收稿日期：30 July 2013
基金：financially supported by the China State Key Program for Basic Research (No. 2011CBA00304);Tsinghua University Initiative Scientific Research Program (No. 2010Z01010);the National Natural Science Foundation of China (Nos. 61106121 and 61174084);
Polarization independent superconducting nanowire detector with high-detection efficiency
He-Yu Yin Han Cai Ri-Sheng Cheng Zheng Xu Zhen-Nan Jiang Jian-She Liu Tie-Fu Li Wei Chen
Tsinghua National Laboratory for Information Science and Technology
Department of Microelectronics and Nanoelectronics, Tsinghua University
Institute of Microelectronics, Tsinghua University
Abstract：
The superconducting nanowire single photon detector(SNSPD) draws much attention because of its attractive performance at ultra violet, visible, and nearinfrared wavelengths, and it can be widespread in quantum information technologies. However, how to increase the absorption which can dramatically increase the quantum efficiency of the SNSPD is still a top research issue. In this study, the effect of incident medium and cavity material on the optical absorptance of cavity-integrated SNSPDs was systematically investigated using finite-element method. The simulation results demonstrate that for photons polarized parallel to nanowire orientation, even though the maximum absorptance of the nanowire is insensitive to cavity material,it does increase when the refractive index of incident medium decreases. For perpendicularly polarized photons, both incident medium and cavity material play significant roles,and the absorptance curves get closer to the parallel case as the refractive index of cavity material increases. Based on these results, two cavity-integrated SNSPDs with frontillumination structure which can enhance the absorptance for both parallel and perpendicular photons are proposed.Finally, a design to realize polarization-independent SNSPDs with high absorptance is presented.
Keyword：
Polarization-independent; Distributed Bragg reflective; High-detection efficiency; Superconducting nanowire single photon detector;
Author： Wei Chen e-mail: weichen@tsinghua.edu.cn;
Received： 30 July 2013
1 Introduction
The superconducting nanowire single photon detector(SNSPD) draws much attention since its first implementation [1], because of its low dark count rate [2], low timing jitter [3–5], and high single-photon counting rate at visible and near-infrared wavelengths [4]. However, owing to the finite absorptance of ultra-thin superconducting nanowires,the SNSPDs generally suffer from low system detection efficiencies, and the absorptance depends heavily on the polarization of incident photons [6], which limits the applications of the SNSPD in quantum optics experiments requiring both high-efficiency single-photon detection and polarization independence, such as linear optical quantum computation [7, 8], quantum key distribution (QKD) [9,10], and loophole-free bell tests [11]. Recently, Verma et al. [12] proposed the three-dimensional superconducting nanowire avalanche photodetector (3D-SNAP) based on WSi nanowires and experimentally realized a peak system detection efficiency of *90 % with negligible polarization dependence. However, the stacked meander structure in this design needs an insulating layer between two detector layers, such as amorphous Si Ox, and superconducting film such as Nb N, which were studied extensively for SNSPD application, cannot be directly deposited on top of this amorphous layer without degradation of its superconducting properties. In addition, because of the extremely low Tcand large time jitter (compared to Nb N nanowire) of the WSi films, polarization-independent SNSPD based on Nb N nanowire is very attractive.
Fig.1 Simplified optical model of cavity-integrated SNSPD a and three-dimensional schematic drawing of cavity-integrated SNSPD with direction of incident photons’polarization b
In this paper, we present an alternative approach, which uses high-refractive-index materials such as Si as cavity material and significantly enhances the absorptance of superconducting nanowires for photons polarized perpendicular to the nanowire orientation, while maintaining high absorptance for parallelly polarized photons. In this new approach, only one layer of superconducting nanowire is needed, and the adoption of SOI substrates combined with wafer-bonding technique could ensure that high-quality superconducting films such as Nb N films can be directly deposited on the top of the epitaxial single-crystal Si layer.
Several factors that influence the total system detection efficiency of the SNSPD were discussed, and finite-element simulation method for calculating the optical absorptance of superconducting nanowires was presented [13]. Based on simulation results, the effects of incident media and cavity materials with different refractive indices on the nanowires’absorptance were systemically discussed. Two practical structures of optical cavity-integrated SNSPDs were given,and cavity optimization method based on finite-element simulation was presented for realizing polarization-independent optical absorptance of the SNSPD.
2 Method of simulation
The system detection efficiency of the SNSPD can be given by the following expression, assuming no transmission loss through the input path:
where gcouplingis the optical coupling efficiency between incident photons and the detection area of the SNSPD;gabsorptionrepresents the optical absorptance of the superconducting nanowire; gintrinsicis the probability of electrical pulse generation after photon absorption. Through selfaligned fiber-to-detector coupling, the gcouplingcould reach as high as 99 % [14, 15], while the gintrinsiccould exceed90 % both in WSi [16] and Nb N nanowires [17]. Therefore, the gabsorptionis the bottleneck of further improving the total system detection efficiency gsystem, because of the limited photon absorptance of ultra-thin nanowires. Integrating an optical cavity with the superconducting nanowire is an effective way of enhancing the absorptance of the nanowire [18–23], and in this section we present the simulation method of calculating the optical absorptance of cavity-integrated nanowires.
Simulation was performed using the radio frequency module of Comsol multi-physics software package (Comsol4.2) on the simplified model as shown in Fig. 1a to obtain the optical absorptance of the superconducting nanowire for both parallelly and perpendicularly polarized photons(Fig. 1b). As shown in Fig. 1a, this model consists of incident medium, superconducting nanowire layer, cavity layer,and reflector. ni, nc, and nd? ikdrepresent the refractive indices of incident medium, cavity material, and detecting material, respectively. h and d are the thickness of the cavity layer and the nanowire layer, while p and w represent the pitch and the width of the superconducting nanowire. Thus,the filling factor of the nanowire is given by f = w/p.
This simulation method models the absorption process of photons by an SNSPD as a plane wave interacting with an infinite grating, the validity of which is justified experimentally by Anant et al. [6] when the photon is normally incident, and the beam spot is smaller than the active detection area of the SNSPD. The illumination is defined by applying scattering boundary condition on the horizontal edges (AA0and BB0) of the unit cell, while Floquet periodical boundary conditions are applied on the parallel vertical edges(AB and A0B0) of the cell to reflect the periodical nature of the detector structure. The absorptance of the Nanowire A was calculated by piding the time-averaged resistive loss in the nanowire region by the incident power [6].
Table 1 Real (n) and imaginary (k) parts of complex refractive indices of materials (All data being measured in condition of wavelength of 1,550 nm) 下载原图
Table 1 Real (n) and imaginary (k) parts of complex refractive indices of materials (All data being measured in condition of wavelength of 1,550 nm)
In this paper, only the absorptance of typical 4 nm thick Nb Nnanowiresattelecommunicationwavelength1,550 nm with different incident media, cavity materials,and reflectors was studied. However, the results for other detecting materials at different wavelengths can be obtained as well using the analysis method given in this paper, if the refractive indices are replaced with corresponding values. The complex refractive indices of materials used in this study are listed in Table 1 [6, 24, 25].
3 Simulated results and discussion
In this section, the effects of incident media and cavity materials with different refractive indices on the Nb N nanowire’s absorptance were discussed. For simplicity,perfect reflector in the cavity structure was used by applying perfect electrical conductance boundary condition on the edge CC0. The Nb N nanowires simulated in this section are4 nm thick and 100 nm wide with 50 % filling factor.
Figure 2a shows the calculated absorptance of Nanowires A as a function of the cavity thickness h for different incident media (ni= 1–4) when nc= 1.444, which is the refractive index value of Si O2. It can be seen from the results that there exists a corresponding optimal value of h to achieve the maximum of absorptance Amaxunder different conditions.Interestingly, Amaxfor parallel-polarized photons Amax//increases with the decrease of ni, which means that frontillumination structure [19] with ni= 1 could obtain larger absorptance than back-illumination structure [18]. Figure 2b illustrates the variation of A with h × ncfor different cavity materials (nc= 1–4) with front-illumination structure(ni= 1). For parallelly polarized photons, all the curves have the peak at one point, that is, Amax//is independent of cavity material. In addition, cavity material plays a significant role in the maximum absorptance for perpendicularly polarized photons Amax⊥, and the absorption curves get closer to the parallel case when the ncincreases. Therefore, in order to achieve both large value of Amax//and Amax⊥, we should consider front-illumination structure with cavity made of high-refractive-index materials, such as Si.
4 Practical cavity-integrated SNSPD with frontillumination structure
Previously, Nejad et al. [26] realized front-illumination structure by integrating SNSPDs with optical cavity based on Ga As/Al As distributed Bragg reflector (DBR). However, owing to the limited refractive index difference between Ga As and Al As, the maximum absorptance is only 50 %, despite that the number of the DBR periods is up to14.5. In this section, we present two cavity-integrated SNSPDs with front-illumination structure using Si/Si O2DBR (DBR-SNSPD, Fig. 3a) or Au film (Au-SNSPD,Fig. 3b) as their bottom mirrors. The high-refractive-index of Si and thus the large refractive index difference between Si and Si O2enable us to realize almost perfect reflection with only four periods, which will be shown in the simulation results below. In addition, the high-reflectivity Au film also makes high absorption of superconducting nanowire possible, despite a little extra loss within the metallic film. Besides, the adoption of SOI substrates combined with wafer-bonding process [27] in the fabrication process would guarantee the quality of superconducting films, which can be directly fabricated on singlecrystal epitaxial Si layer, rather than deposited low-quality polycrystalline cavity material [19], and we expect that the epitaxial Si cavity would also improve the absorptance for perpendicular photons while maintaining the high-absorption for parallel photons.
Fig.2 Calculated absorptance of Nanowires A as a function of cavity thickness h for different incident media(ni=1–4)when nc=1.444 a;variation of absorptance with h × ncfor different cavity materials(nc=1–4)with front-illumination structure(ni=1)b
Fig. 3 Schematic drawings of practical front-illumination cavity-integrated SNSPDs: a DBR-SNSPD and b Au-SNSPD
Fig. 4 Plots of calculated absorptance as a function of filling factor f for DBR-SNSPD and Au-SNSPD compared with perfect-SNSPD a and for DBR4-SNSPD and back-illumination structured SNSPD using HSQ as cavity structure with Au mirror b
FEM calculations were again performed on the model as shown in Fig. 1b, but the perfect reflector was replaced with 100 nm Au or Si/Si O2DBRs with period number ranging from 1 to 4 (DBR1–DBR4). The input medium is air (ni= 1) while the cavity material is Si (nc= 3.48), and the optimized value of cavity thickness for all DBRSNSPDs is 224 nm, while for Au-SNSPD is 90 nm. The thickness of cavity is optimized to achieve the highest absorption for parallel photons, and the optimum thickness does not vary significantly with different value of f.
Figure 4a shows the calculated dependence of absorptance on Nb N nanowire filling factor f for constant values of p = 200 nm, d = 4 nm. Clearly, as the period number of DBR increases, the absorptance of the nanowire increases remarkably, and SNSPD with four periods DBR,that is DBR4-SNSPD, almost has the same absorption as
Fig. 5 Calculated absorptance of DBR4-SNSPD for parallel and perpendicular photons
SNSPD with perfect reflector, which means the reflectivity of DBR enhances with the increase of period number and DBR with four periods has almost 100 % reflectivity just as perfect reflector. Au-SNSPD has absorptance between DBR2-SNSPD and DBR3-SNSPD, and this is because there is a little extra resistive loss within Au film, making the absorption in nanowire decreases slightly. The DBR4-SNSPD was also compared with the back-illumination structure proposed by Rosfjord et al. [18], which comprises sapphire input medium, HSQ cavity, and Au mirror. Figure 4b shows the calculated absorptance A of these two structures as a function of Nb N nanowire filling factor f for constant values of p = 200 nm, d = 4 nm. The simulation results demonstrate that the absorptance for parallel photons increases from 68 % to 88 % for typical nanowire with 50 % filling factor due to the front-illumination structure of DBR4-SNSPD. On the other hand, the absorptance for perpendicular photons increases from 50 %to 83 % which is larger than that for the parallel case because of the high-refractive-index Si cavity compared with HSQ.
5 Polarization-independent SNSPD
In quantum information applications such as QKD, we need to place half-wave plates before the SNSPD if we want to get high performance since the polarization of the photon through the quantum channel is unknown and the detector is polarization-dependent, which increase the system loss and the bit error rate [9, 10]. Hence, SNSPD insensitive to the polarization-state has great significance in those applications. In this section, polarization-independent cavity-integrated SNSPD was proposed through cavity optimization.
Figure 5 shows the calculated absorptance of DBR4-SNSPD for parallel and perpendicular photons for constant values of p=200 nm,d=4 nm,and f=50%.Thanks to the high-refractive-index Si cavity,the curves of parallel and perpendicular case have a point of intersection at h=217 nm,where both the absorptances for parallel and perpendicular photons are 83%.However,it must be noted that the intrinsic efficiency for parallel photons is slightly higher than that of perpendicular photons,which was experimentally observed by Anant et al.[6].Though the origin of this difference is still unclear,we could take it into account by introducing a parameter s,which we define as
where ηintrinsic//and ηintrinsic⊥represent the intrinsic efficiency for parallel photons and perpendicular photons,respectively. From the simulation results shown in Fig. 5,we can see that there exists intersection between curves of A⊥and s 9 A//as long as 0 ＜s ＜6 %, and thus we could make the system efficiency of SNSPD equal for parallel and perpendicular photons, though the absorptance A reduces to 60 % at s = 6 %. Another approach is to use spiral-shaped nanowires [28, 29] to realize polarizationindependent but remove the influence of the difference in intrinsic efficiencies.
6 Conclusion
The effect of incident media and cavity material on the optical absorptance of optical-cavity integrated SNSPDs was systemically investigated by applying finite-element method on this simplified optical model. The simulation results demonstrate that, for photons with the electric fields parallel to the nanowire orientation, the maximum achievable absorptance increases with the decrease of the refractive index of input medium but is insensitive to cavity material. For photons polarized perpendicular to the nanowire, however, both the input medium and cavity material play significant roles and the absorption curves get closer to that of parallel case when the refractive index of the cavity material is larger. Under the guide of these results, we proposed two front-illumination cavity-integrated SNSPDs with DBR and metallic mirrors, respectively. The simulation results show that the absorptance for both parallel and perpendicular photons enhances compared with back-illumination structure, and the adoption of SOI substrate combined with wafer-bonding technique could guarantee the quality of superconducting nanowire which is directly fabricated on the top of the cavity layer.Finally, we presented a design that could realize polarization-insensitive SNSPDs with high absorptance, which is highly desirable in many areas of prospective research such as QKD and other quantum optics experiments. Compared with the 3D-SNAP proposed by the NIST group [12], this design could be applied to superconducting films such as Nb N, and the single layer of superconducting nanowires is beneficial to reduce dark count rates as well as timing jitter.
