Modeling of the field emitter triode (FET) as a displacement/pressure sensor

Abstract

Field emitter triodes (FETs) usually have their current produced and controlled by the gate voltage V g. However, if the emitter is allowed to protrude through the gate opening, the emission current can be controlled by the anode voltage V a and the emitter-anode distance d. In this collector-assisted mode of operation the triode can be used as a displacement/pressure sensor allowing the anode to be mobile. The purpose of this paper is to model this situation. The FET model used has parallel cathode, gate and anode planes, the gate near the emitter having a ‘volcano’ shape. The emitter is conical with a spherical tip. The emitter protrudes through the circular opening of the gate. The Laplace equation is solved numerically and the emission current is obtained through integration of the current density-electric field J( E) Fowler-Nordheim relationship over the emitter area. The sensor can operate in constant current or constant voltage modes and both modes were studied. The sensitivity and resolution of the FET displacement/pressure sensor as a function of the model parameters were derived. Under similar conditions referring to the gate, better sensor sensitivity and resolution are obtained for those situations which assure a higher emission current I. Higher I is obtained for higher V a and emitter height h and also for smaller d, emitter opening angle ϕ and work function Φ. These results can be further used for sensor design improvement. Comparison with experimental results is provided.