The transition from the Fowler-Norheim regime to the space charge limited current regime of a pointed nanometric emitter

We examine the transition from the Fowler-Nordheim (FN) regime to the space charge limited (SCLC) regime of a pointed nanometric emitter of a radius of curvature R for which the traditional FN equations do not hold. To accomplish this, we use the Generalized FN equation [5] for the emission law and the “time of flight” methodology to solve the equations of motion. Taking advantage of the fact that emission from nanometric emitters occurs primarily along the emitter axis we approximate the paths of the electrons as linear, provided, that the anode is far distant from the cathode. In the approach to the SCLC regime the calculated currents of very small R emitters may differ by orders of magnitude compared to the current of planar emitters for a fixed anode-cathode distance D, while the same effect is observed when R is fixed and D is varied.