由水动力声子传输驱动的石墨热特斯拉阀

　　我们首先在Si晶圆上准备了商业2.5μm-thick Sio2，然后用空气等离子体将其烘烤以进行表面处理。使用苏格兰胶带将石墨片通过机械去角质转移到SiO2/Si底物中。我们使用电子束光刻来对特斯拉阀门的初始薄片进行模板，并沉积了Al薄膜，以通过电子束物理蒸气沉积掩盖它们。然后，我们使用O2等离子体在反应性离子蚀刻系统中蚀刻暴露的薄片，并在去除顶部Al薄膜后获得了设计的结构。在两个对称的特斯拉阀的中心，我们沉积了70 nm au垫作为换能器，用于在正向和反向结构中执行热心型测量值。最后，将石墨特斯拉阀用沉积在结构两侧的Au垫与使用蒸气相氢氟酸的基础SIO2蚀刻的AU垫悬挂。 　　我们对整个50×150-μm2薄片（扩展数据）进行了EBSD分析，以研究我们石墨样品的结晶度。如图1B所示，用电子束以70°的倾斜角度将薄片与晶片辐射。电子衍射模式记录了每个晶体平面的信息。反极图（扩展数据图1C – E）显示了所有三个方向的晶体方向（相同颜色）的一致性，即正常方向，横向方向和参考方向。结果，我们确认这项工作中使用的石墨样品是单晶。 　　据报道，带有六角形晶格的材料中的平面上准核糖热传导取决于扶手椅和Zigzag53的不同晶格方向。为了排除这种效果，我们在单晶石墨薄片上制造了样品，以使前向结构中的主和弯曲通道在两种情况下的反向情况下与对应物平行（或具有180°对称性）。 　　次级离子质谱法用于识别单晶石墨样品的同位素组成。使用高压/高温方法54,55的同位素富集后，我们的石墨晶体由99.98％的12C和0.02％13C组成，即世界一流的纯化石墨样品。 　　为了实现特斯拉阀中的热流的逆转，我们通过向另一个旋转180°旋转一个向前和逆转结构。我们制造了两个结构的镜像对称几何形状，适用于泵 - 探针测量中的对称热量耗散。这会导致源/接收器在正向/反向方向的阻力并不严格。但是，在设计样品时，我们考虑了这种差异，并认为其影响可以忽略不计。 　　首先，我们在简化的几何形状中同时进行了蒙特卡洛和FEM模拟，而没有特斯拉阀的臂（即弯曲通道）。这些模拟旨在检查源和水槽对几何差异的影响。扩展数据图3显示，在两个样本中以及衰减时间（在FEM中）中，声子旅行时间（以蒙特卡洛为单位）相同。换句话说，在声子传输的弹道和扩散视图中，源和水槽处的几何形状略有差异都不会有明显的差异。 　　此外，非数学上完美的热源和水槽区域可以平滑接触尺寸的影响。实际上，在桥梁末端恒定散热器温度的理论系统中，接触区域将发挥重要作用。但是在实际的实验系统中，热源区域用高斯激光束缓慢加热至饱和，而散热器是一个远非完美的等温边界的大导电区域。因此，接触的特定形状不太重要。在以下FEM模拟中，这很容易看到，在该模拟中，我们将石墨连接器的宽度更改为散热器，如图8所示。尽管收缩应该具有更强的影响，但只有在比实验样本中，我们才能注意到衰减曲线的差异。 　　我们使用了非接触式的，时域的温度侵占法来分析样品的热传输特性。将642 nm处的激光用2μs的持续时间脉冲，以定期通过AU换能器将热量泵送到特斯拉阀结构。在散热期间，使用514 nm处的连续波激光调查金属传感器上的反射率（ΔR）的变化。使用连续波（探针）激光器检测到AU传感器上反射率（ΔR）的变化，该激光与温度的变化相当于温度的变化（即ΔR/R =CTHΔT）。因此，TDTR信号显示了通过微秒范围内的特斯拉阀结构的脉冲（泵）激光注入的热量的内在衰减，如图1C所示。对于每个测量，LabView程序都以指数关系为〜exp（-t/τ），并收集了最后200个热衰减时间（τ）。每个测量中的相应τ取自其高斯分布的平均值，如图1d所示。在每个温度下进行测量之前，我们花费了足够的时间进行温度稳定，不确定性 <0.1 K to ensure thermal equilibrium between the sample and the holder in the cryostat. Moreover, the decay time and the thermal conductivity were experimentally verified to be independent of the probe laser power heating, even with a more than doubled laser intensity (Extended Data Fig. 9). We assume that the thermal conductivity is also reasonably expected to be independent of the pump laser power, which only induces temporal heat pulse and is more experimentally difficult to be precisely characterized. At each given temperature, we moved the lasers back and forth on the forward and reverse structures and performed repeated measurements up to ten times for each structure (forward or reverse) and the error bars shown in the plots were calculated from their standard deviations. 　　In the μ-TDTR measurement, we first quantify the heat dissipation through the sample by means of the thermal decay time, τ. The thermal conductivity of the Tesla valve is then extracted using FEM simulation implemented in COMSOL Multiphysics. 　　To reproduce the experiment, we built 3D models with the same geometries as the measured Tesla valve in forward and reverse directions, as shown in Extended Data Fig. 10. The pump laser centred on the gold transducer in the experiment is simulated by a Gaussian pulse heat source with the same pulse duration of 2 μs. We set the boundary condition of the heat sinks at the cryostat temperature. And the boundary condition of the edges of the Tesla valve structure is considered adiabatic, at which the thermal radiation loss of the suspended structure was estimated by the Stefan–Boltzmann law and concluded to be neglected, as well as the convection effect56,57. 　　Heat conduction through the entire model follows the heat diffusion equation: 　　in which ρ is the density, Cp is the heat capacity at constant pressure and κ is the thermal conductivity. These parameters are taken from the corresponding material values for the temperature of interest58,59. Thermal boundary conductance between the metal transducer and graphite has a negligible effect on our simulation results, as was investigated in our previous work10. We also consider the anisotropic thermal property in graphite by including the out-of-plane thermal conductivity from the literature59. Thus, the in-plane thermal conductivity of the Tesla valve structure is the only fitting parameter in the simulation. For instance, by sweeping a series of thermal conductivities of the graphite Tesla valve in the forward direction at 45 K, we obtain their corresponding decay curves, as plotted in Fig. 1c. Therefore, the corresponding thermal conductivity value can be obtained through the decay curve that fits our experimental data the best. 　　At 300 K, we obtained the thermal conductivity for the graphite Tesla valve comparable with the literature values. Our values are between those of the bulk graphite59 and the 1.2-μm-wide graphite ribbon with the same isotope contents60, as shown in Extended Data Fig. 6b. As the temperature decreases, these values are much lower than that of the bulk owing to the stronger size effects from the microscale geometry. 　　Our Monte Carlo algorithm traces phonon wave packets through the three-dimensional model of the structure that is assumed to be at temperature T. The phonons are emitted at the hot side and absorbed at the cold side. The phonon frequency (ω) and group velocities are obtained from the Planck distribution at the given temperature and phonon dispersion61. The dispersion was assumed to be isotropic and consisted of three acoustic branches. The temperature variations in the structure are assumed to be too small to cause substantial shift of the Planck distribution. 　　The Umklapp scattering events are simulated as scattering in a random direction that occurs once the time since the previous diffuse scattering event exceeds time t = −ln(r)τR, in which r is a random value between zero and one and τR is the relaxation time. The relaxation time is modelled as: 　　in which B = 3.18 × 10−25 sK−3 and Tdeb = 1,000 K (ref. 62). The impurity scattering is assumed negligible owing to the high purity of our sample. Normal-scattering events are not modelled owing to the nature of the current phonon Monte Carlo algorithm in the single-mode relaxation-time approximation. Thus, the simulations include no hydrodynamic effects and aim to demonstrate the parity of forward and reverse structures in the absence of phonon hydrodynamics. Modelling of boundary scattering depends on the surface roughness (σ), phonon wavelength (λ) and the incident angle to the surface (α). The probability (p) of boundary scattering to be specular or diffuse is evaluated for each scattering according to Soffer’s equation: 　　Then, a random value (r) is drawn to decide whether the scattering event is specular (r < p) or diffuse (r >P）。在弥漫性散射的情况下，散射角分布遵循兰伯特余弦定律。假定侧壁的表面粗糙度为2 nm，顶壁和底壁为0.2 nm。尽管对数千个声子进行了模拟，但声子轨迹的地图仅显示了仅几个第一个声子的路径，为了清楚起见。热量频率图显示了定义为的平面通量，其中QX和QY是QX和QY组件的总和，这些QX和QY组件的总和是汇总的所有声子。热图被计算为随着时间的时间集成给定像素的所有声子的能量（ħΩ）的总和。导热率计算为： 　　其中kb是玻尔兹曼常数，ω（q）是声子频率，v（q）是波形q处的组速度。使用蒙特卡洛模拟作为弥漫散射事件之间的平均时间来测量声子松弛时间τR。 　　先前的实验报告表明，在室温下，独立石墨烯的热导率超过2,500 wm-1 k-1。但是，当受铜的支撑时，热导率会大大降低，降至370 wm -1 k -1。支撑底物的存在引起了显着的声子 - 底物相互作用，从而影响了样品中内在的热性能的研究。因此，为了将大量的热量耗散到支撑底物，并确保通过感兴趣的结构完全耗散热量，在这项研究中，悬浮的石墨特斯拉阀的制造对于精确的热矫正研究至关重要。 　　然而，由于制造过程中固有的残留应力，微观悬浮的结构不可避免地经历了机械不稳定性。在较高的温度下，机械不稳定性引入了连续测量之间的不可避免的差异，从而导致在较高温度下获得的热导率值的差异，如图4所示的误差条所示。这是在材料中，由于材料的高度测量值，这是在材料中的高度测量值，尤其是在材料中，这是一个常见的挑战。 　　尽管存在这些挑战，但值得注意的是，二极管值沿1至300 K的基线表现出一致的变化。为了进一步验证我们的观察结果，在石墨Tesla阀样品S2和S3上进行了进一步的实验。如图4所示，样品S2和S3的发现证实了样品S1中观察到的高温趋势，如主文本中所述。相比之下，在25-60 K的流体动力温度范围内，预计热整流的发生，我们观察到二极管值始终超过1，超出了误差范围。