Generalized High-Energy Thermionic Electron Injection at Graphene Interface
Generalized High-Energy Thermionic Electron Injection at Graphene Interface
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DOI：
10.1103/physrevapplied.12.014057
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发表时间：
2019-07-29
影响因子：
4.6
通讯作者：
Ang, L. K.
中科院分区：
文献类型：
--
作者：
Ang, Yee Sin;Chen, Yueyi;Ang, L. K.
跨越高界面势垒的石墨烯负离子电子发射涉及驻留在远离狄拉克点的高能电子，在狄拉克点处，带结构的狄拉克锥近似被破坏。在这里，我们构建了一个全带模型超越了简单的狄拉克锥近似的高能电子在石墨烯中的电子注入。我们表明，基于狄拉克锥近似的电子发射模型是有效的，只有在石墨烯-半导体肖特基界面工作在室温附近，但在涉及高能电子的情况下，如石墨烯-真空界面或异质结中存在的光子吸收，需要考虑在高电子能量的带结构非线性的全带模型打破。我们确定了一个临界势垒高度，Phi（（c））（B）约为3.5 eV，超过这个临界势垒高度，狄拉克锥近似从低估过渡到高估。在石墨烯-真空界面处的高温电子发射区中，与更精确的全带模型相比，狄拉克锥近似严重高估了电流和热流密度超过50%。两种模型之间的巨大差异证明使用石墨烯为基础的电子冷却器。这些发现揭示了狄拉克锥近似在石墨烯中高能电子的电子注入中的谬误。这里开发的全带模型可以很容易地推广到其他2D材料，并提供了一个改进的理论途径，为准确的分析，建模和设计的石墨烯基电子能量器件。
Graphene thermionic electron emission across a high interface barrier involves energetic electrons residing far away from the Dirac point, where the Dirac cone approximation of the band structure breaks down. Here, we construct a full-band model beyond the simple Dirac cone approximation for the thermionic injection of high-energy electrons in graphene. We show that the thermionic emission model based on the Dirac cone approximation is valid only in the graphene-semiconductor Schottky interface operating near room temperature, but breaks down in the cases involving high-energy electrons, such as the graphene-vacuum interface or heterojunction in the presence of photon absorption, where the full-band model is required to account for the band structure nonlinearity at high electron energy. We identify a critical bar- rier height, Phi((c))(B) approximate to 3.5 eV, beyond which the Dirac cone approximation crosses over from underestimation to overestimation. In the high-temperature thermionic emission regime at the graphene-vacuum interface, the Dirac cone approximation severely overestimates the electrical and heat current densities by more than 50% compared to the more accurate full-band model. The large discrepancies between the two models are demonstrated using a graphene-based thermionic cooler. These findings reveal the fallacy of Dirac cone approximation in the thermionic injection of high-energy electrons in graphene. The full-band model developed here can be readily generalized to other 2D materials and provides an improved theoretical avenue for the accurate analysis, modeling, and design of graphene-based thermionic energy devices.