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An Improved Electrical and Thermal Model of a Microbolometer for Electronic Circuit Simulation

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An Improved Electrical and Thermal Model of a Microbolometer for Electronic Circuit Simulation Adv. Radio Sci., 10, 183–186, 2012 Advances in www.adv-radio-sci.net/10/183/2012/ doi:10.5194/ars-10-183-2012 Radio Science © Author(s) 2012. CC Attribution 3.0 License. An improved electrical and thermal model of a microbolometer for electronic circuit simulation D. Wurfel¨ and H. Vogt Fraunhofer Institute for Microelectronic Circuits and Systems, Duisburg, Germany Correspondence to: D. Wurfel¨ ([email protected]) Abstract. The need for uncooled infrared focal plane arrays istically when these higher order effects are taken into ac- (IRFPA) for imaging systems has increased since the begin- count. A Verilog-A model for electronic circuit simulations ning of the nineties. Examples for the application of IRFPAs is developed based on the improved thermal model of the mi- are thermography, pedestrian detection for automotives, fire crobolometer. Finally, a simulation result of a simple circuit fighting, and infrared spectroscopy. It is very important to is presented. have a correct electro-optical model for the simulation of the microbolometer during the development of the readout inte- grated circuit (ROIC) used for IRFPAs. The microbolome- 1 Introduction ter as the sensing element absorbs infrared radiation which leads to a change of its temperature due to a very good ther- Far infrared (FIR) imager detect the IR-radiation of a warm mal insulation. In conjunction with a high temperature co- body in the wavelength range between 8 and 14 µm passively, efficient of resistance (TCR) of the sensing material (typi- i.e. no further illumination is necessary. Usually in low cost cal vanadium oxide or amorphous silicon) this temperature systems an array of uncooled microbolometers as the sensor change results in a change of the electrical resistance. During elements are used. Typical applications of IRFPAs are ther- readout, electrical power is dissipated in the microbolometer, mal imaging and pedestrian detection for automotive driving which increases the temperature continuously. The standard assistance systems, fire fighting, biological imaging, or mili- model for the electro-optical simulation of a microbolome- tary applications like target recognition (Wurfel¨ et al., 2011). ter includes the radiation emitted by an observed blackbody, radiation emitted by the substrate, radiation emitted by the microbolometer itself to the surrounding, a heat loss through 2 The microbolometer the legs which connect the microbolometer electrically and mechanically to the substrate, and the electrical power dissi- The microbolometer is a temperature dependent resistor. It pation during readout of the microbolometer (Wood, 1997). consists of a membrane which is suspended by two small The improved model presented in this paper takes a closer legs from the CMOS substrate. The legs also contact the look on additional radiation effects in a real IR camera sys- membrane electrically. The microbolometer absorbs the in- tem, for example the radiation emitted by the casing and the coming infrared radiation and converts it into heat energy, lens. The proposed model will consider that some parts of which induces a temperature rise. This results in a change the radiation that is reflected from the casing and the sub- of the electrical resistance. Figure 1 shows a SEM image strate is also absorbed by the microbolometer. Finally, the of a microbolometer fabricated by postprocessing on CMOS proposed model will include that some fraction of the radi- wafers at the Fraunhofer Institute for Microelectronic Cir- ation is transmitted through the microbolometer at first and cuits and Systems (Fraunhofer IMS) “Microsystem Lab & then absorbed after the reflection at the surface of the sub- Fab” (Weiler et al., 2011). The sensor material used for the strate. Compared to the standard model temperature and re- membrane is amorphous silicon. A vacuum package is re- sistance of the microbolometer can be modelled more real- quired to reduce thermal losses by gas convection. Published by Copernicus Publications on behalf of the URSI Landesausschuss in der Bundesrepublik Deutschland e.V. 1 2 3 Figure 1. SEM image of a microbolometer fabricated at the Fraunhofer IMS (left: top view, 4 right: side view) (Weiler et al., 2011) 184 D. Wurfel¨ and H. Vogt: Microbolometer for electronic circuit simulation 5 focal length θ 1 single bolometer 2 Fig. 1. SEM image of a microbolometer fabricated at the Fraun- bolometer- array 3 Figure 1. SEMhofer image IMS of (left: a microbolometer top view, right: fabricated side view) at (Weilerthe Fraunhofer et al., 2011). IMS (left: top view, 4 right: side view) (Weiler et al., 2011) vacuum casing with aperture 3 The Heat Balance Equation blackbody with 5 lens temperatur T Str A single microbolometer detects radiation power according to Fig. 2. The amount of incomingfocal length radiation power PStr de- 6 pends on the solid angle θ (Wood, 1997): 7 Fig. 2. Optical path from blackbody to the microbolometer, based 2 PStr = πLStrABolo sin θ, (1) 8 Figureon (Wood, 2. Optical 1997). path from blackbody to the microbolometer, based on (Wood, 1997) where LStr is the radiance and ABolo is the absorbing mi- 9 θ single bolometer crobolometer area. With the definition of the F -number Fno 4 The enhanced heat balance equation (Wood, 1997) bolometer- array When using the heat balance Eq. (4) it showed out that there 1 Fno = (2) is an energy loss. For example, the microbolometer tem- 2sinθ perature T decreases, when microbolometer temperature T , vacuum casing the power which is absorbed by a singlewith aperture microbolometer is blackbody temperature TStr, and substrate temperature Tsub blackbody with temperatur T given by lens are equal at time t = 0 s without any electrical power dissi- Str 8 pation. According to Eq. (4) for an emissivity εBolo ≈ 0.9 πLStrABoloεBolo QStr = , (3) of a microbolometer and a substrate emissivity εBolo ≈ 0.2 6 4F 2 no with Tsub = TStr = T at time t = 0 s the microbolometer emits 7 where εBolo is the emissivity of the microbolometer. The more power to the substrate Pout than it gets back. It emits in 8 Figure 2. Opticalmicrobolometer path from blackbody heats upto the during microb readoutolometer, due based to on the (Wood, electri- 1997) direction of the substrate cal power dissipation by applying a voltage UBias and a very 4 9 Pout = ABoloεBoloσ T . (5) good thermal insulation. The incoming radiation power PStr from a blackbody and the substrate are absorbed. Through But it only gets back from the substrate the small legs, which connect the microbolometer to the sub- strate, heat energy with the substrate is exchanged. The mi- 4 4 Pin = εBoloABoloεsubσ Tsub = εBoloABoloεsubσ T , (6) crobolometer itself is also a radiation source. In direction of the lens and additional to the substrate radiation is emitted ac- which is smaller by factor of εsub compared to Eq. (5). The cording to Stefan Boltzmann’s law. A heat balance equation result is that the temperature T of the microbolometer de- which describes the microbolometer temperature T when en- creases. The part of the radiation power which is not ab- 8 ergy is exchanged is derived by (Wood, 1997): sorbed by the substrate cannot be lost. In reality a great amount of the radiation power emitted by the microbolome- dT cBolo = UBiasIBolo +εBoloPStr +εBoloPsub ter to the substrate is reflected back to it. Then it is ab- dt sorbed and the microbolometer gets back some of the radi- 4 −gBolo(T−Tsub)−2ABoloεBoloσ T (4) ation power emitted by itself. So the heat balance equation will be enhanced to make it more realistic by taking reflec- where c is the microbolometer’s heat capacitance, I is Bolo Bolo tions and their absorptions into account. Additional the cas- the current through the microbolometer resistance, ε P Bolo sub ing and the lens emits and reflects radiation. Between 8 µm is the absorbed radiation power from the substrate, g is Bolo and 14 µm the transmissivity of the lens is assumed to be the thermal conductance, T is the substrate temperature sub 1. The lens is assumed to be an ideal blackbody for radia- and σ is the Stefan Boltzmann’s constant. tion between 0 and 8 µm wavelength and also from 14 µm to infinity. The microbolometer is assumed to have a transmis- sivity of 1-εBolo and to be part of an array with an infinite expansion. The substrate temperature Tsub, the temperature Adv. Radio Sci., 10, 183–186, 2012 www.adv-radio-sci.net/10/183/2012/ D. Wurfel¨ and H. Vogt: Microbolometer for electronic circuit simulation 185 blackbody 2 QStr,3 (TStr) = εBoloPein(TStr)(1−εcas)(1−εBolo) casing 1 ·( −ε ) − , lens 1 sub 1 2 (9) 4Fno bolometer bolometer array where εcas is the emissivity of the casing. In principle this is repeated infinitely. Of course the amount of radiation power substrate 1 gets smaller and smaller with each absorption. The final re- Fig.2 3. Optical path from blackbody to the microbolometer. sult is the sum of all absorption parts and given by Eq. (10). 3 Figure 3. Optical path from blackbody to the microbolometer QStr (TStr) = QStr,1 (TStr)+QStr,2 (TStr)+QStr,3 (TStr)+... ∞ n = ε πABoloLStr(TStr) · 1+ P (1−ε )n (1−ε )2n (1−ε )n 1− 1 Bolo 4F 2 cas Bolo sub 4F 2 no n=1 no S1 n−1 n−1 2n−1 n 1 +(1−εcas) (1−εBolo) (1−εsub) 1− 2 4Fno 1 (10) + − − − 2 − − 1 1 (1 εcas)(1 εBolo) (1 εsub) 1 2 4Fno πA L (T ) −1 −1 = ε Bolo str str · + (1−εcas) (1−εBolo) + Bolo 4F 2 UBias no − − − 2 − − 1 RBolo 1 (1 εcas)(1 εBolo) (1 εsub) 1 2 4Fno −1 −1 −(1−εcas) (1−εBolo) For all radiation sources the derivation can be done in a sim- ilar way.
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