Design of Plasmonic Coupler with Germanium Spacer Layer for Quantum Well Infrared Photodetectors

A design of a plasmonic coupler, composed of metal hole arrays and a germanium spacer layer, integrated with a quantum well infrared photodetector structure is presented. Insertion of a germanium spacer layer in this hybrid structure enhances absorption and the z-component of an electric field in the quantum well absorption region under both substrate-side and air-side illumination configurations. By changing thickness of the germanium spacer layer, the plasmonic resonance wavelengths can be adjusted with peak quantum well response. This plasmonic coupler is believed to be promising to improve performance of quantum well infrared photodetectors.


Introduction
Quantum well infrared photodetectors (QWIP) have received much attention for applications in night vision, environmental monitoring, and astronomy research [1]. The relatively mature GaAs technology makes QWIP a competitive candidate for long wavelength infrared (LWIR) detectors. However, the major drawback of QWIP is that it cannot detect light at normal incidence and it is only sensitive to an incoming electric field component normal to the QW surface [2] thus necessitates an additional optical coupling scheme to induce a preferred electric field component from normal incident light. Two-dimensional (2D) periodic or random gratings are widely used as an efficient coupling scheme for QWIP focal plane arrays (FPAs) [2,3]. However, realization of such optical gratings involves growth of a thick top grating layer and complex fabrication steps. Photonic crystal structures can also be used to enhance normal incidence absorption and thus detectivity of the QWIP, but suffers from sophisticated fabrication processes [4].
Recently, plasmonic optical couplers have gathered much attention for efficiently coupling the normal incident light to QWIP [5,6]. Integrating a plasmonic coupler, consisting of a simple 2D perforated metal hole arrays (MHA), with the QWIP structure, the performance of the photodetectors can be enhanced [7]. As the commonly used plasmonic metal such as gold (Au) acts as a perfect conductor in the LWIR (8-12 m) range, the surface plasmons excited at the metal/dielectric (semiconductor) interface by 2D MHA at this wavelength range are commonly known as spoof surface plasmons (SSP) [8]. The main challenge involved with the plasmonic coupler integrated with a QWIP structure, referred as a hybrid structure, is to place the active QW region within the SSP decaying field for efficient coupling. This restricts the use of a plasmonic coupler only in a thin QWIP structure [9]. However, for the LWIR range, SSP are loosely bound at the metal/semiconductor interface and the evanescent field penetrates up to few microns into the semiconductor in a typical QWIP structure [10]. In this hybrid structure, a heavily doped top contact layer of the QWIP has low permittivity in the LWIR range [5] and forms an antiguiding structure, resulting enhanced coupling of SSP into substrate radiation and thereby reducing their coupling to the absorber and thus the detectivity of photodetectors [10]. Similar substrate radiation losses have also been observed in a plasmonic coupled type-II superlattice (T2SL) structure due to a low refractive index of a T2SL layer [11].
In this work, a new plasmonic coupler composed of a 2D MHA and germanium (Ge) spacer layer integrated with a LWIR QWIP structure is presented. Insertion of a high refractive index Ge spacer layer between 2D MHA and a heavily doped top contact layer can confine the SSP to the metal/semiconductor interface and enhances absorption as well as induces a strong z-component of the electric field ( E z ) in the QW absorber region. Ge has been found to have good compatibility with n-doped GaAs as it is commonly used as an ohmic contact material and it can be easily deposited by e-beam evaporation [12].

Theoretical Model and Method
The QWIP layer structure considered for this study is shown in Fig. 1a. The layer structure from bottom to top consists of GaAs substrate, a 0.5-m n-doped GaAs bottom contact layer with N d = 1 ×10 18 cm −3 , the multiple quantum well (MQW) absorber consisting of 50 periods of 6.5-nmthick GaAs wells with doping, N d = 1 ×10 18 cm −3 , and 9.5 nm undoped Al 0.25 Ga 0.75 As barriers and atop 0.2 m n-doped GaAs top contact layer with N d = 1 ×10 18 cm −3 . A numerical model is developed based on the finite difference method (FDM) using MATLAB in order to solve self-consistent Schrodinger-Poisson equations. The absorption coeffiecient spectrum of the MQW absorber corresponding to bound-to-bound inter-subband transition of photo-carriers is depicted in Fig. 1b, showing peak absorption at = 9.7 m. Perforated 2D Au hole arrays or MHA are integrated on top of the QWIP structure. The period of the MHA with a square lattice structure, diameter of hole, and thickness of Au film are defined as p, d, and t Au , respectively. A Ge spacer layer of thickness t Ge is inserted in between MHA and an n + -GaAs top contact layer.
The relative permittivity of top and bottom n + -GaAs contact layers is calculated as where p is the plasma frequency defined by where n e , e, ε GaAs , and m * e are free carrier density ( N d =1×10 18 cm −3 ), electron charge, high frequency permittivity of undoped GaAs, and GaAs electron effective mass, respectively. The relative permittivity of the MQW absorber layer is calculated from composition and doping average of the constituent well and barrier materials. The relative permittivity of undoped GaAs, Ge, and Au is taken from ref. [13]. The relative permittivity versus wavelength for different materials used in the simulation is shown in Fig. 1c.
The numerical simulations were performed using Lumerical software package based on the finite difference time domain (FDTD) method. The periodic boundary conditions were adopted in x and y directions and the perfect matched layer (PML) boundary conditions were imposed at top and bottom boundaries along z-direction. Two hybrid structures have been studied and compared under substrateside and air-side illumination configurations. One is a QWIP structure integrated with MHA coupler and the other is the same MHA coupler with a Ge spacer layer inserted between MHA and the top contact layer of QWIP. For convenience, these two plasmonic couplers are referred to as MHA and MHA+Ge coupler, respectively.

Substrate-Side Illumination (SSI)
SSI configuration is compatible with conventional 2D FPAs which are flipped and light is incident through the substrate. In this configuration, incoming light is considered to be incident from the GaAs substrate-side. The SSP at the metal/semiconductor interface are excited directly from GaAs m * e the incident light, and the MHA can be optimized for SSP coupling without concerning about the transmission through the MHA. For the square lattice geometry of MHA on dielectric, the plasmonic resonant wavelength ( ij ) for normal incident light and field penetration depth ( ij ) into the dielectric can be written as [14] and where p is the period of MHA and i, j correspond to the orders of the wavevector, and m and d are relative permittivities of the metal and dielectric (i.e., air or semiconductor), respectively. Figure 2a presents the spectral absorption (=1-T-R, where T and R are the transmission and reflection, respectively) for MHA and MHA+Ge couplers corresponds to p = 3 m, d = p/2, t Au = 100 nm, and t Ge = 100 nm. The Au film is considered sufficiently thicker than the skin depth ( ∼ 30 nm at = 10 m) to avoid direct transmission. The absorption of the QWIP layers without MHA, called reference, is also plotted for comparison. Both MHA and MHA + Ge couplers have absorption peaks nearly at 10 m and 7 m corresponding to the first-and second-order resonance wavelengths, 01 and 11 ( ∼ 01 ∕ √ 2 ), respectively. The little difference in the resonance wavelengths Δ 01 = 0.017 m and Δ 11 = 0.016 m between these two plasmonic couplers is due to difference in relative permittivities of n + -GaAs and Ge layers. For this given period, 01 matches well with the peak absorption of the QWIP structure in the study. For the MHA+Ge coupler, the absorption at 01 is found to be nearly 3 folds higher than that for the MHA coupler. This can be explained on the basis of SSP coupling strength at MHA/ n + -GaAs and MHA/Ge spacer layer interfaces in the hybrid structure. In the LWIR range, as shown in Fig. 1c, the relative permittivity of n + -GaAs top contact layer is reduced due to free carrier contribution and a similar reduction in permittivity is also observed for the MQW absorber layer due to a combined effect of a lower refractive index of the Al 0.25 Ga 0.75 As barrier layer and free carrier contribution from doped QWs. These lower indexed layers confined between MHA coupler and higher refractive index GaAs substrate can act as a leakymode antenna [10] and couples SSP mode directly into the substrate, resulting in lower absorption in the QW region. However, by inserting a higher refractive index Ge spacer layer in between MHA and n + -GaAs top contact layer, MHA restores SSP mode and allows good coupling with the QW absorber layer through the evanescent field that results in the higher absorption. For 01 ≈ 10 m, 01 from Eq. (4) is ∼ 5.2 m for MHA+Ge coupler which is beyond the total QWIP layer thickness, indicating SSP mode coupling with an absorber layer. Also, the absorption enhancement at 01 for MHA and MHA+Ge coupler is found to be nearly 23 and 66 folds higher, respectively, with respect to the reference structure. Figure 2b presents the tuning of the plasmonic resonance wavelengths for MHA+Ge coupler by varying the periods of MHA. As predicted by Eq. (3), the linear dependence of the resonance wavelength with the period of MHA is obtained for different orders. This allows one to achieve perfect spectral overlapping between the plasmonic resonance and the peak QWIP absorption as well as to design multispectral QWIP. The symmetric arrangement of hole arrays in x and y directions makes this plasmonic coupler polarization insensitive as shown in the inset of Fig. 2b. The distribution of the E z field which is the preferred field component for the QW absorption for MHA and MHA+Ge couplers at 01 resonance is shown in Fig. 3. It is found that for the MHA+Ge plasmonic coupler, the E z field in x-y plane at metal/dielectric interface is more strongly confined around opposite edges of a circular hole, indicating dipolar-like plasmonic resonance [15] and a strong E z field in x-z plane almost covers the entire MQW absorber region as compared to those for the MHA coupler. To quantify the enhancement of the E z field at different locations of the QWIP structure for both MHA and MHA+Ge couplers, the quantity F is defined as: where |E z | and |E 0 | are the averaged z-component of the induced electric field and electric field of the normal incident light, respectively. The integration is performed over the entire x-y plane located at a distance (s) from the top n + -GaAs contact layer. As plotted in Fig. 4a, for the MHA+Ge coupler, the averaged |E z | 2 is nearly 15 times stronger than |E 0 | 2 at the center of the MQW active region and at the same location F is 5.5 folds stronger than that for the MHA coupler. For the QWIP, photocurrent is proportional to the averaged |E z | 2 across the entire MQW active region [16]. Therefore, in order to evaluate optical performance of the QWIP integrated with a plasmonic coupler, the coupling efficiency is defined as: where |E z | and |E 0 | have been defined previously. The integration is performed over the entire MQW active region. It is found from Fig. 4b that is nearly four folds stronger for MHA+Ge coupler than that for the MHA coupler at 01 resonance. Hence, an improvement in performance of the QWIP with MHA+Ge coupler is expected.
The tuning of the plasmonic resonance wavelength is also studied by changing the thickness of the Ge spacer layer. As shown in Fig. 5, both 01 and 11 are redshifted with an increase of Ge spacer layer thickness. The redshift is found to be smaller for t Ge ≤ 150 nm and relatively larger for the thicker Ge spacer layer. The resonance wavelength, 01 , is shifted from 9.98 to 10.3 m as the thickness of Ge spacer layer is increased from 50 to 300 nm. However, as the thickness of spacer layer increases, the separation between plasmonic coupler and active region also increases and as a result E z field intensity in Fig. 2 a Absorption spectra for MHA and MHA+Ge plasmonic coupler integrated with QWIP structure at normal incidence under SSI configuration, corresponding to p = 3 m, d = p/2, t Au = 100 nm, and t Ge = 100 nm. Inset shows the period corresponding to the two resonances. The dashed line is the result for the reference structure without plasmonic coupler. b Absorption spectra for the MHA+Ge coupler with different periodicities (p). Inset shows the polarization dependent absorption spectra for p = 3 m the active region decreases. The shift in the resonance wavelength is attributed to change of effective dielectric constant of the dielectric layers. Since the plasmonic field penetrates through the entire QWIP structure including high refractive index Ge spacer layer, the plasmonic resonance strongly depends on the effective dielectric constant of all the dielectric layers. Therefore, with increase in Ge spacer thickness increases the effective dielectric constant of dielectric layers and hence the resonance wavelengths. This allows one to adjust the plasmonic resonance with peak QWIP response without changing MHA lithography masks.

Air-Side Illumination (ASI)
ASI configuration is suitable for single pixel detector characterizations, where light is incident from the air-side (i.e., top side) and hence the critical substrate removal step [17] is not required. In this configuration, the excitation of SSP occurs at both air/metal and metal/semiconductor interfaces. The SSP at the metal/semiconductor interface which is of interest is excited by evanescent waveguide mode through 2D MHA [18] and the corresponding resonance wavelength lies within detection spectrum of the QWIP. Figure 6 presents the absorption spectra for MHA and MHA+Ge couplers in ASI configuration where all the design parameters are kept the same as used in SSI configuration. The resonance wavelengths, 01 = 10.03 m and 11 = 7.07 m for the MHA+Ge coupler, are nearly the same as those obtained in the SSI configuration, suggesting SSP excitation at the metal/semiconductor interface. However, the absorption is found to be lower for both MHA and MHA+Ge couplers as compared to the SSI configuration. This is attributed to the evanescent decay of field intensity at the metal/semiconductor interface. At the air/metal interface, 01 and 11 are found to be 3.04 m and 2.15 m, respectively, which are beyond the detection spectrum of the QWIP. In this configuration, the MHA+Ge coupler is also found to be effective and enhances the absorption by nearly two folds at 01 than that for the MHA coupler as shown in Fig. 6. Also, the MHA+Ge coupler induces 2.4 times stronger E z field intensity at the center of the MQW absorber region as compared to the MHA coupler as shown in the inset of Fig. 6. It is also found that the absorption increases with decrease in the thickness of MHA or Au film as shown in Fig. 7. This may be because evanescent field intensity Fig. 4 a Field enhancement factor, F over x-y plane as a function of distance (s) away from the top n + -GaAs contact layer for MHA and MHA+Ge couplers at the peak resonance wavelength, 01 . b Coupling efficiency, over entire MQW active region versus wavelength for MHA and MHA+Ge couplers, corresponding to p = 3 m, d = p/2, t Au = 100 nm, and t Ge = 100 nm. The shaded region in (a) shows MQW active region  Absorption spectra for MHA and MHA+Ge plasmonic couplers integrated with QWIP structure at normal incidence under ASI configuration, corresponding to p = 3 m, d = p/2, t Au = 50 nm, and t Ge = 100 nm. Inset shows the quantity F over x-y plane as a function of distance (s) away from the top n + -GaAs contact layer for these two couplers at = 01 . The shaded region shows MQW active region increases through thinner MHA and excites SSP at the metal/semiconductor interface.

Conclusion
A design of plasmonic coupler composed of 2D MHA and Ge spacer layer for QWIP is presented. Insertion of Ge spacer layer between MHA and QWIP structure enhances absorption and E z field intensity in the QW absorption region. For the MHA+Ge coupler, the absorption is found to be 3 folds higher than that for the conventional MHA coupler at the resonance wavelength, 01 ≈ 10 m under SSI configuration, while the averaged |E z | 2 is 15 times stronger than |E 0 | 2 at the center of the QW absorber region. However, for ASI configuration, the absorption and field enhancements are limited due to decay of evanescent field intensity at metal/semiconductor interface and these can be maximized with thinner Au film or MHA. The tuning of plasmonic resonance wavelength by changing the thickness of Ge spacer layer allows one to adjust the plasmonic resonance with peak QWIP response without changing MHA lithography masks. This plasmonic coupler is believed to be promising to improve performance of LWIR QWIP FPAs.