We present the concept, the fabrication processes and the experimental results for materials and optics that can be used for terahertz field-effect transistor detector focal plane arrays. More specifically, we propose 3D printed arrays of a new type – diffractive multi-zone lenses of which the performance is superior to that of previously used mono-zone diffractive or refractive elements and evaluate them with GaN/AlGaN field-effect transistor terahertz detectors. Experiments performed in the 300-GHz atmospheric window show that the lens arrays offer both a good efficiency and good uniformity, and may improve the signal-to-noise ratio of the terahertz field-effect transistor detectors by more than one order of magnitude. In practice, we tested 3 × 12 lens linear arrays with printed circuit board THz detector arrays used in postal security scanners and observed significant signal-to-noise improvements. Our results clearly show that the proposed technology provides a way to produce cost-effective, reproducible, flat optics for large-size field-effect transistor THz-detector focal plane arrays.
© 2016 Optical Society of America
Terahertz (THz) imaging has been demonstrated to be a useful tool in applications such as medical diagnostics, security, agriculture and nondestructive quality control [1–3]. The method, however, is problematic because of a lack of effective, powerful and low-cost THz focal plane arrays.
These arrays can be formed by micro-bolometers, Schottky diodes or by field-effect transistors (FETs) [4,5]. The last of these three types of detectors seems to have the most promising properties for producing the arrays because of the maturity of the FET technology [6–14] and recent reports describing the development of large size FET focal plane arrays [15,16]. The performances of FETs THz detector arrays can be improved by placing lenses in front of each detector. These lenses allow the radiation intensity on each sensitive element of the array to be increased while reducing the optical interferences between the detectors (i.e., optical crosstalk) at the same time.
A few reports about lens array fabrication can be found in the literature. They are mainly concerned with refractive optics-based lenses [17–21]. One of the most common elements is mechanically formed/polished lenses. These kinds of lenses are usually used in the case of the single separate detectors. However, they are impractical in the case of large size arrays in which the use of mechanically polished lenses is costly and impractical. These lenses are usually fabricated using silicon that exhibits high (n>3) refractive index leading to important Fresnel losses. Moreover, covering the hemispherical silicon lens by an anti-reflection (AR) coating is problematic. In addition, an important drawback of thick refractive lenses is geometrical aberrations .
Another approach to fabricating lens arrays is related to the matrix of the lenses manufactured by the multi-etch silicon process [17–21], which requires complicated and expensive multilevel etching procedures. For example, the anisotropic etching process required to achieve a depth of hundreds of micrometers is challenging technological task.
In this paper, we propose lens arrays for use in FETs THz detector arrays that have been designed using flat diffractive optics methods [23,24]. To the best of our knowledge this is the first demonstration of arrays consisting of THz diffractive multi-zone lenses arrays. The arrays were produced by employing 3D printing technology allowing for large-scale but low-cost production. Multi-zone design enables the thickness of the lenses to be reduced and the media attenuation to be decreased. Moreover, it leads to suppression of geometrical aberrations . It is worth mentioning that multi-zone lenses are especially useful in the case of sub-THz radiation detector arrays with a detector pitch of the order of a few millimeters. Such a matrix can be technically realized by placing/soldering separate detectors on the electronic printed circuit boards (PCBs).
The experimental validation of these THz lens arrays was performed using GaN/AlGaN high electron mobility transistors (HEMTs) [25,26]. We demonstrated that the 3D printed lens arrays show good uniformity and that the appropriate choice of the lens material and the lens geometry could significantly (more than one order of magnitude) increase the signal-to-noise ratios (SNRs) of the FET THz detectors arrays. Final validation of the 3D printed lens arrays was obtained by designing, manufacturing and integrating of 3 × 12 lens linear arrays with PBC technology FET THz detector arrays. This lenses and detector arrays integration enabled the SNR of the 300-GHz operating focal plane arrays modules to be improved by about one order of magnitude.
2. Lenses–design, materials, fabrication
A description of the design of lens arrays requires us to first consider a specific single lens shown in Fig. 1. When calculating the lenses dimensions one may consider two types of approaches: i) paraxial approximation and ii) a non-paraxial approach. Paraxial approximation means that focal length f is much longer than diameter d (circular) or side a (square shape) of the lens. In this case one may use a basic formula for the complex transmittance of the lossless flat element in Cartesian coordinates may be used:
Here x, y are the Cartesian coordinates in the plane of the lens and z is directed perpendicularly along the lens. We define the origin of the XYZ system in the middle of the lens (axe Z along the optical axe) with the z = 0 at the interface between the lens and its support (see Fig. 1).
In the non-paraxial approach, which requires radiation to be focused into the diffraction limited spot behind the lens for the expected spherical convergent wave, we can write the complex transmittance as:Fig. 1 two dimensional phase distribution (coded modulo π) for a non-paraxial approach f = 10 mm, a = 10 mm, 300 GHz (black – phase retardation 2π; white – phase retardation 0) is shown. Using Eq. (1) and Eq. (2) we estimate the phase error between the lens designed under paraxial approximation and a non-paraxial approach:Eq. (3) is shown in the lower part of Fig. 1. In the case of constant F# = 1 where F# is the ratio of the diameter (d) to the focal length (f) of the lens the phase error increases as the function of the focal length. For f = 10 mm, the error can be as high as 10%. Therefore design in the non-paraxial regime leads to reduction of geometrical aberrations and improves the focusing properties of the element.
The design and modeling of the lenses was performed using wave optics with a scalar approach that was developed as a part of our earlier works [25–27]. Propagation in the Fresnel zone (near field) was calculated by a modified convolution method [25,26], and the modeling was performed in a non-paraxial mode . Current considerations are devoted to cases of in which the plane wave but it may be generalized to illumination occurs. Generally, the matrices of lenses may include more sophisticated beam shaping . We assumed that the square 10 mm apertures were illuminated using a quasi-monochromatic plane wave with a wavelength of 1 mm (300 GHz). For the corresponding circular aperture with diameter d, the size of focal spot size is restricted by the diffraction limit ofEq. (2).
In Fig. 2 we show the XZ cross section (at y = 0) of the 3D radiation pattern of the lens, with f = 10 mm, a = 10 mm (shown in Fig. 1). In the middle part of Fig. 2 we show a few XY cross section scans calculated at constant values of z = 1, 2, 3, 5, 7, and 9 mm respectively. The points of the XY cross sections are marked by arrows on Z axis in Fig. 1.
Before the lens is manufactured, the 2D flat phase distribution should be converted to the local thickness of the 3D printable media. The maximal thickness h corresponding to the phase retardation 2π depends on the refractive index of the media and the wavelength according to:Fig. 1. Specifically, region A is a diffractive lens with a 1-mm-thick substrate layer, region B is an empty space, and region C is the base, in which the mounting hole for the detector (D) is located.
Various polymers can be used in the 3D printing process. Polymer materials have a frequency-independent refractive index in the 0.1 to 1 THz spectral range [29,30]. Based on our previous experience with 3D printed THz optics [27–29,31], we considered two kinds of polymers for the lens array fabrication process here: polyamide PA12 and the acrylate-based polymer EX200. These materials have refractive index values of n = 1.64  and n = 1.66 , respectively. The absorption coefficients for both materials were measured using a standard time-domain spectroscopy (TDS) setup [33–35]. The 300 GHz absorption coefficients were determined as being 1 cm−1 and 4 cm−1 for PA12 and EX200, respectively. Both of these polymers are relatively low-absorption materials, making them suitable for use in the design and fabrication of lenses. EX200 has higher losses (i.e., higher absorption), but it was also considered for lens fabrication because it offers superior mechanical parameters , making it more robust to mechanical damage and deformation, which is especially important for larger sized matrices.
We have used two manufacturing methods: Multi-Jet Printing (MPJ) and Selective Laser Sintering (SLS). MJP printers extrude melted materials, before plotting and forming an object layer-by-layer . In principle, although any thermoplastic material can be used in this 3D printing method , the printing quality is dependent on the melting point, the thermal expansion coefficient, and the elasticity of the material, and thus can vary significantly. The second technique is SLS , which uses the laser as the power source to sinter powdered material in a 3D object. The printing resolution of both methods is of the order of a few tens of microns and depends on the printing direction and the used material. Therefore, both techniques are perfectly suited to the production of series of customized quasi-optical components for the THz range, where the with wavelengths are higher than 100 µm . The 3 × 3 lens matrices were printed using a commercial 3D printer – selective laser sintering for PA12 and MultiJet printing for EX200. In Fig. 3 we show photographs of 3D printed THz lenses that were printed using PA12 with a square aperture of 10 mm × 10 mm. The front (Fig. 3(a)) and the back (Fig. 3(b)) views of the matrices are shown. The holes to be used for mounting of the detectors in the focal points on the backside of the matrix can be seen in Fig. 3(b).
3. Experiments and results
For all spatially resolved measurements, we used THz detectors based on GaN/AlGaN HEMTs that were fabricated in the Institute of High Pressure Physics of the Polish Academy of Sciences. The GaN/AlGaN heterostructures were grown by molecular beam epitaxy (MBE) on GaN/sapphire templates. The growth of the GaN/AlGaN heterostructures was performed at 730°C on GaN/sapphire templates in a VG90 Riber MBE system that was equipped with radio frequency (RF) plasma as an active nitrogen source. The metal-rich conditions (where a thin two-monolayer Ga layer was created and controlled) were used to achieve high quality growth of the GaN and AlGaN layers . First, a 0.5-µm GaN layer doped with Mg (to reduce the parasitic substrate conductivity) at a level of 5 × 1017 cm−3 was grown, followed by a 0.7-µm layer of pure GaN, a 30-nm layer of Al0.14Ga0.86N, and a 3-nm GaN cap layer. The room temperature mobility and the concentration of the two-dimensional electron gas were determined by standard conductivity and Hall measurements, using a six-contact Hall bar structure. The measured mobility and carrier density were 1690 cm2/Vs and 4.4 × 1012 cm−2, respectively.
In Fig. 4 we show the GaN/AlGaN HEMT layout. The transistors were fabricated using HEMT processes based on a laser writing-based photolithography method. The source and drain Ti/Al (20/100 nm) contacts were annealed at 600°C for 1 min under a nitrogen atmosphere. The gate was formed by a Ni/Au (25/75 nm) Schottky contact. The transistor gate length was 2 µm and the channel width was 10 µm. The total dimensions of the single-chip transistor were 400 µm × 260 µm.
In Fig. 4 we show the spectral characteristics of the GaN/AlGaN HEMT detector in the 265–375 GHz range. A sensitivity band (280 GHz–320 GHz) corresponding to the atmospheric window can be seen.
The radiation is coupled to the transistor chip through metallization pads that play the role of antennas, as proven by multiple experiments . As shown in our earlier work , the metallized antennas ensure that radiation not only couples to the transistor but also to the substrate. Different electromagnetic modes can propagate in a thick substrate. Substrates that are conductive cause a great part of incoming radiation to be lost. In the case of dielectric substrates of finite rectangular dimensions standing modes can be generated. In some cases this phenomenon is used to produce so-called “dielectric antennas.” The experimental results in Fig. 4 show relatively sharp resonances of the photo-response versus frequency, a clear indication of the standing modes in the 300 µm × 260 µm × 400 µm cuboid of the detector. A detailed analysis of the radiation coupling mechanism and its optimization is beyond the scope of this work.
The substrate modes may be critical for construction of the transistor focal plane arrays when all transistors are placed on the same wafer. They may lead, for example, to important crosstalk effects. Construction of the focal plane arrays with transistors on PCBs, as proposed in this work, makes it possible to avoid the problems presented by substrate modes.
One of the ways in which to avoid the propagating/standing modes in the detector substrate is to integrate the detector with a lens of the same refractive index (for example silicon). However, this solution is impractical in the case of PCB detector arrays because it requires a large number of expensive silicon lenses and their individual adjustment to each individual transistor. The approach used in this work is more cost effective and allows the SNR of each focal plane array detector to be improved by an order of magnitude.
This improvement is smaller than expected. Indeed, if we assume that the purpose of a lens is to extend the effective area of the detector, collect more power coming from the source, and effectively inject it into the detector, then maximal efficiency of the lens may be obtained by estimations of the lens and its surface. Given the dimensions in Fig. 4, the effective area of the lens corresponds to 79 mm2, which is approximately 50 times larger than the detector area. The measurements show that this lens only leads to an SNR improvement between 2.7 and 10 times. The fact that the lens efficiency is lower than expected may be attributed to the fact that in the proposed solution the light is propagated to the lens (refractive index ~1.5) then back to the air (refractive index is 1) and then to the detector (refractive index ~3). Material attenuation and loss resulting from reflection from interfaces (air-PA12, PA12-air, air-GaN) necessarily cause the focal point radiation intensity (lens efficiency) to decrease. These losses can be reduced by using special 3D printing that allows for a gradient in the refractive index and the full integration of the lens with the detector. In this way, transitioning between the air, lenses, and transistor media can be improved. Such a solution was recently presented by Zhou et al. .
It is important to emphasize that the dimensions of a single chip containing the FET THz detector are smaller than the wavelength corresponding to the 300-GHz radiation (wavelength ~1 mm). Therefore, such an FET THz detector was chosen for the spatially-resolved measurements of the lens matrices.
The matrices were tested using the optical setup shown in Fig. 5. A wide parallel beam was formed using a combination comprising one flat mirror and one parabolic mirror. The data were collected by a single GaN/AlGaN HEMT which was used to scan the radiation intensity along the X-, Y-, and Z-axes.
We performed focal plane scans by registering the detector signal with (S) and without lenses (S0). The intensity distribution (S/S0) that was obtained is shown in Fig. 6. Nine well-defined focal spots with dimensions close to the diffraction limit were registered. The distances between the focal spots correspond very well to the geometry of the matrices (the square aperture of a single lens is 10 mm × 10 mm).
A quantitative comparison (including material attenuation) of the different 3D printing matrices used for the lenses is provided in Table 1. The column on the right presents the ratio (quality factor) of the signal after the lens (S) to the signal without a lens (S0). Lenses fabricated from PA12, for which an intensity increase of one order of magnitude was observed, were found to have the highest quality.
The EX200 lens had an absorption coefficient of approximately 4 cm−1 and showed a relatively small lens-related improvement (less than a factor of 3). Because the refractive indexes of both materials are similar, we attribute this difference in efficiency to the fact that PA12 has a lower absorption coefficient (~1 cm−1). The advantage of EX200, however, is that it offers superior mechanical properties.
Indeed, we observed that optical elements fabricated from PA12 by using 3D printing and lens arrays with a surface exceeding 150 mm × 150 mm and a thickness below 2 mm never retained their flatness. That is, they had a tendency to undergo deformation around one of the diagonal axes – indicating the existence of an extent of internal uniaxial stress. Therefore, large-surface PA12 lens arrays require additional metal frames to retain their flatness (to ensure all lenses remain in the same plane).
In Fig. 7(a) we show four FET panels with lens arrays mounted in front of the detector arrays. They required mechanical fixation to PCBs. These lens arrays were used to enhance the SNR of an array of (3 × 12) FET detectors panels/modules manufactured using PCB technology. One of the panels (without lenses) is shown in Fig. 7(b). These detector panels were used in the postal scanner operating at 300 GHz [30,42,43].
We, indeed found, that the use of the 3D printed lens arrays improved the SNR of the scanner by about one order of magnitude.
In conclusion, we have reported the successful design, fabrication and characterization of 3D printed diffractive multi-zone elements, which have suppressed geometrical aberrations present at their refractive counterparts. We demonstrated that the printed lens arrays have very high yields and show good uniformity, and, by appropriately selecting choice of lens materials and geometries, it is possible to significantly improve the SNR of field effect transistor THz detector arrays. The final validation of the 3D printed lens arrays proposed in this work was carried out by designing, manufacturing, and integrating 3 × 12 lens linear arrays with FET THz detector arrays based on PCB technology. These arrays allowed us to improve the SNR of a postal scanner operating at 300 GHz by about one order of magnitude.
Our results show a clear path towards cost-effective, reproducible, uniform and less cumbersome (i.e., flat) optics for large-sized focal plane arrays, not only fabricated with Thy FETs THz but also with other types of detectors (bolometers, Schottky) detectors. Such THz plane arrays are required in multiple security screening and nondestructive quality control applications. Further improvement of the lens arrays may be obtained by using 3D printing to produce lenses with a refractive gradient index and by integrating the lenses with detectors in such a way as to reduce reflection losses at the lens/air and air/detector interfaces.
This work was partially supported by COST action MP1204 “TERA-MIR Radiation: Materials, Generation, Detection and Applications,” LIA-TERAMIR, the EU Regional Operational Programme, 2007-2013 Masovia (RMA.0101.00-14-04/11-00), the National Center for Research and Development in Poland (THzOnLine grant no. PBS1/A9/11/2012), the National Science Centre (Poland) project allocated on the basis of decision number DEC-2013/10/M/ST3/00705, and by the French Embassy in Warsaw, Poland, financing Doctoral Cotutelle.
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