Contributions to the analytical modeling of distributed thermal and electrical substrate coupling effects in heterojunction bipolar transistors

This work contributes in providing accurate modeling strategies for thermal and electrical effects originating from the substrate region of SiGe-HBTs. Besides arriving at sufficiently compact models in form of equivalent circuits that can directly be employed in circuit simulators emphasis is also put on the development of fast parameterization methodologies to retain advantages w.r.t. efficient model generation and to support aforementioned application scenarios in circuit design.

For self- heating and thermal coupling, calculation of operating temperatures resulting from joule heating is achieved by making use of a solution to the equation of heat conduction in terms of Green's functions. The combination with a surface-element-method enables to consider structural details such as shallow and deep trench enclosure as well as regions with different thermal material properties. In order to account for temperature dependent thermal conductivity the Kirchhoff transform is applied to the calculation of thermal characteristics as well as to the netlist based models for circuit simulation.

For modeling of the electrical coupling between SiGe-HBTs and the substrate physical equivalent circuits are presented for purely junction as well as deep trench isolated devices. Accurate and computationally efficient analytic geometry scaling equations which are partially derived from conformal mapping techniques are presented for two-dimensional vertical cross sections of the devices. The validity of model equations and parameterization methods is verified through comparison with two-dimensional numerical device simulation. For small-signal characteristics up to several hundred GHz, excellent agreement is obtained for a large range of device size and configuration as well as w.r.t. dependencies on d.c. bias.