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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