Thermal resistance modelling of RF high power bipolar transistors

Thermal modelling of RF high power bipolar transistors including the ther mal resistance of the silicon die and the beryllium oxide package as well as the temperature dependence of their thermal conductivities is considered To model power transistors the non linear heat conduction equation is con verted to a linear heat equation using Kirchho s transformation The linear problem is solved using a Green s function method and the Kirchho transformation is e ectuated via a non linear voltage transformation Introduction RF high power transistors are used in base stations for mobile radio radar and satellite com munications to amplify signals to a power level of a few Watts or more Basically these devices consist of a package one or more matching capacitances bonding wires and a silicon die The silicon Si die has a number of active areas and each active area has a number of base and emitter ngers The accurate modelling of the thermal behaviour is of particular relevance since the tem perature in uences the electrical behaviour of the transistor and plays an important role in determining the safe operating area SOA of the device Several methods such as the Finite Element Method FEM and the Finite Di erence Time Domain method FDTD can be used to calculate the temperature at the junction of the devices These methods easily incorporate the temperature dependence of the thermal conduc tivity of the materials involved Simulation times however can be in the order of minutes or hours for the accurate modelling of practical problems Dramatic time savings can be achieved when Green s function methods are employed A principal drawback of this approach is that it fails to incorporate the temperature dependence of the thermal conductivity so that the method is limited to linear problems In this work a robust and e cient implementation of a method for calculating the temper ature distribution and the thermal resistance matrix in Hewlett Packard s Microwave Design System MDS is demonstrated The method is based on proper splitting of the thermal prob lem in a linear problem solved using a Green s function method followed by a non linear Kirchho transformation This division is advantageous in that we obviate the need to recom pute the thermal matrix at every simulation point as is done for example in Simulation times for practical problems are in the order of seconds making the method amendable to CAD applications Computation of the thermal resistance matrix In the thermal model the Si die is placed on top of the beryllium oxide BeO substrate of the package as illustrated in gure The BeO substrate is on top of the mounting base which is maintained at a constant reference temperature Junctions are located in the active areas just below the surface of the Si die where heat is generated due to power dissipation