- Email: [email protected]
Hot-electron photodetection based on embedded asymmetric nano-gap electrodes
Optik - International Journal for Light and Electron Optics 169 (2018) 236–241
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.com/locate/ijleo
Original research article
Hot-electron photodetection based on embedded asymmetric nanogap electrodes
T
Xiaoyi Shi, Wang Xiao, Queqiao Fan, Ting Zhou, Wenjing Song, Chi Zhang, ⁎ Yun Zhang, Zhun Lu, Wei Peng , Yun Zeng Key Laboratory for Micro-/Nano- Optoelectronic Devices of Ministry of Education, School of Physics and Electronics, Hunan University, Changsha 410082, China
A R T IC LE I N F O
ABS TRA CT
Keywords: Hot-electron photodetection Surface plasmons Embedded Asymmetric nano-gap electrodes Schottky barrier
Hot electrons generated from the nonradiative decay of surface plasmons can be employed in photodetection. However, only a small percentage of these hot electrons can be collected. In this paper, a type of hot-electron photodetector based on embedded asymmetric nano-gap electrodes is proposed which can enhance hot-electron collection efficiency. Due to this structure, the device can achieve responsivities as high as 3.75 mA/W and 1.58 mA/W for wavelengths of 1310 nm and 1550 nm, respectively. These insights can enhance efficiencies and lower cost in optical communication systems.
1. Introduction Surface plasmons (SPs), a coherent oscillation of electrons, which can be excited in metal by the electromagnetic wave [1], can promote the ability to trap light [2] by increasing light-matter interaction of the diffraction limit. Nowadays, they have been applied in numerous fields including sub-diffraction-limited inaging [3], photovoltaic devices [4] and environmental sensors [5]. Due to the mechanism of SPs, metal can be excited by the incident light. After excitation, surface plasmons would decay either radiatively into re-emitted photons or nonradiatively by forming hot electrons [6]. The nonradiative decay of plasmons, which can generate hot electrons, can be used for hot-electron photodetection [7]. Hot-electron photodetectors are formed by placing the metal nanoelectrodes in contact with a semiconductor [8], forming a Schottky barrier. Hot electrons generated in metal nanoelectrodes travel to the metal-semiconductor interface and cross Schottky barrier, resulting in photocurrent. Consequently, the bandwidth of photodetectors can be decided by the Schottky barrier height rather than the bandgap of the semiconductor. This allows hot-electron photodetectors to be exploited for optical communications without bonding or extending low-bandgap semiconductors on silicon [9,10], which can reduce the cost of optical communications. Recent years, hot-electron photodetection has been investigated by many groups. Naomi J. Halas et al. accomplished an active optical antenna device of fabricating Au resonant antennas on n-type Si substrate, which achieved tunable peak response at wavelength range of 1250–1600 nm in the order of μA/W [11]. Moreover, the responsivity of silicon-based hot-electron photodetectors in communication band has been greatly improved via pyramid [12], embedded [13], chiral metamaterial [14] nanoelectrode structure. These researches have greatly improved the responsivity of hot-electron photodetectors for optical communications. Generally, the responsivity of hot-electron photodetectors is determined by optical absorption and hot-electron collection. Current researches mostly focus on enhancement of optical absorption.
⁎
Corresponding author. E-mail address: [email protected] (W. Peng).
https://doi.org/10.1016/j.ijleo.2018.05.058 Received 27 December 2017; Accepted 16 May 2018 0030-4026/ © 2018 Elsevier GmbH. All rights reserved.
Optik - International Journal for Light and Electron Optics 169 (2018) 236–241
X. Shi et al.
Fig. 1. (a) Schematic of the embedded asymmetric nano-gap hot electron photodetectors. Wp and Wc are the widths of the plasmon electrodes and the collection electrodes, respectively, H is the height of electrodes, G is the electrode gap, D is the embedding depth of electrodes. (b) Band diagram of the device. The photocurrent is generated by five consecutive steps.
However, hot-electron collection is also a critical factor for photoresponse capability. Hence, realizing effective hot-electron collection will provide further opportunities for the development of hot-electron photodetectors. In our recent researches, a device based on asymmetric nano-gap electrodes is demonstrated to improve responsivity [15] by reducing the traveling length of hot electrons to the order of sub-micron. In this paper, we present a silicon based hot-electron photodetector with embedded asymmetric [16] plasmonic nano-gap electrodes. It realizes a higher responsivity due to the efficient collection of hot electrons. This device has a great potential to replace costly InGaAs and germanium detectors in the field of optical communications. Fig. 1(a) shows an embedded asymmetric nano-gap photodetector based on metal-semiconductor (Au-Si) Schottky barrier [17–19]. Asymmetric gold electrodes are embedded into the silicon substrate. The narrow ones are plasmon electrodes and the wide ones are collection electrodes. The devices can be fabricated by the electron beam lithography [20], etching, the electron beam evaporation and the lift-off process [21]. Excited by incident light of polarization in the x direction, the nonequilibrium photocurrents of plasmon electrodes and collection electrodes, Ip and Ic, will be generated in the device. When the width of collection is 1000 nm, hot electrons induced in the plasmon electrodes are much more than those in the collection electrodes. The net current I can be expressed as I=Ip-Ic [15], and Ic can be ignored in this paper. Thus, this device can work without plus bias voltage due to the asymmetric structure. 2. Computational methods It can be observed from Fig. 1(b) that the process of generating photocurrent consists of five steps. Firstly, when light with frequency ν incidents on the Au electrodes, plasmon resonance will be excited and a large number of hot electrons will be produced. The initial energy of the hot electrons can be calculated as E0 = hν , where h is Planck’s constant. Secondly, hot electrons arrive at the Au-Si interface, and their kinetic energy can be expressed as Ek = E0 e−s / L , where s is total distance of hot electron traveling, L is the mean free path of the electrons. Thirdly, hot electrons cross the Schottky barrier with a certain number of probability [22]. Then, a part of survival hot electrons travel across the gap in the Si substrate. Finally, hot electrons will reach collection electrodes and be collected. The relationship between kinetic energy and momentum of the hot electrons arriving at Au-Si interface in Au electrodes can be expressed by:
Ek =
ℏ2 2 kAu 2me*
(1)
Where ħ is reduced Planck’s constant, me* is the effective mass of the electron, kAu is the total momentum of the hot electron at Au-Si interface in plasmon electrodes, which is given by:. 2 2 2 kAu = kAu , x + kAu, z
(2)
where kAu,x and kAu,z are the momentums of the hot electron in plasmon electrodes in the x and the z directions, respectively. Once the hot electron injects into the Si substrate, both kinetic energy and momentum would change. The kinetic energy can be calculated as:
Ek − φB =
ℏ2 2 kSi 2me*
(3)
Here, φB is the height of Schottky barrier. Similarly, kSi is the total momentum of hot electrons at Au-Si interface in Si substrate:
kSi2 = kSi2 , x + kSi2 , z
(4) 237
Optik - International Journal for Light and Electron Optics 169 (2018) 236–241
X. Shi et al.
Fig. 2. (a) The cross-section of the k-space distribution at Au-Si interface. (b) The emission probability of a hot electron initially moving in directions of z(+z and -z) and x(+x and -x) as the number of reflecting events increases in the left and right, respectively.
where kSi,x and kSi,z are the momentums of the hot electron in plasmon electrodes in the x and the z directions, respectively. In Fig. 2(a), we can see only when kAu,x < kSi,xmax, the hot electrons can escape, so the escape probability can be calculated by a solid angle Ω [23]: 2π Ω ∫0 ∫0 sin θdθdϕ
4π
=
1 1 (1 − cos Ω) = (1 − 2 2
φB s
E0 e − L
)
(5)
In fact, a part of the hot electrons arriving at the Au-Si interface will be reflected, but they still have possibility to cross the Au-Si interface. Here, two assumptions are made: (1) hot electrons excited by nonradiative decay only move in four directions (-x, +x, -z and +z); (2) hot electrons will be reflected elastically which fail to pass the Au-Si interface or travel to the Au-air interface[24]. Thus the emission probability in four directions (P-x(x,z), P+x(x,z), P-z(x,z), P+z(x,z)) can be calculated according to Fig. 2(b). 1
φ
B ), N = 0 ⎧ Pf ,0 (x , z ) = 2 (1 − −s E0 e L ⎪ Pf (x , z ) = P (x , z ) + (1 − P (x , z )) P (x , z )+… f ,0 f ,1 ⎨ f ,0 ⎪+ P (x , z ) ∏N − 1 (1 − P (x , z )), N ≠ 0 f ,N f ,m m=0 ⎩
(6)
Here the initial direction of hot electron movement f, the total distance of hot electron traveling s and the total number of round trip N are shown in Table 1. Because of the image force, the probability of an electron arriving at collection electrodes can reduce to Pf(x,z) mentioned in Eq. (6). The ratio of the thermal electrons moving in each direction can be approximated as the ratio of the electric field difference:
n (x , z ) =
dEx dx
dEz dz
. The total emission probability can be obtained by:
n (x , z ) 1 [ P (x , z ) 1 + n (x , z ) 2 −x 1 1 1 [ P (x , z ) + 2 P−z (x , 1 + n (x , z ) 2 +z
P (x , z ) =
1
+ 2 P+x (x , z )]+ z )]
(7) 238
Optik - International Journal for Light and Electron Optics 169 (2018) 236–241
X. Shi et al.
Table 1 The total distance and the total round trip number of hot electron varied with initial direction of hot electron movement. f [Initial Direction of Hot Electron Movement]
s [Total Distance of Hot Electron Traveling]
N [Total Number of Round Trips]
-x
x + N *Wp
⎛L*ln E0 − x ⎞/ Wp φB ⎠ ⎝
+x
Wp − x + N *Wp
⎛L*ln E0 − Wp + x ⎞/ Wp φB ⎠ ⎝
-z
z + 2N *H
⎛L*ln E0 − z ⎞/(2H ) φB ⎠ ⎝
+z
2H − z + 2N *H
⎛L*ln E0 − 2H + z ⎞/(2H ) φB ⎠ ⎝
The internal quantum efficiency ηi indicates the efficiency of hot electrons collected by collection electrodes, which can be obtained by:
ηi =
H
∫0 ∫0
Wp
r (x , z ) P (x , z ) dxdz
(8)
Where r(x,z) is the probability density of hot electrons appearing at (x,z), which can be calculated by:
r (x , z ) =
E 2 (x , z ) H
Wp 0
∫0 ∫ E 2 (x , z ) dxdz
(9)
Here E(x,z) is the value of the electric field at (x,z) and can be analyzed by finite-difference time domain method (Lumerical FDTD Solutions). Then we can get responsivity as:
R=
A⋅ηi ⋅q hν
(10)
Where ηi the internal quantum efficiency, q is the charge of the electron, A is the absorption, which can also be obtained by the finitedifference time domain method. 3. Result Fig. 3(a) and (b) depict the electric field distribution of plasmon electrodes when the electrodes not embedded and embedded respectively. It can be seen that in plasmon electrodes the electric field in bottom corners is much higher than other regions of the electrode. It indicates that the hot electrons are mainly generated in bottom corners and profiles of plasmon electrodes. Thus, when embedded, the number of hot electrons crossing Au-Si interface, though decreasing in the bottom corners, would increase a lot, enhancing the internal quantum efficiency. In order to achieve higher responsivity by improving internal quantum efficiency, we calculated the relationship between the performance and device dimensions as shown in Fig. 4. We chose three different widths of plasmon electrodes: 100 nm, 120 nm and 140 nm, while other dimensions are fixed as H = 25 nm, Wc = 1 um and G = 200 nm. As shown in Fig. 4(a), for the three considered plasmon electrode widths, before the embedding depth is 19 nm, the internal quantum efficiency curves are all improved as the growth of embedding depth rapidly at first but slowly in the end. For Wp = 100 nm and Wp = 120 nm, the curves peak at D = 19 nm. Fig. 4(b) indicates the relationship between optical absorption and embedding
Fig. 3. The electric field distributions of plasmon electrodes of the device with electrode dimensions: H = 25 nm, Wp = 120 nm, Wc = 1 μm and G = 200 nm at an incident wavelength of 1550 nm. (a) The distribution of electric field, while the electrodes are not embedded in Si substrate. (b) The distribution of electric field, while the embedding depth is 20 nm. 239
Optik - International Journal for Light and Electron Optics 169 (2018) 236–241
X. Shi et al.
Fig. 4. The internal quantum efficiency ηi, the absorption A and the responsivity R vary with embedding depth of electrodes and the width of plasmon electrodes at the wavelength of 1550 nm. (a) The internal quantum efficiency. (b) The absorption. (c) The responsivity.
depth. The curves barely change with embedding depth, which indicates that embedding of electrodes almost has no impact on the total energy absorbed by electrodes, which can also be seen from Fig.3. The responsivity is relative to both absorption and internal quantum efficiency. Therefore the responsivity in this paper are mainly affected by the internal quantum efficiency. In Fig. 4(c), for the curves of Wp = 100 nm and Wp = 120 nm, the responsivity curves peak at the embedding depth of 19 nm and their peak values are 1.41 mA/W and 1.58 mA/W respectively. As for the width of plasmon electrodes, we can also see that as the width increases, internal quantum efficiency is decreased (Fig. 4(a)) while the absorption is increased(Fig. 4(b)). Fig. 4(c) shows that the responsivity of Wp = 120 nm is higher. Consequently, we optimized the device by designing its dimensions with Wp = 120 nm and D = 19 nm. The result of the optimized device is illustrated in Fig. 5. The absorption and internal quantum efficiency spectra are displayed in Fig. 5(a). The absorption is improved with the growth of wavelength, and decreased since the wavelength is more than 1310 nm. The internal quantum efficiency is reduced as the wavelength increased but shows fluctuation. As shown in Fig. 5(b), the peak of responsivity appears at the wavelength of 1310 nm, which is 3.75 mA/W. When the wavelength is 1550 nm, the peak value of responsivity is 1.58 mA/W.
240
Optik - International Journal for Light and Electron Optics 169 (2018) 236–241
X. Shi et al.
Fig. 5. The result of the optimized device. Dimensions of this device are Wp = 120 nm, Wc = 1000 nm, H = 25 nm, D = 19 nm. (a) The absorption and internal quantum efficiency spectra of the optimized device. (b) The responsivity spectra of the optimized device.
4. Conclusion In conclusion, we have proposed a hot-electron photodetector based on embedded asymmetric nano-gap electrodes which achieves higher responsivity at the wavelength for optical-communication. The device can achieve responsivities as high as 3.75 mA/ W and 1.58 mA/W for wavelengths of 1310 nm and 1550 nm, respectively. These results suggest that our design may give rise to additional unforeseen applications in photodetection technologies. Acknowledgement The authors acknowledge support from National Natural Science Foundation of China No. 61705065, Hunan Provincial Natural Science Foundation of China No. 2017JJ3034, Technology Program of Changsha No. kq1703001 and the Students Innovation Training Program of Hunan University No. 201710532122. References [1] J.A. Schuller, E.S. Barnard, W. Cai, Y.C. Jun, J.S. White, M.L. Brongersma, Plasmonics for extreme light concentration and manipulation, Nat. Mater. 9 (2010) 193. [2] W. Li, J.G. Valentine, Harvesting the loss: surface plasmon-based hot electron photodetection, Nanophotonics (2017) 6. [3] N. Fang, H. Lee, C. Sun, X. Zhang, Sub–Diffraction-limited optical imaging with a silver superlens, Science 308 (2005) 534–537. [4] Plasmon-induced hot-electron generation at nanoparticle/metal-oxide interfaces for photovoltaic and photocatalytic devices, Nat. Photon. 8 (2014) 95–103. [5] N. Liu, T. Weiss, M. Mesch, L. Langguth, U. Eigenthaler, M. Hirscher, C. Sönnichsen, H. Giessen, Planar metamaterial analogue of electromagnetically induced transparency for plasmonic sensing, Nano Lett. 10 (2010) 1103. [6] X. Li, D. Xiao, Z. Zhang, Landau damping of quantum plasmons in metal nanostructures, New J. Phys. 15 (2013) 23011–23025 23015. [7] W. Li, J. Valentine, Metamaterial perfect absorber based hot electron photodetection, Nano Lett. 14 (2014) 3510. [8] M.W. Knight, H. Sobhani, P. Nordlander, N.J. Halas, Photodetection with active optical antennas, Science 332 (2011) 702. [9] K. Ueno, H. Misawa, Plasmon-enhanced photocurrent generation and water oxidation from visible to near-infrared wavelengths, Npg Asia Mater. 5 (2013) e61. [10] F.D. Shepherd Jr., A.C. Yang, R.W. Taylor, A 1 to 2 μ;m silicon avalanche photodiode, Proc. IEEE 58 (1970) 1160–1162. [11] M.W. Knight, H. Sobhani, P. Nordlander, N.J. Halas, Photodetection with active optical antennas, Science 332 (2011) 702–704. [12] B. Desiatov, I. Goykhman, J.B. Khurgin, J. Shappir, N. Mazurski, U. Levy, Plasmonic enhanced silicon pyramids for internal photoemission Schottky detectors in the near-infrared regime, Optica 2 (2015) 335. [13] M.W. Knight, Y. Wang, A.S. Urban, A. Sobhani, B.Y. Zheng, P. Nordlander, N.J. Halas, Embedding plasmonic nanostructure diodes enhances Hot electron emission, Nano Lett. 13 (2013) 1687–1692. [14] W. Li, Z.J. Coppens, L.V. Besteiro, W. Wang, A.O. Govorov, J. Valentine, Circularly polarized light detection with hot electrons in chiral plasmonic metamaterials, Nat. Commun. 6 (2015) 8379. [15] J. Ge, M. Luo, W. Zou, W. Peng, H. Duan, Plasmonic photodetectors based on asymmetric nanogap electrodes, Appl. Phy. Exp. 9 (2016) 084101. [16] P.R. Berger, W. Gao, Asymmetric Contacted Metal-Semiconductor-Metal Photodetectors, in, US, (1998). [17] R. Williams, R.H. Bube, Photoemission in the photovoltaic effect in cadmium sulfide crystals, J. Appl. Phys. 31 (1960) 968–978. [18] S.M. Sze, Physics of semiconductor devices, New York 1 (1981) 98–99. [19] C.K. Chen, B. Nechay, B.Y. Tsaur, Ultraviolet, visible, and infrared response of PtSi Schottky-barrier detectors operated in the front-illuminated mode, IEEE Trans. Electron Devices 38 (1991) 1094–1103. [20] H. Duan, H. Hu, K. Kumar, Z. Shen, J.K. Yang, Direct and reliable patterning of plasmonic nanostructures with sub-10-nm gaps, Acs Nano 5 (2011) 7593–7600. [21] Q. Xiang, Y. Chen, Y. Wang, M. Zheng, Z. Li, W. Peng, Y. Zhou, B. Feng, Y. Chen, H. Duan, Low-voltage-exposure-enabled hydrogen silsesquioxane bilayer-like process for three-dimensional nanofabrication, Nanotechnology 27 (2016) 254002. [22] A. Akbari, P. Berini, Schottky contact surface-plasmon detector integrated with an asymmetric metal stripe waveguide, Appl. Phys. Lett. 95 (2009) 824. [23] C. Scales, P. Berini, Thin-film schottky barrier photodetector models, IEEE J. Quantum Electron. 46 (2010) 633–643. [24] L. Yang, P. Kou, J. Shen, E.H. Lee, S. He, Proposal of a broadband, polarization-insensitive and high-efficiency hot-carrier schottky photodetector integrated with a plasmonic silicon ridge waveguide, J. Opt. 17 (2015) 125010.
241
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.com/locate/ijleo
Original research article
Hot-electron photodetection based on embedded asymmetric nanogap electrodes
T
Xiaoyi Shi, Wang Xiao, Queqiao Fan, Ting Zhou, Wenjing Song, Chi Zhang, ⁎ Yun Zhang, Zhun Lu, Wei Peng , Yun Zeng Key Laboratory for Micro-/Nano- Optoelectronic Devices of Ministry of Education, School of Physics and Electronics, Hunan University, Changsha 410082, China
A R T IC LE I N F O
ABS TRA CT
Keywords: Hot-electron photodetection Surface plasmons Embedded Asymmetric nano-gap electrodes Schottky barrier
Hot electrons generated from the nonradiative decay of surface plasmons can be employed in photodetection. However, only a small percentage of these hot electrons can be collected. In this paper, a type of hot-electron photodetector based on embedded asymmetric nano-gap electrodes is proposed which can enhance hot-electron collection efficiency. Due to this structure, the device can achieve responsivities as high as 3.75 mA/W and 1.58 mA/W for wavelengths of 1310 nm and 1550 nm, respectively. These insights can enhance efficiencies and lower cost in optical communication systems.
1. Introduction Surface plasmons (SPs), a coherent oscillation of electrons, which can be excited in metal by the electromagnetic wave [1], can promote the ability to trap light [2] by increasing light-matter interaction of the diffraction limit. Nowadays, they have been applied in numerous fields including sub-diffraction-limited inaging [3], photovoltaic devices [4] and environmental sensors [5]. Due to the mechanism of SPs, metal can be excited by the incident light. After excitation, surface plasmons would decay either radiatively into re-emitted photons or nonradiatively by forming hot electrons [6]. The nonradiative decay of plasmons, which can generate hot electrons, can be used for hot-electron photodetection [7]. Hot-electron photodetectors are formed by placing the metal nanoelectrodes in contact with a semiconductor [8], forming a Schottky barrier. Hot electrons generated in metal nanoelectrodes travel to the metal-semiconductor interface and cross Schottky barrier, resulting in photocurrent. Consequently, the bandwidth of photodetectors can be decided by the Schottky barrier height rather than the bandgap of the semiconductor. This allows hot-electron photodetectors to be exploited for optical communications without bonding or extending low-bandgap semiconductors on silicon [9,10], which can reduce the cost of optical communications. Recent years, hot-electron photodetection has been investigated by many groups. Naomi J. Halas et al. accomplished an active optical antenna device of fabricating Au resonant antennas on n-type Si substrate, which achieved tunable peak response at wavelength range of 1250–1600 nm in the order of μA/W [11]. Moreover, the responsivity of silicon-based hot-electron photodetectors in communication band has been greatly improved via pyramid [12], embedded [13], chiral metamaterial [14] nanoelectrode structure. These researches have greatly improved the responsivity of hot-electron photodetectors for optical communications. Generally, the responsivity of hot-electron photodetectors is determined by optical absorption and hot-electron collection. Current researches mostly focus on enhancement of optical absorption.
⁎
Corresponding author. E-mail address: [email protected] (W. Peng).
https://doi.org/10.1016/j.ijleo.2018.05.058 Received 27 December 2017; Accepted 16 May 2018 0030-4026/ © 2018 Elsevier GmbH. All rights reserved.
Optik - International Journal for Light and Electron Optics 169 (2018) 236–241
X. Shi et al.
Fig. 1. (a) Schematic of the embedded asymmetric nano-gap hot electron photodetectors. Wp and Wc are the widths of the plasmon electrodes and the collection electrodes, respectively, H is the height of electrodes, G is the electrode gap, D is the embedding depth of electrodes. (b) Band diagram of the device. The photocurrent is generated by five consecutive steps.
However, hot-electron collection is also a critical factor for photoresponse capability. Hence, realizing effective hot-electron collection will provide further opportunities for the development of hot-electron photodetectors. In our recent researches, a device based on asymmetric nano-gap electrodes is demonstrated to improve responsivity [15] by reducing the traveling length of hot electrons to the order of sub-micron. In this paper, we present a silicon based hot-electron photodetector with embedded asymmetric [16] plasmonic nano-gap electrodes. It realizes a higher responsivity due to the efficient collection of hot electrons. This device has a great potential to replace costly InGaAs and germanium detectors in the field of optical communications. Fig. 1(a) shows an embedded asymmetric nano-gap photodetector based on metal-semiconductor (Au-Si) Schottky barrier [17–19]. Asymmetric gold electrodes are embedded into the silicon substrate. The narrow ones are plasmon electrodes and the wide ones are collection electrodes. The devices can be fabricated by the electron beam lithography [20], etching, the electron beam evaporation and the lift-off process [21]. Excited by incident light of polarization in the x direction, the nonequilibrium photocurrents of plasmon electrodes and collection electrodes, Ip and Ic, will be generated in the device. When the width of collection is 1000 nm, hot electrons induced in the plasmon electrodes are much more than those in the collection electrodes. The net current I can be expressed as I=Ip-Ic [15], and Ic can be ignored in this paper. Thus, this device can work without plus bias voltage due to the asymmetric structure. 2. Computational methods It can be observed from Fig. 1(b) that the process of generating photocurrent consists of five steps. Firstly, when light with frequency ν incidents on the Au electrodes, plasmon resonance will be excited and a large number of hot electrons will be produced. The initial energy of the hot electrons can be calculated as E0 = hν , where h is Planck’s constant. Secondly, hot electrons arrive at the Au-Si interface, and their kinetic energy can be expressed as Ek = E0 e−s / L , where s is total distance of hot electron traveling, L is the mean free path of the electrons. Thirdly, hot electrons cross the Schottky barrier with a certain number of probability [22]. Then, a part of survival hot electrons travel across the gap in the Si substrate. Finally, hot electrons will reach collection electrodes and be collected. The relationship between kinetic energy and momentum of the hot electrons arriving at Au-Si interface in Au electrodes can be expressed by:
Ek =
ℏ2 2 kAu 2me*
(1)
Where ħ is reduced Planck’s constant, me* is the effective mass of the electron, kAu is the total momentum of the hot electron at Au-Si interface in plasmon electrodes, which is given by:. 2 2 2 kAu = kAu , x + kAu, z
(2)
where kAu,x and kAu,z are the momentums of the hot electron in plasmon electrodes in the x and the z directions, respectively. Once the hot electron injects into the Si substrate, both kinetic energy and momentum would change. The kinetic energy can be calculated as:
Ek − φB =
ℏ2 2 kSi 2me*
(3)
Here, φB is the height of Schottky barrier. Similarly, kSi is the total momentum of hot electrons at Au-Si interface in Si substrate:
kSi2 = kSi2 , x + kSi2 , z
(4) 237
Optik - International Journal for Light and Electron Optics 169 (2018) 236–241
X. Shi et al.
Fig. 2. (a) The cross-section of the k-space distribution at Au-Si interface. (b) The emission probability of a hot electron initially moving in directions of z(+z and -z) and x(+x and -x) as the number of reflecting events increases in the left and right, respectively.
where kSi,x and kSi,z are the momentums of the hot electron in plasmon electrodes in the x and the z directions, respectively. In Fig. 2(a), we can see only when kAu,x < kSi,xmax, the hot electrons can escape, so the escape probability can be calculated by a solid angle Ω [23]: 2π Ω ∫0 ∫0 sin θdθdϕ
4π
=
1 1 (1 − cos Ω) = (1 − 2 2
φB s
E0 e − L
)
(5)
In fact, a part of the hot electrons arriving at the Au-Si interface will be reflected, but they still have possibility to cross the Au-Si interface. Here, two assumptions are made: (1) hot electrons excited by nonradiative decay only move in four directions (-x, +x, -z and +z); (2) hot electrons will be reflected elastically which fail to pass the Au-Si interface or travel to the Au-air interface[24]. Thus the emission probability in four directions (P-x(x,z), P+x(x,z), P-z(x,z), P+z(x,z)) can be calculated according to Fig. 2(b). 1
φ
B ), N = 0 ⎧ Pf ,0 (x , z ) = 2 (1 − −s E0 e L ⎪ Pf (x , z ) = P (x , z ) + (1 − P (x , z )) P (x , z )+… f ,0 f ,1 ⎨ f ,0 ⎪+ P (x , z ) ∏N − 1 (1 − P (x , z )), N ≠ 0 f ,N f ,m m=0 ⎩
(6)
Here the initial direction of hot electron movement f, the total distance of hot electron traveling s and the total number of round trip N are shown in Table 1. Because of the image force, the probability of an electron arriving at collection electrodes can reduce to Pf(x,z) mentioned in Eq. (6). The ratio of the thermal electrons moving in each direction can be approximated as the ratio of the electric field difference:
n (x , z ) =
dEx dx
dEz dz
. The total emission probability can be obtained by:
n (x , z ) 1 [ P (x , z ) 1 + n (x , z ) 2 −x 1 1 1 [ P (x , z ) + 2 P−z (x , 1 + n (x , z ) 2 +z
P (x , z ) =
1
+ 2 P+x (x , z )]+ z )]
(7) 238
Optik - International Journal for Light and Electron Optics 169 (2018) 236–241
X. Shi et al.
Table 1 The total distance and the total round trip number of hot electron varied with initial direction of hot electron movement. f [Initial Direction of Hot Electron Movement]
s [Total Distance of Hot Electron Traveling]
N [Total Number of Round Trips]
-x
x + N *Wp
⎛L*ln E0 − x ⎞/ Wp φB ⎠ ⎝
+x
Wp − x + N *Wp
⎛L*ln E0 − Wp + x ⎞/ Wp φB ⎠ ⎝
-z
z + 2N *H
⎛L*ln E0 − z ⎞/(2H ) φB ⎠ ⎝
+z
2H − z + 2N *H
⎛L*ln E0 − 2H + z ⎞/(2H ) φB ⎠ ⎝
The internal quantum efficiency ηi indicates the efficiency of hot electrons collected by collection electrodes, which can be obtained by:
ηi =
H
∫0 ∫0
Wp
r (x , z ) P (x , z ) dxdz
(8)
Where r(x,z) is the probability density of hot electrons appearing at (x,z), which can be calculated by:
r (x , z ) =
E 2 (x , z ) H
Wp 0
∫0 ∫ E 2 (x , z ) dxdz
(9)
Here E(x,z) is the value of the electric field at (x,z) and can be analyzed by finite-difference time domain method (Lumerical FDTD Solutions). Then we can get responsivity as:
R=
A⋅ηi ⋅q hν
(10)
Where ηi the internal quantum efficiency, q is the charge of the electron, A is the absorption, which can also be obtained by the finitedifference time domain method. 3. Result Fig. 3(a) and (b) depict the electric field distribution of plasmon electrodes when the electrodes not embedded and embedded respectively. It can be seen that in plasmon electrodes the electric field in bottom corners is much higher than other regions of the electrode. It indicates that the hot electrons are mainly generated in bottom corners and profiles of plasmon electrodes. Thus, when embedded, the number of hot electrons crossing Au-Si interface, though decreasing in the bottom corners, would increase a lot, enhancing the internal quantum efficiency. In order to achieve higher responsivity by improving internal quantum efficiency, we calculated the relationship between the performance and device dimensions as shown in Fig. 4. We chose three different widths of plasmon electrodes: 100 nm, 120 nm and 140 nm, while other dimensions are fixed as H = 25 nm, Wc = 1 um and G = 200 nm. As shown in Fig. 4(a), for the three considered plasmon electrode widths, before the embedding depth is 19 nm, the internal quantum efficiency curves are all improved as the growth of embedding depth rapidly at first but slowly in the end. For Wp = 100 nm and Wp = 120 nm, the curves peak at D = 19 nm. Fig. 4(b) indicates the relationship between optical absorption and embedding
Fig. 3. The electric field distributions of plasmon electrodes of the device with electrode dimensions: H = 25 nm, Wp = 120 nm, Wc = 1 μm and G = 200 nm at an incident wavelength of 1550 nm. (a) The distribution of electric field, while the electrodes are not embedded in Si substrate. (b) The distribution of electric field, while the embedding depth is 20 nm. 239
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Fig. 4. The internal quantum efficiency ηi, the absorption A and the responsivity R vary with embedding depth of electrodes and the width of plasmon electrodes at the wavelength of 1550 nm. (a) The internal quantum efficiency. (b) The absorption. (c) The responsivity.
depth. The curves barely change with embedding depth, which indicates that embedding of electrodes almost has no impact on the total energy absorbed by electrodes, which can also be seen from Fig.3. The responsivity is relative to both absorption and internal quantum efficiency. Therefore the responsivity in this paper are mainly affected by the internal quantum efficiency. In Fig. 4(c), for the curves of Wp = 100 nm and Wp = 120 nm, the responsivity curves peak at the embedding depth of 19 nm and their peak values are 1.41 mA/W and 1.58 mA/W respectively. As for the width of plasmon electrodes, we can also see that as the width increases, internal quantum efficiency is decreased (Fig. 4(a)) while the absorption is increased(Fig. 4(b)). Fig. 4(c) shows that the responsivity of Wp = 120 nm is higher. Consequently, we optimized the device by designing its dimensions with Wp = 120 nm and D = 19 nm. The result of the optimized device is illustrated in Fig. 5. The absorption and internal quantum efficiency spectra are displayed in Fig. 5(a). The absorption is improved with the growth of wavelength, and decreased since the wavelength is more than 1310 nm. The internal quantum efficiency is reduced as the wavelength increased but shows fluctuation. As shown in Fig. 5(b), the peak of responsivity appears at the wavelength of 1310 nm, which is 3.75 mA/W. When the wavelength is 1550 nm, the peak value of responsivity is 1.58 mA/W.
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Fig. 5. The result of the optimized device. Dimensions of this device are Wp = 120 nm, Wc = 1000 nm, H = 25 nm, D = 19 nm. (a) The absorption and internal quantum efficiency spectra of the optimized device. (b) The responsivity spectra of the optimized device.
4. Conclusion In conclusion, we have proposed a hot-electron photodetector based on embedded asymmetric nano-gap electrodes which achieves higher responsivity at the wavelength for optical-communication. The device can achieve responsivities as high as 3.75 mA/ W and 1.58 mA/W for wavelengths of 1310 nm and 1550 nm, respectively. These results suggest that our design may give rise to additional unforeseen applications in photodetection technologies. Acknowledgement The authors acknowledge support from National Natural Science Foundation of China No. 61705065, Hunan Provincial Natural Science Foundation of China No. 2017JJ3034, Technology Program of Changsha No. kq1703001 and the Students Innovation Training Program of Hunan University No. 201710532122. References [1] J.A. Schuller, E.S. Barnard, W. Cai, Y.C. Jun, J.S. White, M.L. Brongersma, Plasmonics for extreme light concentration and manipulation, Nat. Mater. 9 (2010) 193. [2] W. Li, J.G. Valentine, Harvesting the loss: surface plasmon-based hot electron photodetection, Nanophotonics (2017) 6. [3] N. Fang, H. Lee, C. Sun, X. Zhang, Sub–Diffraction-limited optical imaging with a silver superlens, Science 308 (2005) 534–537. [4] Plasmon-induced hot-electron generation at nanoparticle/metal-oxide interfaces for photovoltaic and photocatalytic devices, Nat. Photon. 8 (2014) 95–103. [5] N. Liu, T. Weiss, M. Mesch, L. Langguth, U. Eigenthaler, M. Hirscher, C. Sönnichsen, H. Giessen, Planar metamaterial analogue of electromagnetically induced transparency for plasmonic sensing, Nano Lett. 10 (2010) 1103. [6] X. Li, D. Xiao, Z. Zhang, Landau damping of quantum plasmons in metal nanostructures, New J. Phys. 15 (2013) 23011–23025 23015. [7] W. Li, J. Valentine, Metamaterial perfect absorber based hot electron photodetection, Nano Lett. 14 (2014) 3510. [8] M.W. Knight, H. Sobhani, P. Nordlander, N.J. Halas, Photodetection with active optical antennas, Science 332 (2011) 702. [9] K. Ueno, H. Misawa, Plasmon-enhanced photocurrent generation and water oxidation from visible to near-infrared wavelengths, Npg Asia Mater. 5 (2013) e61. [10] F.D. Shepherd Jr., A.C. Yang, R.W. Taylor, A 1 to 2 μ;m silicon avalanche photodiode, Proc. IEEE 58 (1970) 1160–1162. [11] M.W. Knight, H. Sobhani, P. Nordlander, N.J. Halas, Photodetection with active optical antennas, Science 332 (2011) 702–704. [12] B. Desiatov, I. Goykhman, J.B. Khurgin, J. Shappir, N. Mazurski, U. Levy, Plasmonic enhanced silicon pyramids for internal photoemission Schottky detectors in the near-infrared regime, Optica 2 (2015) 335. [13] M.W. Knight, Y. Wang, A.S. Urban, A. Sobhani, B.Y. Zheng, P. Nordlander, N.J. Halas, Embedding plasmonic nanostructure diodes enhances Hot electron emission, Nano Lett. 13 (2013) 1687–1692. [14] W. Li, Z.J. Coppens, L.V. Besteiro, W. Wang, A.O. Govorov, J. Valentine, Circularly polarized light detection with hot electrons in chiral plasmonic metamaterials, Nat. Commun. 6 (2015) 8379. [15] J. Ge, M. Luo, W. Zou, W. Peng, H. Duan, Plasmonic photodetectors based on asymmetric nanogap electrodes, Appl. Phy. Exp. 9 (2016) 084101. [16] P.R. Berger, W. Gao, Asymmetric Contacted Metal-Semiconductor-Metal Photodetectors, in, US, (1998). [17] R. Williams, R.H. Bube, Photoemission in the photovoltaic effect in cadmium sulfide crystals, J. Appl. Phys. 31 (1960) 968–978. [18] S.M. Sze, Physics of semiconductor devices, New York 1 (1981) 98–99. [19] C.K. Chen, B. Nechay, B.Y. Tsaur, Ultraviolet, visible, and infrared response of PtSi Schottky-barrier detectors operated in the front-illuminated mode, IEEE Trans. Electron Devices 38 (1991) 1094–1103. [20] H. Duan, H. Hu, K. Kumar, Z. Shen, J.K. Yang, Direct and reliable patterning of plasmonic nanostructures with sub-10-nm gaps, Acs Nano 5 (2011) 7593–7600. [21] Q. Xiang, Y. Chen, Y. Wang, M. Zheng, Z. Li, W. Peng, Y. Zhou, B. Feng, Y. Chen, H. Duan, Low-voltage-exposure-enabled hydrogen silsesquioxane bilayer-like process for three-dimensional nanofabrication, Nanotechnology 27 (2016) 254002. [22] A. Akbari, P. Berini, Schottky contact surface-plasmon detector integrated with an asymmetric metal stripe waveguide, Appl. Phys. Lett. 95 (2009) 824. [23] C. Scales, P. Berini, Thin-film schottky barrier photodetector models, IEEE J. Quantum Electron. 46 (2010) 633–643. [24] L. Yang, P. Kou, J. Shen, E.H. Lee, S. He, Proposal of a broadband, polarization-insensitive and high-efficiency hot-carrier schottky photodetector integrated with a plasmonic silicon ridge waveguide, J. Opt. 17 (2015) 125010.
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