Heat transport in thin dielectric films

Heat transport in thin dielectric films S.-M. Lee and David G. Cahill Citation: J. Appl. Phys. 81, 2590 (1997); doi: 10.1063/1.363923 View online: http://dx.doi.org/10.1063/1.363923 View Table of Contents: http://jap.aip.org/resource/1/JAPIAU/v81/i6 Published by the American Institute of Physics.

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Heat transport in thin dielectric films S.-M. Lee and David G. Cahilla) Department of Materials Science and Engineering, and the Coordinated Science Laboratory, University of Illinois, Urbana, Illinois 61801

~Received 11 December 1995; accepted for publication 10 December 1996! Heat transport in 20–300 nm thick dielectric films is characterized in the temperature range of 78–400 K using the 3v method. SiO2 and SiNx films are deposited on Si substrates at 300 °C using plasma enhanced chemical vapor deposition ~PECVD!. For films .100 nm thick, the thermal conductivity shows little dependence on film thickness: the thermal conductivity of PECVD SiO2 films is only ;10% smaller than the conductivity of SiO2 grown by thermal oxidation. The thermal conductivity of PECVD SiNx films is approximately a factor of 2 smaller than SiNx deposited by atmospheric pressure CVD at 900 °C. For films ,50 nm thick, the apparent thermal conductivity of both SiO2 and SiNx films decreases with film thickness. The thickness dependent thermal conductivity is interpreted in terms of a small interface thermal resistance R I . At room temperature, R I ;231028 K m2 W21 and is equivalent to the thermal resistance of a ;20 nm thick layer of SiO2 . © 1997 American Institute of Physics. @S0021-8979~97!06406-2#

I. INTRODUCTION

II. EXPERIMENTAL

Thin dielectric films of SiO2 and SiNx are commonly used as interconductor dielectrics and passivation layers in microelectronics. As switching speeds and circuit densities rise, heat transport in these layers becomes increasingly critical in determining the operating temperature and therefore the reliability of microcircuits. The thermal properties of thin dielectric layers are also crucial for understanding the thermal response of magneto-optic storage devices, thin film sensors, optical coatings, and vertical cavity emitting lasers. The thermal conductivity of thin (;100 nm thick! SiO2 films has been the subject of several experimental studies. Often, the apparent thermal conductivity of the film has been observed to depend strongly on film thickness, an effect attributed to an anomalously large interface thermal resistance.1–3 For somewhat thicker films, however, our previous studies of a-Si and sputtered optical coatings have shown no evidence for a large interface thermal resistance.4,5 Recent studies by Goodson and co-workers have also shown that the interface resistance is small in data acquired near room temperature.6,7 To resolve this controversy, we extend the previous studies to include both the temperature and thickness dependence of heat transport in SiO2 and SiNx films, 20–300 nm thick. We find that the thermal conductivity has little dependence on film thickness for films as thin as 100 nm. For films less than 50 nm thick, the apparent thermal conductivity decreases with film thickness and we interpret this result in terms of a temperature dependent interface resistance. The size of the interface resistance, while much smaller than many previous studies, is significantly larger than can be easily accounted for based on simple models of the solidsolid thermal boundary resistance. a!

Electronic mail: [email protected]

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J. Appl. Phys. 81 (6), 15 March 1997

A. Sample film preparation and characterization

Our procedure for preparing samples includes three depositions, and two photolithography and etching steps, see Fig. 1. First, we deposit a 200 nm thick film of SiO2 on a 132 cm2 Si substrate using plasma-enhanced chemical vapor deposition ~PECVD!. Details of the deposition parameters are listed in Table I. Then, using photolithography, a small rectangular window with dimensions 0.130.3 cm2 is etched with a standard buffered oxide etch; the ratio of HF to NH4 F is 1:7. On this ‘‘windowed’’ substrate, we then deposit the sample dielectric film, 20–300 nm thick. Next, the heater/thermometer metallization—a ;2 nm adhesion layer of Cr8 followed by .300 nm of Au—is deposited by thermal evaporation. Finally, the metal film is patterned into the shape shown in Fig. 2 using photolithography and wet chemical etching. The width of the heater line is typically 8 m m and the room temperature resistance of a 1 mm length of the metal line is ;10 V. The two layers of dielectrics are needed to insure that the metallization for the heater/thermometer test pattern is adequately insulated from the Si substrate. Since our measurement method ~see discussion below! makes use of the small non-linear resistance created by the self-heating of a pure metal conductor, any extrinsic non-linearities from electrical contacts between the test pattern and the substrate can easily ruin the measurements. For our thinnest dielectric films, we found that pin-holes, presumably caused by particulates, often lead to an unacceptably large electrical conductance between the metal film and the substrate. The two-layer dielectric described above allows us to insulate the large area contact pads from the substrate using a relatively thick ~200 nm! SiO2 layer that minimizes problems with pin-holes; the electrical resistance between the metallization and substrate is then .40 MV for sample films as thin as 20 nm. Ellipsometry ~Gaertner model L116C! data are analyzed to extract the index of refraction and the film thickness of the

0021-8979/97/81(6)/2590/6/$10.00

© 1997 American Institute of Physics


FIG. 2. Pattern for the heater/thermometer line and contact pads. The width of the heater/thermometer line w is typically 8 m m and the length l51.0 mm.

pore volume fraction of .25% relative to typical APCVD films. B. 3v method for thin films FIG. 1. Process steps for sample preparation. A silicon wafer is first coated with 200 nm of SiO2 by PECVD. A window is etched in the oxide and a thin dielectric film, 20–300 nm thick, is deposited by PECVD. 300 nm of Au on a 2 nm Cr adhesion layer is deposited by thermal evaporation. The heater/ thermometer line and contact pads are patterned using photolithography and wet chemical etching.

dielectric films. In Fig. 3, we plot the film thickness t as a function of deposition time using ‘‘plasma enhanced’’ conditions; in other words, the deposition time is measured by the length of time that the rf power is turned on. The film thickness t does not extrapolate to zero at zero time, showing that the deposition rate is not constant during the initial stages of film growth. We characterize the film composition and density by Rutherford backscattering spectroscopy ~RBS!. Our PECVD films are silicon rich: for SiO2 , the Si:O ratio determined by RBS is 1:1.8 and for SiNx , the Si:N ratio is 1:1.1. In combination with film thickness measurements using ellipsometry, RBS also yields the film densities: for our SiO2 films r 52.160.1 g cm23 ~comparable to SiO2 bulk density of r 52.2 g cm23 ) and for our SiNx films, r 52.260.1 g cm23 . The density of our SiNx film is smaller than typical values, 2.5–2.8 g cm23 for PECVD and 2.8–3.1 g cm23 for APCVD.9 If we assume that the density deficits of the films are due to micropores, we estimate that our SiO2 films have a pore volume fraction of .5%, while our SiNx films have a

Details of the thermal conductivity measurement technique, the 3v method and its extension for thin films, are described in previous publications.4,10 In brief, the 3v method for thin films uses a single metal-line as both the heater and thermometer. An ac driving current at angular frequency v heats the surface of the dielectric film at a frequency 2 v . Since the resistance of a pure metal increases with temperature, these temperature oscillations also produce an oscillation of the electrical resistance at a frequency of 2 v . Consequently, the voltage drop across the metal line has a small component at 3 v that can be used to measure the temperature oscillations and therefore the thermal response of the dielectric film and substrate.

TABLE I. Deposition parameters for plasma enhanced chemical vapor deposition ~PECVD! of SiO2 and SiNx . rf frequency is 13.56 MHz. SiO2

SiNx

sources

5.3% SiH4 /N2 30.9 sccm 5.3% SiH4 /N2 60 sccm N2 O 120 sccm NH3 1.5 sccm total gas pressure ~Torr! 1.0 1.8 RF power ~W! 17.0 16.0 temperature (°C! 300 300

J. Appl. Phys., Vol. 81, No. 6, 15 March 1997

FIG. 3. Film thickness t measured by ellipsometry as a function of the deposition time. The growth rates for SiO2 and SiNx films are 21 and 22 nm min21 , respectively. Deposition time is measured by the time that the rf power is turned on. S.-M. Lee and D. G. Cahill


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FIG. 4. Measured amplitude of the temperature oscillation, DT, of the heater/thermometer line as a function of the frequency of drive current: DT5DT Si1DT f , where DT Si is the calculated thermal response of the Si substrate ~solid and dashed lines! and DT f is the temperature drop through the thickness of the dielectric film. For this example, the dielectric film is 45 nm of SiO2 . Due to the finite thickness of the Si substrate, the data for DT bend upward at low frequencies.

Because the dielectric film is thin, the through-thickness heat transport in the dielectric layer simply adds a frequency independent DT f to the thermal response of the Si substrate DT Si , see Fig. 4. The slope of DT versus ln(v) yields the thermal conductivity of the Si substrate L s . For completeness, the thermal conductivity of the Si substrates used in this work is shown in Fig. 5. These data, in conjunction with literature values for the specific heat of Si13 and the width of the metal line, allow us to calculate the expected thermal response of the substrate DT Si , i.e., the temperature oscillations at the interface between the dielectric layer and the Si wafer. Then, DT f 5DT2DT Si . This method for determining DT f has been previously checked using MgO substrates; for insulating substrates the thermal response can be measured directly but for semiconducting Si substrates used in this work, the bare substrate thermal response must be calculated. We calculate the in-phase component of DT Si using:10,14 DT Si5

F S

D

G

1 L Si P 1 ln ln~ 2 v ! , 2 1h2 l p L Si 2 C Si~ w/2! 2

~1!

where L Si , C Si , w, and l are the thermal conductivity of Si, heat capacity of Si, width of the heater, and length of the heater, respectively. The analytical solution of Ref. 10 gives h 50.923; experiments on a-SiO2 and MgO substrates show that h 51.05 more accurately describes the results of experiments. Since all film thicknesses t studied in this work are far smaller than the width of the heater w, heat flow in the dielectric layer is one-dimensional and the apparent thermal conductivity L a of the layer can be found using DT f 5 2592

P t , La w


~2!

FIG. 5. Thermal conductivity of Si substrates used in this work compared to the data from Ref. 11 and Ref. 12. The thermal conductivity of the substrate is measured by the slope of DT versus ln(v), see Ref. 10.

where P the amplitude of the heater power per unit length. Figure 4 also demonstrates the sensitivity of our method for ultra-thin dielectric layers. At room temperature, DT Si at 1 kHz is approximately the same as the DT created by a ;100 nm thick film of a-SiO2 , i.e., a thermal resistance of 1027 K m2 W21. We believe that our calculation of DT Si is good to 65% and that the uncertainties in this calculation dominate the measurement uncertainty for ultra-thin films;15 therefore, at room temperature, our experimental uncertainty is equivalent to a 5 nm thick layer of SiO2 or a thermal resistance of ;531029 K m2 W21. This source of errors decreases at lower temperatures because the thermal conductivity of Si increases rapidly with decreasing temperature, see Fig. 5. In practice, particularly at low temperatures, DT shows deviations at low frequencies from the expected ln(v) behavior because of the finite thickness of the Si substrate. As shown in Fig. 4, the slope of the DT versus ln(v) plot is steeper at low frequencies, a behavior caused by the thermal resistance between the Si substrate and the Cu sample holder. ~We use silicone vacuum grease to attach the Si wafers to the Cu sample holder.! The raw data, see Fig. 4, are monitored at each temperature to assure that the frequency used to find DT f is high enough to avoid this problem. In most cases, a measuring frequency of ;1 kHz is sufficient. III. RESULTS AND DISCUSSION

Thermal conductivity data for SiO2 and SiNx are summarized in Figs. 6 and 7, respectively. In both cases, as expected, the data show the characteristic temperature dependence of an amorphous solid in this temperature range: a gradual rise in the conductivity with increasing temperature. Data for SiO2 films .100 nm thick are only slightly smaller than data for thermally grown SiO2 , see Fig. 6; we have S.-M. Lee and D. G. Cahill


FIG. 6. Thermal conductivity of PECVD SiO2 films analyzed using Eq. ~2!. For films .100 nm thick, the conductivity approaches data for bulk aSiO2 . For thinner films, the conductivity decreases by a factor that is approximately independent of temperature.

previously shown that the thermal conductivity of a 1 m m thick film of thermally grown SiO2 is equivalent to the bulk glass over the entire temperature range of our measurements, 80–400 K. We also note that the thermal conductivity of PECVD SiO2 films is nearly identical to that of SiO2 grown by magnetron sputter deposition and approximately 30% larger than the thermal conductivity of SiO2 deposited by reactive evaporation.16 Since we are unaware of any data for bulk, amorphous Si3 N4 , our data for PECVD SiNx are compared to results obtained on a SiNx film grown by atmospheric pressure CVD ~APCVD! at 900 °C, see Fig. 7. Even relatively thick PECVD films of SiNx show a significant reduction relative to APCVD films; the conductivity is reduced by a temperature independent factor of ; 2. We cannot at this time be sure of the cause of this reduction although the volume fraction of micropores almost certainly plays a role. Effective medium theory17 provides a simple estimate of the reduction in thermal conductivity produced by nearly spherical voids: L5L m (121.5v ), where L is the thermal conductivity of a material with voids, L m is the conductivity of the ‘‘matrix,’’ i.e., the conductivity in the absence of voids, and v is the volume fraction of voids. If we attribute the density deficit in our films as arising from micro-pores in a fully dense matrix, v 50.25. If we further assume that L m is approximated by data for APCVD SiNx , then L50.63L m in reasonable agreement with our experimental results L PECVD .0.5L APCVD . In all cases, we observe a systematic decrease in the measured thermal conductivity as a function of film thickness; see Figs. 8 and 9. We envision three possible explanations for this result. The first possibility is that the intrinsic conductivity of the films decreases with film thickness beJ. Appl. Phys., Vol. 81, No. 6, 15 March 1997

FIG. 7. Thermal conductivity of PECVD SiNx films compared to data obtained on a 180 nm thick film grown by atmospheric pressure CVD ~APCVD! at 900 °C ~downward pointing triangles!.

cause of an altered microstructure or composition during the initial stages of deposition. While we cannot rule out this mechanism as an explanation of our data, we find it unlikely that the conductivity of films ;20 nm thick can be so drastically reduced relative to thicker films. The second possibility is that phonon boundary scattering reduces the thermal conductivity of the a-SiO2 layer; we argue against this explanation because phonons with mean-free-paths comparable to the thickness of our thinnest films do not contribute sig-

FIG. 8. Thermal conductivity of PECVD SiO2 films at 78 K and 300 K plotted as a function of film thickness. The data at 78 K are compared to data for PECVD films by Swartz and Pohl ~see Ref. 21!; the data at 300 K are compared to data by Goodson and co-workers ~LPCVD films at 400 °C! ~see Ref. 6!, and Ka¨ding and coworkers ~PECVD films at 300 °C! ~see Ref. 7!. The data of Swartz and Pohl were reanalyzed to extract the apparent conductivity, see Eq. ~2!. The solid lines are fits to Eq. ~3!: the decrease in conductivity for decreasing film thickness can be interpreted in terms of an interface thermal resistance of R I ;231028 K m2 W21 at 300 K and ;531028 K m2 W21 at 78 K. S.-M. Lee and D. G. Cahill


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FIG. 9. Thermal conductivity of PECVD SiNx films at 78 K and 300 K plotted as a function of film thickness. The solid lines are fits to Eq. ~3!. The decrease in conductivity for decreasing film thickness can be interpreted in terms of an interface thermal resistance of R I ;231028 K m2 W21 at 300 K and ;631028 K m2 W21 at 78 K.

smaller than the experimental data. Near-surface polishing damage might account for the additional thermal resistance in some cases,23 however, we find it unlikely that substantial polishing damage could exist in the near-surface region of a commercial Si wafer. More realistic models of transport at solid-solid interfaces22 may be required to produce a quantitative understanding of interface properties at T;300 K. Finally, we note the additional contributions to the thermal resistance arising from the finite thermal conductivity of the metal layers. The Au heater/thermometer film contributes to the measured value of R I since heat is generated throughout the metal film and this heat must pass through the Au film before entering the Cr adhesion layer. A straightforward calculation shows that the thermal resistance of a homogeneously heated metal film is given by R5(1/2)t/L. For a 300 nm thick Au film, R Au.231029 K m2 W21 , far smaller than our measured value of R I . The Cr adhesion layer is almost certainly heavily contaminated with oxygen, and therefore we cannot use the bulk thermal conductivity of pure Cr to estimate the contribution to the thermal resistance. However, since R I is comparable to a 20 nm thick layer of amorphous SiO2 , we cannot see how the finite thermal conductivity of this 2 nm Cr layer could significantly affect our results. ACKNOWLEDGMENTS

nificantly to the thermal conductivity at T.50 K.18–20 A third—and we believe, most satisfactory explanation—is that the apparent thermal conductivity is affected by an additional thermal resistance at the interface between the dielectric layer and the Si substrate and the interface between the heater/thermometer metallization and the dielectric layer. The presence of an interface thermal resistance R I can be included in the data analysis using L a5

Li . 11R I L i /t

~3!

Here, L i is the intrinsic thermal conductivity of the film, assumed to be independent of thickness t, and L a is the apparent thermal conductivity derived from Eq. ~2!. Using Eq. ~3! we estimate that R I ;231028 K m2 W21 for our SiO2 films near room temperature and that R I increases with decreasing temperature to R I ;531028 K m2 W21 at 78 K. R I is similar for the SiNx films: R I ;231028 K m2 W21 at 300 K and R I ;631028 K m2 W21 at 78 K. Our values for R I are comparable to R I estimated by Ka¨ding and co-workers7 for a Au/Cr/SiO2 /Si structure prepared in a manner similar to ours. Experiments designed to measure the thermal boundary resistance directly also obtain similar values for R I : data for Rh, Al, and Ti on single crystal Al2 O3 show thermal resistances of 0.522.031028 K m2 W21 near room temperature.21,22 In fact, we are unaware of any measurement of the solid-solid thermal boundary resistance that gives R I ,0.531028 K m2 W21 . Current theoretical understanding of thermal boundary resistance was recently reviewed by Swartz and Pohl:23 while the diffuse-mismatch model is in excellent agreement with data at T,20 K, near room temperature, the predicted thermal resistance is approximately an order of magnitude 2594


The authors thank Nae-Eung Lee for TEM studies, and Ivan Petrov for RBS data. This work was supported by National Science Foundation Grant No. CTS-9421089. Sample characterization was carried out in the Center for Microanalysis of Materials, University of Illinois, which is supported by the U.S. Department of Energy under Grant No. DEFG02-91-ER45439. 1

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