MODEL-BASED OPTIMIZATION OF AN INFRARED GAS SENSOR

MODEL-BASED OPTIMIZATION OF AN INFRARED GAS SENSOR ABSTRACT Ingo Sieber Forschungszentrum Karlsruhe P.O. Box 3640 76021 Karlsruhe Germany sieber@iai.fzk.de Manufacturing test structures of microsensors and microactuators is very expensive in terms of time and materials. In a conventional design process, this limits the number of design variants to be considered. For this reason, computer-supported design techniques are becoming increasingly important in microsystems technologies. The modular structure of hybrid systems requires single components to be manufactured separately and later combined into one total system. Combining single components into one overall system is bound to be subject to certain tolerances. The concept presented in this paper is the computer-- aided design of a modular system rugged enough to be employed in mass fabrication. In mass fabrication, it is not the ideal arrangement of individual components which results in the most effective system. Instead, tolerances in positioning individual optical elements need to be taken into account in modeling already. KEY WORDS Physically-based modeling, simulation optimization, applications, optics simulation 1. Introduction The approach pursued in this article serves to develop a parametrizable model for simulating a large number of possible design variants. This aspect makes for a fast, low-cost systems development, as it allows to minimize the production of laboratory models, a process expensive in terms of time and costs. Moreover, the parametrizable model allows all parameters defined to be optimized in the design. The goal of optimization, in addition to maximizing system performance, can also be an arrangement of the individual components, which results in a system rugged enough to be employed in mass Karl-Heinz Suphan Micro-Hybrid Electronic GmbH Heinrich-Hertz-Straße 8 07629 Hermsdorf Germany fabrication. This means, fabrication tolerances as well as tolerances in positioning individual optical elements need to be taken into account in modeling already. This approach will be applied to an IR gas sensor. Operation of IR analyzers is based on the absorption of certain wavelengths of infrared radiation specific to individual gases. In the wavelength range of 3.0-5.2µm, the characteristic absorption bands of many gases and vapors allow to set up measuring systems combining an IR source, an absorption cell, a wavelength filter (or spectrometer, respectively), and a detector element (Fig. 1). Quantified IR gas analysis employs the Lambert-Beer law, in which absorption is described as a function of the thickness of a layer (and the ray path in the medium to be measured, respectively), the type of molecule, and the concentration of a dissolved substance, which for a constant temperature is proportional to the partial pressure p. The IR radiation passes through the absorption cell (or analysis chamber) on a path of the length, d. In this course, the radiation intensity, I 0,λ, before entering the specimen is reduced to a radiation intensity, I λ, after leaving the specimen. With these quantities, the Lambert- Beer law can be formulated as follows [1]: log I λ = ε cd = E with: I 0λ E = extinction ε = extinction coefficient c = concentration of substance d = beam path in the substance On the basis of these rules, any component in a mix can be determined quantitatively from the IR spectrum, provided that a sufficiently intense absorption band can be found which is not disturbed, or disturbed only to a known extent, by the other components in the mix or by the solvent. IR source Wavelength filter Detector Electronics Absorption cell Figure 1: Schematic representation of an IR gas sensor

This paper is organized as follows: At first, a general description of the IR gas sensor is given. The next two sections deal with the modeling and simulation of the optical components of the gas sensor and the optimization of the geometry of the absorption cell regarding the system s tolerances. The optimization will result in a rugged and stable system design, which can be employed in mass fabrication. 2. The IR Gas Sensor The cost reduction achieved in the last few years with regard to IR components like e.g. sources, optics, and detectors, makes IR measurement increasingly interesting for a broad field of applications. The increasing spread of cost-optimized motion and position detection systems on the basis of pyroelectric IR detectors reflects this trend. A similar development, including an analogous cost reduction, is expected for single gas detectors on the basis of IR gas sensor systems. Fields of use of IR gas sensors are in the surveillance of buildings, mainly in air-scanning purposes of individual rooms. On the other hand these sensors can be employed in environmental measuring techniques. Therefore, application as CO 2 sensor is the primary subject of investigation. Maximum transferability of the results to other gases (e.g. hydrocarbons, CO...) is envisaged. The non-dispersive IR gas sensors (NDIR) considered below allow concentrations of gases to be measured through IR absorption. In the form most commonly used today, the analysis chambers are linear arrays in which the IR emitter and the IR detectors are situated at opposite ends. However, the linear, mostly relatively short ray path is a major constraint in the practical application of these sensors, as the gases to be detected must have a certain minimum absorption. To detect of weakly absorbing gases, the optical ray path in the analysis chamber therefore needs to be extended. If the geometric dimensions, which often are restricted, are to be retained, this can be achieved only by convoluting the ray path and adding additional reflecting elements. The integration of beam-focusing elements is becoming increasingly important in this connection, on the one hand, to achieve sufficient loading of the detector and, on the other hand, to reduce the proportion of rays which, as a result of unintended reflections, have undefined ray paths when incident upon the detector. The disturbing rays with the shorter path lengths act as noise signals relative to the gas sensitivity of the sensor. A thermopile infrared radiation sensor acts as detector. Thermopile sensors belong to the class of thermal infrared sensors [2]. It is common to all detectors of this class that the incident radiation causes a temperature difference between the absorbing medium and the heat sink. This working principle implies that thermal sensors respond unselectively to a wide spectral range and do not require cooling. In thermopile sensors the temperature increase is converted into an electrical signal by means of the Seebeck effect. In order to ensure system stability in the time domain and under changing ambient conditions, the classical gas sensors have an additional reference ray path which, when the same detectors are used, is tuned to a wavelength that, if possible, cannot be influenced by the gas measured. However, as the applications initially considered require regular absolute calibration of the gas sensors, the sensors needed for this purpose are designed as single-beam systems in order to avoid the costs associated with the reference channel. A special clock pulse of the sensor ensures a sufficient system`s stability by using the measured dark quantities as correction values for subsequently measured values. For this reason the signal processor including the controller interface, is an integral part of the sensor system. Interface Detector 3. The Optical Model Source Figure 2: Photograph of a test system of the IR sensor and the controller interface. The subject of optical modeling is to find a description of the IR source and the gas analysis chamber by means of a parametrizable optical model. 3.1 Modeling of the IR Source The IR source consists of a broad-band IR lamp and the lamp reflector. The reflector serves to limit the beam divergence in order to ensure a defined ray path length around a mean distance. In order to adapt the emission characteristics of the source model to the real IR source, measurements were conducted with the incandescent IR lamp [3].

3.2 Modeling of the Absorption Cell The characteristic absorption by the gas to be detected takes place in the analysis chamber. The chamber is therefore, considerable costs. To provide for a cheaper fabrication, an automated assembly of the absorption cell with the source-module and the detecting-module is necessary. The approach to optimizing of system Figure 3: Photograph of the gas analysis chamber (left) and the parametrizable model (right). The reflecting surfaces modifying the beam are shown clearly. designed to match the specific absorption properties of a single gas, i.e. the chamber is tuned to detect a single gas. To detect even weakly absorbing gases, the ray path through the analysis chamber must be extended. As this is to be achieved without a significant increase in the dimensions of the analysis chamber, the boundary surfaces of the chamber must be equipped with a reflective coating and fulfill focusing tasks. Figure 3, on the left-hand side, shows a photograph of the gas analysis chamber. The beam-focusing structures as well as the beam-folding parts (i.e. plane reflecting surfaces causing no beam modifications) can be seen. The analysis chamber in Figure 3 is equipped with a sensor chip (a thermopile element) visible on the right-hand side of the photograph, and also the source inlet can be seen as a circular section on the left-hand side of the chamber bottom. The figure on the right shows the model of the chamber for comparison. Here, the focusing surfaces are also clearly visible. The plane surfaces for beam folding serve as lateral boundaries of the chamber. In Figure 3 these interfaces are not shown to enable view into the interior of the analysis chamber. The optical model of the IR source and the analysis chamber allows the calculation of the ray emission from source to detector in a non-sequential description [4]. On basis of this model, investigations of ray propagation and the raypaths inside the analysis chamber were carried out. Parameter simulations demonstrated the sensitivity of the actual design of the analysis chamber regarding the exact position of the source [4]. The light sources used in the sensor showed a strong uncertainty in the position of the source s filament. This position tolerance of the filament is 1mm. To ensure the functionality of the IR source despite of these oscillations in positioning, the light source has to be assembled actively by means of a power measurement [3]. This procedure is time- consuming and requires a considerable personnel expenditure and, therefore is to find a design of the analysis chamber, which is optimally rugged regarding the system s tolerances. 4. Optimization of the Geometry of the Absorption Cell 4.1 Starting Model for Optimization The starting model for optimization is shown in Fig. 4. It consists of four reflectors: The first reflector has the task of collimating the source s radiation, the second reflector focuses the collimated beam on the detector module. Reflectors three and four are plane mirrors and only serve to convolute of the beam in this starting model. In this model of the absorption cell 86% of the calculated rays hit the detector surface in case of an ideally positioned source. The irradiance distribution for this arrangement is shown in Fig. 5. Mispositioning of the source by half the tolerance range leads to a hit rate of rays on the detector of only 1%. The irradiance distribution of this configuration is shown in Fig. 6. On the basis of this starting model, optimization of the absorption cell s geometry was carried out. The goal of the optimization was to find a rugged design with a consistent and satisfactory performance in the whole tolerance range of source positioning.

Reflector 2 Reflector 4 Reflector 1 Reflector 3 Figure 4: Starting model of the absorption cell. For optimization the following parameters were defined as variables: 1 the position of the reflectors to each other 2 the curvature of the reflectors 3 the source position inside reflector 1 Figure. 6: Irradiance distribution of the starting model in case of a mispositioning of the source of half the value of the tolerance range. 4.1 Optimization In a first step, the shape of the source reflector was optimized in a way that the performance was nearly the same over the entire tolerance range (see Fig.7). The model of the optimized source reflector was inserted into the starting model for optimization of the chamber geometry. Figure 5: Irradiance distribution of the starting model in case of an ideal positioning of the source. Boundary conditions of the optimization runs were the physical dimensions of the chamber, the distance between source and detector, and the ray path inside the chamber. Figure 7: Optimization of the source reflector regarding the position tolerances of the source. In the further cycle of optimization, the plane reflectors 3 and 4 were processed at first, followed by all four reflectors. The resulting optimized model is shown in Fig. 8. Remarkable is the conservation of its plane shape by reflector 3, i.e. reflector 3 only serves as a convolution element of the beam. The most significant change is obvious for reflector 4, which is strongly curved in both x- and y-direction.

References Figure 8: Optimized design of the absorption chamber. Figure 9 shows the irradiance distributions for three positions in the tolerance range. From left to right, the first and third distributions are calculated for the upper and lower boundary of the tolerance range, respectively. The second distribution is determined for the center position of the tolerance range. [1] H. Günzler, H. Heise, MIR-Spektroskopie. (Weinheim, Germany, VCH, 1996) [2] E. Kessler, U. Dillner, V. Baier, J. Müller, A 256 pixel linear thermopile array using materials with high thermoelectric efficiency. ITC 97, 16th International Conference on Thermoelectrics, Dresden, Germany, 1997, 734-737 [3] I. Sieber, H. Eggert, K.-H Suphan, S. Bechtold, Simulation and Modeling of a Chamber of Analysis of an IR Gas Sensor. MICRO SYSTEM Technologies 2001, Düsseldorf, Germany, 2001, 71-76 [4] I. Sieber, H. Eggert, K.H. Suphan, O. Nüssen, Optical Modeling of the Analytical Chamber of an IR Gas Sensor, Design, Test, Integration, and Packaging of MEMS/MOEMS 2001. Proc. of SPIE, Vol. 4408, Cannes, France, 2001, 272-282 Figure 9: Irradiance distribution of the optimized design for three positions of the source inside the tolerance range. The optimized design of the analysis chamber reaches a yield of 30% of the propagated rays on the detector in the whole tolerance range of the source position. Therefore, the optimized design ensures a defined system performance in the whole tolerance range and enables an automated assembly of the analysis chamber. 5. Conclusions A fundamental approach to conceiving a system model of an IR gas sensor was presented in this article. In the first part, modeling and simulation of the analysis chamber were discussed. The second part dealt with the optimization of the optical model of the absorption cell and the IR source. The goal of the optimization was to find a rugged design regarding the position tolerances of the source. Use of the original design of the gas sensor makes it necessary to assemble the source manually by means of a power measurement. The optimized design ensures a well-defined performance over the entire tolerance range of source position. This allows for an automized assembly of the analysis chamber.