MEMS Thermal Effect Sensors

Xiang Zheng Tu

Several MEMS thermal effect sensors have been developed by our company (POSIFA Microsystems). Among them are thermal flow sensors, thermal conductivity sensors, thermal vacuum sensors, thermal motion sensors and thermal humidity/carbon dioxide sensors. These sensors are given a first name as “thermal”, because their behaviors are related to thermal effects. Thermal effects mean the physical or chemical quantities measured by the sensors are caused by heat transfer processes.

All gases conduct heat to differing degrees, and the amount of heat transferred by a gas is determined by its 'Thermal Conductivity' (TC). The thermal conductivity sensor uses this property to accurately measure one of the two gases present in a sample of a binary or pseudo-binary mixture. In order to do so a micro-heater is created in a silicon wafer by MEMS technologies. The micro-heater is suspended over a cavity that is recessed in the silicon wafer. There is a temperature gradient between the micro-heater and the bottom of the cavity, which drives the heat energy generated by applying electrical power to the micro-heater transferring across the cavity by conduction. This results the change in the temperature of the micro-heater, which expresses a certain composition of the binary mixture in the cavity.

On the other hand, the thermal flow sensors operate based on a different type of heat transfer: convective heat transfer. More exactly the thermal flow sensors take advantages of laminar flow. This is why the thermal flow sensor is normally installed on the wall of a tube. When a fluid is forced to flow through the tube laminar flow will occur. The fluid tends to flow parallel in layers without lateral mixing, and adjacent layers slide past one another like playing cards. There are no cross-currents perpendicular to the direction _of flow, nor eddies or swirls of fluids.

Recall that a thermal flow sensor comprises a silicon chip, a resistive heater, one or two thermopiles, and a thermal insulating base. The heater and the hot junctions of the thermopiles are disposed on the surface layer of the base that is burred in the silicon chip and the cold junctions of the thermopiles are disposed outside of the base area. When a fixed electrical power is provided to the heater a temperature difference will be built up between the surface layer of the base and the outside area of the silicon chip. The thermopiles measure the temperature difference and output a voltage signal correspondingly. The temperature difference will be reduced by the forced laminar flow because convective heat transfer will take place.

This is a case of constant heat rate per unit surface area for steady, laminar, fully developed flow. The heat transfer from the surface layer of the thermal flow sensor through convection was first described by Newton and the relation is known as the Newton's Law of Cooling. The equation for convection can be expressed as:

q = h_c A dT,                                     (1)

where q = heat transferred per unit time, A = heat transfer area of the heated surface layer, h_c= convective heat transfer coefficient, and dT = temperature difference between the surface layer and the bulk fluid.

The convection heat transfer coefficient h_c for the surface layer is related to the heated surface layer Nusselt Number Nu_L by,

h_c = ( k/L) Nu_L                                        (2)

In this equation, k is the fluid's thermal conductivity, and L is the length of the heated surface layer.

The Nussult Number for this problem is given by,

Nu_L = 0.664 (Pr)1/3 (Re_L)1/2          (3)

where Pr is the fluid Prandtl Number, and Re_L is the fluid/heated surface layer Reynolds Number.

The Prandtl Number is given by,

Pr = c_p μ/k,                                         (4)

where c_p is the fluid’s thermal capacity and μ is the fluid’s viscosity.

The Reynolds Number is given by,

Re_l = ρu_fL/k,                                        (5)

where ρ is the fluid’s density and u_f  is the fluid’s velocity.

It can be seen that each fluid’s velocity corresponds a certain a certain heat transferred from the heated surface layer of the thermal flow sensor or a fixed input electrical power, because in the above equations only the fluid’s velocity is variable and the others are physical parameters of the fluid or geometrical parameters of the heated surface layer of thermal flow sensor.   

As well known all objects with a temperature above absolute zero emit heat energy in the form of radiation. Usually this radiation isn't visible to the human eye because it radiates at infrared wavelengths, but it can be detected by electronic devices such as MEMS infrared sensors. The MEMS infrared sensors measure temperature by converting infrared energy radiated from target objects into heat with MEMS thermopiles and then measuring the thermo-electromotive force resulting from temperature differences that occur across the contact points of two different types of metal.

The heat received by the thermopiles is very little and easy to dissipate by conduction. To solve this problem a micro-plate has been used to support the hot junction of the thermopiles, which is built over a cavity using low thermal conductivity materials such as a silicon-nitride, silicon dioxide or multilayered combination of these materials.