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These features are added to the Model Builder as subnodes to the heterojunction or the Schottky contact boundary conditions. The Graded Heterojunction Model
This heterojunction tunneling model compares the simulated current density of a graded heterojunction with and without tunneling at different temperatures.
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当电荷载流子的能垒厚度等于或小于衰减长度时，量子隧穿效应将发挥重要作用。为了解释这一效应，我们可以使用 COMSOL® 软件 5.4 版本的“半导体模块”提供的 WKB 隧穿模型 功能来模拟异质结和肖特基接触边界条件。在下文中，我们将通过基准模型演示其用法。
Wentzel-Kramers-Brillouin 近似
根据 K.Yang、J.R.East 和 G.I. Haddad 的参考文献（Ref. 1），若采用 Wentzel-Kramers-Brillouin（WKB）近似假设，隧穿电流会向热离子电流增加一个分数因子 \delta。
COMSOL 博客 -
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In this project, we developed a 3D optoelectronic model for organic bulk-heterojunction solar cells. We validated our COMSOL Multiphysics® model with experimental data and used our simulation to predict the optical and electrical characteristics of a 3D plasmonic OPV device. This work has the potential to open up possibilities for future designs and simulations of nanostructure-enhanced organic bulk-heterojunction solar cells.
论文和技术资料 -
cn.comsol.com/paper/16999
The default finite volume formulation, due to its discontinuous treatment of variables across the mesh interfaces, would require a much finer mesh near the barriers for those systems. See: Heterojunction Tunneling.
The Model Builder with the Continuity/Heterojunction node selected and the corresponding Settings window showing the Continuation Settings section.
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这个基准模型模拟三种不同构型的异质结在正向和反向偏压下的特性，显示了使用连续准费米能级公式与热电子发射公式计算异质结中的电荷转移的差异；通过模拟每种构型的能级并进行比较，阐明了电荷转移的起源，即，主要源自价带中的空穴还是导带中的电子。本例将针对每种构型计算的 I-V 曲线与文献结果进行了比较；并在各个研究步骤的设置过程中演示了提高收敛性的多种方法。
案例下载 -
cn.comsol.com/model/14617
Secondly then we fabricated a ZnO/Silicon nanowires (ZnO/Si NWs) based p-n heterojunction diode which detect Nitric Oxide (NO) gas at least down to 0.5ppm (with dry N2 as the ambience gas). We make a physical model based on p-n heterojunction with analysis of cross-sectional electron microscopy and line energy dispersive spectroscopy.
论文和技术资料 -
cn.comsol.com/paper/83541
Initial tests are done by modeling the heating process on a previously-solved silicon p-n junction as a proof of concept before advancing to a more complicated geometry. Strategies for mapping heterojunction material properties are discussed and estimates for carrier concentrations and current in place of a full carrier model solution are explored.
论文和技术资料 -
cn.comsol.com/paper/13085
此基准模型模拟分级异质结，其中使用热电子发射公式求解异质结上的电荷转移，通过使用 WKB 近似，显示穿过势垒的量子隧穿效应对电流密度的额外贡献。模拟的系统本质上是一维模型，但我们创建了二维模型来演示较常规构型的仿真过程；还演示了如何设置用户定义的三元材料属性。计算出的 I-V 曲线、温度依存性以及能带图都与文献结果高度吻合。
案例下载 -
cn.comsol.com/model/65761
The former can be easily extended to the DG formulation: Just let the quasi-Fermi level and the Slotboom variable be continuous across the heterojunction, which is automatic for Lagrange shape functions. The latter option assumes the thermionic emission process dominates and allows the quasi-Fermi level and the Slotboom variable to be discontinuous across the heterojunction. The same formula as the drift-diffusion theory is used for the thermionic current density, yielding similar results.
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In this research work, we developed a virtual model to examine the electrical conductivity of multilayered thin films when positioned above a single layer and multilayers of graphene, and flexible polyethylene terephthalate (PET) substrate. Additional structured thin films were configure as follows: organic layers of poly(3,4-ethylenedioxythiophene) polystyrene sulfonate (PEDOT:PSS) as a hole conducting layer, poly(3-hexylthiophene-2,5-diyl) (P3HT), as p-type, phenyl-C61-butyric acid methyl ester (PCBM) as n-type, with aluminum (Al) added as a top conductor. COMSOL Multiphysics® was the primary simulation tool used to develop the virtual model, and analyze variations in electric potential and conductivity throughout the thin-film structural system.
论文和技术资料 -
cn.comsol.com/paper/93571
The authors of the paper use COMSOL Multiphysics to show that the local thermal management of a AlGaN/GaN heterojunction field effect transistor (HFET) can be substantially improved via introduction of the additional heat-escaping channels -- top-surface heat spreaders -- made of few-layer graphene (FLG).
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相关案例：
双极晶体管的热分析 MOS 晶体管 (MOSFET) 的直流特性 MOSFET 小信号分析 超晶格带隙工具 异质结隧穿
相关主题网络研讨会：
COMSOL Multiphysics® 5.5 版本软件新增功能简介 COMSOL® 5.5 优化模块新功能 COMSOL® 多物理场仿真的建模技巧
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此模型模拟 GaN 基发光二极管器件，计算了发射强度、光谱和效率随驱动电流变化的情况，模拟了带隙的直接辐射复合，以及非辐射俄歇复合和陷阱辅助复合过程。仿真结果表明，发射强度随着电流的增加而呈次线性增加，这是 LED 器件的共同特性，称为“LED 光效下降”。请注意，该模型未包含薄有源区内的量子限制效应。
案例下载 -
cn.comsol.com/model/20299
Non-charge-based logic is the notion that an electron can be trapped and its spin manipulated through application of gate voltages. Numerical simulations of Spin Single Electron Transistors (SSET) at University at Albany, aimed at practical development of post-CMOS concepts and devices is presented.
We use COMSOL based multiphysics finite element simulation strategy to solve the Schrödinger-Poisson equations self-consistently to obtain realistic confining and gating potentials for realistic device geometries.
论文和技术资料 -
cn.comsol.com/paper/4902
The quantum confinement effect for the quantum well layer is automatically accounted for with the default Continuous quasi-Fermi levels option for the Continuity/Heterojunction boundary condition, active at the well-barrier interfaces.
COMSOL 博客 -
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Solar energy is the cleanest form of renewable energy. The most popular form of utilization of solar energy is through the use of photovoltaic cells. Currently the efficiency of available solar cells lies below 20%. To increase the efficiency, multi-junction can be used in solar cells. While developing such devices we need platform to study various characteristics and parameters to optimize device performance.
论文和技术资料 -
cn.comsol.com/paper/19367
Many optoelectronic devices utilize a heterojunction of a pair semiconducting materials including high-efficiency MEMS devices, solar cells, LEDs, and VCSELs.
论文和技术资料 -
cn.comsol.com/paper/11604
A photoelectrochemical (PEC) cell uses solar energy to split water to hydrogen and oxygen in single integrated device. Electrochemical impedance spectroscopy is a suitable tool to characterize recombination and reaction mechanisms in PEC cell.
Full numerical drift-diffusion calculations of the electrochemical impedance were conducted.
论文和技术资料 -
cn.comsol.com/paper/37021
本教学案例使用密度梯度理论在传统的漂移-扩散公式中引入量子限域效应，以此分析 InSb p 沟道场效应晶体管的直流特性，而不会大量消耗计算资源。量子阱沟道和靠近沟道的顶部绝缘体界面都应用了该限制效应。本例演示各向异性密度梯度有效质量矩阵的使用，以及配置一般场相关迁移率模型的技巧。基于二维模型得到空穴密度分布和 Id-Vg 曲线，并将其与参考资料中发表的数据进行比较，结果表现出高度的一致性。
案例下载 -
cn.comsol.com/model/73551