Hotplates temperature distribution

At low temperatures the average temperatures ealeulated from the individual measurements eorresponded to the temperature setting. They were appreeiably lower at higher temperatures and it was found that the temperature setting eorresponded to the highest temperature that eould be reaehed in the individual measurements. It was also evident that the edge of the hotplate was eolder than the middle, i.e. the effeetive measured temperature was not the same everywhere over the surface of the hotplate a homogeneous temperature distribution is most likely to be found in the center of the plate. 

Heterocyclics 252, 260, 299,416 n-Hexadecanol esters 63 Hexaporphyrin 102 Hexitols 426 Hexobarbital 254,255 Hexoses 161,202 Hexuronic acid 158 Histamine 294,296, 355 Homogentisic acid 166,167 Horizontal chamber 127 Hotplates 93 ff -, temperature distribution 95 Hydrazines 269,284 Hydrazone formation 71 ff -with 2,4-dinitrophenylhydrazine 71, 72, 274... 

The general model assumptions and FEM implementations depend on the geometrical dimensions and the hotplate layouts. Most of the approaches are based on linear approximations, i.e., the temperature coefficients of the heat conductivity are not included. The temperature coefficients, however, are on the order of 10 /°C [103, 104], and will, depending on the geometry, noticeably influence the temperature distribution in the typical operating temperature range of 250-350 °C. 

In case of a homogeneous temperature distribution in the heated area, h corresponds to the temperature coefficient of the heater material, otherwise h includes the effects of temperature gradients on the hotplate. As a consequence of the aheady mentioned self-heating, the applied power is not constant over time, and the hotplate cannot be simply modelled using a thermal resistance and capacitance. Replacing the right-hand term in Eq. (3.28) by Eq. (3.35) leads to a new dynamic equation ... 

A homogeneous temperature distribution in the heated area is highly desirable to make sure that all sensing processes on the hotplate take place at the same defined and precisely controlled temperature. 

The electrochemical etch-stop technology that produces the silicon island is rather complex, so that an etch stop directly on the dielectric layer would simplify the sensor fabrication (Sect. 4.1.2). The second device as presented in Fig. 4.6 was derived from the circular microhotplate design and features the same layout parameters of heaters and electrodes. It does, however, not feature any sihcon island. Due to the missing heat spreader, significant temperature gradients across the heated area are to be expected. Therefore, an array of temperature sensors was integrated on the hotplate to assess the temperature distribution. The temperature sensors (nominal resistance of 1 kfl) were placed in characteristic locations on the microhotplate, which were numbered Ti to T4. 

P. Ruther, M. Ehmann, T. Lindemann, and O. Paul. Dependence of the Temperature Distribution in Micro Hotplates on Heater Geometry and Heating Mode , Proc. IEEE Transducers 03, Boston, MA, USA (2003), 73-76. 

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