A novel MEMS test structure and measurement procedure is presented with which the lateral thermal conductivity of thin films can be easily and accurately ...
2006 International Conference on Microelectronic Test Structures
MEMS test structure for measuring thermal conductivity of thin films L. La Spina, N. Nenadović*, A. W. van Herwaarden**, H. Schellevis, W. H. A. Wien, and L. K. Nanver Laboratory of Electronic Components, Technology & Materials, ECTM, DIMES, Delft University of Technology, P.O. Box 5053, 2600 GB Delft, The Netherlands. * N. Nenadović was with ECTM, DIMES, Delft University of Technology. He is currently with Philips Semiconductors CTO, 6534 AE Nijmegen, The Netherlands. ** A. W. van Herwaarden is with Xensor Integration, P.O. Box 3233, 2601 DE Delft, The Netherlands. achieved by, respectively, a resistor and a thermocouple fabricated in the same polysilicon layer. This gives a higher accuracy than when, for example, an aluminium resistor is used as thermometer [8]. A differential measurement technique is used with a set of two test structures where only the one is patterned with the film-toanalyze (FTA). In this case, the thermal resistance can be regarded as a parallel between the thermal resistances of the supporting membrane and of the FTA. Thus, the measured thermal conductances of the two test structures are subtracted from each other and used to extract the thermal conductivity of the FTA. The method is substantiated also by means of numerical simulations. Moreover, experimental results are given for the thermal conductivities of Al, AlN, and p-type polysilicon thin films.
ABSTRACT A novel MEMS test structure and measurement procedure is presented with which the lateral thermal conductivity of thin films can be easily and accurately extracted. The extraction procedure is discussed in detail and supported by numerical simulations. Experimental examples are given for the determination of the lateral thermal conductivity of aluminium (Al), aluminium nitride (AlN), and p-doped polysilicon (polySi) thin films. INTRODUCTION The performance and reliability of modern microelectronic and micro-electromechanical devices (MEMS) are often limited by the degree to which they and their surroundings can conduct heat. The materials used to form and insulate the devices are increasingly of a thin-film nature, the thermal conductivity of which is difficult to predict from handbook values for the corresponding bulk materials. This is because the thermal transport is to a great extent determined by, for example, phonon scattering on film boundaries and grains [1], [2]. In addition, for polycrystalline films, the thermal conductivity can be strongly anisotropic. Several different techniques have been developed in the past for measuring the thermal conductivity of thin-films [3]-[7]. Most of these require complicated measurement procedures and use of nonstandard, expensive equipment, such as, for example, infrared (IR) microscopes, acousto-optic modulators, lockin amplifiers, and charge-coupled device (CCD) cameras. In this paper, we describe a novel test structure and measurement procedure suitable to readily and accurately determine the lateral thermal conductivity of deposited thin films. Both the fabrication of the structure in silicon technology and the DC measurement procedure are straightforward. Heat generation and monitoring is
1-4244-0167-4/06/$20.00 ©2006 IEEE
TEST STRUCTURES: LAYOUT AND FABRICATION A microscope image, a schematic 3D layout, and a crosssection of the test structure are given in Fig. 1. The two test structures without the FTA and with the FTA are denoted MREF and MFTA, respectively. The processing is straightforward and can be accomplished in most labs equipped with MEMS processing capabilities. The starting material is a p-type silicon wafer that is coated with a 500nm-thick layer of low-stress LPCVD silicon nitride [9]. This layer acts both as a mechanical support for the membrane and as an etch-stop for the backside KOHetching. Then a 300-nm-thick polysilicon layer is deposited on the top of the SiN, implanted by phosphorous and boron through the respective resist masks, annealed, and patterned to form a heater resistor and an n-/p-doped polysilicon thermocouple. This is followed by deposition of a 500-nm-thick LPCVD TEOS layer, which insulates the polysilicon from the 600-nmthick physical-vapor-deposited (PVD) aluminum. The Al
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top of the stack. Finally, using a patterned silicon nitride layer as mask, the silicon substrate below the membrane area is etched away by anisotropic etching in a KOH solution, and the chips are diced, packaged and bonded. The packaged system contains a dedicated structure for
is patterned to form the electrical interconnections and to serve as a heat-spreader that homogenizes the heatdistribution over the whole area of the heating resistor. A 800-nm-thick PECVD SiO2 is deposited as insulation between the metallization and the FTA, which is put on the
Fig. 1. (a) Microscope image of MFTA, (b1) and (b2) schematic 3D layout of MREF and MFTA, respectively, and (c) cross-section along AA’ from (b2) of the test structure MFTA.
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thermocouple calibration, and the two test structures MREF and MFTA. Thus each test structure is comprised of an optional rectangularly patterned FTA, a temperature sensor and a heater all placed on a freestanding SiN membrane. In the absence of the underlying silicon substrate, the membrane confines the heat flow to the lateral direction. The polysilicon heater resistor fully surrounds the n-/ppolysilicon thermocouple fabricated in the middle of the membrane. The thermocouple is used to monitor the temperature difference ∆Ttp between the middle and the
FTA thermal conductance GTH of the FTA, an equivalent thermal resistance network, shown in Fig. 3, is used. Under this approximation, the thermal conductance of MFTA MREF FTA MFTA is GTH = GTH + GTH , and thus
FTA MFTA MREF GTH = GTH − GTH .
(4)
Finally, the thermal conductivity kTH of the film is obtained from the one-dimensional heat conduction equation: FTA L ⋅ GTH kTH = , (5) 2 ⋅W ⋅ d
edge of the membrane. The latter is kept at ambient temperature since the bulk silicon that supports the membrane can be assumed to be an ideal heat sink. Note that ∆Ttp depends both on the dissipated power and on the
where L is the distance between the thermocouple and the edge of the membrane, and d and W are the thickness and the width of FTA, respectively.
thermal conductance of the structure. MEASUREMENT PRINCIPLE In order to minimize the heat convection through air, the measurements are performed in a vacuum chamber at a pressure below 1 mPa. The electrical signals are handled with an Agilent 34970A data-acquisition system. The Seebeck coefficients α s1 and α s 2 , for p- and n-polysilicon respectively, are extracted at different temperatures, and they are reported in Fig. 2. The measured voltage Utp of the thermocouple is related to ∆Ttp through the following equation: U tp = (α s1 − α s 2 ) ∆Ttp .
(1)
The heater that has a resistance of Rh is biased by the voltage U h , which results in a power dissipation of U2 Ph = h . Rh
From (1) and (2), the thermal conductance is (α − α s 2 ) Ph P . GTH = h = s1 ∆Ttp U tp
Fig. 2. Seebeck coefficients of p- and n-doped polysilicon at different temperatures.
(2)
(3)
GTH is measured for both the structures MREF and MFTA, MREF MFTA and the results are denoted with GTH and GTH , respectively. To avoid errors that originate from the temperature dependence of the thermal conductivity, ∆Ttp is kept low
(no more than 20 °C) and equal for the two measurements by properly adjusting U hMREF and U hMFTA . To extract the
Fig. 3. Equivalent thermal resistance network for MFTA.
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be analyzed, is shown to not play any role, due to the differential nature of the measurement approach. Thirdly, the accuracy of modeling the thermal conductance with the network depicted in Fig. 3 is investigated by means of numerical simulations [10]. For a wide range of materials under test, this error proves to be in the order of 2 %. In addition, the one-dimensional approximation of the heat flow through the FTA is also studied by means of numerical simulations. Figs. 4(a) and (b) show temperature maps for the modules MREF and
DISCUSSION AND RESULTS The above extraction methodology is substantiated through analytical calculations and numerical simulations. Firstly, the effect of the radiation is calculated and shown to be negligible, which was expected since the temperature is kept low. Secondly, the heat lost by conduction through the aluminum interconnections, as well as the effect of the heat spreading through the SiO2 layer just below the material to
(a)
(b)
Fig. 4. Simulated temperature distributions. (a) Module MREF, and (b) module MFTA. To maintain
∆Ttp equal in (a) and (b), we set
where the FTA is a layer with a thermal conductivity of 25 Wm -1K -1 . The edges of the membrane are considered isothermal at 300 K.
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Ph( a ) = 16 ⋅ Ph( b ) ,
MFTA, respectively. As illustrated in the Fig. 4(b), the heat flows from the middle to the edges of the membrane in the direction of the y-axis, and the isothermal lines are parallel and equidistant within the FTA. Some inaccuracy is, however, introduced by the limited dimensions of the experimental structures and also by the uncertainties in the measured voltages and currents. The integration of the thermocouple into the test structure reduces the costs required for this kind of measurement, if compared to other techniques based on the usage of an IR camera or external sensors. In principle, an IR camera detects the incoming radiation power intensity and cannot determine temperature itself. The radiation power Q emitted from surface of a specimen can be calculated by the well-known equation Q = Aεσ∆T 4 , (6)
lower than the maximum experimental conductivity of AlN ceramics of about 270 Wm-1K-1 at room temperature [15]. This is not unusual, since the thermal properties of polycrystalline ceramics can depend strongly on the exact deposition conditions, the grain size and shape, the film thickness, and the impurity concentration. The measurements on the p-doped polysilicon also give results comparable to previously published values [3], [12], [16]. For the polysilicon results, it is clear that the thinner the film the lower the kTH , which agrees with the expected increase in thermal resistance due to phonon scattering at the interfaces.
Table I. Measured lateral thermal conductivities of different thin films and thermal conductivities of bulk materials at 300 K.
where A is the section area of the specimen, ε the emissivity of the specimen surface, and σ = 5.67 × 10−8 Wm-2 K -4 is the Stefan-Boltzmann constant. The value of ε can be a source of large uncertainty, especially for dielectric materials that often have very low emissivity. For this reason it is necessary to calibrate the relationship between the infrared intensity sensed by IR camera and the temperature measured by a thermocouple. Moreover, because the calibration is influenced by the environment, it is recommended to repeat the calibration procedure before each measurement [11]. It becomes clear that another advantage of the novel technique described in this paper is represented by the reduced calibration cost. In order to attain a temperature distribution over the material, instead of only a one-point measurement, it is possible to integrate several thermocouples in the test structure, and this is not an expensive step for the fabrication process employed. In conclusion, both the accuracy and cost issues favor the use of the present method. On the other hand, the advantage of an IR camera set-up is the versatility with which it can be used to investigate heat distributions in more complicated structures. Some measurement results are summarized in Table I. The Al and AlN films are deposited by PVD. The lateral thermal conductivity of the LPCVD p-polysilicon is extracted from structures that use the polySi resistor layer also as FTA instead of adding an extra poly deposition. The kTH = 180 Wm -1K -1 determined for the 1.4 µm Al film is lower than the bulk value of 238 Wm-1K-1 and is in reasonable agreement with values reported in literature [12]. The measured lateral thermal conductivity of the AlN films is within the range of values ( 0.4 − 26 Wm -1K -1 ) found by other authors [13], [14]. These values are much
Material
Thickness [µm]
⎡ W ⎤ kTH ⎢ ⎥ ⎣m⋅K⎦
Reference
Al Al AlN AlN AlN AlN AlN Si p-polySi p-polySi p-polySi
Bulk 1.4 Bulk 4 1.7 1 0.7 Bulk 1 0.3 0.15
237 180 270 11.7 10.8 11.0 10.3 148 45.6 27 19.2
[17] [this work] [15] [this work] [this work] [this work] [this work] [17] [16] [this work] [this work]
CONCLUSIONS The simulation and modeling results show that the presented test structure and measurement procedure are well-suited for accurate determination of the lateral thermal conductivity of a wide range of deposited thin– film materials. The experiments on Al, AlN, and doped polysilicon thin films presented in this work give results that are very plausible in view of the values reported by other authors. The general spread in values between the different investigations underlines the fact that thin-film properties can be very dependent on the exact deposition conditions and a determination of the thermal conductivity through measurement is indispensable.
AKNOWLEDGEMENTS The authors would like to thank the staff of the DIMESICP group for their support, in particular E. J. G. Goudena for organization of the experimental runs.
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