Analytical model for the electro-thermal feedback effect in a microbolometer infrared focal plane array

Seung-Man Park; Seungoh Han; Hee Chul Lee

doi:10.1117/1.OE.53.4.043104

3 April 2014 Analytical model for the electro-thermal feedback effect in a microbolometer infrared focal plane array

Seung-Man Park, Seungoh Han, Hee Chul Lee

Author Affiliations +

Optical Engineering, Vol. 53, Issue 4, 043104 (April 2014). https://doi.org/10.1117/1.OE.53.4.043104

Abstract

An analytical model for the electro-thermal feedback effect in a microbolometer infrared focal plane array is presented. The presented model is the integrated optical-electro-thermal model, in which the electro-thermal feedback effect incorporated with the response of incident IR can be described. In addition, since the model is based on physics, the model parameters also have their own physical meaning. This analytical model can be easily utilized to describe the temperature increase caused by the applied heat sources and has a unique feature describing capability of optical-electro-thermal analysis in a quasi-steady-state, which can hardly be performed with thermal analysis tools based on the finite element method. The model shows that the temperature of the microbolometer in this study can be increased 7.1% to 18.6% more by the electro-thermal feedback effect.

1. Introduction

Uncooled microbolometer infrared focal plane array (IRFPA) technology has extended its application to the small-size, low-weight, low-power, and low-cost IR systems.¹^–³ As the density of IRFPA has rapidly increased, several technical challenges, such as process technology, optical fill-factor, thermal isolation, and the thermal drift of their characteristics, have emerged.⁴^–¹¹ The accurate performance prediction of the high-density microbolometer IRFPA is also one of the emerging challenges.⁸^–¹⁶ In order to make a reasonable performance prediction of a highly optimized and high-density microbolometer IRFPA, the correct understanding of the electro-thermal phenomena that occur in a microbolometer IRFPA is essentially required. Since the electro-thermal effect is related to the temperature change and the electronic state change of a sensing material, this effect is inherent in a thermal detector like the microbolometer. Hence, the correct understanding of the electro-thermal effect leads not only to a more accurate signal prediction in the development, but also to the proper use of an IRFPA in the application period.¹³^–¹⁸

In this article, two analytical models for the electro-thermal feedback effect in the microbolometer IRFPA are presented. The electro-thermal feedback effect starts when the bias is applied to read the resistance change of the microbolometer in IRFPA. Once the bias is applied, the bias heat, which is inversely proportional to the resistance of the microbolometer for a constant voltage bias, is produced in a sensing material. This bias heat leads to a rapid temperature increase in the microbolometer. Since the negative temperature coefficient of resistance (NTCR) of IR sensing materials such as VOx and a-Si is used for most microbolometer technology, the bias heat makes the resistance decrease further. Once again, the further the resistance of the microbolometer decreases, the more the bias heat is produced. Therefore, this electro-thermal process is a positive feedback. The electro-thermal feedback increases the apparent signal of the microbolometer IRFPA. Thus, the measured signal voltage may be larger than that predicted without considering the electro-thermal feedback. In order to reduce this positive feedback effect, the biasing time should be decreased. However, decreasing the bias time, which determines the integration time, is not desirable since it increases the noise bandwidth, and hence the noise equivalent temperature differenc.¹⁵^–¹⁷ As a result, it is of high importance to understand the electro-thermal feedback effect as correctly as possible.

2. Electro-Thermal Feedback Models

Since we are interested in the electro-thermal feedback, our primary goal is to find a proper solution to the heat balance equation of a microbolometer in the case, where a constant IR radiation and a voltage bias are applied simultaneously to a microbolometer. The heat balance equation of a microbolometer is given by

Eq. (1)

H \frac{d Δ T}{d t} + K \cdot Δ T = P,

where

H

and

K

are the heat capacity and the thermal conductance, respectively.¹³^–¹⁹

Δ T = T_{d} - T_{a}

. Also,

T_{d}

,

T_{a}

, and

P

are the detector temperature, the constant ambient temperature, and the heat source, respectively.

If $P$ is constant in time, the solution to Eq. (1) is given by the following equation:

Eq. (2)

Δ T = \frac{P}{K} (1 - e^{- t / τ_{th}}) ≅ \frac{P}{H} t,

where

τ_{th} = H / K

is the thermal time constant. The last expression is valid only for

t ≪ τ_{th}

. The electro-thermal feedback effect is not included in Eq. (2) and this equation has been used to describe the temperature change with applied bias with a slight modification of the bias heat term to be constant as the initial power. We call Eq. (2) the conventional linear (CL) model.

As the bias is applied, the $P$ in Eq. (2) is not constant since the bias heat is time dependent. During the constant voltage bias, usually with a pulse form, $P$ can be expressed as follows, in which the bias heat is decomposed into time dependent and independent terms.

Eq. (3)

P = ε ϕ_{e} + \frac{V_{Bias}^{2}}{R_{d}} ≅ (ε ϕ_{e} + \frac{V_{Bias}^{2}}{R_{d 0}}) - \frac{α V_{Bias}^{2}}{R_{d 0}} Δ T,

where

α

,

ε

, and

ϕ_{e}

are the temperature coefficient of resistance of a sensing material, the IR absorption coefficient, and the incident IR power, respectively. The relationship of

R_{d} = R_{d 0} (1 + α Δ T)

is also used. Also, the last approximation in Eq. (3) is valid for

α Δ T ≪ 1

. By putting Eq. (3) into Eq. (2), we can get the following equation:

Eq. (4)

Δ T = (ε ϕ_{e} + \frac{V_{Bias}^{2}}{R_{d 0}}) \frac{t}{H} {(1 + α \frac{V_{Bias}^{2}}{H R_{d 0}} t)}^{- 1} .

From Eq. (4), one can see the feedback characteristic of bias heat. If the incident IR radiation can be negligible, then Eq. (4) becomes the exact same form of a feedback amplifier gain expression²⁰ with a loop gain of $α [(V_{Bias}^{2}) / (H R_{d o})] t$ . The only difference is that the loop gain is negative because of the NTCR of the sensing material, so the electro-thermal feedback modeled by Eq. (4) is a positive feedback, as previously mentioned, and is as intuitive as that in the circuit theory. We call Eq. (4), the feedback amplifier gain (FAG) model, for our discussion.

Another approach is possible. With rearrangement after putting Eq. (3) into Eq. (1), one can get an easily solvable equation as follows:

Eq. (5)

H \frac{d Δ T}{d t} + K_{eff} \cdot Δ T = P_{0},

Eq. (6)

K_{eff} = K + \frac{α V_{Bias}^{2}}{R_{d 0}},

Eq. (7)

P_{0} = ε ϕ_{e} + \frac{V_{Bias}^{2}}{R_{d 0}},

where,

K_{eff}

and

P_{0}

are the effective thermal conductance (ETC) and the time independent heat source, respectively. Whereas the only time independent source term in Eq. (5) with constant incident IR radiation power is treated as a heat source, the time-dependent source term is treated as the term contributing to the ETC. As expected, the solution to Eq. (5) can be found as follows:

Eq. (8)

Δ T = \frac{P_{0}}{K_{eff}} (1 - e^{- t / τ_{eff}}),

where

τ_{eff}

is the effective time constant defined by

τ_{eff} = H / K_{eff}

. Although Eq. (8) has the exact same form as Eq. (2), the increasing shapes in temperature are quite different. This difference stems from the fact that

K_{eff}

is less than

K

, even can be a negative value, then so do

τ_{eff}

. The physical meaning of the

K_{eff}

can be interpreted as follows. If

K_{eff} < 0

, then the heat flows into the microbolometer from the ambient. Accordingly, the heat piled up on the microbolometer will rapidly increase, so this piling up of heat will lead to the rapid increase of its temperature. So,

Δ T

exponentially increased as expected in Eq. (8). If

K_{eff} = 0

, then the heat flowed out to the ambient is precisely balanced with the heat produced by time dependent bias. Accordingly, the heat piled up on the microbolometer will be increased by an amount of time independent heat source

P_{0}

, so

Δ T

is linearly dependent on time with a constant heat source

P_{0}

, as in Eq. (5). We will call Eq. (8), the ETC model.

Two models were derived from the heat balance equation of a microbolometer. Here, one question arises: Which one is better? In the derivation of Eq. (4), three assumptions were made. The first was $t ≪ τ_{th}$ , the second was $α Δ T ≪ 1$ , and the third $P$ was constant in Eq. (2). The first two are very likely. The third is also plausible, in that the mitigation of this assumption was made by quietly inserting the time dependent term of Eq. (3) into Eq. (2). On the other hand, in the derivation of Eq. (8), only the second one was made. So, it can be said that the ETC model is more physical with less assumptions in it. Although Eq. (4) is more intuitive, Eq. (8) is more physical.

3. Applications of the Models and Discussion

In order to demonstrate the utilization of two analytical models for describing the electro-thermal feedback effect, the FAG model of Eq. (4), the ETC model of Eq. (8), and the CL model of Eq. (2) were applied to a typical microbolometer IRFPA. The characteristics of the microbolometer IRFPA used for this study are summarized in Table 1.¹⁶^–¹⁹

Table 1

The characteristic parameters of a microbolometer infrared focal plane array (IRFPA) used for this study.

Parameter	Symbol	Value	Unit	Other
A bolometer in FPA
Pixel pitch		$25 \times 25$	${μ m}^{2}$
Optical fillfactor		0.7
Thermal conductance	$K$	$3 \times 10^{- 8}$	$W / K$
Heat capacity	$H$	$3 \times 10^{- 10}$	$J / K$
IR absorption coefficient	$ε$	0.8
Resistance	$R_{d 0}$	170	$k Ω$	At 298 K
Temperature coefficient of resistance (TCR)	$α$	$- 0.02$	$1 / K$
Reference bolometer
Thermal conductance	$K$	$1 \times 10^{- 3}$	$W / K$
Heat capacity	$H$	$1.2 \times 10^{- 9}$	$J / K$
IR absorption coefficient	$ε$	0		Optical blind
Resistance	$R_{d 0}$	155	$k Ω$	At 298 K
TCR	$α$	$- 0.02$	$1 / K$
# Ref. bolometers per col.		1	ea
IRFPA
Format		$320 \times 240$
Bias voltage	$V_{Bias}$	2	V	const. vol. pulse
Readout type	$C_{int}$	30	pF	columnwise readout with CTIA
Readout type	$T_{int}$	100	μs	columnwise readout with CTIA
Frame time	$T_{f}$	33	ms
Incident IR power	$ф_{e}$	24.3	nW
Ambient temperature	$T_{a}$	298	K	constant

The temperatures of the microbolometer calculated by the CL, FAG, and ETC models, respectively, are shown in Fig. 1. It is presumed that the microbolometer is illuminated by an incident IR radiation from a 35°C extended black body source. The inset of Fig. 1 shows the temperature changes of the microbolometer over the first six frame times. Over one frame time of $T_{f}$ , only for the first 100 μs, the bias is applied to the microbolometer, so the temperature rapidly increases for this biasing time. After the biasing time, the microbolometer is cooled down naturally as the bias heat is dissipated to the substrate mainly by conduction. After three to five frame times, the maximum temperature is reached at the end of the biasing time, while the saturated cooling temperature also reached at the end of cooling time. We call this state the quasi-steady-state of a microbolometer. Figure 1 shows the solution to the heat balance equation of the microbolometer with an electro-thermal feedback effect over several frames up to the quasi-steady-state condition. This capability to describe the quasi-steady-state condition is the most unique feature of our model, distinguishing itself from other thermal analysis tools. The temperatures at the end of the biasing time in the quasi-steady-state calculated with the FAG and ETC models are larger than that with CL, in which the electro-thermal feedback effect was not considered. Whereas the temperature change is 8.90 K calculated with CL, those are 10.55 and 9.53 K with the FAG and ETC models, respectively. Thus, it can be seen that the temperatures from the FAG and ETC models are 18.6% and 7.1% higher than that from CL. These results of the electro-thermal feedback effect may be too large to overlook for making more precise tradeoffs among their performance parameters of a high-density microbolometer IRFPA in both the development and application periods.

Fig. 1

Temperature changes calculated with feedback amplifier gain (FAG), effective thermal conductance (ETC), and conventional linear (CL) models, respectively.

The modeled resistances of the microbolometer are shown in Fig. 2. The inset of Fig. 2 shows the resistance changes of the microbolometer over the first six frame times like in Fig. 1. In the quasi-steady-state, the resistance changes calculated with the FAG and ETC models are larger than that with CL. While the resistance change is $30.4 k Ω$ calculated with CL, those are 42.4 and $35.5 k Ω$ with the FAG and ETC models, respectively. Thus, it can be seen that the resistance changes by considering the electro-thermal feedback effect are 17.3% and 6.7% larger than that from CL. The clear results of the electro-thermal feedback models are shown in Fig. 1 for the temperature and in Fig. 2 for the resistance of the microbolometer.

Fig. 2

Resistance changes calculated with FAG, ETC, and CL models, respectively.

The IR response signals for each temperature of an extended blackbody source can be predicted with the model.¹⁶^–¹⁹ The IR response signals can be predicted from the resistance changes calculated with each model. Figure 3 shows the predicted IR response signals of the previous microbolometer IRFPA of Table 1. Here, it is assumed that the microbolometer IRFPA has a columnwise readout with a capacitive transimpedance amplifier as a column amplifier, as indicated in Table 1.¹⁹^,²¹ The IR response signals from the FAG and ETC models, in which the incident IR radiation incorporated with the electro-thermal feedback effect are considered, are larger than that from CL, in which only the IR radiation is considered. This means that the IR response signals are affected by the electro-thermal feedback effect. Since most IR imaging systems utilizing modern IRFPA technologies to get a high quality image are operated after proper nonuniformity corrections (NUC), the relative response signals are more important. The relative temperature responses extracted from the signals of 20°C and 35°C are 19.5, $18.1 mV / K$ with the FAG, ETC models, respectively, while $17.9 mV / K$ with CL. Compared with the result without an electro-thermal feedback effect, the relative responses with the FAG and ETC models are nearly the same as that with CL. This means that most of the electro-thermal feedback effect can be eliminated by NUC. However, the remaining parts still can affect the nonuniformity of an image even after NUC.

Fig. 3

Infrared response signals calculated with FAG, ETC, and CL models, respectively.

4. Conclusion

The presented analytical model is the integrated optical-electro-thermal model, with which the electro-thermal feedback effect incorporated with the responsivity of the incident IR can be described. In addition, since the model is based on physics, the model parameters also have their own physical meaning. This analytical model can easily be utilized to describe the temperature and resistance change caused by the applied heat sources and has a unique feature, where it can describe the capability of optical-electro-thermal analysis in the quasi-steady-state, which can hardly be performed with finite element method based thermal analysis tools. The model shows that the temperature of the microbolometer in this study can be increased 7.1% to 18.6% more by the electro-thermal feedback effect.

Acknowledgments

This research was supported by the Academic Research Fund of Hoseo University in 2012 (20120239).

References

1.

J. Tissotet al., “High-performance uncooled amorphous silicon video graphics array and extended graphics array infrared focal plane arrays with 17-μm pixel pitch,” Opt. Eng., 50 (6), 061006 (2011). http://dx.doi.org/10.1117/1.3572155 OPEGAR 0091-3286 Google Scholar

2.

R. Breiteret al., “Seize, weight, and power reduction of mercury cadmium telluride infrared detection modules,” Opt. Eng., 50 (6), 061010 (2011). http://dx.doi.org/10.1117/1.3578405 OPEGAR 0091-3286 Google Scholar

3.

C. LiC. J. HanG. Skidmore, “Overview of DRS uncooled VOx infrared detector development,” Opt. Eng., 50 (6), 061017 (2011). http://dx.doi.org/10.1117/1.3593155 OPEGAR 0091-3286 Google Scholar

4.

C. LiG. SkidmoreC. Han, “Uncooled VOx Infrared sensor development and application,” Proc. SPIE, 8012 80121N (2011). http://dx.doi.org/10.1117/12.887113 PSISDG 0277-786X Google Scholar

5.

L. Becker, “Influence of IR sensor technology on the military and civil defense,” Proc. SPIE, 6127 61270S (2006). http://dx.doi.org/10.1117/12.640529 PSISDG 0277-786X Google Scholar

6.

A. Fraenkelet al., “Advanced features of SCD’s uncooled detectors,” Proc. SPIE, 5957 59570N (2005). http://dx.doi.org/10.1117/12.621041 PSISDG 0277-786X Google Scholar

7.

L. Langofet al., “Advanced multi-function infrared detector with on-chip processing,” Proc. SPIE, 8012 80120F (2011). http://dx.doi.org/10.1117/12.883248 PSISDG 0277-786X Google Scholar

8.

A. Fraenkelet al., “SCD’s uncooled detectors and video engines for a wide-range of applications,” Proc. SPIE, 8012 801204 (2011). http://dx.doi.org/10.1117/12.883108 PSISDG 0277-786X Google Scholar

9.

A. Rogalski, “Infrared detectors for the future,” Acta Phys. Pol. A, 116 (3), 389 –406 (2009). ATPLB6 0587-4246 Google Scholar

10.

D. Murphyet al., “ $640 \times 512$ 17 μm microbolometer FPA and sensor development,” Proc. SPIE, 6542 65421Z (2007). http://dx.doi.org/10.1117/12.724345 PSISDG 0277-786X Google Scholar

11.

S. H. Blacket al., “Uncooled detector development at Raytheon,” Proc. SPIE, 8012 80121A (2011). http://dx.doi.org/10.1117/12.887816 PSISDG 0277-786X Google Scholar

12.

P. Ericssonet al., “Towards 17 μm pitch heterogeneously integrated Si/Ge quantum well bolometer FPAs,” Proc. SPIE, 8012 801212 (2011). http://dx.doi.org/10.1117/12.883827 PSISDG 0277-786X Google Scholar

13.

W. ParrishJ. Woolaway, “Improvements in uncooled systems using bias equalization,” Proc. SPIE, 3698 748 –755 (1999). http://dx.doi.org/10.1117/12.354575 PSISDG 0277-786X Google Scholar

14.

E. L. DereniakG. D. Boreman, Infrared Detectors and Systems, 395 –438 Wiley, New York (1996). Google Scholar

15.

F. Niklauset al., “Uncooled infrared bolometer arrays operating in a low to medium vacuum atmosphere: performance model and tradeoffs,” Proc. SPIE, 6542 65421M (2007). http://dx.doi.org/10.1117/12.719163 PSISDG 0277-786X Google Scholar

16.

M. TepegozF. CivitchiT. Akin, “An optimum reference detector design for uncooled microbolometer FPAs,” Proc. SPIE, 6940 694028 (2008). http://dx.doi.org/10.1117/12.786611 PSISDG 0277-786X Google Scholar

17.

A. OguzM. TepegozT. Akin, “A bias heating cancellation method for resistive uncooled microbolometer detectors,” Proc. SPIE, 7298 7298G (2009). http://dx.doi.org/10.1117/12.823720 PSISDG 0277-786X Google Scholar

18.

S. M. ParkS. Han, “Electro-thermal feedback effects on the signal in a pulse voltage biased μ-bolometer focal plane array,” Trans. KIEE., 61 (12), 1886 –1891 (2012). Google Scholar

19.

C. H. Hwanget al., “Readout integrated circuit for microbolometer with an analog non-uniformity correction,” Proc. SPIE, 5987 59870P (2005). http://dx.doi.org/10.1117/12.630755 PSISDG 0277-786X Google Scholar

20.

A. S. SedraK. C. Smith, Microelectronic Circuits, 570 –645 3rd ed.Saunders College Publishing, Philadelphia (1991). Google Scholar

21.

D. JakonisC. SvenssonC. Jansson, “Readout architectures for uncooled IR detector arrays,” Sens. Actuators, 84 (3), 220 –229 (2000). http://dx.doi.org/10.1016/S0924-4247(00)00313-7 SEACDX 0250-6874 Google Scholar

Biography

Seung-man Park received his BS (1984) and MS (1986) in physics from Hanyang University, and his PhD (1997) in electrical engineering from the Korea Advanced Institute of Science and Technology (KAIST). He was with the Agency for Defense Development (1987 to 2008), where he led several projects on infrared (IR) detector development. Since 2008, he has been with Hoseo University as a professor. His research interests are IR detector technologies and related systems. He is a member of several professional societies including SPIE.

Seungoh Han received his BS, MS, and PhD in electrical engineering from Korea University in 1996, 1998, and 2006, respectively. Since 2007, he has been with Hoseo University as a professor. His research interests are NEMS/MEMS, smart sensors, and multiphysics modeling.

Hee Chul Lee received his BS (1978) in electronic engineering from the Seoul National University, Korea, and his MS (1986) and PhD (1989) from the Tokyo Institute of Technology, Japan, respectively. Since 1989, he has been with the Department of Electrical Engineering and Computer Science at KAIST and he was the president of the National Nano-Fab Center (NNFC). His research fields include infrared detectors, readout circuits and polymer memories. He is a program committee member of SPIE and has served as a director of many conferences.

CC BY: © The Authors. Published by SPIE under a Creative Commons Attribution 4.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.

Citation Download Citation

Seung-Man Park, Seungoh Han, and Hee Chul Lee "Analytical model for the electro-thermal feedback effect in a microbolometer infrared focal plane array," Optical Engineering 53(4), 043104 (3 April 2014). https://doi.org/10.1117/1.OE.53.4.043104

Published: 3 April 2014

Access the abstract

JOURNAL ARTICLE
5 PAGES

DOWNLOAD PAPER SAVE TO MY LIBRARY

GET CITATION

KEYWORDS

Microbolometers

Infrared radiation

Resistance

Thermal modeling

Staring arrays

Integrated modeling

Thermography

1.

Introduction

2.

Electro-Thermal Feedback Models

Eq. (1)

Eq. (2)

Eq. (3)

Eq. (4)

Eq. (5)

Eq. (6)

Eq. (7)

Eq. (8)

3.

Applications of the Models and Discussion

Table 1

Fig. 1

Fig. 2

Fig. 3

4.

Conclusion

Acknowledgments

References

Biography

Show All Keywords

Keywords/Phrases

Search In:

Publication Years