Analytical Model for the MOS-Transistor Heater

Starting with the basic model assumptions, the analytical heater model is developed in several steps [126]. The equations include common model equations such as the Shichman-Hodge model [127], the LEVELS model [128] and the BSlMS.vS model [129]. Only selected components of these partly complex models were taken to yield a set of equations that is suitable for modelling the transistor heater. The variables and parameters have been defined in accordance to standard notations. First, a model has been estabhshed that describes the unheated transistor, then, temperature dependencies have been introduced, and, finally, the electrothermal coupHng to the microhotplate has been considered. The result is an implicit equation, which can be iteratively solved. The considered model will be compared to measurement data in Sect. 4.4.4. 

The saturation current is denoted /sd,sat the effective mobihty and the capacitance of the gate oxide Cox- The effective geometrical parameters of the transistor include its overall gate width, W g, and the effective gate length, Leff. 

To be consistent with common equations for NMOS transistors, the polarities of the applied voltages have been inverted. The source-gate voltage is denoted Vsg, the source-drain voltage Vsj, and the threshold voltage Vf. Equation (4.3) corresponds to 

The effects of vertical and lateral fields are assumed to be independent of each other. The modification of the mobihty due to vertical field is expressed as [BSlM3.v3, 

In this equation UA, UB, and UC are a set of parameters from the foundry for the respective CMOS technology. V sbx denotes the potential difference between source and bulk, which is zero in the case of the MOSFET-heater. Finally Cx represents the thickness of the gate oxide. 

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