Low Temperature Enhancement of Z in Silicon “Nanoblade” Micro-Thermoelectric Coolers

To improve thermal management in Si integrated circuits (ICs), micro-thermoelectric coolers (µTECs) compatible with ICs are being investigated. Most research on µTEC technology concentrates on materials having high TE factor <i>Z</i> = (<i>α</i>²<i>σ</i>)/<i>κ</i>, where <i>α</i>, <i>σ</i>, and <i>κ</i> are the thermopower, electrical conductivity, and thermal conductivity. The focus on high <i>Z</i> materials is because the maximum temperature reduction achievable is Δ<i>T</i>_max = (<i>T</i>_source – <i>T</i>_sink) = –½<i>Z</i>(<i>T</i>_source)², where <i>T</i>_source and <i>T</i>_sink are the temperatures of the heat source and sink. However, high <i>Z</i> materials can be expensive, often contain toxic or rare elements, and may be incompatible with IC processing. Si is not usually considered a viable TE material because its high phonon contribution to <i>κ</i> makes its <i>Z</i> ~ 1% of modern high <i>Z</i> materials.<br/> Doped Si nanowires (SiNWs) can have <i>Z</i> values competitive with state-of-the-art high <i>Z</i> materials while being compatible with IC processing. It is believed this enhancement in <i>Z</i> is due to the cross-sectional dimensions of SiNWs being smaller than the phonon mean-free-path (mfp), increasing phonon surface scattering and reducing <i>κ</i>. However, over the past decade µTE devices incorporating SiNWs or other kinds of Si nanostructures have mostly failed to demonstrate substantial enhancements in performance that should result from higher <i>Z</i>.<br/> We report on prototype µTECs using Si_0.97Ge_0.03 as the TE material, made on an industrial Si IC process line. The TE elements were structured by standard lithographic etching into “nanoblades” 80 nm wide by 350 nm tall by 750 nm long. By comparison, the phonon mfp near 300 K is ~ 200 nm. For <i>T</i>_source = 300 K, using bulk material parameter values the ideal Δ<i>T</i>_max ≈ –1.5 K, while our measured Δ<i>T</i>_max = –0.3 K. The reduction from ideal value is due to parasitic series resistances. Near 300 K the inferred <i>Z</i> value of the nanoblades is indistinguishable from bulk material.<br/> However, at <i>T</i>_sink = 150 K, Δ<i>T</i>_max remains nearly constant. That is, these µTECs can still reduce <i>T</i>_source by around –0.3 K below <i>T</i>_sink , and measurable cooling of <i>T</i>_source persists to <i>T</i>_sink ~ 100 K. If the values of all material and device parameters were temperature independent, then we expect Δ<i>T</i>_max(150 K)/Δ<i>T</i>_max(300 K) = ¼. The fact that the measured ratio is actually close to unity cannot be attributed to decreases in parasitic resistances; these tend to increase at lower temperature which should make Δ<i>T</i>_max(150 K)/Δ<i>T</i>_max(300 K) &lt; ¼.<br/> We then infer that the nanoblades’ <i>Z</i>(150 K)/<i>Z</i>(300 K) &gt; 4 to compensate for the temperature decrease. However, using bulk material properties indicates <i>Z</i>(150 K)/<i>Z</i>(300 K) should be &lt; 1. This implies a low temperature increase in <i>Z</i> unrelated to bulk behavior. We believe the likely cause is an increase in the phonon mfp with decreasing temperature; the mfp is estimated to be ~ 3x longer at 150 K compared to 300 K. Thus at 300 K a nanoblade is smaller than the phonon mfp in width only, whereas at 150 K it becomes smaller in both width and height. This makes phonon heat transport effectively one-dimensional, which could significantly reduce the phonon contribution to <i>κ</i> and enhance the nanoblade <i>Z</i>. Full experimental results and comparisons to theoretical analyses of low dimensional phonon transport on <i>Z</i> will be presented.