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J. Semicond. > 2016, Volume 37?>?Issue 12?> 122002

SEMICONDUCTOR PHYSICS

Effect of ultrasound on reverse leakage current of silicon Schottky barrier structure

O.Ya Olikh1, , K.V. Voitenko1, R.M. Burbelo1 and JaM. Olikh2

+ Author Affiliations

 Corresponding author: O. Ya Olikh, Email:olikh@univ.kiev.ua

DOI: 10.1088/1674-4926/37/12/122002

PDF

Abstract: The influence of ultrasonic loading on reverse current-voltage characteristics of Mo/n-n+-Si structures has been investigated. The research of leakage current variation has been carried out for various ultrasonic wave frequencies (4.1 and 8.4 MHz), intensities (up to 0.8 W/cm2) and loading temperatures (130-330 K). The observed reversible acoustically induced increase in reverse currents was as large as 60%. It has been found that dominant charge transfer mechanisms are the thermionic emission (at high temperature) and the phonon-assisted tunneling (at low temperature). The ultrasound loading affects both processes due to the decrease of Schottky barrier height and binding energy of the electron on the trap.

Key words: Schottky contact, leakage current, ultrasound influence



[1]
Savkina R K, Smirnov A B, Sizov F. The effect of high-frequency sonication on charge carrier transport in LPE and MBE HgCdTe layers. Semicond Sci Technol, 2007, 22(2): 97 doi: 10.1088/0268-1242/22/2/016
[2]
Kulakova L, Gorelov V, Lutetskiy A, et al. The rotation of the polarization plane of quantum-well heterolasers emission under the ultrasonic strain. Solid State Commun, 2012, 152(17): 1690 doi: 10.1016/j.ssc.2012.04.065
[3]
Ostrovskii I, Korotchenkov O, Olikh O, et al. Acoustically driven optical phenomena in bulk and low-dimensional semiconductors. J Opt A, 2001, 3(4): S82 https://www.researchgate.net/publication/230991018_Acoustically_driven_optical_phenomena_in_bulk_and_low-dimensional_semiconductors
[4]
Buyukkose S, Vratzov B, van der Veen J, et al. Ultrahighfrequency surface acoustic wave generation for acoustic charge transport in silicon. Appl Phys Lett, 2013, 102(1): 013112 doi: 10.1063/1.4774388
[5]
He J H, Gao J, Guo H Z. Correlated electron transport assisted by surface acoustic waves in micron-separated quasi-onedimensional channels. Appl Phys Lett, 2010, 97(12): 122107 doi: 10.1063/1.3491287
[6]
Ostapenko S S, L Jastrzebski, Sopori B. Change of minority carrier diffusion length in polycrystalline silicon by ultrasound treatment. Semicond Sci Technol, 1995, 10(11): 1494 doi: 10.1088/0268-1242/10/11/011
[7]
Ostapenko S. Defect passivation using ultrasound treatment: fundamentals and application. Appl Phys A: Mater Sci Process, 1999, 69(2): 225 doi: 10.1007/s003390050994
[8]
Sukach A, Teterkin V. Ultrasonic treatment-induced modification of the electrical properties of InAs p-n junctions. Tech Phys Lett, 2009, 35(6): 514 doi: 10.1134/S1063785009060108
[9]
Olikh O. Features of dynamic acoustically induced modification of photovoltaic parameters of silicon solar cells. Semiconductors, 2011, 45(6): 798 doi: 10.1134/S1063782611060170
[10]
Davletova A, Karazhanov S Z. A study of electrical properties of dislocation engineered Si processed by ultrasound. J Phys Chem Solids, 2009, 70(6): 989 doi: 10.1016/j.jpcs.2009.05.009
[11]
Davletova A, Karazhanov S Z. Open-circuit voltage decay transient in dislocation-engineered Si p-n junction. J Phys D: Appl Phys, 2008, 41(16): 165107 doi: 10.1088/0022-3727/41/16/165107
[12]
Melnik V, Olikh Y, Popov V, et al. Characteristics of silicon p-n junction formed by ion implantation with in situ ultrasound treatment. Mater Sci Eng B, 2005, 124/125: 327 doi: 10.1016/j.mseb.2005.08.039
[13]
Olikh O. Effect of ultrasonic loading on current in Mo/n-n+-Si with Schottky barriers. Semiconductors, 2013, 47(7): 987 doi: 10.1134/S106378261307018X
[14]
Olikh O. Reversible influence of ultrasound on γ-irradiated Mo/n-Si Schottky barrier structure. Ultrasonics, 2015, 56: 545 doi: 10.1016/j.ultras.2014.10.008
[15]
Zaveryukhina N, Zaveryukhina E, Vlasov S, et al. Acoustostimulated changes in the density of surface states and their energy spectrum in p-type silicon single crystals. Tech Phys Lett, 2008, 34(3): 241 doi: 10.1134/S106378500803019X
[16]
Mirsagatov S A, Sapaeva I B, Nazarov Z. Ultrasonic annealing of surface states in the heterojunction of a p-Si/n-CdS/n+-CdS injection photodiode. Inorg Mater, 2015, 51(1): 1 doi: 10.1134/S0020168515010148
[17]
Wosinski T, Makosa A, Witczak Z. Transformation of native defects in bulk GaAs under ultrasonic vibration. Semicond Sci Technol, 1994, 9(11): 2047 doi: 10.1088/0268-1242/9/11/003
[18]
Buyanova I A, Ostapenko S S, Sheinkman M K, et al. Ultrasound regeneration of EL2 centres in GaAs. Semicond Sci Technol, 1994, 9(2): 158 doi: 10.1088/0268-1242/9/2/005
[19]
Korotchenkov O, Grimmliss H. Long-wavelength acousticmode-enhanced electron emission from Se and Te donors in silicon. Phys Rev B, 1995, 52(20): 14598 doi: 10.1103/PhysRevB.52.14598
[20]
Ostapenko S S, Bell R E. Ultrasound stimulated dissociation of Fe-B pairs in silicon. J Appl Phys, 1995, 77(10): 5458 doi: 10.1063/1.359243
[21]
Sathaiya D M, Karmalkar S. Thermionic trap-assisted tunneling model and its application to leakage current in nitrided oxides and AlGaN/GaN high electron mobility transistors. J Appl Phys, 2006, 99(9): 093701 doi: 10.1063/1.2191620
[22]
Shan Q, Meyaard D S, Dai Q, et al. Transport-mechanism analysis of the reverse leakage current in GaInN light-emitting diodes. Appl Phys Lett, 2011, 99(25): 253506 doi: 10.1063/1.3668104
[23]
Pipinys P, Lapeika V. Temperature dependence of reverse-bias leakage current in GaN Schottky diodes as a consequence of phonon-assisted tunneling. J Appl Phys, 2006, 99(9): 093709 doi: 10.1063/1.2199980
[24]
Liang Huaguo, Xu Hui, Huang Zhengfeng, et al. Low-leakage and NBTI-mitigated N-type domino logic. Journal of Semiconductors, 2014, 35(1): 015009 doi: 10.1088/1674-4926/35/1/015009
[25]
Bi Xiuwen, Liang Hailian, Gu Xiaofeng, et al. Design of novel DDSCR with embedded PNP structure for ESD protection. Journal of Semiconductors, 2015, 36(12): 124007 doi: 10.1088/1674-4926/36/12/124007
[26]
Abu-Samaha F S, Darwish A A A, Mansour A N. Temperature dependent of the current-voltage (Ⅳ) characteristics of TaSi2/nSi structure. Mater Sci Semicond Process, 2013, 16(6): 1988 doi: 10.1016/j.mssp.2013.07.036
[27]
Jafar M M A G. High-bias current-voltage-temperature characteristics of undoped RF magnetron sputter deposited boron carbide (B5C)/p-type crystalline silicon heterojunctions. Semicond Sci Technol, 2003, 18(1): 7 doi: 10.1088/0268-1242/18/1/302
[28]
Lee C H, Lim K S. Carrier transport through boron-doped amorphous diamond-like carbon p layer of amorphous silicon based p-i-n solar cells. Appl Phys Lett, 1999, 75(4): 569 doi: 10.1063/1.124444
[29]
Pipinys P, Pipiniene A, Rimeika A. Phonon-assisted tunneling in reverse biased Schottky diodes. J Appl Phys, 1999, 86(12): 6875 doi: 10.1063/1.371766
[30]
Tung R T. Recent advances in Schottky barrier concept. Mater Sci Eng, R, 2001, 35(1-3): 1 doi: 10.1016/S0927-796X(01)00037-7
[31]
Olikh O Y, Voytenko K V, Burbelo R M. Ultrasound influence on I-V-T characteristics of silicon Schottky barrier structure. J Appl Phys, 2015, 117(4): 044505 doi: 10.1063/1.4906844
[32]
Wang K, Ye M. Parameter determination of Schottky-barrier diode model using differential evolution. Solid-State Electron, 2009, 53(2): 234 doi: 10.1016/j.sse.2008.11.010
[33]
Rhoderick E H, Williams R H. Metal semiconductor contacts. 2nd ed. Oxford: Clarendon Press, 1988
[34]
Aboelfotoh M. Electrical characteristics of W-Si(100) Schottky barrier junctions. J Appl Phys, 1989, 66(1): 262 doi: 10.1063/1.343867
[35]
Zhua S, Meirhaeghea R L V, Detaverniera C, et al. A BEEM study of the temperature dependence of the barrier height distribution in PtSi/n-Si Schottky diodes. Solid State Commun, 1999, 112(11): 611 doi: 10.1016/S0038-1098(99)00404-4
[36]
Kiveris A, Kudzmauskas S, P P. Release of electrons from traps by an electric field with phonon participation. Phys Stat Sol (a), 1976, 37(1): 321 doi: 10.1002/(ISSN)1521-396X
[37]
Parker G, McGill T, Mead C, et al. Electric field dependence of GaAs Schottky barriers. Solid-State Electron, 1968, 11(2): 201 doi: 10.1016/0038-1101(68)90079-8
[38]
Seebauer E G, Kratzer M C. Charged point defects in semiconductors. Mater Sci Eng R, 2006, 55(3-6): 57 doi: 10.1016/j.mser.2006.01.002
[39]
Lukjanitsa V V. Energy levels of vacancies and interstitial atoms in the band gap of silicon. Semiconductors, 2003, 37(4): 404 doi: 10.1134/1.1568459
[40]
Mitrofanov O, Manfra M. Poole-Frenkel electron emission from the traps in AlGaN/GaN 13 transistors. J Appl Phys, 2004, 95(11): 6414 doi: 10.1063/1.1719264
[41]
Zhdanova N G, Kagan M S, Landsberg E G, et al. Ionization of shallow impurities by the electric field in a random coulomb potential. JETP Lett, 1995, 62(2): 119
[42]
Pavlovich V N. Enhanced diffusion of impurities and defects in crystals in conditions of ultrasonic and radiative excitation of the crystal lattice. Phys Stat Sol (b), 1993, 180(1): 97 doi: 10.1002/(ISSN)1521-3951
[43]
Mirzade F. Elastic wave propagation in a solid layer with laserinduced point defects. J Appl Phys, 2011, 110(6): 064906 doi: 10.1063/1.3633524
[44]
Olikh O, Voytenko K. On the mechanism of ultrasonic loading effect in silicon-based Schottky diodes. Ultrasonics, 2016, 66(1): 1
Fig. 1.  (Color online) (a) Reverse and (b) forward I–V characteristics of Mo/n–Si Schottky structures measured at 10 K intervals without USL. The lines are added to guide the eye.

Fig. 2.  (Color online) (a) Reverse I–V characteristics measured with (open marks) and without (full marks) USL as a function of temperature. (b) Change of the relative AI current variation with the bias and the temperature. fUS=4.1 MHz, WUS=0.65 W/cm2.

Fig. 3.  (Color online) Dependences of relative reverse current variation on ultrasonic intensity.

Fig. 4.  (Color online) Current–temperature characteristics for Mo/n-Si Schottky structures, measured at different reverse bias voltages. The marks are the experimental results, the solid lines are the fitted curves using Equation (11). The dotted and dashed lines represent the TE and the PAT current components respectively for VR=0.5 V, Wus=0.

Fig. 5.  Plot of the temperature-independent factor of TE current component as a function of reverse voltage. Marks are obtained from experimental data, the line is the fitted curve using Equation (10). The calculation was carried out using Vi=0.5VR.

Fig. 6.  (a) Field dependences of the SBH, (b) the trap depth, and (c) the interface state density for the Mo/n–Si Schottky structures with (2, 3) and without (1) USL. Marks are extracted from experimental data, lines are the linear fitting. WUS, W/cm2: 0 (1), 0.17 (2), 0.65 (3). fUS, MHz: 8.4 (2), 4.1 (3).

Fig. 7.  (Color online) (a) Change of the PAT current fractional contribution with the bias and the temperature and (b) its variation under action of ultrasound with fUS=4.1 MHz, WUS=0.65 W/cm2.

Fig. 8.  (Color online) Qualitative pattern of TE (a, c) and PAT (b, d) current variation with decrease of trap depth (a), SBH at zero temperature (b), Poole-Frenkel factor (c) and factor of interface states influence on SBH (d). Equations (2), (4), (12) and (13) were used to calculate the presented data. See details in the text.

Table 1.   Extracted parameters for the Mo/n-Si Schottky structures with and without ultrasonic loading.
[1]
Savkina R K, Smirnov A B, Sizov F. The effect of high-frequency sonication on charge carrier transport in LPE and MBE HgCdTe layers. Semicond Sci Technol, 2007, 22(2): 97 doi: 10.1088/0268-1242/22/2/016
[2]
Kulakova L, Gorelov V, Lutetskiy A, et al. The rotation of the polarization plane of quantum-well heterolasers emission under the ultrasonic strain. Solid State Commun, 2012, 152(17): 1690 doi: 10.1016/j.ssc.2012.04.065
[3]
Ostrovskii I, Korotchenkov O, Olikh O, et al. Acoustically driven optical phenomena in bulk and low-dimensional semiconductors. J Opt A, 2001, 3(4): S82 https://www.researchgate.net/publication/230991018_Acoustically_driven_optical_phenomena_in_bulk_and_low-dimensional_semiconductors
[4]
Buyukkose S, Vratzov B, van der Veen J, et al. Ultrahighfrequency surface acoustic wave generation for acoustic charge transport in silicon. Appl Phys Lett, 2013, 102(1): 013112 doi: 10.1063/1.4774388
[5]
He J H, Gao J, Guo H Z. Correlated electron transport assisted by surface acoustic waves in micron-separated quasi-onedimensional channels. Appl Phys Lett, 2010, 97(12): 122107 doi: 10.1063/1.3491287
[6]
Ostapenko S S, L Jastrzebski, Sopori B. Change of minority carrier diffusion length in polycrystalline silicon by ultrasound treatment. Semicond Sci Technol, 1995, 10(11): 1494 doi: 10.1088/0268-1242/10/11/011
[7]
Ostapenko S. Defect passivation using ultrasound treatment: fundamentals and application. Appl Phys A: Mater Sci Process, 1999, 69(2): 225 doi: 10.1007/s003390050994
[8]
Sukach A, Teterkin V. Ultrasonic treatment-induced modification of the electrical properties of InAs p-n junctions. Tech Phys Lett, 2009, 35(6): 514 doi: 10.1134/S1063785009060108
[9]
Olikh O. Features of dynamic acoustically induced modification of photovoltaic parameters of silicon solar cells. Semiconductors, 2011, 45(6): 798 doi: 10.1134/S1063782611060170
[10]
Davletova A, Karazhanov S Z. A study of electrical properties of dislocation engineered Si processed by ultrasound. J Phys Chem Solids, 2009, 70(6): 989 doi: 10.1016/j.jpcs.2009.05.009
[11]
Davletova A, Karazhanov S Z. Open-circuit voltage decay transient in dislocation-engineered Si p-n junction. J Phys D: Appl Phys, 2008, 41(16): 165107 doi: 10.1088/0022-3727/41/16/165107
[12]
Melnik V, Olikh Y, Popov V, et al. Characteristics of silicon p-n junction formed by ion implantation with in situ ultrasound treatment. Mater Sci Eng B, 2005, 124/125: 327 doi: 10.1016/j.mseb.2005.08.039
[13]
Olikh O. Effect of ultrasonic loading on current in Mo/n-n+-Si with Schottky barriers. Semiconductors, 2013, 47(7): 987 doi: 10.1134/S106378261307018X
[14]
Olikh O. Reversible influence of ultrasound on γ-irradiated Mo/n-Si Schottky barrier structure. Ultrasonics, 2015, 56: 545 doi: 10.1016/j.ultras.2014.10.008
[15]
Zaveryukhina N, Zaveryukhina E, Vlasov S, et al. Acoustostimulated changes in the density of surface states and their energy spectrum in p-type silicon single crystals. Tech Phys Lett, 2008, 34(3): 241 doi: 10.1134/S106378500803019X
[16]
Mirsagatov S A, Sapaeva I B, Nazarov Z. Ultrasonic annealing of surface states in the heterojunction of a p-Si/n-CdS/n+-CdS injection photodiode. Inorg Mater, 2015, 51(1): 1 doi: 10.1134/S0020168515010148
[17]
Wosinski T, Makosa A, Witczak Z. Transformation of native defects in bulk GaAs under ultrasonic vibration. Semicond Sci Technol, 1994, 9(11): 2047 doi: 10.1088/0268-1242/9/11/003
[18]
Buyanova I A, Ostapenko S S, Sheinkman M K, et al. Ultrasound regeneration of EL2 centres in GaAs. Semicond Sci Technol, 1994, 9(2): 158 doi: 10.1088/0268-1242/9/2/005
[19]
Korotchenkov O, Grimmliss H. Long-wavelength acousticmode-enhanced electron emission from Se and Te donors in silicon. Phys Rev B, 1995, 52(20): 14598 doi: 10.1103/PhysRevB.52.14598
[20]
Ostapenko S S, Bell R E. Ultrasound stimulated dissociation of Fe-B pairs in silicon. J Appl Phys, 1995, 77(10): 5458 doi: 10.1063/1.359243
[21]
Sathaiya D M, Karmalkar S. Thermionic trap-assisted tunneling model and its application to leakage current in nitrided oxides and AlGaN/GaN high electron mobility transistors. J Appl Phys, 2006, 99(9): 093701 doi: 10.1063/1.2191620
[22]
Shan Q, Meyaard D S, Dai Q, et al. Transport-mechanism analysis of the reverse leakage current in GaInN light-emitting diodes. Appl Phys Lett, 2011, 99(25): 253506 doi: 10.1063/1.3668104
[23]
Pipinys P, Lapeika V. Temperature dependence of reverse-bias leakage current in GaN Schottky diodes as a consequence of phonon-assisted tunneling. J Appl Phys, 2006, 99(9): 093709 doi: 10.1063/1.2199980
[24]
Liang Huaguo, Xu Hui, Huang Zhengfeng, et al. Low-leakage and NBTI-mitigated N-type domino logic. Journal of Semiconductors, 2014, 35(1): 015009 doi: 10.1088/1674-4926/35/1/015009
[25]
Bi Xiuwen, Liang Hailian, Gu Xiaofeng, et al. Design of novel DDSCR with embedded PNP structure for ESD protection. Journal of Semiconductors, 2015, 36(12): 124007 doi: 10.1088/1674-4926/36/12/124007
[26]
Abu-Samaha F S, Darwish A A A, Mansour A N. Temperature dependent of the current-voltage (Ⅳ) characteristics of TaSi2/nSi structure. Mater Sci Semicond Process, 2013, 16(6): 1988 doi: 10.1016/j.mssp.2013.07.036
[27]
Jafar M M A G. High-bias current-voltage-temperature characteristics of undoped RF magnetron sputter deposited boron carbide (B5C)/p-type crystalline silicon heterojunctions. Semicond Sci Technol, 2003, 18(1): 7 doi: 10.1088/0268-1242/18/1/302
[28]
Lee C H, Lim K S. Carrier transport through boron-doped amorphous diamond-like carbon p layer of amorphous silicon based p-i-n solar cells. Appl Phys Lett, 1999, 75(4): 569 doi: 10.1063/1.124444
[29]
Pipinys P, Pipiniene A, Rimeika A. Phonon-assisted tunneling in reverse biased Schottky diodes. J Appl Phys, 1999, 86(12): 6875 doi: 10.1063/1.371766
[30]
Tung R T. Recent advances in Schottky barrier concept. Mater Sci Eng, R, 2001, 35(1-3): 1 doi: 10.1016/S0927-796X(01)00037-7
[31]
Olikh O Y, Voytenko K V, Burbelo R M. Ultrasound influence on I-V-T characteristics of silicon Schottky barrier structure. J Appl Phys, 2015, 117(4): 044505 doi: 10.1063/1.4906844
[32]
Wang K, Ye M. Parameter determination of Schottky-barrier diode model using differential evolution. Solid-State Electron, 2009, 53(2): 234 doi: 10.1016/j.sse.2008.11.010
[33]
Rhoderick E H, Williams R H. Metal semiconductor contacts. 2nd ed. Oxford: Clarendon Press, 1988
[34]
Aboelfotoh M. Electrical characteristics of W-Si(100) Schottky barrier junctions. J Appl Phys, 1989, 66(1): 262 doi: 10.1063/1.343867
[35]
Zhua S, Meirhaeghea R L V, Detaverniera C, et al. A BEEM study of the temperature dependence of the barrier height distribution in PtSi/n-Si Schottky diodes. Solid State Commun, 1999, 112(11): 611 doi: 10.1016/S0038-1098(99)00404-4
[36]
Kiveris A, Kudzmauskas S, P P. Release of electrons from traps by an electric field with phonon participation. Phys Stat Sol (a), 1976, 37(1): 321 doi: 10.1002/(ISSN)1521-396X
[37]
Parker G, McGill T, Mead C, et al. Electric field dependence of GaAs Schottky barriers. Solid-State Electron, 1968, 11(2): 201 doi: 10.1016/0038-1101(68)90079-8
[38]
Seebauer E G, Kratzer M C. Charged point defects in semiconductors. Mater Sci Eng R, 2006, 55(3-6): 57 doi: 10.1016/j.mser.2006.01.002
[39]
Lukjanitsa V V. Energy levels of vacancies and interstitial atoms in the band gap of silicon. Semiconductors, 2003, 37(4): 404 doi: 10.1134/1.1568459
[40]
Mitrofanov O, Manfra M. Poole-Frenkel electron emission from the traps in AlGaN/GaN 13 transistors. J Appl Phys, 2004, 95(11): 6414 doi: 10.1063/1.1719264
[41]
Zhdanova N G, Kagan M S, Landsberg E G, et al. Ionization of shallow impurities by the electric field in a random coulomb potential. JETP Lett, 1995, 62(2): 119
[42]
Pavlovich V N. Enhanced diffusion of impurities and defects in crystals in conditions of ultrasonic and radiative excitation of the crystal lattice. Phys Stat Sol (b), 1993, 180(1): 97 doi: 10.1002/(ISSN)1521-3951
[43]
Mirzade F. Elastic wave propagation in a solid layer with laserinduced point defects. J Appl Phys, 2011, 110(6): 064906 doi: 10.1063/1.3633524
[44]
Olikh O, Voytenko K. On the mechanism of ultrasonic loading effect in silicon-based Schottky diodes. Ultrasonics, 2016, 66(1): 1

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    Received: 12 February 2016 Revised: 23 June 2016 Online: Published: 01 December 2016

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      O.Ya Olikh, K.V. Voitenko, R.M. Burbelo, JaM. Olikh. Effect of ultrasound on reverse leakage current of silicon Schottky barrier structure[J]. Journal of Semiconductors, 2016, 37(12): 122002. doi: 10.1088/1674-4926/37/12/122002 ****O. Y. Olikh, K. V. Voitenko, R. M. Burbelo, J. M. Olikh. Effect of ultrasound on reverse leakage current of silicon Schottky barrier structure[J]. J. Semicond., 2016, 37(12): 122002. doi:? 10.1088/1674-4926/37/12/122002.
      Citation:
      O.Ya Olikh, K.V. Voitenko, R.M. Burbelo, JaM. Olikh. Effect of ultrasound on reverse leakage current of silicon Schottky barrier structure[J]. Journal of Semiconductors, 2016, 37(12): 122002. doi: 10.1088/1674-4926/37/12/122002 ****
      O. Y. Olikh, K. V. Voitenko, R. M. Burbelo, J. M. Olikh. Effect of ultrasound on reverse leakage current of silicon Schottky barrier structure[J]. J. Semicond., 2016, 37(12): 122002. doi:? 10.1088/1674-4926/37/12/122002.

      Effect of ultrasound on reverse leakage current of silicon Schottky barrier structure

      DOI: 10.1088/1674-4926/37/12/122002
      • 1.

        Faculty of Physics, Taras Shevchenko National University of Kyiv, Kyiv 01601, Ukraine

      • 2.

        V Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine, Kyiv 03028, Ukraine

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      • Corresponding author: O. Ya Olikh, Email:olikh@univ.kiev.ua
      • Received Date: 2016-02-12
      • Revised Date: 2016-06-23
      • Published Date: 2016-12-01

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