4.- Current - Voltage Relationship in a Diode

We have analyzed a diode formed by a cathode and an anode closely spaced and formed by parallel plane surfaces. In figure 4 we can see the interface of the simulation of a two dimensional diode. Our model is as follow, an electric field is applied between the two plane electrodes while a constant rate of particles per unit time is provided to the space between plates, emitted by the cathode. The movement of a particle is the result of the action of the applied electric field and the interaction with the other charged particles, this result in a current flow between plates.

For a given temperature of the cathode, a saturation of the current occurs as the applied potential increases (Hemenway 1962). In our study we can simulate this fact modifying the rate of particles injected into the space. In figure 5 the current versus the applied voltage for different temperatures are shown, these curves had been obtained with the simulation. The saturation of the current is clearly appreciated and the variation with the temperature agrees qualitatively with the experiments.

Figure 5: Current versus the applied voltage for different temperatures. Data obtained from the simulation

The relationship between the electric current and the voltage is well known and was established by Child and Langmuir (Owen 1929) in the three-half power law for the non saturated region.

Where d is the distance from the cathode to the anode. The curves we obtain are qualitatively coincident with Child Langmuir law, but with quantitative deviations in respect to the 3/2 law. This is so because we have not been able of properly modeling the cathode and anode metallic electrodes (as constant potential bodies in the presence of the emitted electrons). Work in this respect is being carried out.

Download applet: ejs_diodeV_10.jar