Electronics calculations for an ideal planar parallel vacuum microelectronics diode

Potential distribution function, electric field distribution function and electron velocity distribution function inside an ideal planar parallel vacuum microelectronics (P-VME) diode are derived through solving a simplified cubic equation from a three halves power relationship between the anode current density and the anode voltage. The calculated values of the anode voltage, the anode electric field intensity and the anode electron velocity increases to about 50.00%, 73.21% and 22.47%, respectively, when the influence of space charge inside the P-VME diode is considered.