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Temperature-Dependent Thermal Conductivity of Single-Crystal M. Asheghi Temperature-Dependent Thermal M. N. Touzelbaev Conductivity of Single-Crystal Silicon Layers in SOI Substrates K. E. Goodson Self heating diminishes the reliability of silicon-on-insulator (SOI) transistors, partic­ [email protected] Mechanical Engineering Department, ularly those that must withstand electrostatic discharge (ESD) pulses. This problem Stanford University, is alleviated by lateral thermal conduction in the silicon device layer, whose thermal Stanford, CA 94305-3030 conductivity is not known. The present work develops a technique for measuring this property and provides data for layers in wafers fabricated using bond-and-etch-back (BESOI) technology. The room-temperature thermal conductivity data decrease with Y. K. Leung decreasing layer thickness, ds, to a value nearly 40 percent less than that of bulk silicon for ds = 0.42 \xm. The agreement of the data with the predictions of phonon transport analysis between 20 and 300 K strongly indicates that phonon scattering S. S. Wong on layer boundaries is responsible for a large part of the reduction. The reduction is also due in part to concentrations of imperfections larger than those in bulk Electrical Engineering Department, samples. The data show that the buried oxide in BESOI wafers has a thermal conduc­ Stanford University, tivity that is nearly equal to that of bulk fused quartz. The present work will lead to Stanford, CA 94305-3030 more accurate thermal simulations of SOI transistors and cantilever MEMS struc­ tures. 1 Introduction bulk material. The higher concentrations result from steps in the wafer fabrication process, such as SIMOX implantation Silicon-on-insulator (SOI) circuits promise advantages in (e.g., Cellar and White, 1992) and the epitaxial growth process speed and processing expense compared to circuits made from bulk silicon (e.g., Peters, 1993). The buried silicon-dioxide of BESOI wafers (Maszara, 1991). While the impact of these layer in SOI circuits has a very low thermal conductivity, which imperfections on electrical transport has been studied, there has results in a large thermal resistance between the device and the been little progress on modeling or measuring their impact on chip packaging. This is a major problem for transistors that heat transport. Finally, the impurities and additional free carriers experience brief pulses of heating, such as ESD protection de­ in doped semiconducting regions impede heat transport com­ vices (e.g., Amerasekera et al, 1992), for which the tempera­ pared to that in bulk intrinsic silicon (Goodson and Cooper, ture rise is dominated by conduction within micrometers of 1995). There are data available for the thermal conductivity of active regions. Lateral conduction parallel to the plane of the bulk doped samples (Touloukian et al., 1970a) which show a strong reduction for impurity concentrations greater than about wafer in the silicon device layer can strongly reduce the temper­ 19 -3 ature rise in active regions, such as the transistor channel (Good- 5 X 10 cm , but it is not clear if the bulk data are appropriate son et al., 1995). However, this effect cannot be accurately for layers doped using thin-film implantation and diffusion tech­ predicted at present because the thermal conductivity of the niques. device layer is not known. The lateral thermal conductivity of Previous work (Paul et al., 1993, 1994; Von Arx and Baltes, the silicon layer in SOI substrates is also important for the 1992; Von Arx et al, 1995; Mastrangelo and Miiller, 1988; Tai design of many MicroElectroMechanical Systems (MEMS) et al., 1988) measured the lateral thermal conductivity of doped which use single-crystal silicon cantilevers that are etched from polysilicon layers. These authors reported a reduction of up to SOI substrates. One example is the cantilever of Chui et al. 80 percent compared to the conductivity of bulk intrinsic silicon. (1996), which uses heat pulses to make sub-micrometer pits in While it is not clear which of the mechanisms shown in Fig. 1 PMMA for high-density data storage. is responsible for the reduction in the polysilicon layers for Heat conduction in silicon is dominated by phonon transport, which data are available, it is likely that the grain boundaries even in the presence of large concentrations of free charge are responsible for a fraction of the reduction. It would therefore carriers. The device-layer thermal conductivity is reduced com­ be inappropriate to assume that the thermal conductivity of the pared to that of bulk silicon due to scattering mechanisms in crystalline layers in SOI substrates can be determined using the the layer that are not present in the bulk material, such as those existing data for poly crystalline samples. depicted in Fig. 1. Phonon-boundary scattering is particularly Very few data are available for the thermal conductivity of important at low temperatures, where the mean free path would single-crystal silicon samples with submillimeter dimensions. otherwise become arbitrarily large. While phonon-boundary in­ Savvides and Goldsmid (1973) measured the thermal conduc­ teractions govern the thermal conductivity of any silicon sample tivity of pure and neutron-irradiated crystalline silicon with di­ at low enough temperatures, the reduction is more severe and mensions comparable to 20, 40, 60, and 100 p,m at temperatures extends to higher temperatures for thin layers than for bulk of 200 and 300 K. They did not observe a size effect on the samples. Also important is phonon scattering on imperfections, thermal conductivity even for the thinnest pure silicon specimen which exist in larger concentrations in SOI substrates than in at 200 K. Yu et al. (1996) measured the thermal diffusivity of a 4 fim thick, free-standing silicon film at room temperature and observed no significant reduction in the thermal diffusivity Contributed by the Heat Transfer Division for publication in the JOURNAL OF compared to that of bulk samples. However, a recent study HEAT TRANSFER and presented at the 1996 ASME IMECE. Manuscript received by the Heat Transfer Division August 21, 1996; revision received September 23, reported a two orders of magnitude reduction in the thermal 1997; Keywords: Conduction; Measurement Techniques; Thermophysical Proper­ conductivity of a 0.15 //m thick silicon layer made using SI­ ties. Associate Technical Editor: A. S. Lavine. MOX technology at temperatures between 330 and 380 K 30 / Vol. 120, FEBRUARY 1998 Copyright © 1998 by ASME Transactions of the ASME Downloaded 21 Nov 2008 to 171.64.49.29. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm PHONON- PHONON- PHONON- PHONON- scattering. The potential for such fundamental study is particu­ BOUNDARY IMPERFECTION IMPURITY ELECTRON SCATTERING SCATTERING SCATTERING SCATTERING larly large in SOI wafers, whose device layers resemble the bulk material in purity and microstructural quality. yfV IMPERFECTION PHONON PHONON 2 Experimental Structures and Procedure PHONON ds Figure 2 shows a cross-sectional schematic and an electron micrograph of the experimental structure used to measure the „..,,.,„., IMPURITY • lateral thermal conductivity of the SOI device layer. The wafers PHONON ATnM „ crTnn„ in the present study are fabricated using BESOI technology, in which ap+ epitaxial layer doped with about 1020 boron atoms Fig. 1 Phonon scattering mechanisms which reduce the thermal con­ 3 ductivity of SOI device layers compared to that of bulk intrinsic silicon. ever serves as the etch stop. The device layer is grown on the The thermal conductivity of silicon is dominated by phonon transport. etch-stop layer and is doped with less than 1015 boron atoms cm"3 due to the residual boron in the chamber. After the bond­ ing, the silicon substrate is etched with a KOH/isopropyl alco­ + + (Zheng et al, 1996). These data motivate the present study, hol solution which stops at the p layer. The p layer is then which provides a systematic measurement of the thermal con­ removed using a 1:3:8 solution of 49 percent HF, 70 percent ductivities of single-crystal silicon layers of thickness compara­ HN03, and 98 percent CH3COOH. This solution selectively + ble to and less than one micrometer. The resulting data are of etches the p region and stops at the undoped layer. The moder­ practical relevance for SOI devices and are of fundamental ately doped bridge, which is used here as a heater for the thermal interest because of the information they provide about phonon conductivity measurements, is fabricated using a 50 keV im­ 15 2 free paths in the bulk material. plantation of BF2+ with dosage 5 X 10 cm" and a subsequent This work develops a technique for measuring the lateral 30 minute anneal at 1220 K. Two sets of structures are used in thermal conductivity of SOI device layers. The technique has the present study, distinguished by the die from which they are the advantage that it uses doping and photolithography tech­ fabricated. Data reported here over the temperature range of 20 niques that are compatible with CMOS technology, such that it to 300 K are obtained from die no. 1 with silicon device layer can be directly integrated onto an SOI wafer for parallel device thicknesses ds = 0.42, 0.83, and 1.6 p,m and buried oxide thick­ and thermal-property characterization. The measurements yield ness d0 = 3 /xm. Data are obtained from die no. 2 at room the vertical thermal resistance of the buried silicon dioxide as temperature, with silicon device layer thicknesses ds = 0.42, well as the lateral thermal conductivity of the silicon device 0.72, and 1.42 /jm. The dies are attached within a 68-pin leadless layer using two separate structures. This manuscript reports data chip carrier device package, wire bonded, and mounted on the for BESOI silicon layers of thickness between 0.4 and 1.6 /jm chip-carrier assembly of an open-circuit MTD-160 cryogenic at temperatures between 20 and 300 K.
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