Owing to its superlative carrier mobility and atomic thinness, graphene exhibits great promise for interconnects in future nanoelectronic integrated circuits. Chemical vapor deposition (CVD), the most popular method for wafer-scale growth of graphene, produces monolayers that are polycrystalline, where misoriented grains are separated by extended grain boundaries (GBs). Theoretical models of GB resistivity focused on small sections of an extended GB, assuming it to be a straight line, and predicted a strong dependence of resistivity on misorientation angle. In contrast, measurements produced values in a much narrower range and without a pronounced angle dependence. Here we study electron transport across rough GBs, which are composed of short straight segments connected together into an extended GB. We found that, due to the zig-zag nature of rough GBs, there always exist a few segments that divide the crystallographic angle between two grains symmetrically and provide a highly conductive path for the current to flow across the GBs. The presence of highly conductive segments produces resistivity between 10² to 10⁴ Ω μm regardless of misorientation angle. An extended GB with large roughness and small correlation length has small resistivity on the order of 10³ Ω μm, even for highly mismatched asymmetric GBs. The effective slope of the GB, given by the ratio of roughness and lateral correlation length, is an effective universal quantifier for GB resistivity. Our results demonstrate that the probability of finding conductive segments diminishes in short GBs, which could cause a large variation in the resistivity of narrow ribbons etched from polycrystalline graphene. We also uncover spreading resistance due to the current bending in the grains to flow through the conductive segments of the GB and show that it scales linearly with the grain resistance. Our results will be crucial for designing graphene-based interconnects for future integrated circuits.

由于其最高的载流子迁移率和原子厚度，石墨烯在未来纳米电子集成电路中的互连方面表现出巨大的潜力。化学气相沉积 (CVD) 是最流行的石墨烯晶圆级生长方法，可生产多晶单层，其中错误取向的晶粒被扩展的晶界 (GB) 隔开。GB 电阻率的理论模型侧重于扩展 GB 的小部分，假设它是一条直线，并预测电阻率对错误取向的角度有很强的依赖性。相比之下，测量产生的值范围要窄得多，并且没有明显的角度依赖性。在这里，我们研究了穿过粗糙 GB 的电子传输，这些 GB 由连接在一起的短直段组成一个扩展的 GB。我们发现，由于粗糙 GB 的锯齿形特性，总是存在一些部分，它们对称地划分两个晶粒之间的结晶角，并为电流流过 GB 提供高导电路径。高导电段的存在产生的电阻率在 10²至 10 ⁴ Ω μ m，与错误定向角度无关。具有大粗糙度和小相关长度的扩展 GB 具有 10 ³ Ω μ量级的小电阻率m，即使对于高度不匹配的非对称 GB。GB 的有效斜率由粗糙度和横向相关长度的比值给出，是 GB 电阻率的有效通用量词。我们的结果表明，在短 GB 中找到导电段的可能性降低，这可能导致从多晶石墨烯蚀刻的窄带的电阻率发生很大变化。我们还发现了由于颗粒中的电流弯曲流过 GB 的导电段而导致的扩散电阻，并表明它与颗粒电阻成线性比例。我们的结果对于为未来的集成电路设计基于石墨烯的互连至关重要。