Physical loss mechanisms for resonant acoustical waves in boron doped poly-SiGe deposited with hydrogen dilution

Abstract

In this paper, the physical loss mechanisms in boron doped poly-SiGe are analyzed theoretically and experimentally. The phonon losses were calculated theoretically for different germanium and doping concentrations. The theoretical analysis showed that Akhiezer damping sets a fundamental lower limit to the internal damping. Calculated limits for the f×Q due to Akhiezer damping were ∼1×1014 Hz for SiGe with low Ge content and ∼2×1013 Hz for SiGe with high Ge content. However, in the experiments it was found that an internal friction loss mechanism limits the maximum achievable f×Q in our material to 3×1012 at a frequency of 130 MHz. Experimentally the loss mechanisms were studied further by preparing SiGe layers with different Ge/H/B content. The acoustical losses were measured by fabricating a micromechanical resonator from the layers. The measurements identified a thermally activated loss mechanism. By studying the microstructure of the SiGe layers, we identified interface defects and interstitial as the most important loss mechanisms. Furthermore, the experiments show that at high frequencies (>130 MHz) the achievable f×Q-products of SiGe are close to the values, which can be achieved with single crystal materials.

Design strategies for controlling damping in micromechanical and nanomechanical resonators

“…For example, the free surfaces of silicon, titanium, and aluminum are invariably covered with ultrathin coatings of native oxide under typical processing and operating conditions. Similarly, internal oxide layers and interfaces can be created due to unintentional oxidation during deposition [87].…”

“…Quantifying these details, especially in micrometer and nanometer scale structures, requires extensive experimental studies using a suite of microscopic and spectroscopic techniques (see, for example, [82,87,89]). Even when such information is available, it is difficult to model the dynamics of defects over multiple scales of length, time, and energy.…”

Research progress on energy dissipation mechanisms in micro- and nano-mechanical resonators

“…Akhiezer 阻 尼 和 Landau-Rumer 阻 尼 模 型 具 有 相 同的物理耗散机理, 即局部声子-声子相互作用, 两 种模型均适用于某一特定的频率区域, 两区域之间 的过渡频率满足条件 [27] ph [27] , 过渡 频率f tr 和材料的热传导特性密切相关.…”

“…(ⅰ) 谷内声子-电子散射. 谷内声子-电子耗散 指的是电子与长波声子作用, 长波声子能量小, 散射 前后能量改变很小, 为弹性散射, 该耗散的阻尼f×Q 优值为 图 9 (网络版彩色)Akhiezer和Landau-Rumer阻尼损耗与频率之间的 关系 [27] Figure 9 (Color online) Frequency dependency of the Akhiezer and Landau-Rumer losses [27]…”

“…Wang等人 [83] Figure 19 (Color online) Relative quality factor plotted against the thickness of H-and oxide-terminated paddle resonators [83] 图 20 (网络版彩色)多层结构谐振器. (a) 界面形成; (b) 界面耗散 [27] Figure 20 (Color online) Multi-layer structure resonators. (a) The formed interface between the two PECVD layers; (b) interfacial dissipation [27] 谐振器固体和固体形成的边界面, 采用等离子体增 强化学气相沉积法(PECVD)淀积的两个SiGe层之间 形成的界面清晰可见 [27] , 振动能量在边界面处产生耗 散, 边界效应会使谐振器的品质因子下降, 如图20(b) 所示, 界面损耗直接影响多层结构谐振器的性能.…”