Abstract

We develop the device models for the far-infrared interband photodetectors (IPs) with the graphene-layer (GL) sensitive elements and the black Phosphorus (b-P) or black-Arsenic (b-As) barrier layers (BLs). These far-infrared GL/BL-based IPs (GBIPs) can operate at the photon energies $\hbar \Omega$ smaller than the energy gap, ΔG, of the b-P or b-As or their compounds, namely, at $\hbar \Omega \lesssim 2\Delta _G/3$ corresponding to the wavelength range $\lambda \gtrsim (6 - 12)~\mu$m. The GBIP operation spectrum can be shifted to the terahertz range by increasing the bias voltage. The BLs made of the compounds b-AsxB1−x with different x, enable the GBIPs with desirable spectral characteristics. The GL doping level substantially affects the GBIP characteristics and is important for their optimization. A remarkable feature of the GBIPs under consideration is a substantial (over an order of magnitude) lowering of the dark current due to a partial suppression of the dark-current gain accompanied by a fairly high photoconductive gain. Due to a large absorption coefficient and photoconductive gain, the GBIPs can exhibit large values of the internal responsivity and dark-current-limited detectivity exceeding those of the quantum-well and quantum-dot IPs using the intersubband transitions. The GBIPs with the b-P and b-As BLs can operate at longer radiation wavelengths than the infrared GL-based IPs comprising the BLs made of other van der Waals materials and can also compete with all kinds of the far-infrared photodetectors.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2019 (2)

A. Rogalski, “Graphene-based materials in the infrared and terahertz detector families: a tutorial,” Adv. Opt. Photonics 11(2), 314–379 (2019).
[Crossref]

M. Ryzhii, V. Ryzhii, V. Mitin, M. S. Shur, and T. Otsuji, “Vertical hot-electron terahertz detectors based on black-As1−xPx/graphene/black-As1−yPy heterostructures,” Sens. Mater. 31(7), 2271–2279 (2019).
[Crossref]

2018 (6)

Yu Li, Yi Shi, and X. Wang, “Electrically tunable optical properties of few-layer black arsenic phosphorus,” Nanotechnology 29(48), 484001 (2018).
[Crossref]

Y. Chen, C. Chen, R. Kealhofer, H. Liu, Z. Yuan, L. Jiang, J. Suh, J. Park, C. Ko, H. S. Choe, J. Avila, M. Zhong, Z. Wei, J. Li, S. Li, H. Gao, Y. Liu, J. Analytis, Q. Xia, M. C. Asensio, and J. Wu, “Black Arsenic: a layered semiconductor with extreme in-plane anisotropy,” Adv. Mater. (Weinheim, Ger.) 30(30), 1800754 (2018).
[Crossref]

W. C. Tan, L. H. Huang, E. J. Ng, L. Wang, D. Md. Naruddin Hasan, T. J. Duffin, K. S Kumar, C. A. Nijhuism, C. Lee, and K.-W. Ang, “A black phosphorus carbide infrared phototransistor,” Adv. Mater. (Weinheim, Ger.) 30(6), 1705039 (2018).
[Crossref]

S. Yuan, C. Shen, B. Deng, X. Chen, Q. Guo, Y. Ma, A. Abbas, B. Liu, R. Haiges, C. Ott, T. Nilges, K. Watanabe, T. Taniguchi, O. Sinai, D. Naveh, C. Zhou, and F. Xia, “Air-stable room-temperature mid-infrared photodetectors based on hBN/black arsenic phosphorus/hBN heterostructures,” Nano Lett. 18(5), 3172–3179 (2018).
[Crossref]

V. Ryzhii, T. Otsuji, V. E. Karasik, M. Ryzhii, V. G. Leiman, V. Mitin, and M. S. Shur, “Comparison of intersubband quantum-well and interband graphene-layer infrared photodetectors,” IEEE J. Quantum Electron. 54(2), 1–8 (2018).
[Crossref]

D. Palaferri, Y. Todorov, A. Bigioli, A. Mottaghizadeh, D. Gacemi, A. Calabrese, A. Vasanelli, L. Li, A. G. Davies, E. H. Linfield, F. Kapsalidis, M. Beck, J. Faist, and C. Sirtori, “Room-temperature nine-μm-wavelength photodetectors and GHz-frequency heterodyne receivers,” Nature 556(7699), 85–88 (2018).
[Crossref]

2017 (7)

K. K. Choi, S. C. Allen, J. G. Sun, Y. Wei, K. A. Olver, and R. X. Fu, “Resonant structures for infrared detection,” Appl. Opt. 56(3), B26–B36 (2017).
[Crossref]

B. Paulillo, S. Pirotta, H. Nong, P. Crozat, S. Guilet, G. Xu, S. Dhillon, L. H. Li, A. G. Davies, E. H. Linfield, and R. olombelli, “Ultrafast terahertz detectors based on three-dimensional meta-atoms,” Optica 4(12), 1451–1456 (2017).
[Crossref]

V. Ryzhii, M. Ryzhii, D. Svintsov. V. Leiman, V. Mitin, M. S. Shur, and T. Otsuji, “Infrared photodetectors based on graphene van der Waals heterostructures,” Infrared Phys. Technol. 84, 72–81 (2017).
[Crossref]

V. Ryzhii, M. Ryzhii, V. Leiman, V. Mitin, M. S. Shur, and T. Otsuji, “Effect of doping on the characteristics of infrared photodetectors based on van der Waals heterostructures with multiple graphene layers,” J. Appl. Phys. 122(5), 054505 (2017).
[Crossref]

V. Ryzhii, M. Ryzhii, D. Svintsov, V. Leiman, V. Mitin, M. S. Shur, and T. Otsuji, “Nonlinear response of infrared photodetectors based on van der Waals heterostructures with graphene layers,” Opt. Express 25(5), 5536–5549 (2017).
[Crossref]

W. C. Tan, Y. Cai, R. J. Ng, L. Huang, X. Feng, G. Zhang, Y.-W. Zhang, C. A. Nijhuis, X. Liu, and K.-W. Ang, “Few-layer black phosphorus carbide field-effect transistor via carbon doping,” Adv. Mater. (Weinheim, Ger.) 29(24), 1700503 (2017).
[Crossref]

M. Long, A. Gao, P. Wang, H. Xia, C. Ott, C. Pan, Y. Fu, E. Liu, X. Chen, W. Lu, T. Nilges, J. Xu, X. Wang, W. Hu, and F. Miao, “Room temperature high-detectivity mid-infrared photodetectors based on black arsenic phosphorus,” Sci. Adv. 3(6), e1700589 (2017).
[Crossref]

2016 (1)

X. Wang and S. Lan, “Optical properties of black phosphorus,” Adv. Opt. Photonics 8(4), 618–655 (2016).
[Crossref]

2015 (7)

Z. Guo, H. Zhang, S. Lu, Z. Wang, S. Tang, J. Shao, Z. Sun, H. Xie, H. Wang, X.-F. Yu, and P. K. Chu, “From black phosphorus to phosphorene: Basic solvent exfoliation, evolution of Raman scattering, and applications to ultrafast photonics,” Adv. Funct. Mater. 25(45), 6996–7002 (2015).
[Crossref]

B. Liu, M. Kopf, A. N. Abbas, X. Wang, Q. Guo, Y. Jia, F. Xia, R. Weihrich, F. Bachhuber, F. Pielnhofer, H. Wang, R. Dhall, S. B. Cronin, M. Ge, X. Fang, T. Nilges, and C. Zhou, “Black Arsenic-Phosphorus: layered anisotropic infrared semiconductors with highly tunable compositions and properties,” Adv. Mater. 27(30), 4423–4429 (2015).
[Crossref]

Ling Xi, “The renaissance of black phosphorus,” Proc. Natl. Acad. Sci. U. S. A. 112(15), 4523–4530 (2015).
[Crossref]

V. Ryzhii, T. Otsuji, M. Ryzhii, V. Ya. Aleshkin, A. A. Dubinov, V. Mitin, and M. S. Shur, “Vertical electron transport in van der Waals heterostructures with graphene layers,” J. Appl. Phys. 117(15), 154504 (2015).
[Crossref]

Y. Cai, G. Zhang, and Y.-W. Zhang, “Layer-dependent band alignment and work function of few-layer phosphorene,” Sci. Rep. 4(1), 6677 (2015).
[Crossref]

H. Liu, Y. Du, Y. Deng, and P. D. Ye, “Semiconducting black phosphorus: synthesis, transport properties and electronic applications,” Chem. Soc. Rev. 44(9), 2732–2743 (2015).
[Crossref]

V. Ya. Aleshkin, A. A. Dubinov, M. Ryzhii, V. Ryzhii, and T. Otsuji, “Electron capture in van der Waals graphene based heterostructures with WS2 barrier layers,” J. Phys. Soc. Jpn. 84(9), 094703 (2015).
[Crossref]

2014 (4)

S. D. Gunapala, S. V. Bandara, J. K. Liu, J. M. Mumolo, S. B. Rafol, D. Z. Ting, A. Soibel, and C. Hill, “Quantum well infrared photodetector technology and applications,” IEEE J. Sel. Top. Quantum Electron. 20(6), 154–165 (2014).
[Crossref]

A. Tredicucci and M. S. Vitielo, “Device concepts for graphene-based terahertz photonics,” IEEE J. Sel. Top. Quantum Electron. 20(1), 130–138 (2014).
[Crossref]

V. Ryzhii, A. Satou, T. Otsuji, M. Ryzhii, V. Mitin, and M. S. Shur, “Graphene vertical hot-electron terahertz detectors,” J. Appl. Phys. 116(11), 114504 (2014).
[Crossref]

F. Xia, H. Wang, and Y. Jia, “Rediscovering black phosphorous as an anisotropic layered material for optoelectronics and electronics,” Nat. Commun. 5(1), 4458 (2014).
[Crossref]

2013 (3)

C. Downs and T. E. Vandervelde, “Progress in infrared photodetectors since 2000,” Sensors 13(4), 5054–5098 (2013).
[Crossref]

G. Gong, H. Zhang, W. Wang, L. Colombo, R. M. Wallace, and K. Cho, “Band alignment of two-dimensional transition metal dichalcogenides: Application in tunnel field effect transistors,” Appl. Phys. Lett. 103(5), 053513 (2013).
[Crossref]

A. Rogalski, “Semiconductor detectors and focal plane arrays for far-infrared imaging,” Opto-Electron. Rev. 21(4), 404–426 (2013).
[Crossref]

2012 (2)

S. Kalchmair, R. Gansch, S. I. Ahn, A. M. Andrews, H. Detz, T. Zederbauer, E. Mujagic, P. Reininger, G. Lasser, W. Schrenk, and G. Strasser, “Detectivity enhancement in quantum well infrared photodetectors utilizing a photonic crystal slab resonator,” Opt. Express 20(5), 5622–5628 (2012).
[Crossref]

V. Ryzhii, N. Ryabova, M. Ryzhii, N. V. Baryshnikov, V. E. Karasik, V. Mitin, and T. Otsuji, “Terahertz and infrared photodetectors based on multiple graphene layer and nanoribbon structures,” Opto-Electron. Rev. 20(1), 15–25 (2012).
[Crossref]

2011 (1)

A. V. Barve, J. Montaya, Y. Sharma, T. Rotter, J. Shao, W.-Y. Jang, S. Meesala, S. J. Lee, and S. Krishna, “High temperature operation of quantum dots-in-a-well infrared photodetectors,” Infrared Phys. Technol. 54(3), 215–219 (2011).
[Crossref]

2010 (3)

T. Mueller, F. N. A. Xia, and P. Avouris, “Graphene photodetectors for high speed optical communications,” Nat. Photonics 4(5), 297–301 (2010).
[Crossref]

V. Ryzhii, M. Ryzhii, V. Mitin, and T. Otsuji, “Terahertz and infrared photodetection using p-i-n multiple-graphene layer structures,” J. Appl. Phys. 107(5), 054512 (2010).
[Crossref]

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
[Crossref]

2009 (1)

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[Crossref]

2007 (1)

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1(2), 97–105 (2007).
[Crossref]

2005 (1)

S. Chakrabarti, A. D. Stiff-Roberts, X. H. Su, P. Bhattacharya, G. Ariyawansa, and A. G. U. Perera, “High-performance mid-infrared quantum dot infrared photodetectors,” J. Phys. D: Appl. Phys. 38(13), 2135–2141 (2005).
[Crossref]

2004 (1)

V. Ryzhii, M. Ryzhii, and V. Mitin, “Comparison of dark current, responsivity and detectivity in different intersubband infrared photodetectors,” Semicond. Sci. Technol. 19(1), 8–16 (2004).
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2001 (2)

V. Ryzhii, I. Khmyrova, V. Mitin, M. Stroscio, and M. Willander, “On the detectivity of quantum-dot infrared photodetectors,” Appl. Phys. Lett. 78(22), 3523–3525 (2001).
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V. Ryzhii and R. A. Suris, “Nonlocal hot-electron transport and capture model for multiple quantum well structures excited by infrared radiation,” Jpn. J. Appl. Phys. 40(Part 1, No. 2A), 513–517 (2001).
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2000 (1)

V. Ryzhii, I. Khmyrova, M. Ryzhii, R. Suris, and C. Hamaguchi, “Phenomenological theory of electric-field domains induced by infrared radiation in multiple quantum well structures,” Phys. Rev. B 62(11), 7268–7274 (2000).
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1998 (2)

V. Ryzhii, I. Khmyrova, and M. Ryzhii, “Impact of transit-time and capture effects on high-frequency performance of multiple quantum-well infrared photodetectors,” IEEE Trans. Electron Devices 45(1), 293–298 (1998).
[Crossref]

V. Ryzhii, “High-frequency performance of single quantum well infrared photodetectors at high power densities,” IEEE Trans. Electron Devices 45(8), 1797–1803 (1998).
[Crossref]

1997 (1)

V. Ryzhii, “Characteristics of quantum-well infrared photodetectors,” J. Appl. Phys. 81(9), 6442–6448 (1997).
[Crossref]

1996 (2)

L. Thibaudeau, P. Bois, and J. Y. Dubos, “A self - consistent model for quantum well infrared photodetectors,” J. Appl. Phys. (Melville, NY, U. S.) 79(1), 446–454 (1996).
[Crossref]

V. Ryzhii, “The theory of quantum-dot infrared phototransistors,” Semicond. Sci. Technol. 11(5), 759–765 (1996).
[Crossref]

1995 (3)

H. C. Liu, G. E. Jenkins, E. R. Brown, K. A. McIntosh, K. B. Nichols, and M. J. Manfra, “Optical heterodyne detection and microwave rectification up to 26 GHz using quantum well infrared photodetectors,” IEEE Electron Device Lett. 16(6), 253–255 (1995).
[Crossref]

H. C. Liu, J. Li, E. R. Brown, K. A. McIntosh, K. B. Nichols, and M. J. Manfra, “Quantum well intersubband heterodyne infrared detection up to 82 GHz,” Appl. Phys. Lett. 67(11), 1594–1596 (1995).
[Crossref]

M. Ershov, V. Ryzhii, and C. Hamaguchi, “Contact and distributed effects in quantum well infrared photodetectors,” Appl. Phys. Lett. 67(21), 3147–3149 (1995).
[Crossref]

1994 (1)

E. Rosencher, B. Vinter, F. Luc, L. Thibaudeu, P. Bois, and J. Nagle, “Emission and capture of electrons in multiquantum-well structures,” IEEE J. Quantum Electron. 30(12), 2875–2888 (1994).
[Crossref]

1992 (1)

H. C. Liu, “Photoconductive gain mechanism of quantum well intersubband infrared detectors,” Appl. Phys. Lett. 60(12), 1507–1509 (1992).
[Crossref]

1988 (1)

S. Luryi, “Quantum capacitance devices,” Appl. Phys. Lett. 52(6), 501–503 (1988).
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1986 (1)

A. Morita, “Semiconducting black phosphorus,” Appl. Phys. A 39(4), 227–242 (1986).
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1984 (1)

H. Asahina and A. Morita, “Band structure and optical properties of black phosphorus,” J. Phys. C: Solid State Phys. 17(11), 1839–1852 (1984).
[Crossref]

1957 (1)

R. B. Dingle, “Fermi-Dirac integrals,” Appl. Sci. Res. 6(1), 225–239 (1957).
[Crossref]

1953 (1)

R. W. Keyes, “The electrical properties of black phosphorus,” Phys. Rev. 92(3), 580–584 (1953).
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Abbas, A.

S. Yuan, C. Shen, B. Deng, X. Chen, Q. Guo, Y. Ma, A. Abbas, B. Liu, R. Haiges, C. Ott, T. Nilges, K. Watanabe, T. Taniguchi, O. Sinai, D. Naveh, C. Zhou, and F. Xia, “Air-stable room-temperature mid-infrared photodetectors based on hBN/black arsenic phosphorus/hBN heterostructures,” Nano Lett. 18(5), 3172–3179 (2018).
[Crossref]

Abbas, A. N.

B. Liu, M. Kopf, A. N. Abbas, X. Wang, Q. Guo, Y. Jia, F. Xia, R. Weihrich, F. Bachhuber, F. Pielnhofer, H. Wang, R. Dhall, S. B. Cronin, M. Ge, X. Fang, T. Nilges, and C. Zhou, “Black Arsenic-Phosphorus: layered anisotropic infrared semiconductors with highly tunable compositions and properties,” Adv. Mater. 27(30), 4423–4429 (2015).
[Crossref]

Ahn, S. I.

Allen, S. C.

Analytis, J.

Y. Chen, C. Chen, R. Kealhofer, H. Liu, Z. Yuan, L. Jiang, J. Suh, J. Park, C. Ko, H. S. Choe, J. Avila, M. Zhong, Z. Wei, J. Li, S. Li, H. Gao, Y. Liu, J. Analytis, Q. Xia, M. C. Asensio, and J. Wu, “Black Arsenic: a layered semiconductor with extreme in-plane anisotropy,” Adv. Mater. (Weinheim, Ger.) 30(30), 1800754 (2018).
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Andrews, A. M.

Ang, K.-W.

W. C. Tan, L. H. Huang, E. J. Ng, L. Wang, D. Md. Naruddin Hasan, T. J. Duffin, K. S Kumar, C. A. Nijhuism, C. Lee, and K.-W. Ang, “A black phosphorus carbide infrared phototransistor,” Adv. Mater. (Weinheim, Ger.) 30(6), 1705039 (2018).
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W. C. Tan, Y. Cai, R. J. Ng, L. Huang, X. Feng, G. Zhang, Y.-W. Zhang, C. A. Nijhuis, X. Liu, and K.-W. Ang, “Few-layer black phosphorus carbide field-effect transistor via carbon doping,” Adv. Mater. (Weinheim, Ger.) 29(24), 1700503 (2017).
[Crossref]

Ariyawansa, G.

S. Chakrabarti, A. D. Stiff-Roberts, X. H. Su, P. Bhattacharya, G. Ariyawansa, and A. G. U. Perera, “High-performance mid-infrared quantum dot infrared photodetectors,” J. Phys. D: Appl. Phys. 38(13), 2135–2141 (2005).
[Crossref]

Asahina, H.

H. Asahina and A. Morita, “Band structure and optical properties of black phosphorus,” J. Phys. C: Solid State Phys. 17(11), 1839–1852 (1984).
[Crossref]

Asensio, M. C.

Y. Chen, C. Chen, R. Kealhofer, H. Liu, Z. Yuan, L. Jiang, J. Suh, J. Park, C. Ko, H. S. Choe, J. Avila, M. Zhong, Z. Wei, J. Li, S. Li, H. Gao, Y. Liu, J. Analytis, Q. Xia, M. C. Asensio, and J. Wu, “Black Arsenic: a layered semiconductor with extreme in-plane anisotropy,” Adv. Mater. (Weinheim, Ger.) 30(30), 1800754 (2018).
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Avila, J.

Y. Chen, C. Chen, R. Kealhofer, H. Liu, Z. Yuan, L. Jiang, J. Suh, J. Park, C. Ko, H. S. Choe, J. Avila, M. Zhong, Z. Wei, J. Li, S. Li, H. Gao, Y. Liu, J. Analytis, Q. Xia, M. C. Asensio, and J. Wu, “Black Arsenic: a layered semiconductor with extreme in-plane anisotropy,” Adv. Mater. (Weinheim, Ger.) 30(30), 1800754 (2018).
[Crossref]

Avouris, P.

T. Mueller, F. N. A. Xia, and P. Avouris, “Graphene photodetectors for high speed optical communications,” Nat. Photonics 4(5), 297–301 (2010).
[Crossref]

Bachhuber, F.

B. Liu, M. Kopf, A. N. Abbas, X. Wang, Q. Guo, Y. Jia, F. Xia, R. Weihrich, F. Bachhuber, F. Pielnhofer, H. Wang, R. Dhall, S. B. Cronin, M. Ge, X. Fang, T. Nilges, and C. Zhou, “Black Arsenic-Phosphorus: layered anisotropic infrared semiconductors with highly tunable compositions and properties,” Adv. Mater. 27(30), 4423–4429 (2015).
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Bandara, S. V.

S. D. Gunapala, S. V. Bandara, J. K. Liu, J. M. Mumolo, S. B. Rafol, D. Z. Ting, A. Soibel, and C. Hill, “Quantum well infrared photodetector technology and applications,” IEEE J. Sel. Top. Quantum Electron. 20(6), 154–165 (2014).
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Barve, A. V.

A. V. Barve, J. Montaya, Y. Sharma, T. Rotter, J. Shao, W.-Y. Jang, S. Meesala, S. J. Lee, and S. Krishna, “High temperature operation of quantum dots-in-a-well infrared photodetectors,” Infrared Phys. Technol. 54(3), 215–219 (2011).
[Crossref]

Baryshnikov, N. V.

V. Ryzhii, N. Ryabova, M. Ryzhii, N. V. Baryshnikov, V. E. Karasik, V. Mitin, and T. Otsuji, “Terahertz and infrared photodetectors based on multiple graphene layer and nanoribbon structures,” Opto-Electron. Rev. 20(1), 15–25 (2012).
[Crossref]

Beck, M.

D. Palaferri, Y. Todorov, A. Bigioli, A. Mottaghizadeh, D. Gacemi, A. Calabrese, A. Vasanelli, L. Li, A. G. Davies, E. H. Linfield, F. Kapsalidis, M. Beck, J. Faist, and C. Sirtori, “Room-temperature nine-μm-wavelength photodetectors and GHz-frequency heterodyne receivers,” Nature 556(7699), 85–88 (2018).
[Crossref]

Bhattacharya, P.

S. Chakrabarti, A. D. Stiff-Roberts, X. H. Su, P. Bhattacharya, G. Ariyawansa, and A. G. U. Perera, “High-performance mid-infrared quantum dot infrared photodetectors,” J. Phys. D: Appl. Phys. 38(13), 2135–2141 (2005).
[Crossref]

Bigioli, A.

D. Palaferri, Y. Todorov, A. Bigioli, A. Mottaghizadeh, D. Gacemi, A. Calabrese, A. Vasanelli, L. Li, A. G. Davies, E. H. Linfield, F. Kapsalidis, M. Beck, J. Faist, and C. Sirtori, “Room-temperature nine-μm-wavelength photodetectors and GHz-frequency heterodyne receivers,” Nature 556(7699), 85–88 (2018).
[Crossref]

Bois, P.

L. Thibaudeau, P. Bois, and J. Y. Dubos, “A self - consistent model for quantum well infrared photodetectors,” J. Appl. Phys. (Melville, NY, U. S.) 79(1), 446–454 (1996).
[Crossref]

E. Rosencher, B. Vinter, F. Luc, L. Thibaudeu, P. Bois, and J. Nagle, “Emission and capture of electrons in multiquantum-well structures,” IEEE J. Quantum Electron. 30(12), 2875–2888 (1994).
[Crossref]

Bonaccorso, F.

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
[Crossref]

Brown, E. R.

H. C. Liu, G. E. Jenkins, E. R. Brown, K. A. McIntosh, K. B. Nichols, and M. J. Manfra, “Optical heterodyne detection and microwave rectification up to 26 GHz using quantum well infrared photodetectors,” IEEE Electron Device Lett. 16(6), 253–255 (1995).
[Crossref]

H. C. Liu, J. Li, E. R. Brown, K. A. McIntosh, K. B. Nichols, and M. J. Manfra, “Quantum well intersubband heterodyne infrared detection up to 82 GHz,” Appl. Phys. Lett. 67(11), 1594–1596 (1995).
[Crossref]

Cai, Y.

W. C. Tan, Y. Cai, R. J. Ng, L. Huang, X. Feng, G. Zhang, Y.-W. Zhang, C. A. Nijhuis, X. Liu, and K.-W. Ang, “Few-layer black phosphorus carbide field-effect transistor via carbon doping,” Adv. Mater. (Weinheim, Ger.) 29(24), 1700503 (2017).
[Crossref]

Y. Cai, G. Zhang, and Y.-W. Zhang, “Layer-dependent band alignment and work function of few-layer phosphorene,” Sci. Rep. 4(1), 6677 (2015).
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Calabrese, A.

D. Palaferri, Y. Todorov, A. Bigioli, A. Mottaghizadeh, D. Gacemi, A. Calabrese, A. Vasanelli, L. Li, A. G. Davies, E. H. Linfield, F. Kapsalidis, M. Beck, J. Faist, and C. Sirtori, “Room-temperature nine-μm-wavelength photodetectors and GHz-frequency heterodyne receivers,” Nature 556(7699), 85–88 (2018).
[Crossref]

Castro Neto, A. H.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[Crossref]

Chakrabarti, S.

S. Chakrabarti, A. D. Stiff-Roberts, X. H. Su, P. Bhattacharya, G. Ariyawansa, and A. G. U. Perera, “High-performance mid-infrared quantum dot infrared photodetectors,” J. Phys. D: Appl. Phys. 38(13), 2135–2141 (2005).
[Crossref]

Chen, C.

Y. Chen, C. Chen, R. Kealhofer, H. Liu, Z. Yuan, L. Jiang, J. Suh, J. Park, C. Ko, H. S. Choe, J. Avila, M. Zhong, Z. Wei, J. Li, S. Li, H. Gao, Y. Liu, J. Analytis, Q. Xia, M. C. Asensio, and J. Wu, “Black Arsenic: a layered semiconductor with extreme in-plane anisotropy,” Adv. Mater. (Weinheim, Ger.) 30(30), 1800754 (2018).
[Crossref]

Chen, X.

S. Yuan, C. Shen, B. Deng, X. Chen, Q. Guo, Y. Ma, A. Abbas, B. Liu, R. Haiges, C. Ott, T. Nilges, K. Watanabe, T. Taniguchi, O. Sinai, D. Naveh, C. Zhou, and F. Xia, “Air-stable room-temperature mid-infrared photodetectors based on hBN/black arsenic phosphorus/hBN heterostructures,” Nano Lett. 18(5), 3172–3179 (2018).
[Crossref]

M. Long, A. Gao, P. Wang, H. Xia, C. Ott, C. Pan, Y. Fu, E. Liu, X. Chen, W. Lu, T. Nilges, J. Xu, X. Wang, W. Hu, and F. Miao, “Room temperature high-detectivity mid-infrared photodetectors based on black arsenic phosphorus,” Sci. Adv. 3(6), e1700589 (2017).
[Crossref]

Chen, Y.

Y. Chen, C. Chen, R. Kealhofer, H. Liu, Z. Yuan, L. Jiang, J. Suh, J. Park, C. Ko, H. S. Choe, J. Avila, M. Zhong, Z. Wei, J. Li, S. Li, H. Gao, Y. Liu, J. Analytis, Q. Xia, M. C. Asensio, and J. Wu, “Black Arsenic: a layered semiconductor with extreme in-plane anisotropy,” Adv. Mater. (Weinheim, Ger.) 30(30), 1800754 (2018).
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Cho, K.

G. Gong, H. Zhang, W. Wang, L. Colombo, R. M. Wallace, and K. Cho, “Band alignment of two-dimensional transition metal dichalcogenides: Application in tunnel field effect transistors,” Appl. Phys. Lett. 103(5), 053513 (2013).
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Choe, H. S.

Y. Chen, C. Chen, R. Kealhofer, H. Liu, Z. Yuan, L. Jiang, J. Suh, J. Park, C. Ko, H. S. Choe, J. Avila, M. Zhong, Z. Wei, J. Li, S. Li, H. Gao, Y. Liu, J. Analytis, Q. Xia, M. C. Asensio, and J. Wu, “Black Arsenic: a layered semiconductor with extreme in-plane anisotropy,” Adv. Mater. (Weinheim, Ger.) 30(30), 1800754 (2018).
[Crossref]

Choi, K. K.

Chu, P. K.

Z. Guo, H. Zhang, S. Lu, Z. Wang, S. Tang, J. Shao, Z. Sun, H. Xie, H. Wang, X.-F. Yu, and P. K. Chu, “From black phosphorus to phosphorene: Basic solvent exfoliation, evolution of Raman scattering, and applications to ultrafast photonics,” Adv. Funct. Mater. 25(45), 6996–7002 (2015).
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Colombo, L.

G. Gong, H. Zhang, W. Wang, L. Colombo, R. M. Wallace, and K. Cho, “Band alignment of two-dimensional transition metal dichalcogenides: Application in tunnel field effect transistors,” Appl. Phys. Lett. 103(5), 053513 (2013).
[Crossref]

Cronin, S. B.

B. Liu, M. Kopf, A. N. Abbas, X. Wang, Q. Guo, Y. Jia, F. Xia, R. Weihrich, F. Bachhuber, F. Pielnhofer, H. Wang, R. Dhall, S. B. Cronin, M. Ge, X. Fang, T. Nilges, and C. Zhou, “Black Arsenic-Phosphorus: layered anisotropic infrared semiconductors with highly tunable compositions and properties,” Adv. Mater. 27(30), 4423–4429 (2015).
[Crossref]

Crozat, P.

Davies, A. G.

D. Palaferri, Y. Todorov, A. Bigioli, A. Mottaghizadeh, D. Gacemi, A. Calabrese, A. Vasanelli, L. Li, A. G. Davies, E. H. Linfield, F. Kapsalidis, M. Beck, J. Faist, and C. Sirtori, “Room-temperature nine-μm-wavelength photodetectors and GHz-frequency heterodyne receivers,” Nature 556(7699), 85–88 (2018).
[Crossref]

B. Paulillo, S. Pirotta, H. Nong, P. Crozat, S. Guilet, G. Xu, S. Dhillon, L. H. Li, A. G. Davies, E. H. Linfield, and R. olombelli, “Ultrafast terahertz detectors based on three-dimensional meta-atoms,” Optica 4(12), 1451–1456 (2017).
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Deng, B.

S. Yuan, C. Shen, B. Deng, X. Chen, Q. Guo, Y. Ma, A. Abbas, B. Liu, R. Haiges, C. Ott, T. Nilges, K. Watanabe, T. Taniguchi, O. Sinai, D. Naveh, C. Zhou, and F. Xia, “Air-stable room-temperature mid-infrared photodetectors based on hBN/black arsenic phosphorus/hBN heterostructures,” Nano Lett. 18(5), 3172–3179 (2018).
[Crossref]

Deng, Y.

H. Liu, Y. Du, Y. Deng, and P. D. Ye, “Semiconducting black phosphorus: synthesis, transport properties and electronic applications,” Chem. Soc. Rev. 44(9), 2732–2743 (2015).
[Crossref]

Detz, H.

Dhall, R.

B. Liu, M. Kopf, A. N. Abbas, X. Wang, Q. Guo, Y. Jia, F. Xia, R. Weihrich, F. Bachhuber, F. Pielnhofer, H. Wang, R. Dhall, S. B. Cronin, M. Ge, X. Fang, T. Nilges, and C. Zhou, “Black Arsenic-Phosphorus: layered anisotropic infrared semiconductors with highly tunable compositions and properties,” Adv. Mater. 27(30), 4423–4429 (2015).
[Crossref]

Dhillon, S.

Dingle, R. B.

R. B. Dingle, “Fermi-Dirac integrals,” Appl. Sci. Res. 6(1), 225–239 (1957).
[Crossref]

Downs, C.

C. Downs and T. E. Vandervelde, “Progress in infrared photodetectors since 2000,” Sensors 13(4), 5054–5098 (2013).
[Crossref]

Du, Y.

H. Liu, Y. Du, Y. Deng, and P. D. Ye, “Semiconducting black phosphorus: synthesis, transport properties and electronic applications,” Chem. Soc. Rev. 44(9), 2732–2743 (2015).
[Crossref]

Dubinov, A. A.

V. Ya. Aleshkin, A. A. Dubinov, M. Ryzhii, V. Ryzhii, and T. Otsuji, “Electron capture in van der Waals graphene based heterostructures with WS2 barrier layers,” J. Phys. Soc. Jpn. 84(9), 094703 (2015).
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V. Ryzhii, T. Otsuji, M. Ryzhii, V. Ya. Aleshkin, A. A. Dubinov, V. Mitin, and M. S. Shur, “Vertical electron transport in van der Waals heterostructures with graphene layers,” J. Appl. Phys. 117(15), 154504 (2015).
[Crossref]

Dubos, J. Y.

L. Thibaudeau, P. Bois, and J. Y. Dubos, “A self - consistent model for quantum well infrared photodetectors,” J. Appl. Phys. (Melville, NY, U. S.) 79(1), 446–454 (1996).
[Crossref]

Duffin, T. J.

W. C. Tan, L. H. Huang, E. J. Ng, L. Wang, D. Md. Naruddin Hasan, T. J. Duffin, K. S Kumar, C. A. Nijhuism, C. Lee, and K.-W. Ang, “A black phosphorus carbide infrared phototransistor,” Adv. Mater. (Weinheim, Ger.) 30(6), 1705039 (2018).
[Crossref]

Ershov, M.

M. Ershov, V. Ryzhii, and C. Hamaguchi, “Contact and distributed effects in quantum well infrared photodetectors,” Appl. Phys. Lett. 67(21), 3147–3149 (1995).
[Crossref]

Faist, J.

D. Palaferri, Y. Todorov, A. Bigioli, A. Mottaghizadeh, D. Gacemi, A. Calabrese, A. Vasanelli, L. Li, A. G. Davies, E. H. Linfield, F. Kapsalidis, M. Beck, J. Faist, and C. Sirtori, “Room-temperature nine-μm-wavelength photodetectors and GHz-frequency heterodyne receivers,” Nature 556(7699), 85–88 (2018).
[Crossref]

Fang, X.

B. Liu, M. Kopf, A. N. Abbas, X. Wang, Q. Guo, Y. Jia, F. Xia, R. Weihrich, F. Bachhuber, F. Pielnhofer, H. Wang, R. Dhall, S. B. Cronin, M. Ge, X. Fang, T. Nilges, and C. Zhou, “Black Arsenic-Phosphorus: layered anisotropic infrared semiconductors with highly tunable compositions and properties,” Adv. Mater. 27(30), 4423–4429 (2015).
[Crossref]

Feng, X.

W. C. Tan, Y. Cai, R. J. Ng, L. Huang, X. Feng, G. Zhang, Y.-W. Zhang, C. A. Nijhuis, X. Liu, and K.-W. Ang, “Few-layer black phosphorus carbide field-effect transistor via carbon doping,” Adv. Mater. (Weinheim, Ger.) 29(24), 1700503 (2017).
[Crossref]

Ferrari, A. C.

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
[Crossref]

Fu, R. X.

Fu, Y.

M. Long, A. Gao, P. Wang, H. Xia, C. Ott, C. Pan, Y. Fu, E. Liu, X. Chen, W. Lu, T. Nilges, J. Xu, X. Wang, W. Hu, and F. Miao, “Room temperature high-detectivity mid-infrared photodetectors based on black arsenic phosphorus,” Sci. Adv. 3(6), e1700589 (2017).
[Crossref]

Gacemi, D.

D. Palaferri, Y. Todorov, A. Bigioli, A. Mottaghizadeh, D. Gacemi, A. Calabrese, A. Vasanelli, L. Li, A. G. Davies, E. H. Linfield, F. Kapsalidis, M. Beck, J. Faist, and C. Sirtori, “Room-temperature nine-μm-wavelength photodetectors and GHz-frequency heterodyne receivers,” Nature 556(7699), 85–88 (2018).
[Crossref]

Gansch, R.

Gao, A.

M. Long, A. Gao, P. Wang, H. Xia, C. Ott, C. Pan, Y. Fu, E. Liu, X. Chen, W. Lu, T. Nilges, J. Xu, X. Wang, W. Hu, and F. Miao, “Room temperature high-detectivity mid-infrared photodetectors based on black arsenic phosphorus,” Sci. Adv. 3(6), e1700589 (2017).
[Crossref]

Gao, H.

Y. Chen, C. Chen, R. Kealhofer, H. Liu, Z. Yuan, L. Jiang, J. Suh, J. Park, C. Ko, H. S. Choe, J. Avila, M. Zhong, Z. Wei, J. Li, S. Li, H. Gao, Y. Liu, J. Analytis, Q. Xia, M. C. Asensio, and J. Wu, “Black Arsenic: a layered semiconductor with extreme in-plane anisotropy,” Adv. Mater. (Weinheim, Ger.) 30(30), 1800754 (2018).
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Adv. Funct. Mater. (1)

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Adv. Mater. (1)

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Adv. Mater. (Weinheim, Ger.) (3)

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Adv. Opt. Photonics (2)

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Figures (6)

Fig. 1.
Fig. 1. The GBIP band diagrams (a) at relatively small ( $V < V_0$ ), (b) $V = V_0$ , and (c) high ( $V > V_0$ ) bias voltages. Panels (d) and (e) show enlarged fragments of the device band diagrams demonstrating the processes of the holes (black circles) an electrons (open circles) transitions indicated by arrows. The wavy vertical arrow shows the electron transfer from the valence band in the GL to its conduction band due to the photon absorption.
Fig. 2.
Fig. 2. The dark current gain $g_{dark}$ versus the capture probability $p$ for the GBIPs with different BLs: (a) with the b-P BL and (b) with the b-As BL. Dashed lines correspond to $T = 300$ K and solid lines correspond to $T = 200$ K. Dotted lines correspond to $g = (1/p - 1/2)$ .
Fig. 3.
Fig. 3. The normalized dark current $j_{dark}/j_{GL}$ versus bias voltage $V$ for the GBIPs with (a) b-P BLs and (b) b-As BLs at $T = 300$ K (dashed lines) and $T = 200$ K (solid lines) calculated for different Fermi energies $\mu _D$ .
Fig. 4.
Fig. 4. The GBIP responsivity $R_{\Omega }$ versus the photon energy $\hbar \Omega$ and Fermi energy $\mu _D$ (donor density in the GL-base) for (a) b-P BLs ( $\mu _A = 100$ meV, $dE_T = 3$ V, and $V = 1$ V) and (b) b-As ( $\mu _A = 50$ meV, $dE_T = 1$ V, and $V = 1$ V).
Fig. 5.
Fig. 5. Variation of the GBIP (with the b-As BLs) spectral characteristics with varying bias voltages $V$ at (a) $T= 300$ K and (b) $T = 200$ K.
Fig. 6.
Fig. 6. (a) The Fermi energy in the GL-base $\mu _{dark}|_{V=V_0}$ at the threshold voltage $V_0$ and (b) the threshold voltage $V_0$ as function of the Fermi in the emitter GL $\mu _A$ at fixed $V_D$ (fixed $\mu _D = 50$ meV).

Equations (37)

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Θ E , p = Σ G L τ e s c exp ( μ E Δ V k B T ) , Θ C , p = Σ G L τ e s c exp ( μ C Δ V k B T ) ,
Θ E , n = Σ G L τ e s c exp ( μ E + Δ C k B T ) Θ C , n = Σ G L τ e s c exp ( μ C + Δ C k B T ) ,
μ E = μ A 2 + κ 2 v W 2 E E 4 e μ A ( 1 + e E E d 2 e V A ) , μ C = μ A 2 κ 2 v W 2 E C 4 e μ A ( 1 + e E C d 2 e V A ) ,
Θ p = Σ G L τ e s c exp ( μ + Δ V k B T ) , Θ n = Σ G L τ e s c exp ( μ Δ C k B T ) ,
G p h = β F Ω ξ Ω I Ω .
F Ω = 1 exp [ ( μ Ω / 2 ) / k B T ] + 1 .
1 ξ Ω = 1 + τ e s c τ r e l a x { exp [ 4 2 m z ( Δ V Ω / 2 ) 3 / 2 3 e E E θ ( E E ) ] + exp [ 4 2 m z ( Δ V Ω / 2 ) 3 / 2 3 e E C θ ( E C ) ] } ,
V V D V T [ F 1 ( μ k B T ) F 1 ( μ k B T ) ] = 2 E E d .
F 1 ( a ) = 0 d ξ ξ exp ( ξ a ) + 1 .
j G L e exp ( Δ G 2 k B T ) [ exp ( μ 0 + μ A k B T ) exp ( e E E d k B T ) + exp ( μ 0 + μ A k B T ) exp ( e E C d k B T ) ] p = G t h + G p h ,
G t h = j G L e exp ( Δ G 2 k B T ) [ exp ( μ 0 μ k B T ) exp ( μ 0 μ k B T ) exp ( e E E d k B T ) ] .
j = j G L exp ( Δ G 2 k B T ) × { exp ( μ 0 + μ A k B T ) exp ( e E E d k B T ) exp ( μ 0 + μ A k B T ) exp ( e E C d k B T ) ( 1 p ) 1 2 exp ( μ 0 μ k B T ) + exp ( μ 0 μ k B T ) [ exp ( e E E d k B T ) 1 2 exp ( e E C d k B T ) ] } e 2 G p h ,
j = j G L exp ( Δ G 2 k B T ) × { [ exp ( μ 0 μ k B T ) exp ( μ 0 μ k B T ) exp ( e E E d k B T ) ] ( 1 p 1 2 ) [ 1 exp ( e V / k B T ) 1 + exp ( e V / k B T ) ] + 1 2 exp ( μ 0 μ k B T ) exp ( e E E d k B T ) [ 1 exp ( e V / k B T ) ] } + e β F Ω ξ Ω I Ω [ 1 exp ( e V / k B T ) 1 + exp ( e V / k B T ) ] ( 1 p 1 2 ) .
exp ( e E E d k B T ) = exp [ 2 ( μ 0 μ d a r k ) / k B T ] 1 + exp [ ( 2 μ 0 + μ A μ d a r k / k B T ] p [ 1 + exp ( e V / k B T ) ] .
j d a r k = g d a r k j G L exp ( Δ V + μ d a r k k B T ) [ 1 exp ( e V k B T ) 1 + exp ( e V k B T ) ]
g d a r k = { exp ( 2 μ 0 + μ A μ d a r k k B T ) p ( 1 p 1 2 ) + 1 2 1 + exp ( 2 μ 0 + μ A μ d a r k k B T ) p [ 1 + exp ( e V k B T ) ] } [ 1 + exp ( e V k B T ) ]
μ d a r k k B T μ D k B T ( 1 V 2 V D ) = μ D γ e V k B T ,
j d a r k = g d a r k j G L exp ( Δ V + μ D γ e V k B T ) [ 1 exp ( e V k B T ) 1 + exp ( e V k B T ) ] .
g d a r k exp ( 2 μ 0 + μ A μ D k B T ) p ( 1 p 1 2 ) [ 1 + exp ( e V k B T ) ] 1 + exp ( 2 μ 0 + μ A μ D k B T ) p [ 1 + exp ( e V k B T ) ] .
j p h = g p h e β F Ω ξ Ω I Ω [ 1 exp ( e V k B T ) 1 + exp ( e V k B T ) ] .
g p h = ( 1 p 1 2 ) 1 p
F Ω = 1 exp [ ( μ d a r k Ω / 2 ) / k B T ] + 1 1 exp [ ( μ D γ V Ω / 2 ) / k B T ] + 1 .
R Ω g p h e β F Ω ξ Ω Ω [ 1 exp ( e V k B T ) 1 + exp ( e V k B T ) ] ,
R Ω R g p h ( 1 + τ e s c / τ r e l a x ) g p h ( 2 Δ V Ω ) [ exp ( μ D Ω / 2 k B T ) + 1 ]
D Ω = G p h 2 Ω I Ω G t h .
D Ω = β F Ω ξ Ω 2 Ω e j G L exp ( Δ V + μ D 2 k B T ) 1 + K .
D Ω D Ω ¯ = β F Ω ξ Ω 2 Ω e j G L exp ( Δ V + μ D 2 k B T ) .
exp ( Δ G 2 k B T ) exp [ 4 d 2 m z 3 e ( Δ G 2 ) 3 / 2 ] = exp [ 2 d E T 3 e V ( Δ G Δ V ) 3 / 2 ]
e V k B T < 4 d m z Δ G 3 .
D Ω D Ω Q W I P r 1 + K N exp ( 4 μ D Ω 4 k B T ) , D Ω D Ω Q D I P r 1 + K N exp ( 2 μ D Ω 4 k B T ) ,
f n = [ exp [ ( p v W μ k B T ) + 1 ] 1 , f p = [ exp ( p v W + μ k B T ) + 1 ] 1 .
e Σ = 2 e π 2 0 d p p [ 1 exp ( p v W + μ k B T ) + 1 1 exp ( p v W μ k B T ) + 1 ] = 2 e T 2 π 2 v W 2 [ F 1 ( μ k B T ) F 1 ( μ k B T ) ] ,
F 1 ( a ) = 0 d ξ ξ exp ( ξ a ) + 1
p exp ( μ A + μ 0 k B T ) = 2 sinh ( μ 0 μ d a r k | V = V 0 k B T ) ,
μ d a r k | V = V 0 = μ 0 k B T ln { p 2 exp ( μ A + μ 0 k B T ) + [ p 2 exp ( μ A + μ 0 k B T ) ] 2 + 1 } .
V 0 = V D + V T [ F 1 ( μ d a r k | V = V 0 k B T ) F 1 ( μ d a r k | V = V 0 k B T ) ] .
j d a r k | V = V 0 = e Σ G τ e s c exp ( Δ G 2 k B T ) { ( 1 p 2 ) exp ( μ A + μ 0 k B T ) + 1 2 { p 2 exp ( μ A + μ 0 k B T ) + [ p 2 exp ( μ A + μ 0 k B T ) ] 2 + 1 } 1 e Σ G τ e s c exp ( Δ G 2 k B T ) { ( 1 p 2 ) exp ( μ A + μ 0 k B T ) = e Σ G τ e s c ( 1 p 2 ) exp ( μ A Δ V k B T ) .

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