The Copper Oxide Rectifier

It is shown that the conductivity in the ohmic part of the cuprous oxide layer can be explained with the usual band picture of semiconductors only by assuming the presence of some donor-type impurities in addition to the usual acceptor type. The energy difference between the acceptors and the filled band is 0.3 electron volt, and the total number of impurity atoms is about ${10}^{14}$ to ${10}^{16}$ per ${\mathrm{cm}}^3$, the number of donors being less than but of the same order as the number of acceptors. Applying the Schottky theory of the space charge exhaustion layer, one finds from the dependence of capacity of the rectifier on bias voltage that the density of ion charge in the rectifying layer is of the same order of magnitude as the difference between the donors and acceptors found from the conductivity, thus furnishing a check for the theory. The field at the copper-cuprous oxide interface calculated from the space charge is about 2×${10}^4$ volts/cm; the height of the potential at the surface as compared with the oxide interior is about 0.5 volt; and the thickness of the space charge layer about 5.0×${10}^{-5\mathrm{}}$ cm. The diffusion equation for flow of current through this space charge region can be integrated to give the current in terms of the field at the interface and the applied potential across the space charge layer. Two currents are involved, one from the semiconductor to the metal ($I_s$) and one from the metal to the semiconductor ($I_m$) which is similar to a thermionic emission current into the semiconductor. The net current is, of course, $I=I_m-I_s$. One can get this "emission" current ($I_m$) by dividing the true current by the factor $1-\exp (-\frac{e{V}_a}{\mathrm{kT}})$, where $V_a$ is the applied potential. This emission current depends on the absolute temperature and on the field at the copper-cuprous oxide interface. At high fields the logarithm of the current is proportional to the square root of the field, and at low fields the current decreases more rapidly indicating a patchy surface having small areas of low potential maximum from which all the emission comes when the field is large. This effective potential maximum measured from the Fermi level in the copper is about 0.5 ev, and the fraction of the total area effective ranges from ${10}^{-2\mathrm{}}$ to ${10}^{-5\mathrm{}}$ depending on how the rectifier was made. This last factor—the fraction of the area having this low potential maximum—is by far the most important variable, resulting in low reverse currents when the fraction is small and large reverse currents when the fraction is large.