Analytical electrostatic model of silicon conical field emitters. I

We present an analytical electrostatic model for a conical field emitter surrounded by a circular gate. The model is based on a radially symmetric orthonormal expansion of the potential throughout all space in the basis of Legendre functions of nonintegral degrees. The "bowling pin" model (BPM) makes it possible to calculate the total emission current and electron trajectories. The calculated values of the emitted current are in good agreement with the data. The value for the tip radius of curvature (ROC) obtained as the adjustable parameter in the model is in good agreement with that obtained from independent numerical modeling of the same devices.