Characterization of Gas Conductance of a Thermal Device With a V-Groove Cavity

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IEEE ELECTRON DEVICE LETTERS, VOL. 33, NO. 2, FEBRUARY 2012 275

Characterization of Gas Conductance of a

Thermal Device With a V-Groove Cavity

Chung-Nan Chen

Abstract—The gas conductance of a V-groove thermal sensor is characterized by the simulation of effective collisions inside the cavity and further verified by the measurements of frequency responses in vacuum and in air. The effective gap depths of a polysilicon microbolometer with an active area of 44 μm× 27 μm and a V-groove cavity of 48 μm× 45 μm were estimated as 4.37 and 4.24 μm by the respective calculations based on the simulation and measurement results which are much lower than those calculated by early models of published papers. The gas conductance of the sensor in atmosphere was further evaluated as 1.4× 10−5W/K which dominates the heat loss of the thermal sensor.

Index Terms—Gas conductance, microbolometer, polysilicon, thermal sensor, V-groove.

I. INTRODUCTION

T

HERMAL devices were widely and popularly used and served as thermal sensors, heating components, infrared emitters, and power generators, such as microbolometers [1]– [3] and thermopiles [4], [5] for infrared sensing, micro Pirani gauges for pressure sensing [6], [7], heating elements for gas sensors [8], microemitters for infrared sources [9], and thermoelectric devices for power generation [10], [11]. The performance of a thermal device is extremely dependent on the behavior of heat transfer of the device. The thermal time constants and responsivity of microbolometers and thermopile infrared sensors are inversely proportional to their thermal conductance [5]. The output voltage of a thermoelectric power generator is also in inverse ratio to its thermal conductance [10]. Moreover, the sensitivity of a micro Pirani gauge is indirectly proportional to the ratio of gas conductance to the sum of solid conductance and radiation loss [7]. In general, the gas conduction may dominate the heat loss for most of the micromachined thermal devices due to their narrow gaps between the active areas of devices and their heat sinks [1], [2], [5]–[7]. Therefore, the characterization of gas conduction of a thermal device becomes critical for the design of an excellent thermal device. For a thermal device with a heat sink paralleled to its active area, the gas conductance of the device

Manuscript received September 8, 2011; revised November 9, 2011; accepted November 12, 2011. Date of publication December 19, 2011; date of current version January 27, 2012. This work was supported in part by the National Science Council of Taiwan under Grant NSC-97-2221-E-151-006. The review of this letter was arranged by Editor W. T. Ng.

The author is with the Institute of Photonics and Communications, National Kaohsiung University of Applied Sciences, Kaohsiung 807, Taiwan (e-mail: cn_chen@ kuas.edu.tw).

Color versions of one or more of the figures in this letter are available online at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/LED.2011.2176712

is near directly proportional to the pressure in the low-pressure molecular state and independent of the gap depth between the active area and heat sink. At high pressure, gas conduction occurs in the viscosity state which is almost independent of the gas pressure, and the magnitude of gas conductance is in inverse ratio to the gap depth [6]. However, a lot of thermal devices with V-groove cavities were fabricated on 100-oriented silicon substrates by adopting front-side anisotropic etching process [1], [2], [4]–[10], [12], [13]. The gap depth between each active layer and its corresponding heat sink is not uniform anymore. The calculations of gas conductance for thermal devices with V-grooves have been reported in published articles by using the concept of effective gap depth [2], [6], [7]. X. He took the average gap as the effective gap depth. The group of P. K. Weng and J.-S. Shie adopted a numerical calculation of heat flux to estimate the effective gap depth and revealed that the effective depth was 18% of the V-groove width for most of the cases. In this letter, the effective gap depth of a thermal device with a V-groove cavity is estimated by adopting the 3-D simulation of heat flow using ray tracing software. This letter also proposes a novel and simple experimental method to further verify the simulation results and estimate the gas conductance of a V-groove thermal device. This experiment is based on the fact that the ratio of thermal time constants of a thermal device in air and in vacuum is directly proportional to the reciprocal of the ratio of thermal conductance in air and in vacuum. Furthermore, the gas conductance could become negligible at suitably low pressure.

II. THEORY ANDSIMULATION

In this study, the gas conductance of a polysilicon mi-crobolometer infrared sensor with an active area of 44 μm× 27μm and a V-groove cavity of 48 μm× 45 μm was simulated and characterized. The infrared sensor consists of two heavily phosphorus-doped polysilicon electrodes with low resistivity and a lightly doped polysilicon sensor area with high temper-ature coefficient of resistance (TCR), as shown in Fig. 1.

The responsivity RV of a microbolometer is given by [1]

RV = εαV G 1 √ 1 + ω2_τ2 = RV 0 √ 1 + ω2_τ2 (1) where ε is the emissivity of the infrared absorber, α is the TCR,

V is the bias voltage, G is the thermal conductance, ω is the

angular frequency of the modulated incident infrared, and τ =

C/G is the thermal time constant of the sensor in which C is

the heat capacitance and RV 0is the flatband responsivity. There