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This article is an open-access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

This paper adopts Taguchi’s signal-to-noise ratio analysis to optimize the dynamic characteristics of a SAW gas sensor system whose output response is linearly related to the input signal. The goal of the present dynamic characteristics study is to increase the sensitivity of the measurement system while simultaneously reducing its variability. A time- and cost-efficient finite element analysis method is utilized to investigate the effects of the deposited mass upon the resonant frequency output of the SAW biosensor. The results show that the proposed methodology not only reduces the design cost but also promotes the performance of the sensors.

Owing to its many advantages of high sensitivity, simplicity, low cost and ability to perform rapid measurements, the piezoelectric quartz crystal resonator has been widely used as a mass sensitive detector in electrochemical experiments recently. The application of an alternating electrical field perpendicular to the surface of the piezoelectric quartz crystal (PQC) induces a mechanical vibration of the piezoelectric surface, whose frequency is changed by loading effects generated when a small mass is deposited on the resonator surface [^{−9} ∼ 10^{−15} g, a rapid response, low cost, small physical size, and a straightforward fabrication process [

SAW sensors consist of a thin ST-cut quartz disk sandwiched between metal electrodes and then coated with sensitive membranes. Traditionally, the design and development of these devices has relied heavily upon an experimental approach. However, the effects of operative error, or of faulty apparatus, are virtually impossible to eliminate in such a case. Consequently, discrepancies frequently exist between the design specification and the experimental results. Modern computer-aided design finite element method (FEM) techniques provide powerful simulation tools for the task of designing piezoelectric systems [

The Taguchi robust design method enables the main effects of certain designated design parameters to be evaluated. This method ensures the reproducibility of the experimental results and enables the optimum combination of design parameters (i.e. the control factors) to be determined from a minimum number of experiments. Taguchi parameter design can be divided into static and dynamic cases, in which the former case has no signal factor, while the latter has signal factors for the output optimization goals. Generally speaking, the accuracy of a measurement system is influenced by dynamic characteristics such as time-varying input signals or by the presence of noise [

Surface acoustic wave sensors are highly sensitive to mass changes on their surfaces. Even the deposition of a small mass on the surface of ST-cut quartz crystal in air causes a reduction of its original resonant frequency as shown in

The resonant frequency shift of a SAW sensor is directly proportional to the deposited mass per unit area, and hence provides an indication of the mass sensitivity of the device. In general, the sensitivity, _{1} =−9.33×10^{−8} m^{2}s/kg, k_{2} = −4.16×10^{−8} m^{2}s/kg are the mass sensitivity constant, _{0} is resonant frequency, and _{s}

Studies have shown that a robust measurement system has the following capabilities: 1) it minimizes variability as the input signal changes, 2) it provides consistent measurements for the same input, 3) it continues to give an accurate reading as the input values changes, 4) it adjusts the sensitivity of the design in transforming the input signal into an output, and 5) it is robust to noise [_{0}

This equation describes a straight line of slope

The dynamic S/N ratio is closely related to the static case and can be expressed conceptually in mathematical form as:
_{ij}_{j}_{o}

In _{i}

Dynamic robust design is an engineering methodology which renders a product or a process insensitive to the effects of variability. This methodology is applied during the research and development stage to ensure that high-quality products can be produced quickly and at low cost. The Taguchi method is an established robust design technique which has been successfully applied to the development of many products. The fundamental objective of robust design is to optimize the product and process designs such that they become insensitive to variations in the uncontrollable noise sources without actually eliminating these sources. The Taguchi method incorporates two principal tools, namely a S/N ratio to measure the quality of the design and an orthogonal array (OA), which permits the simultaneous consideration of many design parameters. In the SAW sensor, the frequency shift is related to the deposited mass via a linear

In the SAW design, the frequency shift value is treated as the characteristic value and is ideally as large as possible in order to enhance the detection capabilities of the device. Therefore, the present robust design case is defined as a dynamic larger-the-better problem and the main objective of the design activity is to maximize the S/N ratio defined in _{18}(2^{1}×3^{7}) orthogonal array as _{1}^{−9} g, _{2}^{−8} g, and _{3}^{−7} g, crossed with a three-level noise factor, i.e. _{1}^{0}, _{2}^{0}, and _{3}^{0}, where N is the cut angle of the quartz. It is noted that these noise factors represent the dimensional errors in quartz crystal cutting angle introduced during manufacturing.

In accordance with the design parameter combinations in the OA table, eighteen different SAW finite element models were constructed using the model presented previously by Wu [

In the two-step optimization of the current larger-the-better dynamic problem, the quality is first optimized by identifying the control factors which significantly influence the S/N ratio and the sensitivity, and then appropriate control factor level settings are established to reduce the variability and to increase the sensitivity of the measurement system. Two statistical analysis methods, namely, the Analysis of Mean (ANOM) and the Analysis of Variance (ANOVA) are utilized to establish the optimum design conditions. In order to obtain the optimum combination of design parameters, the control factor effects are analyzed using ANOM to identify the factors which are primarily responsible for inducing variation in the S/N ratio and in the sensitivity.

The results of these figures enable the optimum level of each control factor to be identified. The ANOVA approach is a mathematical technique commonly known as the sum of squares. Using this method, the relative contribution of each control factor can be estimated quantitatively and the overall measured response can be expressed as a percentage. In this study, ANOVA is used to identify the control factors which significantly reduce the variability and which bring the sensitivity toward its target value.

Having identified the factors which have a significant influence on the S/N ratio and sensitivity, appropriate settings of each design parameter must be chosen in order to reduce the variability and increase the sensitivity. However, if the design objective is to maximize the device sensitivity β and reduce variability, then from _{1}B_{2}C_{1}D_{2}E_{1}F_{3}G_{3}H_{2}. It can be seen that there is a contradiction between these two sets of results, and hence some degree of compromise is necessary. Of the five control factors, factor F can be considered as an adjustable factor whose setting is dependent on economic or manufacturing considerations.

The aim of this step is to verify that the optimum control factor treatment combination established in the above analysis is correct. It has been shown that the optimum factor level settings depend on whether it is the S/N ratio or the sensitivity β which is to be optimized. Two separate tests are conducted for verification purposes. In the first test, an additive model is used for prediction purposes, while in the second, a simulation experiment is performed. The optimum factor level settings for the original design are found to be A_{2}B_{2}C_{2}D_{2}E_{2}F_{2}G_{2}H_{2}, which compare to A_{1}B_{2}C_{1}D_{2}E_{1}F_{3}G_{3}H_{2} for the robust dynamic design. As shown in

The purpose of this paper has been to establish a dynamic measurement system design for a piezoelectric SAW biosensor. The following brief conclusions can be drawn:

This study represents the first time that the Taguchi dynamic design method has been integrated with computer simulation in the study of SAW devices. The results indicate that the adopted methodology enables the device sensitivity to be increased while reducing its variability.

FEM simulation is convenient, rapid, accurate, inexpensive, and straightforward to implement and learn. This technique provides a new and effective coupled field piezoelectric design tool.

The present robust dynamic design has confirmed that the control factors such as the thickness of sensor membrane, DDT, electrode thickness, No. of electrode finger pairs and the electrodes are essential design parameters in that they significantly influence the precision and sensitivity of the SAW biosensor. It is noted that for reasons of simplicity, this study has considered only a single noise factor. It is recommended that future studies implement more noise factors in order to reflect a more realistic working environment.

The financial assistance provided by the National Science Council Taiwan under contract NSC 93-2212-E-020-007 is gratefully acknowledged.

Stiffness matrix of Quartz

Piezoelectric strain matrix of Quartz

Permittivity matrix of Quartz

Piezoelectric stress matrix of ST-cutX

Permittivity matrix of ST-cutX

Schematic of SAW sensor model.

IDT_{S} structure.

Procedure of Taguchi analysis.

SAW sensor 3D geometry model.

SAW sensor 3D FE model.

(a) Half FEM model (b)FE simulation of Rayleigh wave propagation of SAW.

The S/N cause effects graph of control factors.

The gain cause effects graph of control factors.

Comparisons of original and robust design for sensitivity β analysis.

Control factor and level.

| |||
---|---|---|---|

A Types of ST quartz | ST-cutX Quartz | ST-cutY Quartz | |

B No. of electrode finger pairs | 20 | 40 | 60 |

C Delay distance (×10^{−3} m) |
95λ = 2.28 | 100λ = 2.4 | 105 |

D Electrode thickness _{e} |
1800 | 1900 | 2000 |

E Electrode overlay W(×10^{−3} m) |
5.76 | 6 | 6.24 |

F Types of sensor membrane | rubbery | glassy-rubbery | glassy |

G Sensor membrane thickness _{f} |
0.21 | 0.22 | 0.23 |

H dimensions of matrix(×10^{−3} m) |
9.8×6.8×1 | 10×7×1 | 10.2×7.2×1 |

L_{18}(2^{1}×3^{7}) Orthogonal array.

1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |

1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | |

1 | 1 | 3 | 3 | 3 | 3 | 3 | 3 | |

1 | 2 | 1 | 1 | 2 | 2 | 3 | 3 | |

1 | 2 | 2 | 2 | 3 | 3 | 1 | 3 | |

1 | 2 | 3 | 3 | 1 | 1 | 2 | 2 | |

1 | 3 | 1 | 2 | 1 | 3 | 2 | 3 | |

1 | 3 | 2 | 3 | 2 | 1 | 3 | 1 | |

1 | 3 | 3 | 1 | 3 | 2 | 1 | 2 | |

2 | 1 | 1 | 3 | 3 | 2 | 2 | 1 | |

2 | 1 | 2 | 1 | 1 | 3 | 3 | 2 | |

2 | 1 | 3 | 2 | 2 | 1 | 1 | 3 | |

2 | 2 | 1 | 2 | 3 | 1 | 3 | 2 | |

2 | 2 | 2 | 3 | 1 | 2 | 1 | 3 | |

2 | 2 | 3 | 1 | 2 | 3 | 2 | 1 | |

2 | 3 | 1 | 3 | 2 | 3 | 1 | 2 | |

2 | 3 | 2 | 1 | 3 | 1 | 2 | 3 | |

2 | 3 | 3 | 2 | 1 | 2 | 3 | 1 |

Simulation data of dynamic analysis.

_{1} |
_{2} |
_{3} | |||||||
---|---|---|---|---|---|---|---|---|---|

_{1} |
_{2}^{*} |
_{3}^{*} |
_{1} |
_{2} |
^{*} |
_{1}^{*} |
_{2}^{*} |
_{3}^{*} | |

5.9544 | 5.6137 | 4.9526 | 59.5442 | 56.1371 | 49.5256 | 595.4416 | 561.3709 | 495.2558 | |

7.1123 | 5.7219 | 4.9320 | 71.1227 | 57.2190 | 49.3202 | 711.2268 | 572.1900 | 493.2021 | |

5.5450 | 5.5383 | 5.3513 | 55.4500 | 55.3828 | 53.5127 | 554.4994 | 553.8276 | 535.1274 | |

5.4662 | 5.3247 | 5.2557 | 54.6623 | 53.2474 | 52.5567 | 546.6235 | 532.4737 | 525.5666 | |

5.4200 | 5.1293 | 4.9677 | 54.1996 | 51.2925 | 49.6774 | 541.9964 | 512.9252 | 496.7736 | |

6.3338 | 5.8331 | 5.3219 | 63.3379 | 58.3312 | 53.2185 | 633.3791 | 583.3116 | 532.1852 | |

6.8546 | 6.0335 | 5.3645 | 68.5457 | 60.3350 | 53.6445 | 685.4569 | 603.3505 | 536.4451 | |

5.7614 | 5.2287 | 4.7018 | 57.6145 | 52.2869 | 47.0182 | 576.1448 | 522.8694 | 470.1817 | |

5.7140 | 5.4216 | 5.2758 | 57.1402 | 54.2158 | 52.7585 | 571.4015 | 542.1579 | 527.5847 | |

5.7761 | 5.2158 | 4.9665 | 57.7609 | 52.1579 | 49.6647 | 577.6092 | 521.5794 | 496.6465 | |

6.4332 | 5.8204 | 5.5289 | 64.3322 | 58.2037 | 55.2894 | 643.3219 | 582.0373 | 552.8947 | |

6.3500 | 5.8675 | 5.2588 | 63.5002 | 58.6746 | 52.5882 | 635.0022 | 586.7465 | 525.8818 | |

5.9821 | 5.7190 | 5.6693 | 59.8209 | 57.1903 | 56.6933 | 598.2086 | 571.9030 | 566.9328 | |

5.9668 | 5.2947 | 4.4197 | 59.6676 | 52.9465 | 44.1973 | 596.6765 | 529.4654 | 441.9732 | |

6.8332 | 5.5468 | 5.0760 | 68.3321 | 55.4676 | 50.7604 | 683.3214 | 554.6763 | 507.6042 | |

5.6545 | 5.3507 | 5.0336 | 56.5454 | 53.5073 | 50.3358 | 565.4542 | 535.0729 | 503.3581 | |

6.1350 | 5.7287 | 5.4108 | 61.3502 | 57.2874 | 54.1076 | 613.5021 | 572.8741 | 541.0759 | |

5.8872 | 5.4612 | 5.1292 | 58.8720 | 54.6125 | 51.2920 | 588.7199 | 546.1248 | 512.9201 |

S/N Dynamic results.

^{11}) |
^{11}) |
||||||
---|---|---|---|---|---|---|---|

| |||||||

255982.28^{2} |
154.13 | 155.59 | 208368.03^{2} |
148.89 | 157.08 | ||

554690.05^{2} |
165.75 | 149.51 | 231941.75^{2} |
165.91 | 157.09 | ||

55255.11^{2} |
153.33 | 168.87 | 274784.63^{2} |
163.05 | 155.47 | ||

53940.54^{2} |
149.71 | 168.87 | 84458.61^{2} |
162.06 | 165.66 | ||

115161.77^{2} |
144.77 | 161.99 | 389818.28^{2} |
146.30 | 151.49 | ||

254263.75^{2} |
163.17 | 156.15 | 457088.89^{2} |
162.86 | 151.04 | ||

375054.86^{2} |
170.29 | 153.14 | 156034.23^{2} |
149.64 | 159.64 | ||

266243.53^{2} |
146.40 | 154.81 | 901749.61^{2} |
133.18 | 143.39 | ||

112131.85^{2} |
153.11 | 162.71 | 190940.61^{2} |
153.73 | 158.12 | ||

| |||||||

274328.24^{2} |
154.79 | 157.25 |

The results of ANOVA.

| |||||||
---|---|---|---|---|---|---|---|

| |||||||

59.2562 | 1 | 59.2562 | 12.5668 | 1 | 12.5668 | ||

45.6002 | 2 | 22.8001 | 166.5850 | 2 | 83.2925 | ||

164.4157 | 2 | 82.2078 | 192.4940 | 2 | 96.2470 | ||

7.3055 | 2 | 3.6528 | 248.9454 | 2 | 124.4727 | ||

70.2703 | 2 | 35.1351 | 300.8786 | 2 | 150.4393 | ||

40.1874 | 2 | 20.0937 | 83.0479 | 2 | 41.5239 | ||

334.6497 | 2 | 167.3248 | 92.9377 | 2 | 46.4689 | ||

13.5930 | 2 | 6.7965 | 240.5441 | 2 | 120.2721 | ||

17.9588 | 2 | 8.9794 | 205.9727 | 2 | 102.9864 | ||

| |||||||

753.2366 | 17 | 1543.9724 | 17 |

The comparisons of S/N ratio between original design and Taguchi design.

^{11}) |
163.81 | 175.26 | 11.45 |

149.89 | 170.08 | 20.20 |