Model performance improvement for a calibration-free temperature measurement based on p±n junctions Olfa Kanoun * , Hans-Rolf Tra Ènkler Institute for Measurement and Automation, University of the Bundeswehr Munich, 85577 Neubiberg RFA, Germany Received 21 February 2001; received in revised form 3 June 2002; accepted 10 June 2002 Abstract The p±n junction I±U characteristic offers the possibility to realize an easy applicable calibration-free measurement. In this paper, we present a new measurement method making use of an inverse problem consideration. A new p±n junction I±U characteristic model is specially developed for this method and taking into account semiconductor secondary effects is presented and compared to the reduced reduced Gummel±Poon Model (RGP). The experimental results show an improvement of one order relative to previous calibration-free methods like the method by Goloub (2.8 K). The temperature calculation procedure is more stable and converges much faster than with the RGP. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Temperature measurement; Diode temperature sensors; Silicon transistor thermometers; p±n junction; Modeling 1. Introduction The knowledge about the real behavior of a sensor con- tributes considerably to the de®nition of its optimal opera- tion parameters and consequently leads to a signi®cant improvement of measurement accuracy. For this reason, several calibration processes are generally required all through the service lifetime of a sensor specimen. Right after production and during the implementation of sensor systems, a sensor calibration process is generally required in order to examine the specimen scattering due to ¯uctuations throughout the technological manufacturing process. Later during maintenance processes of sensor systems, several calibrations are carried out in order to investigate or to verify the in¯uence of the aging processes on the sensor operation parameters. During calibration, the sensor output should be documen- ted by de®nite well known input values. Especially for temperature sensors, and in order to guarantee a well known and constant temperature during calibration, the sensor must remain in the calibration equipment until the thermal equi- librium is reached between the sensor itself, the liquid bath and the temperature regulation process. This process requires an expensive equipment and takes generally a long time. For several applications, in which a long lifetime and low maintenance costs are required, the additional calibra- tion costs are supplementary costs that should be preferably avoided. 2. Calibration-free temperature measurement The possibilities of a calibration-free temperature measurement are quite limited. Generally, only the well known primary thermometers like gas thermometers, acoustic thermometers, noise thermometers and total radiation thermometers are regarded as calibration free [1]. They generally reach a very high accuracy level (e.g. Table 1) and are therefore, used in the de®nition of the international temperature scale. These methods are conceived for laboratories, not for industrial applica- tions [2]. In industrial applications, a considerably lower accuracy is accepted, if the experimental effort remains reasonable. In fact, a calibration-free temperature measurement is de®ned as a method that guarantees a certain accuracy level without the necessity of a calibration process neither per batch nor per unit. Regarding this de®nition, it is also possible that methods with restricted accuracy be calibration free. The quantity being measured must be only calculable without need of the predetermination of any unknown parameters. Sensors and Actuators A 101 (2002) 275±282 * Corresponding author. Tel.: 49-89-6004-3740; fax: 49-89-6004-2557. E-mail address: olfa.kanoun@unibw-muenchen.de (O. Kanoun). 0924-4247/02/$ ± see front matter # 2002 Elsevier Science B.V. All rights reserved. PII:S0924-4247(02)00207-8