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Analytical model for base transit time of a bipolar transistor with Gaussian-doped base

机译：高斯掺杂基极双极晶体管基极渡越时间的解析模型

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摘要

The present analysis for base transit time τ_b of a modern high-speed npn bipolar transistor is done for Gaussian-doped base considering doping dependence of mobility, bandgap narrowing effect and carrier velocity saturation effect at base-collector junction. First the minority carrier current density and electron density equations incorporating all the effects are analytically solved. The collector current density J_c and base stored charge Q_b are then separately expressed as a function of the injected electron density n(0) in the base in order to find base transit time. The modeling of J_c Q_b and τ_b are essential for the design of high-speed bipolar transistor. The equations are applicable for low level of injection. The base transit time calculated analytically is compared with numerical results in order to demonstrate the validity of the assumptions made in deriving the equations. The closed form equations for collector current density and base transit time offer a physical insight into device operation and are a useful tool in device design and optimization.
机译：考虑到迁移率，带隙变窄效应和基极-集电极结的载流子速度饱和效应的掺杂相关性，对高斯掺杂基极进行了现代高速npn双极晶体管基极渡越时间τ_b的分析。首先，分析了包含所有影响的少数载流子电流密度和电子密度方程。然后，将集电极电流密度J_c和基极存储电荷Q_b分别表示为基极中注入的电子密度n（0）的函数，以便找到基极渡越时间。 J_c Q_b和τ_b的建模对于高速双极晶体管的设计至关重要。该方程式适用于低水平的进样。将分析计算出的基本渡越时间与数值结果进行比较，以证明推导方程式的假设的有效性。集电极电流密度和基本传输时间的闭合形式方程式提供了对器件操作的物理洞察力，并且是器件设计和优化中的有用工具。

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