A framework of shape optimisation based on the isogeometric boundary element method toward designing thin-silicon photovoltaic devices
A framework of shape optimisation based on the isogeometric boundary element method toward designing thin-silicon photovoltaic devices
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DOI：
10.1007/s00366-018-0606-6
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发表时间：
2018-04
影响因子：
8.7
通讯作者：
Toru Takahashi;Tatsuro Yamamoto;Yuta Shimba;H. Isakari;Toshiro Matsumoto
中科院分区：
文献类型：
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作者：
Toru Takahashi;Tatsuro Yamamoto;Yuta Shimba;H. Isakari;Toshiro Matsumoto
我们提出了一种基于梯度的优化框架来设计周期性分层结构中的界面形状，该框架可以根据所需的电磁特性来模拟光伏器件、光纤光栅等。为此，我们首先发展了一种等距边界元方法(IGBEM)来分析层状介质中二维Helmholtz方程的单周期边值问题。从本质上讲，与传统的边界和域型求解器相比，IGBEM不仅具有数值精度，而且适用于形状优化。然后，基于伴随变量法推导出目标函数的形状导数(或形状敏感度)与磁场强度或能量吸收率的关系。用IGBEM求解原始问题和伴随问题，即可求出形状导数。随后，我们将形状优化问题映射为非线性规划问题，以开发用于解决后者的通用软件。在通过与精确解的比较严格地验证了我们的优化框架之后，我们在一个薄硅光伏器件模型中演示了硅-金属界面的形状优化：确定界面是至关重要的，这样当硅层的厚度反常地很小时，入射光的能量可以尽可能地限制在硅层中；在我们的模型中是1微米。最佳形状的吸收率是参考(扁平)形状的8.6倍。这一模拟表明，该框架能够为分析和设计光伏器件以及由单周期层组成的光子和等离子体器件做出基础性贡献。
We propose a gradient-based optimisation framework to design the shape of the interfaces in periodic layered structures, which can model photovoltaic devices, optical gratings, etc., according to a desired electromagnetic property. To this end, we first develop an isogeometric boundary element method (IGBEM) to analyse singly periodic boundary value problems for 2D Helmholtz equation in layered media. By nature, the IGBEM is not only numerically accurate but also suitable for the shape optimisation in comparison with the conventional boundary- and domain-type solvers. Next, we derive the shape derivative (or shape sensitivity) of the objective function in terms of the magnetic field strength or energy absorption rate on the basis of the adjoint variable method. The shape derivative can be computed by solving the primal and adjoint problems with the IGBEM. Subsequently, we map our shape optimisation problems to nonlinear programming problems in order to exploit a general-purpose software for the latter problems. After verifying our optimisation framework rigorously by comparing with the exact solutions, we demonstrate a shape optimisation of the silicon-metal interface in a model of thin-silicon photovoltaic devices: it is crucial to determine the interface so that the energy of the incident light can be confined in the silicon layer as much as possible when the thickness of the layer is unconventionally small; one micrometre in our model. The optimal shape achieved 8.6 times higher absorption rate than the reference (flat) shape. This simulation shows that the proposed framework is capable of making a fundamental contribution to analysing and designing photovoltaic devices as well as photonic and plasmonic devices that consist of singly periodic layers.