Online proceedings - EDA Publishing Association

7-9 October 2009, Leuven, Belgium
Because D is finite, there is a finite delay before AC
ETF
power dissipated in the heater creates temperature fluctuations
at the thermopile. As such, an ETF can be seen as a thermaldomain
low-pass filter with temperature-dependent filtering
φ constant
characteristics.
f ETF
(T)
(a)
The filtering characteristics of an ETF can be analyzed by
modeling the thermal transfer impedance between the heater
and the junctions of the surrounding thermopile. For complex
heater geometries, such as in the ETF of Fig. 2, this can be
done by approximating the heater’s volume by a number of
spheres, for which the heat equation is solvable [15, 19]. Using
this model, the hot and cold junctions of the thermopile can be
located on contours of constant phase shift [15], so that the
vector sum of the various thermocouple voltages, and hence the
ETF’s output amplitude, is maximized.
Heater
Thermopile
Phase shift in degrees
100
80
60
f constant
ETF
φ ETF
f ETF
φ ETF (T)
(b)
(c)
160
110
60
Frequency in kHz
S
-60
0 60 120
Temperature in °C
Figure 3: Temperature-dependent ETF output characteristics for both phaseand
frequency readout.
100 µm
Figure 2: Photo of a CMOS ETF; the thermocouple junctions are aligned to
have the same thermal impedance to the center of the heater.
To understand how an ETF can be used to measure
temperature, we consider a simplified ETF, consisting of a
point heater and a point temperature sensor. When such an ETF
is driven at a frequency f ETF , it has a phase shift φ ETF , which can
be approximated by:
φ ∝ s
ETF
fETF
D( T )
If either f ETF or φ ETF is kept constant, as shown in Fig. 3a
and 3b respectively, the other will be a function of temperature.
Simulation results are shown in Fig. 3c (for s =20 μm, f constant =
85kHz, φ constant = 90°, D(300K) = 0.89cm/s 2 ).
(1)
From Eq. 1, it follows that in constant phase mode, f ETF (T)
is proportional to 1/T 1.8 , and that in constant frequency
mode, φ ETF (T) is proportional to T 0.9 . The effect of thermal
expansion on s is at the 0.05% level, and is neglected here.
The absolute accuracy of an ETF depends on the accuracy
of its geometry, defined by s, and on D. For IC-grade bulk
silicon, D is well-defined. For low doping levels, it is also
insensitive to process spread [4]. The temperature-sensing
inaccuracy of an ETF is therefore defined by spread in the
distance s, which is caused by lithographic error (e.g. mask
misalignment). This error can be minimized by making s
sufficiently large.
III. ETF READOUT ARCHITECTURES
The main problem associated with reading out an ETF is
its low output amplitude. Self-heating and power
consumption issues limit the amount of power that can be
dissipated in the ETF heater. Since silicon is a good thermal
conductor, this means that, for a heater power of say 2.5mW,
the temperature gradient across the thermocouples is only in
the order of 40mK. Assuming a thermopile made up of 20
thermocouples, each with a sensitivity of 0.5mV/K, this
leads to a thermopile output voltage with an amplitude of
about 400μV pp . Due to the presence of wideband white noise
from the thermopile’s resistance, the measurement
bandwidth then needs to be limited to about 0.5Hz to obtain
a temperature-sensing resolution of 0.05ºC.
©EDA Publishing/THERMINIC 2009 141
ISBN: 978-2-35500-010-2