Optical and Quantum Electronics

, Volume 45, Issue 7, pp 665–672 | Cite as

Crosstalk suppressing design of GaAs microlenses integrated on HgCdTe infrared focal plane array

  • Yang Li
  • Zhen-Hua Ye
  • Chun Lin
  • Xiao-Ning Hu
  • Rui-Jun Ding
  • Li He
Article

Abstract

In this study, crosstalk suppressing design of dielectric GaAs microlenses integrated on a traditional HgCdTe infrared focal plane array is presented, by exploiting the finite difference time domain technique. Responsive photocurrent of the objective pixel and crosstalk between adjacent detectors have been numerically simulated, using commercial TCAD software Apsys, for a mid-wavelength planar array with a pitch of 20\(\upmu \)m. By properly adjusting both the microlens radius and the absorber thickness, crosstalk can be notably suppressed to less than 1 % while the photoresponse is maintained or even enhanced.

Keywords

Microlens IRFPA Crosstalk suppressing FDTD method 

1 Introduction

The mercury cadmium telluride (HgCdTe) alloy has become one of the most important and widely used material systems among others (Guo et al. 2011, 2012) for infrared (IR) imaging applications, since its first synthesis in 1958 (Rogalski 2005; Hu et al. 2009, 2011; Hu et al. 2012; Yin et al. 2009; Ye et al. 2011; Wang et al. 2011; Chen et al. 2012; Li et al. 2012). The third generation HgCdTe IR detectors at present, despite no distinct definition, are commonly believed to feature large-format arrays, high operating temperature, multi-color detection and other flexible capabilities (Rogalski 2003). Unfortunately, as the pixel dimension is continuously reduced to achieve higher resolution, IRFPA detectors encounter a decreased optical efficiency as well as an increased spatial crosstalk. Large crosstalk may cause misleading signals at adjacent pixels, resulting in degraded device performance and illegible output images.

The magnitude of crosstalk depends on a number of factors that characterize the material properties and the device geometry (Musca et al. 1999; Dhar et al. 1998). For a conventional planar IRFPA, crosstalk can be partially suppressed by optimizing related parameters such as the minority carrier lifetime, but its actual effect is usually limited by its side effect of decrease in responsivity. To suppress crosstalk effectively, two methods have been developed concerning the device structure, i.e., mesa isolation and integrated microlenses (Kozlowski et al. 1999). Mesa isolation directly interrupts photogenerated carriers’ transport towards other pixels, but it may bring etching-induced damage that is relatively hard to completely recover for HgCdTe material. Microlenses integrated against photodiodes, on the other hand, can redirect and focus incident light into the central part of corresponding active regions, suppressing crosstalk by reducing the possibility of photogenerated carriers diffusing to neighboring detectors.

Both design and fabrication of such microlenses have been investigated for devices of various material systems including HgCdTe (Peake et al. 1997; Piotrowski et al. 2003; Huang et al. 2010; Guo et al. 2011). Different from most studies that are based on traditional geometrical optics, the finite difference time domain (FDTD) method is utilized in this paper to calculate the optical energy distribution inside the device, fully considering the wave characteristics of incoming radiation. Thereafter, the photoresponse and crosstalk of the microlensed HgCdTe IRFPA are computed through numerical simulations, and the optimal values of microlens radius and absorber thickness can then be obtained.

This paper is organized as below: a brief description of the device structure and the simulation method is given in Sect. 2; the simulation results are presented in Sect. 3, followed by a discussion in Sect. 4 and the conclusion finally in Sect. 5.

2 Model and method

Figure 1 shows the cross-sectional schematic of the microlensed HgCdTe planar array investigated in this paper. Three adjacent pixels, with a pitch of 20 \(\upmu \)m, are to be simulated in two-dimensional mode to enable evaluation of crosstalk. Each pixel comprises an \(n^{+}\)-on-\(p\) Hg\(_{1-x}\)Cd\(_{x}\)Te mid-wavelength (MW) photodiode (\(x=0.29\)) and a spherical microlens formed on the back of GaAs substrate. A 6-\(\upmu \)m-thick CdTe buffer layer partitions the active region and the substrate. The donor density in the ion-implanted \(n\)-type region is \(2\times 10^{17}\mathrm {cm}^{-3}\), and the acceptor density in the \(p\)-type absorption layer is \(8\times 10^{15}\mathrm {cm}^{-3}\). The width and depth of \(n\)-region are 18 and 1\(\upmu \)m, respectively, and the total thickness of GaAs substrate, including the height of lenses, is fixed at 21\(\upmu \)m. Thickness of the absorber and radius of the microlenses are chosen as adjustable parameters in this work. The device is modeled to operate at zero bias, 77 K, with the central pixel illuminated independently from backside through the corresponding microlens by 5\(\upmu \)m monochromatic IR plane wave. Thus the crosstalk can be evaluated as a ratio of the photocurrent at one most adjacent photodiode to that at the objective pixel itself.
Fig. 1

Schematic of the micro-lensed HgCdTe IRFPA to be investigated in 2D mode

At the first stage of simulation, light intensity distribution inside the device is determined through applying the FDTD algorithm, a recurrence algorithm based on the Maxwell’s curl equations (Keasler and Bellotti 2011). The refractive index of GaAs is 3.65, and the model we have invoked for the optical properties of HgCdTe can be found in Hougen (1989). An excitation source of 50 %-TE, 50 %-TM mode is adopted to simulate natural light, and the boundary condition of perfectly matched layer (PML) around the device is used to restrict the calculation in finite space. Once the light distribution (hence the optical generation rate) is available, photoelectrical characteristics of the detector array can be thereafter derived according to the Van Roosbroeck model, i.e., the coupled system of continuity equations, Poisson equation and the drift-diffusion current equations. Numerical calculations here are performed using commercial computer aided design (TCAD) package Apsys from Crosslight Software Inc., and all other indispensable parameters are set as presented in Rogalski (2005).

3 Simulation results

The Hg\(_{0.71}\)Cd\(_{0.29}\)Te active region has a relatively high absorption coefficient (\({\sim }5,000\,\mathrm {cm^{-1}}\) at 5\(\upmu \)m wavelength), and the incoming IR radiation will be largely absorbed within a thin layer near the HgCdTe–CdTe interface. As a consequence, variation in absorber thickness \(d\), compared with that in microlens radius \(r\), does not notably affect the light distribution inside the device. To put it another way, modeled devices with various \(d\)’s might share identical optimal value of \(r\), while it might not be the case contrariwise. Therefore, we will firstly determine the optimal value of \(r\) with a fixed \(d\), and later adjust the value of \(d\) to further optimize the device performance.

A series of simulations are carried out with \(d\) fixed at 7\(\upmu \)m while \(r\) changing from 13 \(\upmu \)m to infinite, and the calculated optical field distributions within the central pixel are partially depicted in Fig. 2. As can be seen, the incident light gets increasingly concentrated with decreasing microlens radius until \(r\approx 25\,\upmu \)m is reached, and then begins to disperse with even smaller \(r\). Correspondingly, the focusing spot of the microlens gradually moves from inside the HgCdTe layer (or even farther) to within the GaAs substrate. When \(r=25\,\upmu \)m, the focus is located right near the interface of CdTe buffer and HgCdTe absorber, producing a narrowest area for photoinduced carrier generation in front of the pixel center, in which case we expect that crosstalk can be suppressed at the most.
Fig. 2

Light energy distributions with different microlens radii

Figure 3a, b present the relative responsivity of the central detector and the crosstalk between most adjacent pixels, respectively, as a function of microlens radius \(r\) with various electron lifetime values from 2 to 100 ns. For an electron lifetime value of 100 ns, the responsivity of the central pixel without microlens is 1.644 A/W, corresponding to a low quantum efficiency of 40.6 %, which will be discussed later in Sect. 4. This value is viewed as unity in all figures throughout this paper where relative values of photoresponse are given. As illustrated in Fig. 3a, the responsive photocurrent basically exhibits an increasing tendency as \(r\) decreases until a maximum is obtained at \(r=18\,\upmu \)m. On the other hand, it can be seen from Fig. 3b that the minimum crosstalk value appears at \(r\approx 25\,\upmu \)m as we have expected, independent from the electron lifetime value. For an electron lifetime value of 100 ns, crosstalk between neighboring pixels can be suppressed to about 7 %, half of the value when no microlenses integrated, with the photoresponsivity enhanced by about 17 %. To achieve such an optimized effect, the microlens radius \(r\) can be adjusted within the range of 22–30 \(\upmu \)m, where the crosstalk and responsivity are both relatively insensitive to the change in \(r\).
Fig. 3

Simulation results for various electron lifetimes with \(d\) fixed at 7\(\upmu \)m. a Relative responsive current as a function of \(r\). b Crosstalk as a function of \(r\)

Having obtained the optimal microlens radius, we can next proceed to determine the appropriate values of absorber thickness \(d\). The simulated photoresponse and crosstalk as functions of \(d\) are displayed in Fig. 4a, b, respectively, for different electron lifetime values with fixed \(r=25\,\upmu \)m. The peak photoresponse appears somewhere in the range \(d=4\sim 5\,\upmu \)m for the lifetime value of 100 ns, and at smaller thickness values for shorter lifetimes, due to a balanced competition between photon absorption and carrier collection. Meanwhile, the crosstalk shows a strong dependence on \(d\) and rapidly decreases from about 10 % to 0.3 % with \(d\) changing from 9 to \(2\,\upmu \)m. Thus a crosstalk value of about 1.1 % can be obtained by using \(d=4\,\upmu \)m, simultaneously with the photoresponse almost at its maximum.
Fig. 4

Simulation results for various electron lifetimes with \(r\) fixed at 25\(\upmu \)m. a Relative responsive current as a function of \(d\). b Crosstalk as a function of \(d\)

We have also performed simulations on absorber thickness optimization without integrating microlenses for a comparison. Most results are qualitatively similar to those in Fig. 4, so we only plot the results when the electron lifetime equals 100ns in Fig. 5 to enable clearer illustration. We can find that for any \(d\) value the photoresponse of the microlensed IRFPA is overall increased by about 15 %, compared with that without microlenses. Moreover, it should be noted that crosstalk for the conventional planar IRFPA varies between about 20 % to 3 %, demonstrating a much weaker absorber thickness dependence than the microlensed IRFPA does in the same argument range. In a word, compared with conventional HgCdTe planar IRFPAs, the microlensed IRFPA can be optimized to have both 1.1 % crosstalk and 15 % higher responsivity, or to have crosstalk as low as 0.5 % at least without loss of photoresponse.
Fig. 5

Comparison of optimization results by adjusting absorber thickness, between a microlensed array and a conventional array. The electron lifetime is 100 ns

4 Discussion

Although this study is based on solution of differential equations, most of its results are still phenomenologically understandable by considering the Kamins-Fong model or the Dhar model (Dhar et al. 1998). In these models, the magnitude of crosstalk is notably influenced by the contrast between the field angles subtended by adjacent depletion regions viewing from the cite where a photoinduced carrier is generated. When incident radiation is focused so that carrier generation is restricted near the central CdTe–HgCdTe interface of the illuminated pixel, almost all photogenerated minority carriers have a largest angular field towards the objective depletion region but a smallest angular field towards side ones, leading to minimized crosstalk. It also explains the absorber thickness dependence of crosstalk as well as why this dependence is more considerable for a microlensed IRFPA than a conventionl one.

When optimizing the structure to suppress crosstalk, the subsequent side effect exerted on the responsivity needs balanced consideration. As shown in Fig. 3a, the integrated microlens is able to enhance the photoresponse; however, we can find that the total responsive photocurrent, including contribution from both side pixels, exhibits no evident increase until the lens radius \(r\) decreases to about 22\(\,\upmu \)m. That is to say, the increased photoresponse of the central pixel at \(r=25\,\upmu \)m arises mainly from the reduction in the photocurrent collected by side pixels, which have diverted about 22.4 % of the total responsive current and partially caused the low responsivity and low quantum efficiency without microlenses as mentioned in Sect. 3. The rise in the total photocurrent when \(r<25\,\upmu \)m possibly results from increased light absorption brought by successive mutual reflection between neighboring microlenses’ surfaces, which requires further investigation.

Similarly, when adjusting the absorber thickness \(d\), variation in the responsivity of the central pixel is also coupled with the change in crosstalk value. After checking Fig. 4, we find again that the peak total photoresponse appears at the thickness value about \(1\upmu \)m larger than what we have claimed previously for the maximum responsivity of the central pixel. In other words, thinning the absorption layer by this \(1\upmu \)m leads to more decrease in crosstalk than in total response so that the responsivity of the central pixel even increases. Therefore, we can infer that the optimal value of absorber thickness might be overestimated in those one-dimensional simulations or multi-dimensional simulations with one single pixel modeled, where crosstalk does exist but cannot be considered.

By now we have focused on a specific, representative configuration of planar IRFPA, i.e., an MBE-grown HgCdTe IRFPA with spherical microlenses exposed directly to vacuum. However, the principle and results presented still qualitatively apply to other types of planar IRFPA despite some quantitative differences. The microlenses are susceptible to real fabrication processes and not necessarily spherical, but they will still be effective against crosstalk as long as concentrating the incident light to the proper region. As another example, an LPE-made Hg\(_{1-x}\)Cd\(_x\)Te \(n\)-on-\(p\) IRFPA per se already has fairly low crosstalk because of its longitudinal built-in electric field that drives photo-generated electrons towards the junction and reduces the transverse diffusion (Dhar et al. 1998). For such an array, crosstalk can be suppressed even further by redirecting the incoming IR light to the central quasi-interface between the absorber and the transition layer (instead of a distinct substrate-absorber interface), only with the expectable difference that there would be no conspicuous increase in the objective pixel’s responsivity. Moreover, the low quantum efficiency presented in Sect. 3 is also considerably due to the GaAs substrate that keeps out about 30 % of the total light energy, since no antireflection coating is applied. We believe that this issue can be settled by an immersed microlens structure, which is to be designed in a similar way after noting the fact that the GaAs substrate would then have a smaller relative refractive index.

In this paper, we have also chosen to control the position of focusing spot by adjusting the microlens radius with a fixed substrate thickness. Of course, we can alternatively adjust the substrate thickness with a fixed microlens curvature to accomplish similar optimization results, since the key to suppressing crosstalk is to constrain the photoinduced carrier generation within a focusing region as narrow as possible at the central CdTe–HgCdTe interface. However, in both cases, the dependence of optimization results on the fixed parameter needs to be examined to allow tolerance for actual fabrication process. In addition, perpendicularly incident plane wave has been used to evaluate crosstalk, which may be different from the real case when the IRFPA operates with the optical system. Therefore, it remains our important future work to improve the current design for stronger flexibility and applicability.

5 Conclusion

A planar HgCdTe MW IRFPA integrated with microlenses against corresponding photodiodes is designed. Photoresponse of the objective detector and crosstalk between adjacent pixels have been numerically simulated by exploiting the FDTD method with TCAD software \(Apsys\). With appropriate radius value, the spherical microlenses can successfully reduce crosstalk to half its magnitude and meanwhile enhance the responsivity, by focusing the incoming infrared plane wave into a small region near the buffer-absorber interface. Moreover, adjusting the absorber thickness of the microlensed detector array further suppresses crosstalk. For the configuration in this paper, crosstalk can be optimized to be as low as 1.1 % with responsivity increased by about 15 %, or as low as 0.5 % without loss of photoresponse.

Notes

Acknowledgments

We thank C. S. Xia, Y. Sheng and M. Yang from Crosslight Software Inc., Shanghai Office for technical assistance and helpful discussions. We also acknowledge the support provided by the National Natural Science Foundation of China (Grant No. 6070612).

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Yang Li
    • 1
    • 2
  • Zhen-Hua Ye
    • 1
  • Chun Lin
    • 1
  • Xiao-Ning Hu
    • 1
  • Rui-Jun Ding
    • 1
  • Li He
    • 1
  1. 1.Key Laboratory of Infrared Imaging Materials and Detectors, Shanghai Institute of Technical PhysicsChinese Academy of SciencesShanghaiChina
  2. 2.University of Chinese Academy of SciencesBeijingChina

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