Noise of short-time integrators for readout of uncooled infrared bolometer arrays

Transcription

1 Adv. Radio Sci., 8, 9 33, 00 doi:0.594/ars8900 Authors 00. CC Attribution 3.0 License. Advances in Radio Science Noise of shorttime integrators for readout of uncooled infrared bolometer arrays D. Würfel, D. Weiler, B. J. Hosticka, and H. Vogt Fraunhofer Institute for Microelectronic Circuits and Systems, Duisburg, Germany Abstract. As stateoftheart readout circuits shorttime integrators in Far Infrared FIR uncooled bolometer arrays are commonly used. This paper compares the transfer functions of an ideal continuoustime integrator with that of a real integrator with focus an OTA parameters and noise analysis. Beside the noise sources at the noninverting input of the OTA special care has to be taken to account for capacitances at the inverting input. The Noise Equivalent Temperature Difference NETD as the key parameter for bolometer applications for a real shorttime integrator will be derived. As the result it will be shown, that the NETD is /f noise limited. Introduction The need for uncooled infrared focal plane arrays IRFPA for imaging systems has increased since the beginning of the nineties. Examples for the application of IRFPAs are thermography, pedestrian detection for automotive, firefighting and infrared spectroscopy. According to Plank s law, each body with a temperature above absolute zero point emits electromagnetic radiation. The wavelength and intensity depends on the temperature of the body. For example, a body at a temperature of 300 K has its maximum emittance at a wavelength of approx. 0 µm. FIR imager uses the IRradiation of a warm body in the wavelength range between 8..4 µm. The FIRsensitive element is the bolometer which changes its resistance by absorbing the radiation of the warm body. A pulsed bias with a constant voltage is applied to the bolometer and the resulting current is integrated for a fixed time. An offset current is subtracted before integration. Conventional readout circuits use a columnwise architecture. Correspondence to: D. Würfel daniel.wuerfel@ims.fraunhofer.de Bolometer The bolometer is fabricated by postprocessing on CMOS wafers in Fraunhofer IMS Microsystem Lab. The realization of a microbolometer is shown in Fig. as a cross section. A micromachined membrane consisting of amorphous silicon is suspended by two via stacks of metal from the CMOS substrate. The membrane forms with two other layers a good interferometric structure for radiation absorption. On top of the membrane an antireflection layer with a sheet resistance of 377 /sq is deposited. The bottom structure consists of a nearly perfect reflecting metal layer Ruß et al., 007. To increase the thermal resistance the membrane is fixed by two small legs Fig.. The optical distance between membrane and reflection metal reaches an optimum for one quarter of the radiation wavelength. To reduce thermal losses by gas conduction a vacuum package is required. The bolometer converts the infrared radiation into heat energy and this induces a temperature rise resulting in a change of the electrical resistance. Typical bolometers have pixel pitch values of 35 µm or 5 µm. Figure shows a bolometer array with 4 4 sensor elements. 3 Shorttime integrator In Sect., the ideal integrator model is analysed. In Sect., the real integrator circuit is presented, analysed and compared to the ideal model. 3. Ideal model Figure 3 shows the ideal shorttime integrator model in the timedomain. By applying a bias voltage pulse v Bias t = V Bias to the bolometer resistor R Bolo T 0 the bolometer current i Bolo t is generated and integrated at the integration capacitor. Only a small part of the bolometer current depends on the IRradiation, so a bias current i Bias t = I Bias is Published by Copernicus Publications on behalf of the URSI Landesausschuss in der Bundesrepublik Deutschland e.v.

2 Figure. Realization of a bolometer cross section 30 D. Würfel et al.: Noise of shorttime integrators Fig.. Realization of a bolometer cross section. Figure. Realization of a bolometer cross section subtracted at the first summation node in order to cancel a corresponding offset at the integrator output. The integration stops after readout time. This is modelled in the following way: the second summation node subtracts the replica of the bolometer current delayed by the readout time and integrates it. The integration constant is /. In this way we obtain a timewindowed integration. Otherwise the ideal integration would never end. The output voltage V out s is calculated in the Laplacedomain in Eq.. V out s = e s s UBias s R Bolo T 0 I Biass Thus the transfer functions for output voltage V out s over input voltage V Bias s and input current I Bias s are given by Eqs. and 3. H in,ideal Figure s = V outs. VLayout Bias s = of e a bolometer st srarray Bolo T 0 H in,ideal s = V outs I Bias s = e s s 3 3. Real integrator i Bolot v Biast Figure 4 shows the real readout integrated circuit ROIC R consisting of an OTA BoloT with 0 an integration capacitor in the feedback and all relevant noise sources. The output resistance is assumed to be infinity. The i Biast singlestage OTA is compensated by a load capacitance C L. The integrator is reseted by the switch reset. A parasitic capacitor C p caused e.g. Figure by a column 3. Ideal lineintegratormodel is placed the inverting input of the OTA. After the reset phase bolometer and a current source are connected to the inverting OTA input by the switch select for the readout time. The current from the current source is a constant during the integration, but there is no current if the switch select is off. Then the output voltage is held and sampled by a following stage not shown here. The switch resistance R s in series with the bolometer resistor R Bolo T 0 can be neglected, because R Bolo T 0 R s. If the transconductance of the OTA is sufficiently high, so that R Bolo T 0 and R Bolo T 0 C L, the output voltage V out s is given by Figure. Layout of a bolometer array Fig.. Layout of a bolometer array. V out s = e s V n,a s s C p RBolo T 0 I Bias sr Bolo T 0 V Bias s s R Bolo T 0 sce i g Bolot v Biast mota with R BoloT 0 i Biast scint = C L C p C LC p. 5 From Eq. 4 3 transfer functions can be derived: Figure 3. Ideal integratormodel H in s = V outs V Bias s s = e s 6 sc int R Bolo T 0 v s outt Cint H in s = V outs s I Bias s = e s 7 s s H in3 s = V outs V n,a s = s R Bolo T 0 C p s e s H in s and H in s compared to H in,ideal s and H in,deal s, respectively, shows that there is now a zero in the transfer function and an additional nondominant pole, which is given by the gain bandwith product GBW of the OTA. If the zero is not dominant, its effect can be 4 8 t Pixe Adv. Radio Sci., 8, 9 33, 00

3 D. Würfel et al.: Noise of shorttime integrators 3 v Biast i Bolot R BoloT 0 v outt Cint i Biast Fig. 3. Ideal integratormodel. Figure 3. Ideal integratormodel Rreset reset v n,rreset Cint v n,rbolo RBoloT0 select R s vd v out VBias Cp v n,a gmotavd CL i n,ibias I Bias Fig. 4. RealFigure ROIC with 4. an Real OTA ROIC noise sources with an included. OTA noise sources included neglected. But H in3 s is of special interest. Noise at the noninverting input of the OTA is integrated but additionally amplified by C p / up to the GBW. There could be a high amplification if there is a large parasitic capacitance and a small integration capacitance with a large bandwith dependent on OTA s GBW. 4 Noise calculation and NETD The power noise density S RBolo including white and /f noise for the bolometer resistor is given by v n,rbolo,/f S RBolo f = v n,rbolo,w = 4kT 0 R Bolo T 0 VBias k fbolo f with k as Boltzman s constant, k fbolo the /f noise parameter and T 0 as the reference temperature. The power noise density S A including white and /f noise for the OTA is given by 9 with W as the width of the input transistor, L as the length of the input transistor, C ox as the capacitance per unit of the transistor, n the weak inversion slope parameter, γ as the noise parameter and as the /f noise parameter of the input transistor Anelli, 000. K a and K b account for the effect of OTA s remaining transistors on total OTA s white noise and /f noise respectively. The power noise density of the current source depends on the realization. In the simplest case it could be a resistor with the same resistance as the bolometer resistance. To make it easy it is assumed that the current source is ideal, but has a power noise density given by S IBias = i n,ibias,w = 4kT 0 R Bolo T 0. At first the noise power at the integrator output caused by the bolometer for white noise is calculated. S A f = v n,a,w v n,a,/f = 4K akt 0 nγ K b WLC ox f 0 Adv. Radio Sci., 8, 9 33, 00

4 3 D. Würfel et al.: Noise of shorttime integrators v n,out,rbolo,w = vn,bolo,w H in f = sinπf t 4kT 0 R Bolo T 0 πf R Bolo T 0 sinπf t 4kT 0 R Bolo T 0 πf R Bolo T 0 kt 0 R Bolo T 0 Cint R Bolo T 0 sinπf t 4kT 0 R Bolo T 0 πf R Bolo T 0 πf πf πf πf 4kT 0 R Bolo T 0 πf R Bolo T 0 πf This result has been obtained using several approximations. The noise power at the output caused by the current source is calculated similarly as: vn,out,ibias,w = in,ibias,w H in f t kt 0 R Bolo T 0. 3 R Bolo T 0 C int The noise power caused by OTA s white noise is determined as vn,out,a,w = vn,a,w H in3f 4K akt 0 nγ sinπf t R Bolo T 0 πf 4K akt 0 nγ R Bolo T 0 C P K a kt 0 nγ. The noise power caused by the bolometer resistor s /f noise is described as vn,out,rbolo,/f = f V Bias f v n,bolo,/f H in f = VBias f k fbolo sinπf t f R Bolo T 0 πf k fbolo f πf πf sinπf R Bolo T 0 πf VBias k fbolo cosξ ξ sinξξ Ciξ ξ RBolo T 0Cint tpixel VBias k fbolo R Bolo T 0 ln πf πf VBias k t fbolo ln R Bolo T 0 πf R Bolo T 0 ln. C πf e C P πf πf 4 5 where ξ = π f, cosξ, sinξ ξ, the Cosine Integral Ciξ lnξ with lnξ and πf /. A mechanical shutter in front of the IRFPA is periodically closed. This can be modelled as a high Adv. Radio Sci., 8, 9 33, 00 pass filter. The lower frequency f is assumed to be Wood, 997 f 4t shutter. 6

5 D. Würfel et al.: Noise of shorttime integrators 33 t shutter is the shutter time, where t shutter. The contribution of the /f noise of the OTA with same approximations as above is given by v n,out,a,/f = K b f f W LCox f K b W LC ox v n,a,/f H in3 f sinπf πf R Bolo T 0 C P 4 C int πf Ce t ln R Bolo T 0 π f ln 4 C P. πf Ce 7 During the reset of the integrator the ktcnoise is stored on the integration capacitor. Thus vn,reset = kt 0. 8 The current responsitivity of the bolometer at the input is given for a constant voltage across the bolometer by V Bias α R I. 9 R Bolo T 0 g Bolo where α is the temperature coefficient TCR and g Bolo is the heat conductance of the bolometer derived from Wood, 997 with g Bolo g eff, I Bolo = V Bias /R Bolo T 0, α < 0, I Bolo as the constant bolometer current, g eff as the effective heat conductance. The TCR α is assumed to be constant. The total output noise power is refered to the input by multiplying by the square of the DC value of the transferfunction H in f and converted into a current by division by R Bolo T 0. The NETD is defined as 4F no π A Bolo ε Bolo dl dt t arget i n,total R I 0 where i n,total is the total noise current, F no is the fnumber of the optic, A Bolo the area of the bolometer, ε Bolo is the emission coefficient which is equal to the absorption coefficient and dl/dt target is the differential change of radiance over the change of the target temperature Wood, 997. Finally, total NETD is calculated to 4Fno RBoloT0 C dl πa Boloε Bolo R BoloT0 int dtt arget v n,out,rbolo,w vn,out,rbolo,/f v n,reset vn,out,ibias,w v n,out,a,w v n,out,a,/f Assuming that there is only noise from the bolometer resistor white and /f noise and current source white noise with, C L, WL the NETD reaches 4Fno g Bolo dl πa Boloε Bolo dtt arget 4kT 0 R Bolo T 0 t V Bias k tshutter fbololn π V Bias α. NETD caused by white noise can be decreased by increasing the readout time and bias voltage and by decreasing the bolometer resistance assuming that the bolometer parameters and fnumber are fixed. NETD caused by /f noise is independent of the bias voltage, because it cancels out. Because of the logarithm there won t be much change when varying for a fixed shutter time. Thus white noise can be reduced, but /f noise cannot. So /f noise will limit NETD. 5 Conclusions The ideal and real shorttime integrator have been modelled. The effect of the finite integration time has been included. The total noise power and the resulting NETD have been calculated. For long integration the limiting factor as far as NETD is concerned is /f noise. References Ruß, M., Bauer, J., and Vogt, H.: The geometric design of microbolometer elements for uncooled focal plane arrays, Proc. of SPIE Conference Infrared Technology and Applications XXXIII, Volume 654, , 007. Anelli, G.: Design and Characterization of Radiation Tolerant Integrated Circuits in Deep Submicron CMOS Technologies for the LHC Experiments, Ph.D. Thesis, Institut National Polytechnique de Grenoble, France, 000. Wood, R. A.: Monolithic Silicon Microbolometer Arrays, in Uncooled Infrared Imaging Arrays and Systems, edited by: Kruse, P. and Skatrud, D., Semiconductors and Semimetals, 47, 45, Academic Press, 997. R I Adv. Radio Sci., 8, 9 33, 00