石墨烯与金属的欧姆接触理论研究

石墨烯材料应用于多种电子器件时不可避免地要与金属电极接触，它们之间的接触电阻直接影响了器件的性能.为了揭示影响金属电极与石墨烯间接触电阻的因素，提出有效地抑制这些影响的措施，本文建立了一种求解接触电阻的物理模型，将载流子的输运分为金属与正下方石墨烯之间、正下方石墨烯与邻近石墨烯之间的两个过程，分别研究各个过程的输运概率；结合金属电极与石墨烯接触对载流子分布的影响分析接触电阻，据此分别探讨了金属电极材料、栅极电压、掺杂浓度、金属与石墨烯原子距离等对接触电阻的影响.为验证理论分析结果的正确性，制作了金与石墨烯接触的实验样品，实验测得的接触电阻与理论分析结果符合.理论分析结果表明，可通过选择与石墨烯功函数接近的金属材料，降低二氧化硅层厚度，增加载流子平均自由程，改进金属材料的表面形态使其更光滑，减小金属与石墨烯耦合长度等方法降低石墨烯与金属电极的接触电阻.

Theoretical study on ohmic contact between graphene and metal electrode

Graphene has excellent electrical, optical, thermal and mechanical properties, so it has been used in high-performance field effect transistors, sensors, optoelectronic devices, and quantized devices. It is crucial to realize a high-quality junction between metal electrode and graphene. For example, in the field of electrical measurement, due only to the contact resistance in a proper order of magnitude, the quantum Hall effect can be realized. The lower the contact resistance, the higher the measurement accuracy of Hall resistance is. In order to reveal the factors affecting the contact resistance we propose an effective method to reduce it, and a physical model is established in this paper. The carrier transport between the metal electrode and graphene is divided into two cascaded processes. Carriers first transport from the metal electrode to the graphene underneath it, then transport between the graphene underneath metal and the adjacent graphene. The transport probability of first step is considered through the effective coupling length and the mean free path. The transport probability of second step is considered through the effective length of potential step change between the graphene under the metal and the adjacent graphene. The contact resistance is analyzed by combining the distribution of carriers. In order to verify the correctness of the theoretical results, an experimental sample with gold as the metal electrode is fabricated. The transport line model is used to measure the contact resistance. The length of contact area is 4 μm. The lengths of graphene channel are set to be 2, 4, 6, 8, and 10 μm, respectively. The current values are set to be 10, 20, 40, 60, and 80 μA, respectively. The results show that the relationship between current and voltage is almost linear. The total resistance can be obtained with different lengths of graphene. According to the transmission line model, the resistance value can be estimated as (160±30) Ω when the graphene length is zero. Considering that the measured result is obtained under two metal electrodes contacting the graphene, the contact resistance of experimental result is (320±30) Ω·μm which agrees well with the theoretical result. From the analysis of theoretical process, the factors that affect the contact resistance is determined by material, drain-source voltage, gate voltage, doping concentration, distance between metal electrode and graphene atoms, distance between graphene and gate. Finally, in order to reduce the contact resistance between graphene and metal electrode, we propose some corresponding solutions for choosing the metal material whose work function is close to graphene's, reducing the thickness of the silicon dioxide layer, increasing carrier mean free path, improving the surface morphology of the metal material, and reducing the coupling length between metal and graphene.