Thermal resistance measurement

Oettinger, EE and Blackburn, D.L. 1990. Semiconductor Measurement Technology Thermal Resistance Measurements. NIST Special Pub. 400-86, Washington, DC. 

This temperature coefficient k will vary from device type to device type and from wafer lot to wafer lot. Therefore, to obtain accurate temperature measurements, each wafer lot must be calibrated by running a temperature vs. Vp curve as shown in Figure 3.27. However, for many applications, accurate measurements are not required to detect defects in assembly. A large amount of voiding will show up as an abrupt change from nominal in the thermal resistance measurement. 

C-SAM is a nondestructive test that provides voiding information on the heat path. By correlating the location and amount of voiding in conjimction with thermal modeling, C-SAM becomes a method that indirectly provides thermal resistance measurements. 

Curves of Figure 19 compare the data published for (a) boron nitride [37,40] (b) aluminium (c) diamond-[37-39] (d) aluminium nitride [37-42] (e) crystalline silica. It can be seen that, at 45 vol.%, the maximum thermal conductivity achieved with diamond powder is 1.5 W m K, while crystalline boron nitride at 35 vol.% affords 2.0Wm K. The thermal conductivity of silver-filled adhesives was studied by using silicon test chips attached to copper and molybdenum substrates [43]. The authors outline the importance of the shape factor A, related to the aspect ratio of the particles, to achieve the highest level of thermal conductivity. Another study reports the variation of the effective thermal resistance, between a test chip and the chip carrier, in relation to the volume fraction of silver and the thickness of the bond layer [44]. The ultimate value of bulk thermal conductivity is 2 W m at 25 vol.% silver. However, the effective thermal conductivity, calculated from the thermal resistance measurements, is only one-fifth of the bulk value when the silicon chip is bonded to a copper substrate. 

Phosphatase Test. The phosphatase [9001-78-9] test is a chemical method for measuring the efficiency of pasteurization. AH raw milk contains phosphatase and the thermal resistance of this enzyme is greater than that of pathogens over the range of time and temperature of heat treatments recognized for proper pasteurization. Phosphatase tests are based on the principle that alkaline phosphatase is able, under proper conditions of temperature and pH, to Hberate phenol [108-95-2] from a disodium phenyl phosphate substrate. The amount of Hberated phenol, which is proportional to the amount of enzyme present, is determined by the reaction of Hberated phenol with 2,6-dichloroquinone chloroimide and colorimetric measurement of the indophenol blue formed. Under-pasteurization as well as contamination of a properly pasteurized product with raw milk can be detected by this test. 

A guarded hot-plate method, ASTM D1518, is used to measure the rate of heat transfer over time from a warm metal plate. The fabric is placed on the constant temperature plate and covered by a second metal plate. After the temperature of the second plate has been allowed to equiUbrate, the thermal transmittance is calculated based on the temperature difference between the two plates and the energy required to maintain the temperature of the bottom plate. The units for thermal transmittance are W/m -K. Thermal resistance is the reciprocal of thermal conductivity (or transmittance). Thermal resistance is often reported as a do value, defined as the insulation required to keep a resting person comfortable at 21°C with air movement of 0.1 m/s. Thermal resistance in m -K/W can be converted to do by multiplying by 0.1548 (121). 

As predicted by the Arrhenius equation (Sec. 4), a plot of microbial death rate versus the reciprocal or the temperature is usually linear with a slope that is a measure of the susceptibility of microorganisms to heat. Correlations other than the Arrhenius equation are used, particularly in the food processing industry. A common temperature relationship of the thermal resistance is decimal reduction time (DRT), defined as the time required to reduce the microbial population by one-tenth. Over short temperature internals (e.g., 5.5°C) DRT is useful, but extrapolation over a wide temperature internal gives serious errors. 

The PMV index can be determined when the activity (metabolic rate) and the clothing (thermal resistance) are estimated and the following environmental parameters are measured air temperature, mean radiant temperature, relative air velocity, and partial water vapor pressure (see ISO EN 7726). 

Thermal resistance is the reciprocal of thermal conductance. It is expressed as m KTW. Since the purpose of thermal insulation is to resist heat flow, it is convenient to measure a material s performance in terms of its thermal resistance, which is calculated by dividing the thickness expressed in meters by the thermal conductivity. Being additive, thermal resistances facilitate the computation of overall thermal transmittance values (t/-values). 

Conducted heat is that going in through cold store surfaces, tank sides, pipe insulation, etc. It is normally assumed to be constant and the outside temperature an average summer temperature, probably 25-2/°C for the UK, unless some other figure is known. Coldroom surfaces are measured on the outside dimensions and it is usual to calculate on the heat flow through the insulation only, ignoring other construction materials, since their thermal resistance is small. 

In 1941, Kapitza [54] reported his measurements of the temperature drop at the boundary between helium and a solid (bronze) when heat flows across the boundary. More than ten years later, Khalatnikov (1952) presented a model, an approximation to what is now known as the acoustic mismatch model , to explain that a thermal resistance Rk (thermal boundary resistance) occurs at boundaries with helium [55],... 

Bridges give a mean resistance value around 7 = 0. Strictly, they should be used only for linear components. In both cases (d.c. or a.c.), the resistance measurements are made in four-wire configuration, since the resistor to be measured is at low temperature whereas the measuring instrument is at room temperature the electric connection is usually made by low thermal conductivity wires which are also poor electrical conductors (remind the Wiedeman-Franz law). 

The thermal resistance between the ends of the sample and the copper blocks must be negligible compared with the thermal resistance of the sample. This assumption must be verified especially for short samples at low temperature where the contact resistance is higher. For this reason, a second measurement of the thermal conductivity of Torlon in the 4.2-25 K range was carried out. The second sample had a different length (L = 24.51 mm) and the same section A. This additional measurement gave the same value of k within 2%. Moreover, we see from Fig. 11.15 that data of thermal conductivity at 4.2 K well join data at lower temperatures (within 3%) obtained on a sample of much smaller geometrical factor and with a different method (integrated thermal conductivity method) and a different apparatus [38], Finally, at room temperature, we find k = 0.26 W/mK, which is the data sheet value. 

Let us examine in Fig. 12.1 a schematics of a set up for heat capacity measurement a support (Sp) of heat capacity CSp is thermally linked to the thermal bath through a thermal resistance RG = l/G. 

It can be observed that the bulk thermal conductance of the tin cylinders [23] and of the NbTi wires [24] are respectively about two orders of magnitude higher and four order of magnitudes lower than the measured G(7). Therefore, the main contribution to G is the thermal conductance of the contacts Cu/Sn and Sn/Te02. The exponent between 2 and 3 has been already reported for measurements of contact thermal resistances between solids at very low temperatures [25]. 

Cone. This type of crucible shape (Fig. 8 c) provides an increased contact area between crucible and its counterpart on the crucible holder. Especially in the combination TG-DTA this decreases the thermal resistance and allows a better resolution of the measured DTA-effect. 

The thermal resistance will be temperature-dependent as canbe seen in Eq. (3.24), which is not only a consequence of the temperature dependence of the thermal heat conduction coefficients. The measured membrane temperature, Tm, is related to the location of the temperature sensor, so that the temperature distribution across the heated area will also influence the thermal resistance value. The nonlinearity in Eq. (3.24) is, nevertheless, small. The expression thermal resistance consequently often refers to the coefficient t]o only, which is used as a figure of merit and corresponds, according to Eqs. (3.24) and (3.25), to the thermal resistance or thermal efficiency of the microhotplate at ambient temperature, Tq. The temperature Tm can be determined from simulations with distinct heating powers. The thermal resistance then can be extracted from these data. 

The relationship between the temperature difference, AT, and the input power is shown in Fig. 4.5 for microhotplate simulations and measurements. The simulated values are plotted together with the mean value of the experimental data for a set of three hotplates of the same wafer. The experimental curve was fitted with a second-order polynomial according to Eq. (3.24). As a result of the curve fit, the thermal resistance at room temperature, tjo, is 5.8 °C/mW with a standard deviation of 0.2 °C/mW, which is mainly due to variations in the etching process. 

The coefficients of thermal resistance can either be measured for existing devices or be calculated with the thermal microhotplate model presented in Chap. 3. In analogy to resistor-heated membranes, the model can be used for evaluation and optimization of new designs. A combination of the presented transistor model equations with the lumped microhotplate model in Sect. 3.4 would allow to also derive an AHDL model for coupled-system simulations. 

The thermal resistance of the circular hotplate was measured to be 5.8 °C/mW for the coated and uncoated transducer. An increased thermal resistance is desirable for sensor arrays with one approach being the reduction of the heated membrane area. At the moment the smallest possible diameter of drop-deposited tin-oxide is 100 pm. A microhotplate with a heated area of 100 pm in diameter was fabricated and featured an increased thermal resistance of approximately 10 °C/mW. 

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