Physics-based microwave GaN HEMT statistical modeling

集成微波电路的设计依赖于数值电路仿真，而晶体管模型的质量是获得高精度仿真结果的关键因素。通常，使用所谓的紧凑型晶体管模型，该模型基于非线性等效电路来描述晶体管的电热行为。通过参数化函数定义了等效电路元件。这种方法允许基于物理的晶体管模型的一般定义，该模型可以通过参数拟合来适应特定的晶体管工艺。但在现实中，并不是两个晶体管是完全相同的。例如，存在取决于晶体管在波形器上的位置的系统参数分布，以及外延和工艺技术的随机变化。如果晶体管模型忽略了这些变化，而只描述了理想晶体管，那么设计者将错过任何有关晶体管参数扩展如何影响集成电路性能的信息，成品率将低于最优。因此，将紧凑型晶体管模型的参数视为随机变量势在必行。这样的模型在下文中将被称为统计模型。本项目的目标是定义GaN HEMT的统计模型。通过考虑控制电气性能的物理效应，我们的目标是最小化独立随机变量的数量。在这方面，基于物理的GaN器件紧凑模型直到最近才被提出，这提出了一个具体的科学挑战。这些模型不仅比硅晶体管模型更年轻，而且更多地依赖于物理驱动的拟合公式。另一个重大挑战是GaN HEMT中存在深陷阱，导致电学行为中的色散，而对GaN HEMT色散的建模本身仍是一个正在进行的研究问题。

The design of integrated microwave circuits relies on numerical circuit simulation, where the quality of the transistor model is the key factor to obtain highly precise simulation results. Usually, so-called compact transistor models are used, that describe the transistor's electrothermal behavior based on a nonlinear equivalent circuit. The equivalent circuit elements are defined through parameterized functions. This approach allows for a general physics-based definition of a transistor model, which can be adapted to a specific transistor process by parameter fitting. But in reality, not two transistors are identical. There are, for example, systematic parameter spreads depending on where the transistor is positioned on the waver, and stochastic variations in epitaxy and process technology. If a transistor model ignores these variations and only describes the ideal transistor, the designer will miss any information on how the transistor parameter spread impacts integrated circuit performance and yield will be below optimum. Hence, it is imperative to treat the compact transistor model's parameters as stochastic variables. Such a model will be called a statistical model in the following. It is the goal of this project, to define a statistical model for GaN HEMTs. By considering the physical effects governing the electrical performance, we aim at minimizing the number of independent stochastic variables. In this respect, it poses a specific scientific challenge that physics-based compact models for GaN devices were formulated only recently. Not only are these models younger than their silicon transistor counterparts, they also rely more often on physics-motivated fitting formulae. Another significant challenge is the presence of deep traps in GaN HEMTs, leading to dispersion in the electrical behavior, and modeling of GaN HEMT dispersion is in itself still a matter of ongoing research.