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Research Papers: Conduction

Cross-Plane Phonon Conduction in Polycrystalline Silicon Films

[+] Author and Article Information
Jungwan Cho

Department of Mechanical Engineering,
Stanford University,
Stanford, CA 94305
440 Escondido Mall,
Bldg 530/Rm 224,
Stanford, CA 94305-3030
e-mail: jungwan.cho@stanford.edu

Daniel Francis

Element Six Technologies,
Santa Clara, CA 95054
e-mail: daniel.francis@e6.com

Pane C. Chao

Microelectronics Center,
BAE Systems,
Nashua, NH 03060
e-mail: pane.chao@baesystems.com

Mehdi Asheghi

Department of Mechanical Engineering,
Stanford University,
Stanford, CA 94305
e-mail: masheghi@stanford.edu

Kenneth E. Goodson

Fellow ASME
Department of Mechanical Engineering,
Stanford University,
Stanford, CA 94305
e-mail: goodson@stanford.edu

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received September 10, 2014; final manuscript received February 5, 2015; published online March 24, 2015. Assoc. Editor: Zhuomin Zhang.

J. Heat Transfer 137(7), 071303 (Jul 01, 2015) (9 pages) Paper No: HT-14-1609; doi: 10.1115/1.4029820 History: Received September 10, 2014; Revised February 05, 2015; Online March 24, 2015

Silicon films of submicrometer thickness play a central role in many advanced technologies for computation and energy conversion. Numerous thermal conductivity data for silicon films are available in the literature, but they are mainly for the lateral, or in-plane, direction for both polycrystalline and single crystalline films. Here, we use time-domain thermoreflectance (TDTR), transmission electron microscopy, and semiclassical phonon transport theory to investigate thermal conduction normal to polycrystalline silicon (polysilicon) films of thickness 79, 176, and 630 nm on a diamond substrate. The data agree with theoretical predictions accounting for the coupled effects of phonon scattering on film boundaries and defects related to grain boundaries. Using the data and the phonon transport model, we extract the normal, or cross-plane thermal conductivity of the polysilicon (11.3 ± 3.5, 14.2 ± 3.5, and 25.6 ± 5.8 W m−1 K−1 for the 79, 176, and 630 nm films, respectively), as well as the thermal boundary resistance between polysilicon and diamond (6.5–8 m2 K GW−1) at room temperature. The nonuniformity in the extracted thermal conductivities is due to spatially varying distributions of imperfections in the direction normal to the film associated with nucleation and coalescence of grains and their subsequent columnar growth.

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Figures

Grahic Jump Location
Fig. 1

Cross-sectional TEMs of: (a) the 79 nm polysilicon film, (b) the 176 nm polysilicon film, and (c) the 630 nm polysilicon film on diamond. (d) The higher magnification image of the 630 nm sample near the polysilicon–diamond interface shows that the minimum grain dimension of the film at its growth interface (with the diamond) is approximately of the order of a few tens of nanometers. Overall, the micrographs indicate that the grain structure of the polysilicon film becomes columnar with increasing film thickness, and the columnar gains are aligned with respect to the film-normal direction. Approximately 45-nm-thick, evaporated Al films on top of these samples serve as the transducer for thermoreflectance measurements.

Grahic Jump Location
Fig. 2

Sensitivity of the TDTR amplitude signal, calculated via Eq. (1), for the three polysilicon samples to the thermal boundary resistance between the Al and polysilicon Rb,Al–Si, the cross-plane thermal conductivity of the polysilicon film kSi (cross-plane), the in-plane thermal conductivity of the polysilicon film kSi (in-plane), the thermal boundary resistance between the polysilicon and diamond Rb,Si–Diam, and the thermal conductivity of the diamond substrate kDiam. The values of the sensitivity coefficients are evaluated at a pump modulation frequency of 2 MHz and as a function of the pump–probe delay time. The thickness of the polysilicon film is 79 nm in (a), 176 nm in (b), and 630 nm in (c).

Grahic Jump Location
Fig. 3

(a) TDTR data for the 176 nm polysilicon sample (solid line) along with the best analytical fit (dashed line) yielding the optimal parameter set Rb,Al–Si = 6.7 m2 K GW−1, kSi = 14.7 W m−1 K−1, and Rb,Si–Diam = 7.7 m2 K GW−1. The dashed–dotted and dotted curves represent the analytical fits obtained by varying best-fit Rb,Si–Diam by −10% and +10%, respectively, and then by reoptimizing Rb,Al–Si and kSi. The re-optimized polysilicon thermal conductivity varies by −4.1% (dashed–dotted line) and +4.5% (dotted line) from its original optimal value of 14.7 W m−1 K−1. The variations in Rb,Al–Si are negligible. (b) TDTR data for the 79 nm polysilicon sample (solid line) along with the best analytical fit (dashed line) yielding the optimal parameter set Rb,Al–Si = 7.5 m2 K GW−1, kSi = 12.0 m2 K GW−1, and Rb,Si–Diam = 6.8 m2 K GW–1. The best-fit curve assumes kDiam = 1500 W m−1 K−1 (from manufacturer's specification). The dashed–dotted and dotted curves represent the analytical fits obtained by varying this diamond thermal conductivity by −30% and +30%, respectively, and by assuming best-fit values for each of the fitted variables.

Grahic Jump Location
Fig. 5

Room-temperature thermal conductivity of silicon films as a function of film thickness. The cross-plane thermal conductivity data for our three polysilicon films and a suspended 500-nm-thick single crystalline silicon film [3] are depicted by the filled squares and the filled circle, respectively. The in-plane thermal conductivity data for doped polysilicon films [14] and an undoped polysilicon film [15] are depicted by the up-facing and down-facing filled triangles, respectively. The MD calculation for the cross-plane thermal conductivity of a 10-nm-thick polysilicon film [56] (unfiled diamond) is shown for comparison. This MD calculation assumes a random shape of grains and an average grain size of 4 nm. The results of the BTE model for the cross-plane polysilicon thermal conductivity from Eq. (3) (with the boundary resistances removed) are shown with the solid (random grain structure) and dashed (columnar grain structure) lines.

Grahic Jump Location
Fig. 4

Total summed thermal resistance RT for conduction normal to the polysilicon films as a function of film thickness, including the volume resistance of the polysilicon and the boundary resistances at its interfaces (with the Al and with the diamond), along with the predictions of the BTE model (Eq. (3)). (a) The BTE model considers the minimum grain dimensions dG0 of 20 and 50 nm for the two cases of randomly oriented grains and entirely columnar grains. The number density of point defects per unit grain boundary area nGB,P is assumed to be 1.5 × 1019m−2. (b) The point defect density nGB,P is varied from 1.5 × 1019 to 3.0 × 1019m−2 while assuming dG0 = 50 nm.

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