The Thermal Conductivity of Porous Silicon
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The development of thermal sensors and transducers is an important challenge in applied microsystem technology. Here, very often a sensor structure must be thermally isolated to get a large temperature signal from a small amount of power. An example are thermal infrared sensors (bolometers, thermocouples) and thermal gas sensors (pellistors, thermal conductivity sensors). Normally the thermal isolation is performed by the use of free standing membranes or bridges made of an insulating material like silicon nitride, oxide or carbide. To realize the free standing structure, anisotropic etching or surface micromachining is used. Another possibility for thermal isolation is the use of a thick silicon oxide made by the oxidation of porous silicon 1. Since porous silicon has a very low thermal conductivity itself, it can be directly used for the purpose of thermal isolation. To evaluate the opportunities it is necessary to obtain data on the thermal conductivity of porous silicon.
561
Mat. Res. Soc. Symp. Proc. Vol. 358 0 1995 Materials Research Society
Experimental The characteristics of the samples investigated are given in Table 1. The electrochemical cell we used and the way we anodized the samples are described in Ref 2. Due to its large inner surface area, porous silicon is easily oxidized without high-temperature treatment. Since oxidation changes the thermal conductivity, we also investigated oxidized material. The oxidation was performed in 02 at a temperature of 3000C for 1 hour.
Name of
I
II
III
sample
(DB16)
(DC161)
(DK3)
Doping
p(B)
n(P)
p(B)
Resistivity
(acm
38.0 52.0
1 -2
0.010 0.018
Current density
mA/cm 2
30
10
50
Etching time
s
420
900
240
Light applied
none
visible 500 W
none
Porosity
40%
53%
45%
10
10
Type
p"
n
10 p+
Morphology
nano
nano + macro
meso
Thickness
Pm
Thermal conductivity as prepared
W/mK
1.2
1.75
80
Thermal conductivtiy oxide
W/mK
1.3
1.85
2.7
Table 1:
-
The samples used: Doping, etching parameters, measurement results. 562
In order to determine the thermal properties of porous silicon, a dynamic method of measurement was used 3. The surface of the sample is exposed to a periodic temperature modulation. This way an oscillating temperature field in the sample is generated. For this specific boundary condition, the thermal conduction equation can be solved by a temperature field which looks like a critically damped wave. The phase shift of this "thermal wave" is analysed. While the heat is transported by heat conduction, a phase difference arises between the point of measurement and the point where the waves have been created. With increasing distance from this point, the thermal wave is increasingly damped. When the sample consists of several layers which possess different thermal properties (thermal conductivity X, heat capacity cp) a reflection of the thermal waves occurs at the boundary of each layer. The system is shown in Fig. 1: The flat sample (approximately 25 mm x 25 mm) is held by a clamp between the heater and the
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