Micromachined Thermal Conductivity Sensor

with a Thermopile on a Hot-plate

Xiang Zheng Tu

  

The thermal conductivity sensor with a heater and a thermopile is manufactured by POSIFA Microsystems Company. The sensor is created in a silicon substrate and constructed with a thin membrane suspending over a cavity recessed into the substrate. A resistive heater and a plural of hot junctions of a thermopile are disposed on the membrane and a plural of cold junctions of the thermopile are disposed the top of the substrate which is surrounded the membrane. The cavity is configured to have a bottom surface parallel with the top membrane allowing heat generated by the heater transfers perpendicular through the cavity to the bottom. The path length is optimized to have a maximum heat conduction transfer efficient.

The sensors rely on the thermal conductivity of a gas mixture which affects thermal phenomenon by way of heat conduction transfer that, in turn, is converted into a varying electrical signal capturing the sensor response to its component concentration change. As shown in the top figure, the sensors are thermally isolated so only heat transfer due to thermal conductivity through a cavity. Other heat transfer pathways such as through substrate or electrical leads result in thermal losses that degrade sensor performance and have been minimized in the device design.

In sensor operation the heat P_heat generated inside the heater by a DC voltage U_DC applied to the output terminals of the thermopile sensor follows the equation

P_heat = U ² R_sensor . (1)

We can assume that the thermal contact between the periphery and the ambient is so good that the temperatures of the periphery and the ambient environment are identical. They are equal to T_amb. Since the heat P_heat is generated on the membrane, its temperature T_mem depends on the thermal conductivity λ_mem of the hot plate and the thermal conductivity λ_gas of the gas filled in the cavity as

T_mem = P_heat / (λ_mem + λ_gas) + T_amb. (2)

The generated thermopile voltage U is proportional to the temperature difference between the membrane and the periphery as

U_DC ∝ ΔT = T_mem − T_per ≈ Pheat / (λ_mem + λ_gs) . (3)

Thus,

U_DC ∝ U ² / ( λ_mem + λ_gas) . (4)

Each gas has a known thermal conductivity. The thermal conductivities of some gases can be found in the table below.

Gas	Thermal Conductivity
ACETYLENE	4.400
AMMONIA	5.135
ARGON	3.880
CARBON DIOXIDE	3.393
CARBON MONOXIDE	5.425
CHLORINE	1.829
ETHANE	4.303
ETHYLENE	4.020
HELIUM	33.60
HYDROGEN	39.60
HYDROGEN SULPHIDE	3.045
METHANE	7.200
NEON	10.87
NITRIC OXIDE	5.550
NITROGEN	5.680
NITROUS OXIDE	3.515
OXYGEN	5.700
SULPHUR DIOXIDE	1.950

The sensors can be used not only measure all the gases listed in the table but also to analyze a whole range of binary gas mixtures provided that there are only two gases present and that the two gases have significantly different thermal conductivities.  Example is nitrogen and hydrogen or a pseudo-binary mix. Air is an example of a pseudo-binary mix: it has a fixed proportion of oxygen and nitrogen, both having very similar thermal conductivities and so behaves much like a single gas.

Other examples include:

• 0 – 100% Hydrogen in Air
• 0 – 100% Methane in Air
• 0 – 100% Carbon Dioxide in Air
• 0 – 100% Carbon Dioxide in Methane
• 0 – 100% Helium in Air

Thermal conductivity sensor with a heater and a thermopile utilizes micromachining technology which is amenable to creating micro-heaters and thermal conductivity sensors with no moving parts required, thus simplifying fabrication and operational design requirements. Another reason for the large interest in thermal conductivity sensors is the advantages gained through miniaturization: low power consumption, higher sensitivity to low conductivity, fast response and ease of use with different modes of operation.