With the increasing availability of large-area graphene, the ability to rapidly and accurately assess the quality of the electrical properties has become critically important. For practical applications, spatial variability in carrier density and carrier mobility must be controlled and minimized. We present a simple framework for assessing the quality and homogeneity of large-area graphene devices. The field effect in both exfoliated graphene devices encapsulated in hexagonal boron nitride and chemical vapor-deposited (CVD) devices was measured in dual current–voltage configurations and used to derive a single, gate-dependent effective shape factor, β, for each device. β is a sensitive indicator of spatial homogeneity that can be obtained from samples of arbitrary shape. All 50 devices investigated in this study show a variation (up to tenfold) in β as a function of the gate bias. Finite element simulations suggest that spatial doping inhomogeneity, rather than mobility inhomogeneity, is the primary cause of the gate dependence of β, and that measurable variations of β can be caused by doping variations as small as 10¹⁰ cm⁻². Our results suggest that local variations in the position of the Dirac point alter the current flow and thus the effective sample shape as a function of the gate bias. We also found that such variations lead to systematic errors in carrier mobility calculations, which can be revealed by inspecting the corresponding β factor.

中文翻译：

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石墨烯的质量评估：迁移率测量的连续性，均匀性和准确性

随着大面积石墨烯可用性的提高，快速而准确地评估电性能的质量变得至关重要。对于实际应用，必须控制并最小化载流子密度和载流子迁移率的空间变异性。我们提出了一个简单的框架，用于评估大面积石墨烯设备的质量和同质性。在双电流-电压配置中测量了封装在六角形氮化硼中的片状石墨烯器件和化学气相沉积（CVD）器件中的场效应，并用于得出每个器件的单个取决于栅极的有效形状因数β。β是可以从任意形状的样本获得的空间均匀性的敏感指标。本研究中研究的所有50种器件都显示出β随栅极偏置的变化（最大十倍）。有限元模拟表明，空间掺杂不均匀性，而不是流动性的不均匀性，是的栅极依赖性的主要原因β，以及可测量的变化β可以通过掺杂的变化小而引起10 ¹⁰厘米^-2。我们的结果表明，狄拉克点位置的局部变化会改变电流，因此有效采样形状会随栅极偏置而变化。我们还发现，这种变化会导致载流子迁移率计算出现系统误差，这可以通过检查相应的β因子来揭示。