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Design and optimization of planar mesa termination for diamond Schottky barrier diodes
Diamond & Related Materials 36 (2013) 51–57
Contents lists available at SciVerse ScienceDirect
Diamond & Related Materials journal homepage: www.elsevier.com/locate/diamond
Design and optimization of planar mesa termination for diamond Schottky barrier diodes A. Nawawi a,⁎, K.J. Tseng a, Rusli a, G.A.J. Amaratunga a, b, H. Umezawa c, S. Shikata c a b c
School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, Singapore Department of Engineering, University of Cambridge, Cambridge, United Kingdom Diamond Research Center, National Institute of Advanced Industrial Science and Technology, Tokyo, Japan
a r t i c l e
i n f o
Article history: Received 1 January 2013 Received in revised form 20 March 2013 Accepted 23 April 2013 Available online 30 April 2013 Keywords: Diamond Schottky barrier diodes Termination Simulation Planar mesa
a b s t r a c t In this paper, we present planar mesa termination structure with high k dielectric Al2O3 for high-voltage diamond Schottky barrier diode. Analysis, design, and optimization are carried out by simulations using finite element technology computer-aided design (TCAD) Sentaurus Device software. The performances of planar mesa termination structure are compared to those of conventional field plate termination structure. It is found that optimum geometry of planar mesa terminated diode requires shorter metal plate extension (1/3 of the field plate terminated diode). Consequently, planar mesa terminated diode can be designed with bigger Schottky contact to increase its current carrying capability. Breakdown performance of field plate termination structure is limited at 1480 V due to peak electric field at the corner of Schottky contact (no oxide breakdown occurs). In contrast, peak electric field in planar mesa termination structure only occurs in the field oxide such that its breakdown performance is highly dependent on the oxide material. Due to Al2O3 breakdown, planar mesa termination structure suffers premature breakdown at 1440 V. Considering no oxide breakdown occurs, planar mesa termination structure can realize higher breakdown voltage of 1751 V. Therefore, to fully realize the potential of planar mesa terminated diode, it is important to choose suitable high k dielectric material with sufficient breakdown electric field for the field oxide. © 2013 Elsevier B.V. All rights reserved.
1. Introduction Among the wide band gap materials, diamond has very significant properties such as large band gap of 5.47 eV, high critical electric fields of 10–20 MV/cm, high carrier mobility (3800 cm2/Vs for hole and 4500 cm2/Vs for electron), high saturation velocity of 2.7 × 107 cm/s, and high thermal conductivity of 22–24 W/cmK [1–4]. Such properties make diamond potentially very attractive for power devices applications that require high-voltage, high-power, high-speed, and hightemperature capability. Diamond Schottky barrier diodes (SBD) with high breakdown voltage (6.5 kV, 7.5 kV, and 10 kV) and high breakdown electric field (7–9.5 MV/cm) have been reported in the literature [5–8]. However, the breakdown electric field achieved by most of the fabricated SBDs up to this date is usually less than 3–4 MV/cm [7,9]. While improvement in the quality of synthetic single crystal diamond is crucial to improve the breakdown electric field, the design and optimization of termination structure is another key factor that should be taken into considerations. Because of high ionization energy of n-type dopant in diamond, termination techniques that require n-type diamond region such as junction termination are not applicable at this moment. Instead, ⁎ Corresponding author. E-mail address: [email protected] (A. Nawawi). 0925-9635/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.diamond.2013.04.009
termination techniques that utilize field plate extension such as field plate termination, three step termination, and ramp oxide termination have been developed [10]. High k dielectric oxide and semiresistive materials have also been employed in order to prevent breakdown in oxide [11–13]. In this paper, we propose planar mesa termination structure [14] for p-type diamond SBD to improve the trade-off between forward and reverse bias characteristics. Design and optimization are carried out by simulation in finite element physics-based technology computer-aided design (TCAD) Sentaurus Device software. High k dielectric Al2O3 is used as the field oxide in this simulation study. The electrical performance of planar mesa termination structure has been investigated and compared with that of field plate termination structure. 2. Termination structures for diamond Schottky barrier diode In any practical diode devices, any metallic contact has to terminate at a certain point on the device. The early SBD was fabricated without any special termination structure as shown in Fig. 1(a) [15]. While the fabrication process for this structure is very simple, it suffers from low breakdown voltage due to the electric field enhancement at the abrupt edge of Schottky contact termination. To prevent premature breakdown, other more sophisticated termination structures are needed to redistribute the electric field more uniformly.
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Fig. 1. Different structure of SBD. (a) Diode without termination structure. (b) Diode with field plate type of termination structure. (c) Diode with planar mesa type of termination structure. (d) Ideal parallel plate diode.
The most common termination structure considered for diamond SBD currently is the field plate termination, as shown in Fig. 1(b). Although this structure is able to increase the breakdown voltage of the diode, peak electric field still occurs at the edge of Schottky metal–semiconductor interface. This can cause Schottky barrier lowering and consequently an increase in leakage current. At high reverse bias, the leakage current is further increased due to multiplication effects [15], which can lead to breakdown at small area under the edge of Schottky contact. In this work, we propose the planar mesa termination structure to improve the performance of diamond SBD. This structure has the potential to reduce the peak electric field at the Schottky metal– diamond interface. Applications of this structure in conventional silicon SBD have demonstrated vast improvement in reverse bias performance with minimal effect on forward bias performance [14,16]. The proposed planar mesa termination structure for diamond SBD is shown in Fig. 1(c). The mesa region is surrounded by an oxide layer to reduce electric field crowding at the corner of the Schottky contact.
This mesa structure can be obtained by inductively coupled plasma (ICP) etching technique using O2 and CF4 reactant gases [17,18]. Possible process flow for fabrication is shown in Fig. 2. In this process, the center area for Schottky contact is firstly masked. Then, ICP process is carried out to selectively etch the p− region at the edge of device. Next, oxide is deposited to fill the trench region created by the etching process, followed by Schottky contact metallization. In order to investigate the performance of proposed planar mesa termination structure for diamond SBD, we performed two dimensional numerical simulation studies as elaborated in the next section. 3. Modeling and simulation Our simulation studies are carried out in two-dimensional finite element physics-based TCAD Sentaurus Device software because of its ability to simulate various physics phenomena in the semiconductor devices. To produce the simulations, it was necessary to first implement various physics-based models and their parameters
Fig. 2. Process flow for fabrication of planar mesa termination for diamond SBD. (a) Masking of p− region at center area for Schottky contact. (b) Selective ICP etching to create diamond mesa structure. (c) Oxide deposition to fill in the trench region for termination purposes. (d) Schottky contact metallization.
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which are suitable for diamond materials. Doping concentrationdependent and temperature-dependent bulk mobility models of the University of Bologna have been applied with parameters based on [19–21] to model the carrier transport in the Boron doped diamond devices. Furthermore, incomplete ionization can occur due to high ionization energy of Boron acceptor in diamond (~ 0.37 eV) [22]. This phenomenon is modeled by implementing incomplete ionization model given by Eq. (1) for Boron concentration less than NA,crit of 3 × 10 19 cm −3 [16,20]. For concentrations greater than NA,crit, hopping conduction occurs and activation energy starts to decrease rapidly; therefore, we assume complete ionization for these cases. −
NA ¼
NA −EF 1 þ g A exp EAkT
ð1Þ
In the Eq. (1), NA− is the number of ionized acceptor, NA is the acceptor doping concentration, EF is Fermi level, and EA is the concentrationdependent activation energy given by 1=3
EA ¼ EA0 −α ðNA −N D Þ
ð2Þ
with EA0 = 0.37 eV and α = 4.1 × 10−8 eV cm−1 [23]. gA in Eq. (1) is temperature-dependent degeneracy factor given by −Δ g A ¼ 4 þ 2 exp kT
ð3Þ
with Δ = 6 meV [24]. To simulate breakdown phenomena in the device, we implemented impact ionization (avalanche generation) model. The electron–hole pair generation rate G ii from impact ionization at high electric field is given by [16,20] ii
G ¼ α n nvn þ α p pvp
ð4Þ
vn(vp) is the electron (hole) velocity and n(p) is the number of electron (hole).αn(αp) is the ionization rate for electron (hole), i.e., the number of electron–hole pairs generated by electron (hole), accelerated along the direction of electric field per unit distance. When Gii goes to a large number, avalanche breakdown occurs. The model implemented in our simulations is van Overstraeten–de Man model given by [20] bnðpÞ α nðpÞ Ef ¼ anðpÞ exp − Ef
! ð5Þ
with Ef as electric field and an(p) and bn(p) as the impact ionization coefficients for electron (hole). In addition, the Caughey–Thomas formula with saturation velocity model is activated to take into account high field transport [20]. Breakdown simulation in diamond devices is always challenging and somewhat approximate because there is no accurate measurement on the values of impact ionization coefficients in diamond up to this date. Several values have been proposed in the literature by Trew et al. [4], Rashid et al. [21], and Isberg [25], as shown in Table 1. To investigate the effect of different impact ionization coefficients on device's breakdown characteristics, we performed reverse bias
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simulation on ideal parallel plate diamond SBD structure as shown in Fig. 1(d). The p+ region is 20 μm thick and it has high Boron doping of 1 × 10 20 cm −3. The p− drift region has Boron doping of 5 × 10 15 cm −3 and thickness of 10 μm. These doping concentrations can be easily achieved in experimental fabrication using current technology. The diamond is oxygen terminated with electron affinity of 1.3 eV. The Schottky metal work function is fixed at 4.27 eV to yield Schottky barrier height of 2.5 eV. Ideal parallel plate is chosen because it exhibits no electric field crowding such that breakdown is largely dependent on the values of impact ionization coefficients. The breakdown voltage is extracted when reverse current density reaches 1 × 10 −4 A/cm 2 [26]. Values of simulated breakdown voltage VBr and maximum electric field at breakdown corresponding to the applied impact ionization coefficients for the ideal parallel plate SBD are shown in Table 1. The distributions of electric field in the device along y-axis for different applied impact ionization coefficients are shown in Fig. 3. We can observe that the maximum electric field at breakdown is less than ~ 3 MV/cm for these various applied impact ionization coefficients in the simulations. While this range of breakdown electric field is commonly found in experimental diamond SBDs [18,27,28], it is much lower than the normally quoted value of 10–20 MV/cm for diamond material [1,2,26]. Furthermore, Volpe et al. [7,8] claimed to have achieved diamond SBD with breakdown electric field of approximately 7–9.5 MV/cm, which led to a conclusion that the currently available impact ionization coefficients underestimate the real capability of diamond material. Through simulations, the wide range of impact ionization coefficients can be designed to achieve certain value of simulated maximum electric field at breakdown. For example, both αn = αp = 5.48 × 106exp(−8 × 107/Ef) and αn = αp = 0.22 × 106 exp(−5 × 107/Ef) can be applied in the simulations to achieve simulated breakdown electric field of ~10 MV/cm for ideal parallel plate diamond SBD structure. Therefore, there are no unique and accurate impact ionization coefficients for diamond that can be deduced through simulations. Rather than stipulating the values of impact ionization coefficients, we apply values suggested by Rashid et al. in our simulations work. While the simulated breakdown voltage might be lower than what can be achieved in single crystal diamond material, these values serve as references in comparing the performances of different edge termination structures. Moreover, we did not consider non-ideal factors such as defects, imperfect metal–diamond interface, etc., in these simulation studies. 4. Results and discussion To assess the performance of planar mesa termination structure in comparison with field plate termination structure for diamond SBD, we carried out simulations of both termination structures with identical properties (thickness and doping of p+ and p− layer, metal work function, etc.) as the simulated ideal parallel plate diamond SBD in Section 3, except for the termination structures. In both structures, the width of the Schottky contact LS is selected as 30 μm and high k dielectric Al2O3 with dielectric constant of 8.7 [26] is used as the oxide layer. To find optimum device's geometry for high breakdown voltage
Table 1 Different impact ionization coefficients for diamond reported in the literature. an (cm−1) Trew et al. [4] Rashid et al. [21] Isberg et al. [25]* Isberg et al. [25]**
1.935 × 10 1.89 × 105 – –
ap (cm−1) 8
1.935 × 10 5.48 × 106 0.6 × 106 4 × 106
bn (V cm−1) 8
7.749 × 10 1.7 × 107 – –
6
bp (V cm−1) 7.749 × 10 1.42 × 107 0.8 × 107 1.1 × 107
6
Breakdown voltage (V)
Maximum electrical field (MV/cm)
222.5 1755 2320 1940
0.846 2.55 3.11 2.73
Symbols * and ** are used to refer to different values of impact ionization parameters reported by the same author in the same report (Isberg et. al [25]). These symbols are related to the results shown in Fig. 3 for different values of impact ionization parameters.
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Fig. 3. Distribution of electric field along the y-axis in the ideal parallel plate diamond SBD at breakdown. The Schottky contact is located at y = 0 μm. Different curves correspond to different impact ionization coefficients that are applied in the simulations.
applications, we conducted many simulations with different values of metal plate extension length LF and the oxide thickness TOX for both termination structures (refer to Fig. 1(b) and (c)). Variations of simulated breakdown voltage VBr for different LF and TOX for field plate terminated diamond SBD are shown in Fig. 4(a).
Fig. 4. (a) Variations of simulated breakdown voltage for different field plate length LF and oxide thickness TOX for field plate terminated diamond SBD. (b) Distribution of reverse current density in the field plate terminated diamond SBD at 1480 V.
While longer LF can result in higher VBr, this effect starts to saturate for LF > 15 μm. We can also see that small variations in TOX affect the VBr significantly. From Fig. 4(a), it can be observed that optimum geometry for field plate terminated SBD (with LF = 15 μm and TOX = 1 μm) exhibits VBr of 1480 V. Fig. 4(b) shows the distribution of current density in the device at breakdown. The breakdown mainly occurs at small region at the corner of Schottky contact due to high electric field. The distribution of electric field at breakdown in this structure is shown in Fig. 5(a) and (b). Peak electric field can be observed at 2 points, i.e., Ef = 5.76 MV/cm at the corner of Schottky contact (x = 15 μm, y = 0 μm) and Ef = 9.38 MV/cm in the oxide layer at the end of field plate termination (x = 30 μm, y = −1 μm). As peak Ef in the oxide layer is lower than Al2O3 breakdown electric field (10 MV/cm) [29,30], no oxide breakdown occurs in optimum field plate terminated SBD. For planar mesa terminated diamond SBD, variations of simulated breakdown voltage VBr for different LF and TOX are shown in Fig. 6(a). Increasing LF and TOX up to certain values can increase the VBr significantly. The optimum geometry for planar mesa terminated SBD can be realized with LF = 5 μm and TOX = 2 μm. Without considering oxide breakdown, this structure is able to achieve VBr of 1751 V. From the distribution of current density in the device at breakdown (shown in Fig. 6(b)), we can observe that breakdown occurs at large area (bulk diamond) under the Schottky contact. The electric field distribution in the device at 1751 V is shown in Fig. 7(a) and (b). In this structure, electric field is distributed almost uniformly under the Schottky contact (channel area) and
Fig. 5. Distribution of electric field in the field plate terminated diamond SBD at 1480 V: (a) In the half of symmetric device and (b) along the line y = 0 μm (oxide– diamond) and y = −1 μm (metal–oxide).
A. Nawawi et al. / Diamond & Related Materials 36 (2013) 51–57
Fig. 6. (a) Variations of simulated breakdown voltage for different field plate length LF and oxide thickness TOX for planar mesa terminated diamond SBD. (b) Distribution of reverse current density in the planar mesa terminated diamond SBD at 1751 V.
peak Ef occurs only at 1 point, i.e., Ef = 11.41 MV/cm in the oxide region at the end of metal plate extension (x = 20 μm, y = 0 μm). This prevents Schottky barrier lowering and breakdown due to electric field crowding at the Schottky contact. However, peak Ef = 11.41 MV/cm in the oxide is beyond the breakdown electric field of Al2O3. By limiting peak Ef in oxide to 10 MV/cm as the limit of Al2O3 breakdown, optimum planar mesa terminated SBD yields VBr = 1440 V. The distribution of electric field in the device at 1440 V along line y = 0 μm is shown in Fig. 7(b), with peak Ef = 9.84 MV/cm (at x = 20 μm, y = 0 μm). By comparing the optimum geometry of field plate termination and planar mesa termination structure for diamond SBD, it is clear that the later consumes less area due to shorter metal plate extension required. Therefore, for the same total device's area, planar mesa terminated SBD can be designed with bigger Schottky contact area which increases its current carrying capability. To compare forward I − V characteristics of both termination structures, we simulated the SBDs with circular contact occupying the same total device's area (total device's diameter of 230 μm) as shown in Fig. 8 based on optimum structure design. Schottky contact area in planar mesa terminated SBD (LS = 220 μm, Schottky contact area = 91.49% of total device's area) is 1.21 times bigger than Schottky contact area in field plate terminated SBD (LS = 200 μm, Schottky contact area = 75.61% of total device's area). The applied parasitic resistance on both devices is 8 mΩ.cm 2 [18]. The simulated forward I − V characteristics for both structures are shown in Fig. 9(a) and (b). Even though planar mesa terminated SBD has slightly lower forward current density
55
Fig. 7. Distribution of electric field in the planar mesa terminated SBD: (a) At 1751 V in the half of symmetric device. (b) At 1751 V and at 1440 V along the line y = 0 μm.
compared to that of field plate terminated SBD, it has higher total forward current (lower on resistance) due to larger Schottky contact area. Table 2 summarizes the performance comparisons between optimum field plate terminated SBD and planar mesa terminated SBD.
Fig. 8. Top view schematic diagram of optimum field plate terminated SBD and planar mesa terminated SBD occupying the same total device's area (diameter of 230 μm). LS and LF are the diameter of Schottky contact and length of metal plate extension in the corresponding structures.
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underestimate the real capability of diamond (breakdown electric field of 10–20 MV/cm). By applying other coefficients such as αn = αp = 5.48 × 10 6exp(−8 × 10 7/Ef) (mentioned in Section 3) for a test case, optimum planar mesa terminated SBD yields simulated VBr of 9190 V. At breakdown, peak Ef in the Al2O3 region at the end of metal plate extension (x = 20 μm, y = 0 μm) reaches high value of 48.15 MV/cm. This value is about 4 times of the maximum Ef in the diamond (~ 12 MV/cm under Schottky contact) and well beyond the capability of Al2O3. Therefore, to fully realize potential of diamond power devices, we need to utilize material with higher dielectric constant and sufficient breakdown electric field to prevent oxide breakdown. The development of such material for diamond SBD can gain insight from research on high k material to replace SiO2 in complementary metal oxide semiconductor (CMOS) technology. In addition, high k materials are also being developed for applications in diamond field effect transistors (FETs). Some of the high k materials of interest for applications in diamond devices are Ta2O5 (k ~ 16–29) [31], SrTiO3 [32], PZT [33–36], Yb2O3 (k ~ 15), HfO2 (k ~ 25), TiO2 (k ~ 80–95), ZrO2 (k ~ 29), etc. [30,37].
5. Conclusions
Fig. 9. Simulated forward I − V characteristics of the field plate terminated (FP) and planar mesa terminated (PM) diamond SBD with the same total device's area (diameter of 230 μm). (a) Comparison of forward current density. (b) Comparison of total forward current.
With the usage of Al2O3 as the oxide layer (considering breakdown in Al2O3), planar mesa terminated SBD yields slightly lower VBr and forward current density compared to field plate terminated SBD. However, it requires shorter metal plate extension. Therefore, it can accommodate larger Schottky contact for the same total device's area which results in higher total forward current. From Table 2, we can also observe that the reverse performances of planar mesa terminated SBD is limited by the breakdown of Al2O3 layer. Unlike field plate terminated SBD, VBr of planar mesa terminated SBD can be increased further to 1751 V if breakdown does not occurs in oxide layer. This can only be realized by replacing Al2O3 with suitable high k material that can support sufficient electric field. Moreover, it is worthy to point out that the impact ionization coefficients used in these simulations (suggested by Rashid et al.)
In conclusion, we have presented planar mesa termination structure for high-voltage diamond Schottky barrier diode. Analysis, design, and optimization are carried out using simulation in TCAD Sentaurus Device software. The performance of planar mesa terminated SBD is compared with that of field plate terminated SBD. In both termination structures, Al2O3 is used as the field oxide. Through many simulations, we found out that the optimum geometry of planar mesa termination structure requires shorter metal plate extension (less area consumption for termination structure) compared to field plate termination structure. For the same total device's area, planar mesa terminated SBD can be designed with larger Schottky contact which increases its current carrying capability. Using Al2O3 as the field oxide, the optimum field plate terminated SBD and planar mesa terminated SBD yield breakdown voltage of 1480 V and 1440 V, respectively. In the field plate terminated SBD, breakdown occurs at small area at the corner of Schottky contact due to high peak electric field (without breakdown in Al2O3 layer). On the contrary, premature breakdown in planar mesa terminated SBD at 1440 V is caused by breakdown of Al2O3 layer (at electric field of 10 MV/cm). Although planar mesa termination structure is able to reduce electric field crowding at Schottky contact, the peak electric field inside the oxide is around 4 times of maximum electric field in the diamond. Assuming that oxide breakdown does not occur, breakdown voltage of planar mesa terminated SBD can further be increased to 1751 V where breakdown occurs in bulk diamond (under the schottky contact). Therefore, special attention must be paid on the choice of the field oxide to prevent oxide breakdown. With the right choice of field oxide material, planar mesa termination structure can realize high breakdown voltage diamond SBD. Further studies on the development and integration of alternative high k materials suitable for diamond devices are crucial to fully realize potential of diamond material.
Table 2 Performances comparisons between optimum field plate and planar mesa termination structure for diamond SBD. Termination structure
Field plate Planar mesa
Optimum geometry LF (μm)
TOX (μm)
15 5
1 2
VBr considering Al2O3 breakdown (V)
1480 1440
VBr without considering oxide breakdown (V)
1480 1751
Forward I − V for total device's diameter of 230 μm (refer to Fig. 8) Current density at 5 V (A/cm2)
Total current at 5 V (A)
23.73 22.74
0.00746 0.00864
A. Nawawi et al. / Diamond & Related Materials 36 (2013) 51–57
Prime novelty statement We propose planar mesa termination structure with high k dielectric to improve the breakdown performance of p-type diamond Schottky barrier diode. Analysis conducted by simulations in finite element physics based software shows that planar mesa terminated diode has the potential to achieve higher breakdown voltage and higher current carrying capability compared to alternatively used field plate termination structure. References [1] L.M. Tolbert, B. Ozpineci, S.K. Islam, M.S. Chinthavali, Power and Energy Systems, Proceedings, 2003, pp. 317–321. [2] B. Ozpineci, L. Tolbert, Comparison of wide-bandgap semiconductors for power electronics applications, U.S.D.o. Energy, 2004. [3] J. Isberg, J. Hammersberg, E. Johansson, T. Wikstrom, D.J. Twitchen, A.J. Whitehead, S.E. Coe, G.A. Scarsbrook, Science 297 (2002) 1670–1672. [4] R.J. Trew, J.B. Yan, P.M. Mock, Proc. IEEE 79 (1991) 598–620. [5] D.J. Twitchen, A.J. Whitehead, S.E. Coe, J. Isberg, J. Hammersberg, T. Wikstrom, E. Johansson, IEEE Trans. Electron Dev. 51 (2004) 826–828. [6] J.E. Butler, M.W. Geis, K.E. Krohn, J. Lawless, S. Deneault, T.M. Lyszczarz, D. Flechtner, R. Wright, Semicond. Sci. Technol. 18 (2003) S67–S71. [7] P.N. Volpe, P. Muret, J. Pernot, F. Omnes, T. Teraji, Y. Koide, F. Jomard, D. Planson, P. Brosselard, N. Dheilly, B. Vergne, S. Scharnholz, Appl. Phys. Lett. 97 (2010). [8] P.N. Volpe, P. Muret, J. Pernot, F. Omnes, T. Teraji, F. Jomard, D. Planson, P. Brosselard, N. Dheilly, B. Vergne, S. Scharnholtz, Phys. Status Solidi A: Appl. Mater. Sci. 207 (2010) 2088–2092. [9] H. Umezawa, K. Ikeda, N. Tatsumi, K. Ramanujam, S. Shikata, Diamond Relat. Mater. 18 (2009) 1196–1199. [10] M. Brezeanu, M. Avram, S.J. Rashid, G.A.J. Amaratunga, T. Butler, N.L. Rupesinghe, F. Udrea, A. Tajani, M. Dixon, D.J. Twitchen, A. Garraway, D. Chamund, P. Taylor, G. Brezeanu, Int. Symp. Power Semicond. (2006) 73–76. [11] K. Ikeda, H. Umezawa, N. Tatsumi, K. Ramanujam, S. Shikata, Diamond Relat. Mater. 18 (2009) 292–295. [12] M. Brezeanu, T. Butler, N.L. Rupesinghe, G.A.J. Amaratunga, S.J. Rashid, F. Udrea, M. Avram, G. Brezeanu, Diamond Relat. Mater. 16 (2007) 1020–1024. [13] F. Thion, K. Isoird, D. Planson, M.L. Locatelli, H. Ding, Diamond Relat. Mater. 20 (2011) 729–732.
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Diamond & Related Materials journal homepage: www.elsevier.com/locate/diamond
Design and optimization of planar mesa termination for diamond Schottky barrier diodes A. Nawawi a,⁎, K.J. Tseng a, Rusli a, G.A.J. Amaratunga a, b, H. Umezawa c, S. Shikata c a b c
School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, Singapore Department of Engineering, University of Cambridge, Cambridge, United Kingdom Diamond Research Center, National Institute of Advanced Industrial Science and Technology, Tokyo, Japan
a r t i c l e
i n f o
Article history: Received 1 January 2013 Received in revised form 20 March 2013 Accepted 23 April 2013 Available online 30 April 2013 Keywords: Diamond Schottky barrier diodes Termination Simulation Planar mesa
a b s t r a c t In this paper, we present planar mesa termination structure with high k dielectric Al2O3 for high-voltage diamond Schottky barrier diode. Analysis, design, and optimization are carried out by simulations using finite element technology computer-aided design (TCAD) Sentaurus Device software. The performances of planar mesa termination structure are compared to those of conventional field plate termination structure. It is found that optimum geometry of planar mesa terminated diode requires shorter metal plate extension (1/3 of the field plate terminated diode). Consequently, planar mesa terminated diode can be designed with bigger Schottky contact to increase its current carrying capability. Breakdown performance of field plate termination structure is limited at 1480 V due to peak electric field at the corner of Schottky contact (no oxide breakdown occurs). In contrast, peak electric field in planar mesa termination structure only occurs in the field oxide such that its breakdown performance is highly dependent on the oxide material. Due to Al2O3 breakdown, planar mesa termination structure suffers premature breakdown at 1440 V. Considering no oxide breakdown occurs, planar mesa termination structure can realize higher breakdown voltage of 1751 V. Therefore, to fully realize the potential of planar mesa terminated diode, it is important to choose suitable high k dielectric material with sufficient breakdown electric field for the field oxide. © 2013 Elsevier B.V. All rights reserved.
1. Introduction Among the wide band gap materials, diamond has very significant properties such as large band gap of 5.47 eV, high critical electric fields of 10–20 MV/cm, high carrier mobility (3800 cm2/Vs for hole and 4500 cm2/Vs for electron), high saturation velocity of 2.7 × 107 cm/s, and high thermal conductivity of 22–24 W/cmK [1–4]. Such properties make diamond potentially very attractive for power devices applications that require high-voltage, high-power, high-speed, and hightemperature capability. Diamond Schottky barrier diodes (SBD) with high breakdown voltage (6.5 kV, 7.5 kV, and 10 kV) and high breakdown electric field (7–9.5 MV/cm) have been reported in the literature [5–8]. However, the breakdown electric field achieved by most of the fabricated SBDs up to this date is usually less than 3–4 MV/cm [7,9]. While improvement in the quality of synthetic single crystal diamond is crucial to improve the breakdown electric field, the design and optimization of termination structure is another key factor that should be taken into considerations. Because of high ionization energy of n-type dopant in diamond, termination techniques that require n-type diamond region such as junction termination are not applicable at this moment. Instead, ⁎ Corresponding author. E-mail address: [email protected] (A. Nawawi). 0925-9635/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.diamond.2013.04.009
termination techniques that utilize field plate extension such as field plate termination, three step termination, and ramp oxide termination have been developed [10]. High k dielectric oxide and semiresistive materials have also been employed in order to prevent breakdown in oxide [11–13]. In this paper, we propose planar mesa termination structure [14] for p-type diamond SBD to improve the trade-off between forward and reverse bias characteristics. Design and optimization are carried out by simulation in finite element physics-based technology computer-aided design (TCAD) Sentaurus Device software. High k dielectric Al2O3 is used as the field oxide in this simulation study. The electrical performance of planar mesa termination structure has been investigated and compared with that of field plate termination structure. 2. Termination structures for diamond Schottky barrier diode In any practical diode devices, any metallic contact has to terminate at a certain point on the device. The early SBD was fabricated without any special termination structure as shown in Fig. 1(a) [15]. While the fabrication process for this structure is very simple, it suffers from low breakdown voltage due to the electric field enhancement at the abrupt edge of Schottky contact termination. To prevent premature breakdown, other more sophisticated termination structures are needed to redistribute the electric field more uniformly.
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Fig. 1. Different structure of SBD. (a) Diode without termination structure. (b) Diode with field plate type of termination structure. (c) Diode with planar mesa type of termination structure. (d) Ideal parallel plate diode.
The most common termination structure considered for diamond SBD currently is the field plate termination, as shown in Fig. 1(b). Although this structure is able to increase the breakdown voltage of the diode, peak electric field still occurs at the edge of Schottky metal–semiconductor interface. This can cause Schottky barrier lowering and consequently an increase in leakage current. At high reverse bias, the leakage current is further increased due to multiplication effects [15], which can lead to breakdown at small area under the edge of Schottky contact. In this work, we propose the planar mesa termination structure to improve the performance of diamond SBD. This structure has the potential to reduce the peak electric field at the Schottky metal– diamond interface. Applications of this structure in conventional silicon SBD have demonstrated vast improvement in reverse bias performance with minimal effect on forward bias performance [14,16]. The proposed planar mesa termination structure for diamond SBD is shown in Fig. 1(c). The mesa region is surrounded by an oxide layer to reduce electric field crowding at the corner of the Schottky contact.
This mesa structure can be obtained by inductively coupled plasma (ICP) etching technique using O2 and CF4 reactant gases [17,18]. Possible process flow for fabrication is shown in Fig. 2. In this process, the center area for Schottky contact is firstly masked. Then, ICP process is carried out to selectively etch the p− region at the edge of device. Next, oxide is deposited to fill the trench region created by the etching process, followed by Schottky contact metallization. In order to investigate the performance of proposed planar mesa termination structure for diamond SBD, we performed two dimensional numerical simulation studies as elaborated in the next section. 3. Modeling and simulation Our simulation studies are carried out in two-dimensional finite element physics-based TCAD Sentaurus Device software because of its ability to simulate various physics phenomena in the semiconductor devices. To produce the simulations, it was necessary to first implement various physics-based models and their parameters
Fig. 2. Process flow for fabrication of planar mesa termination for diamond SBD. (a) Masking of p− region at center area for Schottky contact. (b) Selective ICP etching to create diamond mesa structure. (c) Oxide deposition to fill in the trench region for termination purposes. (d) Schottky contact metallization.
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which are suitable for diamond materials. Doping concentrationdependent and temperature-dependent bulk mobility models of the University of Bologna have been applied with parameters based on [19–21] to model the carrier transport in the Boron doped diamond devices. Furthermore, incomplete ionization can occur due to high ionization energy of Boron acceptor in diamond (~ 0.37 eV) [22]. This phenomenon is modeled by implementing incomplete ionization model given by Eq. (1) for Boron concentration less than NA,crit of 3 × 10 19 cm −3 [16,20]. For concentrations greater than NA,crit, hopping conduction occurs and activation energy starts to decrease rapidly; therefore, we assume complete ionization for these cases. −
NA ¼
NA −EF 1 þ g A exp EAkT
ð1Þ
In the Eq. (1), NA− is the number of ionized acceptor, NA is the acceptor doping concentration, EF is Fermi level, and EA is the concentrationdependent activation energy given by 1=3
EA ¼ EA0 −α ðNA −N D Þ
ð2Þ
with EA0 = 0.37 eV and α = 4.1 × 10−8 eV cm−1 [23]. gA in Eq. (1) is temperature-dependent degeneracy factor given by −Δ g A ¼ 4 þ 2 exp kT
ð3Þ
with Δ = 6 meV [24]. To simulate breakdown phenomena in the device, we implemented impact ionization (avalanche generation) model. The electron–hole pair generation rate G ii from impact ionization at high electric field is given by [16,20] ii
G ¼ α n nvn þ α p pvp
ð4Þ
vn(vp) is the electron (hole) velocity and n(p) is the number of electron (hole).αn(αp) is the ionization rate for electron (hole), i.e., the number of electron–hole pairs generated by electron (hole), accelerated along the direction of electric field per unit distance. When Gii goes to a large number, avalanche breakdown occurs. The model implemented in our simulations is van Overstraeten–de Man model given by [20] bnðpÞ α nðpÞ Ef ¼ anðpÞ exp − Ef
! ð5Þ
with Ef as electric field and an(p) and bn(p) as the impact ionization coefficients for electron (hole). In addition, the Caughey–Thomas formula with saturation velocity model is activated to take into account high field transport [20]. Breakdown simulation in diamond devices is always challenging and somewhat approximate because there is no accurate measurement on the values of impact ionization coefficients in diamond up to this date. Several values have been proposed in the literature by Trew et al. [4], Rashid et al. [21], and Isberg [25], as shown in Table 1. To investigate the effect of different impact ionization coefficients on device's breakdown characteristics, we performed reverse bias
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simulation on ideal parallel plate diamond SBD structure as shown in Fig. 1(d). The p+ region is 20 μm thick and it has high Boron doping of 1 × 10 20 cm −3. The p− drift region has Boron doping of 5 × 10 15 cm −3 and thickness of 10 μm. These doping concentrations can be easily achieved in experimental fabrication using current technology. The diamond is oxygen terminated with electron affinity of 1.3 eV. The Schottky metal work function is fixed at 4.27 eV to yield Schottky barrier height of 2.5 eV. Ideal parallel plate is chosen because it exhibits no electric field crowding such that breakdown is largely dependent on the values of impact ionization coefficients. The breakdown voltage is extracted when reverse current density reaches 1 × 10 −4 A/cm 2 [26]. Values of simulated breakdown voltage VBr and maximum electric field at breakdown corresponding to the applied impact ionization coefficients for the ideal parallel plate SBD are shown in Table 1. The distributions of electric field in the device along y-axis for different applied impact ionization coefficients are shown in Fig. 3. We can observe that the maximum electric field at breakdown is less than ~ 3 MV/cm for these various applied impact ionization coefficients in the simulations. While this range of breakdown electric field is commonly found in experimental diamond SBDs [18,27,28], it is much lower than the normally quoted value of 10–20 MV/cm for diamond material [1,2,26]. Furthermore, Volpe et al. [7,8] claimed to have achieved diamond SBD with breakdown electric field of approximately 7–9.5 MV/cm, which led to a conclusion that the currently available impact ionization coefficients underestimate the real capability of diamond material. Through simulations, the wide range of impact ionization coefficients can be designed to achieve certain value of simulated maximum electric field at breakdown. For example, both αn = αp = 5.48 × 106exp(−8 × 107/Ef) and αn = αp = 0.22 × 106 exp(−5 × 107/Ef) can be applied in the simulations to achieve simulated breakdown electric field of ~10 MV/cm for ideal parallel plate diamond SBD structure. Therefore, there are no unique and accurate impact ionization coefficients for diamond that can be deduced through simulations. Rather than stipulating the values of impact ionization coefficients, we apply values suggested by Rashid et al. in our simulations work. While the simulated breakdown voltage might be lower than what can be achieved in single crystal diamond material, these values serve as references in comparing the performances of different edge termination structures. Moreover, we did not consider non-ideal factors such as defects, imperfect metal–diamond interface, etc., in these simulation studies. 4. Results and discussion To assess the performance of planar mesa termination structure in comparison with field plate termination structure for diamond SBD, we carried out simulations of both termination structures with identical properties (thickness and doping of p+ and p− layer, metal work function, etc.) as the simulated ideal parallel plate diamond SBD in Section 3, except for the termination structures. In both structures, the width of the Schottky contact LS is selected as 30 μm and high k dielectric Al2O3 with dielectric constant of 8.7 [26] is used as the oxide layer. To find optimum device's geometry for high breakdown voltage
Table 1 Different impact ionization coefficients for diamond reported in the literature. an (cm−1) Trew et al. [4] Rashid et al. [21] Isberg et al. [25]* Isberg et al. [25]**
1.935 × 10 1.89 × 105 – –
ap (cm−1) 8
1.935 × 10 5.48 × 106 0.6 × 106 4 × 106
bn (V cm−1) 8
7.749 × 10 1.7 × 107 – –
6
bp (V cm−1) 7.749 × 10 1.42 × 107 0.8 × 107 1.1 × 107
6
Breakdown voltage (V)
Maximum electrical field (MV/cm)
222.5 1755 2320 1940
0.846 2.55 3.11 2.73
Symbols * and ** are used to refer to different values of impact ionization parameters reported by the same author in the same report (Isberg et. al [25]). These symbols are related to the results shown in Fig. 3 for different values of impact ionization parameters.
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Fig. 3. Distribution of electric field along the y-axis in the ideal parallel plate diamond SBD at breakdown. The Schottky contact is located at y = 0 μm. Different curves correspond to different impact ionization coefficients that are applied in the simulations.
applications, we conducted many simulations with different values of metal plate extension length LF and the oxide thickness TOX for both termination structures (refer to Fig. 1(b) and (c)). Variations of simulated breakdown voltage VBr for different LF and TOX for field plate terminated diamond SBD are shown in Fig. 4(a).
Fig. 4. (a) Variations of simulated breakdown voltage for different field plate length LF and oxide thickness TOX for field plate terminated diamond SBD. (b) Distribution of reverse current density in the field plate terminated diamond SBD at 1480 V.
While longer LF can result in higher VBr, this effect starts to saturate for LF > 15 μm. We can also see that small variations in TOX affect the VBr significantly. From Fig. 4(a), it can be observed that optimum geometry for field plate terminated SBD (with LF = 15 μm and TOX = 1 μm) exhibits VBr of 1480 V. Fig. 4(b) shows the distribution of current density in the device at breakdown. The breakdown mainly occurs at small region at the corner of Schottky contact due to high electric field. The distribution of electric field at breakdown in this structure is shown in Fig. 5(a) and (b). Peak electric field can be observed at 2 points, i.e., Ef = 5.76 MV/cm at the corner of Schottky contact (x = 15 μm, y = 0 μm) and Ef = 9.38 MV/cm in the oxide layer at the end of field plate termination (x = 30 μm, y = −1 μm). As peak Ef in the oxide layer is lower than Al2O3 breakdown electric field (10 MV/cm) [29,30], no oxide breakdown occurs in optimum field plate terminated SBD. For planar mesa terminated diamond SBD, variations of simulated breakdown voltage VBr for different LF and TOX are shown in Fig. 6(a). Increasing LF and TOX up to certain values can increase the VBr significantly. The optimum geometry for planar mesa terminated SBD can be realized with LF = 5 μm and TOX = 2 μm. Without considering oxide breakdown, this structure is able to achieve VBr of 1751 V. From the distribution of current density in the device at breakdown (shown in Fig. 6(b)), we can observe that breakdown occurs at large area (bulk diamond) under the Schottky contact. The electric field distribution in the device at 1751 V is shown in Fig. 7(a) and (b). In this structure, electric field is distributed almost uniformly under the Schottky contact (channel area) and
Fig. 5. Distribution of electric field in the field plate terminated diamond SBD at 1480 V: (a) In the half of symmetric device and (b) along the line y = 0 μm (oxide– diamond) and y = −1 μm (metal–oxide).
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Fig. 6. (a) Variations of simulated breakdown voltage for different field plate length LF and oxide thickness TOX for planar mesa terminated diamond SBD. (b) Distribution of reverse current density in the planar mesa terminated diamond SBD at 1751 V.
peak Ef occurs only at 1 point, i.e., Ef = 11.41 MV/cm in the oxide region at the end of metal plate extension (x = 20 μm, y = 0 μm). This prevents Schottky barrier lowering and breakdown due to electric field crowding at the Schottky contact. However, peak Ef = 11.41 MV/cm in the oxide is beyond the breakdown electric field of Al2O3. By limiting peak Ef in oxide to 10 MV/cm as the limit of Al2O3 breakdown, optimum planar mesa terminated SBD yields VBr = 1440 V. The distribution of electric field in the device at 1440 V along line y = 0 μm is shown in Fig. 7(b), with peak Ef = 9.84 MV/cm (at x = 20 μm, y = 0 μm). By comparing the optimum geometry of field plate termination and planar mesa termination structure for diamond SBD, it is clear that the later consumes less area due to shorter metal plate extension required. Therefore, for the same total device's area, planar mesa terminated SBD can be designed with bigger Schottky contact area which increases its current carrying capability. To compare forward I − V characteristics of both termination structures, we simulated the SBDs with circular contact occupying the same total device's area (total device's diameter of 230 μm) as shown in Fig. 8 based on optimum structure design. Schottky contact area in planar mesa terminated SBD (LS = 220 μm, Schottky contact area = 91.49% of total device's area) is 1.21 times bigger than Schottky contact area in field plate terminated SBD (LS = 200 μm, Schottky contact area = 75.61% of total device's area). The applied parasitic resistance on both devices is 8 mΩ.cm 2 [18]. The simulated forward I − V characteristics for both structures are shown in Fig. 9(a) and (b). Even though planar mesa terminated SBD has slightly lower forward current density
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Fig. 7. Distribution of electric field in the planar mesa terminated SBD: (a) At 1751 V in the half of symmetric device. (b) At 1751 V and at 1440 V along the line y = 0 μm.
compared to that of field plate terminated SBD, it has higher total forward current (lower on resistance) due to larger Schottky contact area. Table 2 summarizes the performance comparisons between optimum field plate terminated SBD and planar mesa terminated SBD.
Fig. 8. Top view schematic diagram of optimum field plate terminated SBD and planar mesa terminated SBD occupying the same total device's area (diameter of 230 μm). LS and LF are the diameter of Schottky contact and length of metal plate extension in the corresponding structures.
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underestimate the real capability of diamond (breakdown electric field of 10–20 MV/cm). By applying other coefficients such as αn = αp = 5.48 × 10 6exp(−8 × 10 7/Ef) (mentioned in Section 3) for a test case, optimum planar mesa terminated SBD yields simulated VBr of 9190 V. At breakdown, peak Ef in the Al2O3 region at the end of metal plate extension (x = 20 μm, y = 0 μm) reaches high value of 48.15 MV/cm. This value is about 4 times of the maximum Ef in the diamond (~ 12 MV/cm under Schottky contact) and well beyond the capability of Al2O3. Therefore, to fully realize potential of diamond power devices, we need to utilize material with higher dielectric constant and sufficient breakdown electric field to prevent oxide breakdown. The development of such material for diamond SBD can gain insight from research on high k material to replace SiO2 in complementary metal oxide semiconductor (CMOS) technology. In addition, high k materials are also being developed for applications in diamond field effect transistors (FETs). Some of the high k materials of interest for applications in diamond devices are Ta2O5 (k ~ 16–29) [31], SrTiO3 [32], PZT [33–36], Yb2O3 (k ~ 15), HfO2 (k ~ 25), TiO2 (k ~ 80–95), ZrO2 (k ~ 29), etc. [30,37].
5. Conclusions
Fig. 9. Simulated forward I − V characteristics of the field plate terminated (FP) and planar mesa terminated (PM) diamond SBD with the same total device's area (diameter of 230 μm). (a) Comparison of forward current density. (b) Comparison of total forward current.
With the usage of Al2O3 as the oxide layer (considering breakdown in Al2O3), planar mesa terminated SBD yields slightly lower VBr and forward current density compared to field plate terminated SBD. However, it requires shorter metal plate extension. Therefore, it can accommodate larger Schottky contact for the same total device's area which results in higher total forward current. From Table 2, we can also observe that the reverse performances of planar mesa terminated SBD is limited by the breakdown of Al2O3 layer. Unlike field plate terminated SBD, VBr of planar mesa terminated SBD can be increased further to 1751 V if breakdown does not occurs in oxide layer. This can only be realized by replacing Al2O3 with suitable high k material that can support sufficient electric field. Moreover, it is worthy to point out that the impact ionization coefficients used in these simulations (suggested by Rashid et al.)
In conclusion, we have presented planar mesa termination structure for high-voltage diamond Schottky barrier diode. Analysis, design, and optimization are carried out using simulation in TCAD Sentaurus Device software. The performance of planar mesa terminated SBD is compared with that of field plate terminated SBD. In both termination structures, Al2O3 is used as the field oxide. Through many simulations, we found out that the optimum geometry of planar mesa termination structure requires shorter metal plate extension (less area consumption for termination structure) compared to field plate termination structure. For the same total device's area, planar mesa terminated SBD can be designed with larger Schottky contact which increases its current carrying capability. Using Al2O3 as the field oxide, the optimum field plate terminated SBD and planar mesa terminated SBD yield breakdown voltage of 1480 V and 1440 V, respectively. In the field plate terminated SBD, breakdown occurs at small area at the corner of Schottky contact due to high peak electric field (without breakdown in Al2O3 layer). On the contrary, premature breakdown in planar mesa terminated SBD at 1440 V is caused by breakdown of Al2O3 layer (at electric field of 10 MV/cm). Although planar mesa termination structure is able to reduce electric field crowding at Schottky contact, the peak electric field inside the oxide is around 4 times of maximum electric field in the diamond. Assuming that oxide breakdown does not occur, breakdown voltage of planar mesa terminated SBD can further be increased to 1751 V where breakdown occurs in bulk diamond (under the schottky contact). Therefore, special attention must be paid on the choice of the field oxide to prevent oxide breakdown. With the right choice of field oxide material, planar mesa termination structure can realize high breakdown voltage diamond SBD. Further studies on the development and integration of alternative high k materials suitable for diamond devices are crucial to fully realize potential of diamond material.
Table 2 Performances comparisons between optimum field plate and planar mesa termination structure for diamond SBD. Termination structure
Field plate Planar mesa
Optimum geometry LF (μm)
TOX (μm)
15 5
1 2
VBr considering Al2O3 breakdown (V)
1480 1440
VBr without considering oxide breakdown (V)
1480 1751
Forward I − V for total device's diameter of 230 μm (refer to Fig. 8) Current density at 5 V (A/cm2)
Total current at 5 V (A)
23.73 22.74
0.00746 0.00864
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Prime novelty statement We propose planar mesa termination structure with high k dielectric to improve the breakdown performance of p-type diamond Schottky barrier diode. Analysis conducted by simulations in finite element physics based software shows that planar mesa terminated diode has the potential to achieve higher breakdown voltage and higher current carrying capability compared to alternatively used field plate termination structure. References [1] L.M. Tolbert, B. Ozpineci, S.K. Islam, M.S. Chinthavali, Power and Energy Systems, Proceedings, 2003, pp. 317–321. [2] B. Ozpineci, L. Tolbert, Comparison of wide-bandgap semiconductors for power electronics applications, U.S.D.o. Energy, 2004. [3] J. Isberg, J. Hammersberg, E. Johansson, T. Wikstrom, D.J. Twitchen, A.J. Whitehead, S.E. Coe, G.A. Scarsbrook, Science 297 (2002) 1670–1672. [4] R.J. Trew, J.B. Yan, P.M. Mock, Proc. IEEE 79 (1991) 598–620. [5] D.J. Twitchen, A.J. Whitehead, S.E. Coe, J. Isberg, J. Hammersberg, T. Wikstrom, E. Johansson, IEEE Trans. Electron Dev. 51 (2004) 826–828. [6] J.E. Butler, M.W. Geis, K.E. Krohn, J. Lawless, S. Deneault, T.M. Lyszczarz, D. Flechtner, R. Wright, Semicond. Sci. Technol. 18 (2003) S67–S71. [7] P.N. Volpe, P. Muret, J. Pernot, F. Omnes, T. Teraji, Y. Koide, F. Jomard, D. Planson, P. Brosselard, N. Dheilly, B. Vergne, S. Scharnholz, Appl. Phys. Lett. 97 (2010). [8] P.N. Volpe, P. Muret, J. Pernot, F. Omnes, T. Teraji, F. Jomard, D. Planson, P. Brosselard, N. Dheilly, B. Vergne, S. Scharnholtz, Phys. Status Solidi A: Appl. Mater. Sci. 207 (2010) 2088–2092. [9] H. Umezawa, K. Ikeda, N. Tatsumi, K. Ramanujam, S. Shikata, Diamond Relat. Mater. 18 (2009) 1196–1199. [10] M. Brezeanu, M. Avram, S.J. Rashid, G.A.J. Amaratunga, T. Butler, N.L. Rupesinghe, F. Udrea, A. Tajani, M. Dixon, D.J. Twitchen, A. Garraway, D. Chamund, P. Taylor, G. Brezeanu, Int. Symp. Power Semicond. (2006) 73–76. [11] K. Ikeda, H. Umezawa, N. Tatsumi, K. Ramanujam, S. Shikata, Diamond Relat. Mater. 18 (2009) 292–295. [12] M. Brezeanu, T. Butler, N.L. Rupesinghe, G.A.J. Amaratunga, S.J. Rashid, F. Udrea, M. Avram, G. Brezeanu, Diamond Relat. Mater. 16 (2007) 1020–1024. [13] F. Thion, K. Isoird, D. Planson, M.L. Locatelli, H. Ding, Diamond Relat. Mater. 20 (2011) 729–732.
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