Wednesday, June 15, 2016

Temperature Detected by MEMS Thermopile Flow Sensors

Tu Xiang Zheng

A MEMS thermopile flow sensor provided by POSIFA Microsystems is composed of a membrane, a resistor, a thermopile and a silicon chip. The resistor and the hot junctions of the thermopile are disposed on the membrane that is suspending over a cavity. The cavity is recessed in a silicon chip and the bridges of the membrane is expended to and supported by the silicon chip. The legs of the thermopile pass through the bridges so that the cold junctions of the thermopile are disposed on the silicon chip.

When air flows over the surface of the sensor and the resistor of the sensor is heated up by a fixed input power, the output voltage of the thermopile depends on the temperature of the air.  This dependence can be seen from the input power expression:

Power = I * V = Am * km * (T – T0) / Lm + h * kair ((T – T0) + Am * Jr      (1)

I is the current being passed through the resistor, V is the voltage measured across the resistor, T is the temperature of the membrane and T0 is the temperature of the air. Am is the effective cross section area that heat is transported across the membrane, km is the thermal conductivity of the membrane, and Lm is the distance along the membrane that the temperature gradient is established, Am is the surface area of the membrane, hair is air natural or free convection coefficient, kair is the thermal conductivity of air and Jr is radiation heat flux of the membrane.

The air natural convection coefficient hair can be expressed as:

h   =   C*(kair / L) * {[ρ * gc * β * L3 * (T – T0)] / [μ * kair]}n       (2)

L is the length of the membrane, ρ is the density of air, gc is the gravitational acceleration, β is the coefficient of thermal expansion of air and μ is the dynamic viscosity. The value of constant C and exponent n are equal to 0.54 - 0.25, 1.32 – 0.25, respectively. Actually, equation (2) is an empirical formula the natural convection h of air is approximately equal to 10.45.  So it is true that the output voltage of the thermopile depends on the temperature of the air, if the membrane is kept a constant temperature above the temperature of air.

One widespread method of temperature measurement of air is thermistor-based temperature measurement, typically platinum (Pt) resistors-based. The reason is that Pt resistors are superior in terms of accurate temperature coefficient of resistivity (TCR) and, therefore, have better defined temperature dependence.

However, during the temperature measurement, one significant problem in Pt resistors based temperature measurement is that the self-heating effect causes a temperature rise in the sensor element. Self-heating effect is that when a current flows through a thermistor, it will generate heat which will raise the temperature of the thermistor above that of its environment. If the thermistor is being used to measure the temperature of the environment, this electrical heating will introduce a significant error if a correction is not made.

One of the temperature measurement methods which do not have the problem of self-heating or poorly IC-process compatible is thermopile-based temperature measurement. In additional, thermopiles is based on the self-generating Seebeck effect, this ensures that:
  • the output signal generated by the thermopile which has no offset or no offset drift, because there cannot be any output signal without input power,
  • the thermopile does not suffer from interference from power supplies or any physical or chemical signals except light (which can easily be shielded),because the Seebeck effect and the photoelectric effect are the only two self-generating effect in silicon,
  • the thermopile does not need any biasing, and
  • the read-out circuit is quite simple, only a voltmeter is required.


Moreover, the sensitivity of the thermopile is hardly influenced by variations in the electrical parameters across the wafer or by the temperature of the environment. Unlike transistors and resistors, whose sensitivity and offset depend on the position on the wafer and the temperature.

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