes were removed after the I–V measurements for the defect analysis of the p− layer. Dislocations in the sample were analyzed using XRT. XRT is a two-dimensional image of X-ray diffraction intensities, and acts as a defect distribution map for a single crystal. The Burgers vector b can be determined by this method because the dislocation image disappears when b is perpendicular to the diffraction vector g. The bright area in the image is virtually free of any defects. Moreover, the dislocation vector t is suggested by the dislocation figure in the projection image of the dislocation. XRT measurements were carried out at BL14B and BL20B of the Photon Factory in Japan. The used wavelength range of monochromatic X-rays from a double-bounced Si (111) crystal was 0.7–1.0 Å. Diffraction plans g were set to {404}, {113} and (220). Because the X-ray wave length is 0.9 Å and incident angle is set to 0.5° in the case of {404}, the extinction distance of X-ray ξ is about 7 μm [18]. This surface sensitivity is enough for discussion about p− layer (17.8 μm). In the case of {113}, a stainless steel put in front of the sample as x-ray shield for surface sensitive measurement. Because XRT of (220) is measured with the transmission geometry (Laue case), this XRT image is bulk sensitive.
3. Results and discussion Fig. 3 shows an XRT image (g = 0–44). Fig. 3a shows the overall view of the sample. A lot of black/white contrast can be observed; this is caused by defects, mainly dislocations. For discussing the effect of defects on device characteristics, this figure is trimmed to the size of a Schottky electrode, as shown in Fig. 2b. From these figures, we were able to observe the defects in each Schottky electrode. The average number of defects in a Schottky electrode was 8.5. The defect distribution varied between the electrodes. The minimum and maximum defect densities were about 3 × 103 and about 9 × 104/cm2, respectively. Because this defect density was almost consistent with dislocation density in the Ib substrate [6] and epitaxial layer (p− layer) [15] as per previous papers, the crystal quality of our sample was similar to commonly used samples. By using XRT, we were estimated five types of defects: edge dislocation (ED), threading mixed dislocation (TMD), mixed dislocation on {111} (MD), large unknown defect (LUD), and small unknown defect (SUD). The “small”
Fig. 2. I–V curves of diamond Schottky barrier diode (SBD). (a) Forward and (b) reverse characteristics of diamond SBD with electrode sizes of 200 μm.
Please cite this article as: Y. Kato, et al., X-ray topographic study of defect in p− diamond layer of Schottky barrier diode, Diamond Relat. Mater. (2015), http://dx.doi.org/10.1016/j.diamond.2015.03.021
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Fig. 3. X-ray topographic (XRT) image of p− layer. g vector is set to [0−44]. (a) XRT image of the p− layer of a sample. The sample size is 3 mm × 3 mm. (b) Trimmed XRT images. There are 25 Schottky electrodes with several defects. The average number of defects in a Schottky electrode is 8.5. It means that the average defect density is about 2.7 × 104/cm2.
in SUD implies that the XRT contrast size was similar to the dislocation size. Fig. 4 and Table 1 show the one example of dislocation analysis. Analyzed device (group 2) is shown in Fig. 3b. The vertical axis on left in Fig. 5 represents the defect density of each Schottky electrode, the vertical axis on right in Fig. 5 represents the defect number of each Schottky electrode and the horizontal axis represents VR (1 mA). As shown by the red dotted line, there was one group whose defect density agreed but VR (1 mA) varied. On the other hand, there was another group whose defect density varied but VR (1 mA) agreed, as shown by the blue dotted line.
These observations suggest that there was a correlation between the defect density and VR (1 mA). For quantitative analysis, we used a correlation coefficient, C, given by the following equation. X ðx−xÞðy−yÞ ffi C ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X X 2 2 ðx−xÞ ðy−yÞ
In the case of discussion on defect density and VR (1 mA), x is VR (1 mA), x is the average of VR (1 mA), y is defect density, and y is the average of VR (1 mA). A C value exceeding implies high VR (1 mA); thus, a good device can be fabricated using diamond with high defect density. A C value below zero implies high VR (1 mA); thus, a good device can be fabricated using diamond with low defect density. Because the correlation coefficient between defect density and VR (1 mA) was −0.09, it means that there was no correlation between the two parameters. Next, we discuss about the correlation between each type of defect (ED, TMD, MD, LUD, and SUD) and VR (1 mA). The vertical axis of Fig. 6 represents the defect density of the Schottky electrodes, and the horizontal axis represents VR (1 mA). In the cases of ED and TMD, correlation coefficients CED and CTMD were −0.21 and −0.14, respectively. Fig. 6a and b shows this weak correlation. In the case of MD, it was assumed that there was a correlation because CMD was 0.57. However, the CMD value and Fig. 6c for high VR (1 mA) samples contradict each other. For example, in the case of samples that showed high VR (1 mA), one of them had a defect density of 6 × 103/cm2, but another
Table 1 Burgers vector, dislocation vector, and dislocation type of each dislocation shown in Fig. 3. The analysis data of dislocation type in device shown in Fig. 3. In device shown in Figs. 3, there are five dislocations. One of dislocations is mixed dislocation on {111} and others are edge dislocations.
Fig. 4. X-ray topographic (XRT) image of one device (group 2) which is marked by red line in Fig. 3b. (a) This is XRT image (g = 0−44) of one of device. Because of the reflection geometry (Bragg case), this is surface sensitive image. (b) This figure is same as Fig. 2a, but g = − 404. (c) This figure is same as Fig. 2a, but g = 113. (d) This figure is same as Fig. 2a, but g = 404. (e) This figure is same as Fig. 2a, but g = −113. (f) This figure is same as Fig. 2a, but g = 220. Because of the transmission geometry (Laue case), this is bulk sensitive image. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
0−44 −404 404 113 −113 220 b t Type of dislocation
a
b
○ ○ N.D. ○ ○ ○ [10−1] or [−101] 1−12 Mixed on {111}
○ ○ ○ ○ ○ ○ ○ ○ ○ ○ N.D. N.D. [1−10] or [−110] 001 001 Edge Edge
c
d
e
○ ○ ○ ○ ○ N.D.
○ ○ ○ ○ ○ N.D.
001 Edge
001 Edge
Please cite this article as: Y. Kato, et al., X-ray topographic study of defect in p− diamond layer of Schottky barrier diode, Diamond Relat. Mater. (2015), http://dx.doi.org/10.1016/j.diamond.2015.03.021
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Fig. 5. Dislocation density and reverse voltage at 1 mA/cm2 (VR (1 mA)). This figure is for the discussion about the correlation between the dislocation density of a Schottky electrode and the reverse voltage at 1 mA/cm2. (a) The vertical axis shows the defect density of each Schottky electrode, and the horizontal axis shows VR (1 mA). As shown by the red dotted line, there is one group whose defect density agrees but VR (1 mA) varies. On the other hand, there is one group whose defect density varies but VR (1 mA) agrees, as shown by the blue dotted line. We could not able find a correlation from this figure. (b) A schematic image for explaining VR (1 mA). VR (1 mA) is the reverse voltage when the leakage current density is 1 mA/cm2. We defined this parameter for an easy discussion about correlations between device characteristics and defect distribution in Schottky electrodes. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
had a defect density of 2 × 104/cm2. Fig. 6d shows about the correlation for LUD and SUD. Because CLUD was −0.05, there was no correlation between LUD and VR (1 mA). In the case of SUD, we cannot discuss about
anything with correlation coefficient because CSUD is −0.29. However, in Fig. 6d, there are not any SUDs in high withstand-voltage devices having VR (1 mA) is 800 V or higher. These trends indicate that SUDs will cause current leakage at low voltage. Thus, we could find a clear correlation between dislocation and the withstand-voltage performance via the analysis of individual defect types. Finally, we show a correlation between the dislocation type and device performance by using the following assumption. If each defect acts as a different type of resistance, the SBD circuit includes various conductance depend on the distribution of dislocation. Because the conductance measurement for each defect in the p− layer is difficult in the case of our sample, we defined that one factor includes conductance factor. This factor named “contribution factor” (mdefect). The conductance of one SBD circuit is denoted as G and can be calculated using mdefect G ¼ nED mED þ nTMD mTMD þ nMDonf111g mMDonf111g þ nLUD mLUD þ nSUD mSUD
Fig. 6. Each type of dislocation density and reverse voltage at 1 mA/cm2 (VR (1 mA)). (a) The vertical axis shows the defect density and the number of ED, and the horizontal axis shows VR (1 mA). There is a weak correlation between ED density and VR (1 mA). (b) This is similar to Fig. 4a, but the vertical axis shows the defect density and the number of TMD. There is also a weak correlation between the TMD density and VR (1 mA). (c) This is similar to Fig. 4a but the vertical axis shows the defect density and the number of MD. CMD is 0.57; however, the MD density varies widely at high VR (1 mA). (d) This is similar to Fig. 4a, but the vertical axis shows the defect density and the number of LUD and SUD. Two squares mean LUD data and cross-marks mean SUD data. SUDs will cause current leakage at low voltage because we could not observe SUD in the Schottky electrode whose VR (1 mA) was higher than 800 V.
where ndefect is the number of defects. mdefect is estimated by parameter for evaluating the discrepancy between the experimental data and the estimation model, residual sum of squares (RSS). When RSS is minimum value, it means that mismatch between experimental data and estimation model is small. Table 2 is the contribution factors mdefect with normalized mdefect by mED. Fig. 7 is for comparison between VR (1 mA) and calculated reverse voltage. The vertical and horizontal axes of Fig. 7 represent VR (culc) and VR (1 mA), respectively. Because the correlation coefficient in this figure is 0.57, it is assumed that VR (culc) is in good agreement with VR (1 mA). For evaluation that this result is threshold-independent, other thresholds' results are shown in Fig. 7 and Table 2. For 0.5 mA/cm2 and 1 mA/cm2, we found the same results as shown Fig. 7. In the case of 1 μA/cm2, the absolute value of each m is different from other high leak current region, but the magnitude relation is same as others. In the future work, we will discuss this difference of absolute value in detail. 4. Conclusions In this paper, we reported the correlation between defect density and device performance for various SBDs. We couldn't find any type of dislocation which is worked as device performance killer, but it was
Please cite this article as: Y. Kato, et al., X-ray topographic study of defect in p− diamond layer of Schottky barrier diode, Diamond Relat. Mater. (2015), http://dx.doi.org/10.1016/j.diamond.2015.03.021
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Table 2 Contribution factors mdefect normalized by mED with different threshold current densities, 1 μA, 0.5 mA, 1 mA and 2 mA. For showing an influence of conclusion degree of the threshold of current density, contribution factors under other condition are shown. When threshold is 0.5 mA/cm2 or 2 mA/cm2, each contribution factors are similar to mdefect at 1 mA/cm2. In the case of 1 μA/cm2, the absolute value of each m is different from other high leak current region, but the magnitude relation is same as others. In the future work, we will discuss this difference of absolute value in detail. Thresholds
1 μA
0.5 mA
1 mA
2 mA
Edge Threading Mixed Mixed on {111} Large unknown Small unknown Correlation coefficient
2.64E+6 (1.00) 3.20E+6 (0.83) 3.30E+6 (0.80) 1.00E+7 (0.26) 2.50E+5 (10.56) 0.79
1.79E+6 (1.00) 8.70E+6 (0.21) 6.30E+6 (0.28) 4.00E+8 (0.01) 7.60E+5 (2.36) 0.55
1.77E+6 (1.00) 9.35E+6 (0.19) 6.20E+6 (0.29) 3.00E+8 (0.01) 7.90E+5 (2.24) 0.57
1.90E+6 (1.00) 9.65E+6 (0.20) 6.30E+6 (0.30) 1.00E+8 (0.02) 7.75E+5 (2.45) 0.58
assumed that the device performance depends on several types of defects, each having its own contribution factor, mdefect. This correlation doesn't depend on the threshold, 1 mA. In future work, we will fabricate a vertical SBD. When the current route is clearly vertical to the p− layer, the discussion about a killer defect will be simple. In addition, we will design new electrode pattern for the simple description of electric circuit. For example, we will make the guard ring for leakage current and field plate for electrode edge effects. The guard rings play a major role in reducing the leakage of extraneous charge to the collecting electrode. A field plate will act as a suppressor of leak occurrence due to local electric field concentration. In other words, it would block the occurrence of extra current routes.
Prime novelty statement The suggestion of correlation between the types of defect dislocation density of Schottky electrode for the fabrication of high performance diode is new in this manuscript.
Fig. 7. Calculated reverse voltage at various threshold from 1 μA/cm2 to 2 mA/cm2 (VR(threshold)) and reverse voltage at various threshold (VR(threshold)). This figure was drawn under the assumption that each defect has a various contribution factor. X-axis shows experimental data and Y-axis shows calculated data. Blue square shows the Calculated reveres voltage at 1 mA/cm2 (VR (1 mA)) and reverse voltage at 1 mA/cm2 (VR (1 mA)). Black triangle, red cross and green circle mean the case of VR (1 μA), VR (0.5 mA) and VR (2 mA), respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Acknowledgments This work has been performed under the approval of the Photon Factory (Proposal No. 2014G036). This work was supported in part by grants from JSPS KAKENHI(25820128).
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Please cite this article as: Y. Kato, et al., X-ray topographic study of defect in p− diamond layer of Schottky barrier diode, Diamond Relat. Mater. (2015), http://dx.doi.org/10.1016/j.diamond.2015.03.021