Sensitive and Robust Millimeter-Wave/Terahertz Photonic Crystal Chip for Biosensing Applications

In recent years terahertz (THz) technology has attracted great interest in biosensing applications. Due to the interaction between analyte and electromagnetic (EM) field, a THz resonator is sensitive to changes in the refractive index of the analyte and can be used as a thin-film sensor for rapid pathogen diagnosis. To achieve high sensitivity and reliability, the sensor should have a high Q factor, a high field concentration at the site of the analyte, and the ability to compensate for temperature effects. However, conventional metamaterial methods have a low Q factor, which may lead to ambiguous detection and no attention has been paid to address the temperature effects. Here, we present a photonic crystal (PhC) based chip consisting of a reference channel and a sensing channel with two identical PhC slot resonators. The resonance difference between the resonators is temperature invariant and can be used for analyte detection. The dual-channel PhC chip has a Q factor of 5063 and a figure of merit of 3.1 /RIU/ $\mu \text{m}$ (RIU is refractive index unit), which are higher than that of metamaterial sensors. The chip is designed and simulated for the W band by 3D field simulations and is verified by measurements. Our results suggest that THz PhC resonators can provide high sensitivity and high resistance to environmental effects. We anticipate our work to be a starting point for future biosensing applications.

This article is organized as follows: In Section 2, 96 we present the structure design and simulation results 97 of the single resonator and the dual-channel sensor 98 chip. In Section 3, the fabrication and the experimental 99 setup are described. Section 4 presents the measurement 100 results in terms of sensitivity and temperature dependence. 101 Section 5 contains the conclusions. To achieve a high sensitivity and a high Q factor, a PhC res-105 onator with a slot in the middle is firstly designed as shown in 106 Fig. 1 (a). Based on this design, a PhC chip consisting of two 107 channels with the slot resonator in each channel is proposed 108 as shown in Fig. 2 (a). They are based on a PhC slab with a tri-109 angular lattice of air holes in a high-resistivity silicon (HRSi) 110 slab, which can be easily fabricated by micro-and nanotech-111 nology. HRSi is used because of its low loss (loss tangent = 112 0.00015) and high permittivity of 11.68 in THz regime [14]. 113 EM waves are reflected at each air/silicon interface and inter-114 fere with each other. This leads to a suppression of waves in a 115 hedral mesh type with adaptive mesh refinement was chosen.  Since an intuitive relationship between dimensions and 137 resonance frequency and Q factor, respectively, is not found, 138 the photonic crystal slab is studied with numerical tools by 139 sweeping structural dimensions [16]. In our work, the layouts 140 were designed iteratively in CST. In every step, we swept 141 the dimensions and observe the S parameters and electric 142 field distribution. After the desired properties were found, 143 we swept the dimensions with a finer step width to search 144 the optimum performance. Based on this guideline, we design 145 the resonator step by step: (a) finding an optimum photonic 146 crystal design, (b) building a resonator by removing holes, 147 (c) introducing a slot, and (d) shifting the holes near the 148 resonator to achieve an optimum Q factor. 149 We started to design the single slot resonator with the goal 150 to achieve a high Q factor and a high field concentration in 151 the slot. Three parameters define the PhC slab: the lattice 152 period p (the distance between the centers of two adjacent 153 holes), the radius of the holes r, and the thickness of the 154 slab t. These parameters determine the center frequency and 155 the bandwidth of the bandgap [15]. Considering the cost 156 effectiveness for the later fabrication, a standard HRSi wafer 157 with a thickness of t = 725µm was used. Hence, only the 158 parameters p and r were optimized in CST for maximum 159 bandgap bandwidth. For p = 1100µm and r = 400µm, 160 a bandgap which covers 75 GHz to 110 GHz was found. 161 In a second step, 5 holes were removed in the center of the 162 PhC slab to obtain a resonator with a high Q factor [17]. 163 Because the resonator has the largest field concentration in 164 the silicon, where the analyte under test cannot be placed, the 165 interaction between the analyte and electric field is limited. 166 To enhance the interaction and improve thus the sensitivity, 167 a slot is introduced in the middle of the resonator. Now, the 168 maximum electric field is in the air-filled slot as shown in 169 Fig. 1 (b). Thus, the thin film analyte can be placed on the 170 wall of the slot for detection.

171
The Q factor of the slot resonator depends on radia-172 tion losses, coupling losses with waveguides, and material 173 losses [15]. Among them, the radiation losses make the 174 largest contribution. Moving the adjacent holes around the 175 resonator can adjust electric field profile and reduce the radi-176 ation losses [17]. In this work, the first and the third adjacent 177 holes along the resonator were shifted towards the outside 178 with a displacement of S1 and S3, respectively. The second 179 hole was shifted towards the inside with a displacement of S2 180 as shown in Fig. 1 (a). The holes below and above the res-181 onator were shifted towards the outside with a displacement 182 of S4. The displacements of the holes and the width of the slot 183 were optimized in CST to achieve the maximum Q factor. 184 The optimized S1, S2, S3, S4 and the width of the slot are 185 219 µm, 50 µm, 120 µm, and 197 µm, respectively. As the 186 next step, waveguides and tapers were designed for excitation 187 and detection of the resonator. The waveguides were realized 188 by removing holes in a line. A short distance between the 189 waveguides and the resonator favors a strong coupling. This 190 leads to a high transmission magnitude but a low Q factor. 191 Here, the waveguides were placed three holes away from 192 the resonator as a trade-off between good coupling and a 193 high Q factor. To save space, the waveguides were aligned 194 with the resonator. Then, a taper transition connected to the 195 waveguide was built for the sake of minimal reflection and 196 efficient energy coupling between the PhC waveguides and 197 the WR10 rectangular metallic waveguides. The taper con-198 sists of a straight silicon waveguide with the same width as 199 VOLUME 10, 2022 the PhC waveguides and a taper with a continuous transition.   the captured bacteria forms a thin film with a thickness in the 255 micrometer range and changes refractive index on the sensor 256 surface.

257
The effect of the analyte on the resonance frequency can be 258 explained using the perturbation theory. Here, it is assumed 259 that the perturbated EM field can be approximated by the 260 unperturbed EM field, since the volume of the analyte is much 261 smaller than the resonator. The resonance shift f r due to the 262 analyte can be expressed by [15]: where V a is the volume of the resonator and V 0 is the volume 265 of the whole area including the resonator, the analyte, and 266 the surrounding air. It can be seen that the fractional change 267 in resonance frequency is related to the fractional change in 268 refractive index and the fraction of the electric field energy 269 in the analyte. The minus symbol means that increasing 270 in refractive index and the volume of the analyte result in 271 decreasing the resonance frequency.

272
The thin film analyte was modeled in CST and covers the 273 wall of the slot of the resonator as shown in Fig. 3. Because 274 the thickness of the PhC slab t = 725µm is much larger 275 than the thickness of the film, errors may occur during the 276 simulation. For a reliable result, the thin film analyte was set 277 as an independent mesh with fine mesh step width in the local 278 mesh properties. According to the results in [21], the real part 279 of the permittivity of different bacteria ranges from 2.75 to 280 4.11 at 1 THz. In our simulation, the refractive index n of 281 the analyte was changed from 1.0 (air) to 2.0 to simulate the 282 empty and analyte-loaded resonator.

283
First, the transmission parameter S21 of the resonator was 284 simulated with h a = 0.5µm and a variation of n from 1.0 to 285 2.0 as shown in Fig. 4 (a). The empty resonator (n = 1.0) 286 has a resonance frequency of f r = 91.108 GHz as shown in 287 Fig. 4 (a) (black line). The FWHM of the unloaded resonator 288 is 14.4 MHz. The Q factor is calculated to be 6327 by using 289 the expression [11]: (2) 291 With the increasing n, the transmission spectrum shifts to 292 lower frequencies as expected from (1). Since the volume 293  shift has a reciprocal relation to n as expected. To evalu-302 ate overall sensing performance for the thin film analyte, a 303 figure-of-merit (FOM) parameter regarding the unit thickness 304 of the analyte is defined as [3]: The FOM of the resonator with varying n is plotted in 307 Fig. 4 (b), where RIU is the refractive index unit. With (1), 308 the FOM can be expressed as We further investigate the effects of the analyte's thickness 317 by sweeping h a from 0.1 µm to 1 µm while keeping n = 1.5 318 constant. The resonance shift increases with increasing h a as 319 shown in Fig. 4 (c). In this case, the volume of the analyte 320 V a increases linearly with increasing h a . Since V a is much 321 smaller than V 0 , it is assumed that the electric field distri-322 bution is the same as the unperturbed field and the electric 323 field does not change along the thickness in the analyte. As a 324 results, the integration in the nominator is linearly related 325 to the thickness and the integration in the denominator is 326 constant. Then, (1) can be approximated by f r = B · h a , 327 where B is a constant. The resonance shift with varying h a can 328 be linearly fitted with a COD of 0.9941. Its COD is smaller 329 than that in the simulation with varying n, because the mesh 330 of the analyte can change with h a in spite of the setup of 331 the independent mesh. As a result, the calculated FOM is 332 between 5.6 /RIU/µm and 6.9 /RIU/µm. With the slope of 333 the resonance shift with varying thickness, the average FOM 334 is calculated to be 5.8 /RIU/µm. 335 Second, the PhC chip with two channels was investigated 336 by loading one resonator with the analyte as the sensing chan-337 nel and keeping the other resonator empty as the reference 338 channel. The transmission parameter S21 was simulated with 339 h a = 0.5µm and a variation of n from 1.0 to 2.0 as shown 340 in Fig. 5 (a). The frequency spectrum for n = 1.0 shows 341 that the empty chip has only one resonance at 91.130 GHz 342 with an FWHM of 18 MHz. The Q factor is calculated to be 343 5063, which is lower than that of the single resonator. The 344 reason is that the coupling between the waveguide and the 345 resonator of the two-channel sensor chip is stronger than in 346 the single resonator, which leads to higher coupling losses 347 and a higher transmission at the resonance frequency. The 348 resonance frequency of the sensing resonator is shifted to a 349 lower frequency. From n = 1.2, the S21 parameter starts 350 to show two peaks: one peak with a lower frequency f r,l 351 VOLUME 10, 2022 oscillation at f r,h . Fig. 5 (a) shows that the amplitude at f r,l 359 is greatly reduced, while the amplitude of the peak at f r,h is 360 similar to that of the empty chip and f r,h is slightly shifted 361 to lower frequencies. As n increases, f r,l shifts further to 362 lower frequencies and the amplitude increases slightly. This 363 is due to interference between the two resonators through 364 the air holes and the PhC waveguides [23]. As the refractive 365 index of the analyte increases, the resonance frequency of 366 the sensing resonator is further reduced and the interference 367 gets weaker. As a result, the amplitude at f r,l increases. The 368 interference is difficult to eliminate in passive components 369 with a small footprint. However, the resonance difference 370 between f r,l and f r,h can be easily used for analyte detection. 371 Additionally, the difference frequency of the two resonances 372 is temperature independent as both resonators act identically 373 to a temperature change. 374 Fig. 5 (b) shows the resonance difference with varying n. 375 For n< 1.3 the resonance peak at f r,h is not separated and 376 the resonance difference cannot be plotted. The resonance 377 difference increases as n increases. Similarly, the resonance 378 difference is fitted using a reciprocal function with a COD 379 of 0.9960 and the FOM is fitted using a reciprocal function 380 with a COD of 0.9830. The FOM ranges from 1.7 /RIU/µm 381 to 3.3 /RIU/µm, which is smaller than that of the single 382 resonator. The reason is that the decreased Q factor and the 383 interference between the two resonators depress the FOM. 384 However, to guarantee that the sensing resonator and the 385 reference resonator react to the temperature in the same 386 manner, their resonance frequency are designed identical. 387 In addition, the dependence on the analyte thickness was 388 investigated by sweeping h a from 0.1 µm to 1 µm while 389   HRSi wafer with a resistivity higher than 10 k cm for pro-418 totyping due to its low cost. During fabrication, the HRSi 419 wafer was cut by a high energy laser for fast prototyping. The 420 production was carried out by a waterjet-laser system. The laser and an ultrafine waterjet simultaneously. This process 424 makes it possible to produce parts accurately without damag-425 ing the material and provide high surface quality of the inner 426 sides of the cut holes. Structures larger than 30 µm with a 427 height-to-width ratio of up to 400:1 can be produced with 428 high accuracy. A precision of +/-1 µm is given from the 429 manufacturer. Fig. 8 (a) and (b) show the fabricated single 430 resonator and dual-channel sensor chip, respectively.

432
To investigate the sensing performance of the fabricated res-433 onator and chip, NaCl was used as the analyte. NaCl can be 434 easily resolved in water and washed off from the wall of the 435 slot in the resonator, so that the resonator can be reused for the 436 experiments. Furthermore, NaCl is easy to handle, and a high-437 level biological lab is not needed. Dry NaCl was resolved 438 in distilled water to prepare NaCl solutions with different 439 concentration (1, 2, 3, 5 and 10 µg/µL). In the experiments, 440 2 µL of the prepared solution were transferred using a pipette. 441 The solution was slowly dropped into the two holes connected 442 to the slot to prevent the liquid leaking to other places and let 443 the liquid flow into the slot. According to our observation, the 444 solution stays inside the slot and dries on the walls. After the 445 solution dried, only the NaCl stays on the walls with a weight 446 of 2, 4, 6, 10 and 20 µg on the resonator, respectively. After 447 resonator was characterized with different concentration of 483 NaCl solution as mentioned above. First, the single resonator 484 was connected to the network analyzer and the transmis-485 sion parameter S21was measured at room temperature. Then, 486 2 µL of the prepared NaCl solution was dropped in the slot of 487 the resonator using a pipette. A decrease of the maximum S21 488 was observed which is due to losses in the water. As the drop 489 dries, the transmission increases. The drying of the drop ends 490 when the S21 parameter becomes static. At this point, the S21 491 parameter was recorded. After that, the resonator was washed 492 with water to remove the dried NaCl and was dried to perform 493 the next measurement. This procedure was repeated 5 times 494 for each concentration of the solution and the mean value of 495 the measurement was calculated to minimize random effects. 496 An example measurement result from the single resonator for 497 a concentration of 5 ug/µL is shown in Fig. 10 (a). The empty 498 resonator has a resonance frequency of 92.070 GHz with a 499 FWHM of 15 MHz, which is in good agreement with the 500 simulated results. The Q factor was calculated to be 6138. The 501 loading of the dried NaCl results in a shift of the resonance 502 frequency.

503
The measured resonance shift increases with increasing 504 concentration as shown in Fig. 10 (b). As explained for the 505 simulation results with varying thickness of the analyte, the 506 electric field distribution is assumed to be unchanged in 507 the whole area and constant along the thickness of the analyte, since the volume of the analyte is much smaller than the 509 resonator. As a result, the resonance shift is linearly related 510 to the electric field energy in the volume of the analyte.

511
If the NaCl is uniformly distributed on the wall of the slot, 512 the resonance shift is linearly related to the volume or the 513 thickness of the NaCl. The linear relationship is shown in 514 the simulation results with varying thickness of the analyte 515 in Fig. 4 (c). On the other side, the measurement results with 516 varying concentration shows a high linearity. The measured 517 resonance shift with varying concentration can be linearly 518 fitted with a slope of 4.5 MHz/(µg/µL) and a COD of 0.9974.

519
The volume of the analyte is linearly corelated to the concen-520 tration as expressed:

522
where V drop is the volume of one drop of the solution, C is the 523 concentration and ρ is the density of dry NaCl. If the NaCl is 524 assumed to be uniformly distributed on the wall, the thickness 525 is linearly corelated to the volume as expressed:

527
where S is the area of the slot surface as shown in Fig. 3.

528
The thickness of the NaCl on the wall of the slot is calculated NaCl, while the reference resonator of the chip was kept 561 empty. A measurement result of the chip without the NaCl 562 (empty) and with dried NaCl from 2 µL of the solution with 563 a concentration 5 ug/µL is depicted in Fig. 11 (a). The empty 564 chip shows two resonance peaks: f r,l = 92.045 GHz and 565 f r,h = 92.098 GHz. The FWHM at f r,h is 20 MHz and the 566 Q factor is 4604. The reason, why two resonance peaks in 567 the transmission spectrum are present can be attributed to the 568 fabrication tolerance of the resonators. In particular, the width 569 of the slots plays a major role in the resonance frequency. 570 However, the resonance differences can still be used for the 571 analyte detection. Loading the sensing channel with NaCl 572 causes a shift of the lower resonance frequency f r,l and an 573 increase in amplitude as expected from the simulations. 574 Fig. 11 (b) shows the measured resonance differences, 575 which are linearly related to the concentration. The slope 576 of the linear fit is 3.9 MHz/(µg/µL). This corresponds to 577 1.95 MHz/µg or 39 MHz/µm of dry NaCl. The standard devi-578 ation of the resonance differences ranges between 0.5 MHz 579 and 2.7 MHz. With the estimation of the refractive index 580 of dry NaCl n = 1.55, the calculated FOM is between 581 2.6 /RIU/µm and 3.5 /RIU/µm as shown in Fig. 11 (b). With 582 the slope of the resonance difference, the average FOM is cal-583 culated to be 3.5 /RIU/µm, which agrees with the simulated 584 FOM (3.1 /RIU/µm). It is noted that the measured FOM is 585 slightly higher than the simulated FOM. One reason can be 586  air heater. The temperature was measured by placing a ther-611 mal probe near to the chip and recording the measured 612 temperature as shown in Fig. 9. The distance between the 613 heater and chip was adjusted to heat the chip to temper-614 atures from 26 to 42 • C. The measured resonance fre-615 quency of the single resonator decreases linearly as the 616 temperature increases as shown in Fig. 13 (a). This can be 617 attributed to the change in the refractive index and the thermal 618 expansion of the silicon [25]. The slope of the fitted line is - Fig. 13 (b) shows the transmission parameter of 620 the dual-channel chip for increasing temperature. Both reso-621 nance peaks shift to lower frequency in the same manner. The 622 resonance differences between both resonance frequencies 623 are calculated and plotted in Fig. 13 (c). The resonance differ-  the analyte to the sensor. Additionally, it will be interesting to 674 test other rapid prototyping methods with high permittivity 675 materials such as ceramic 3-D printing [27]. 676 Since 2021, he has been employed as a Researcher