Field emission in an array of homogeneous identical nanometer-long nanotubes

Abstract

We consider the problem of field emission based on carbon nanotubes. The length of these nanotubes differs from several nanometers to several hundreds of nanometers. We obtain the particle transmission function, considering the difference of potentials on the ends of nanotubes to be \(U = 2 \div 3.5{\text{ V}}\). Basing on the transmission function we calculate emission current. We establish the dependence of the Nordheim function on the length of nanotubes. The limiting transition is considered for the transmission coefficient for field emission from the cathode surface in the absence of nanotubes on it. We establish the linear dependence of current I on the field strength W and the linear dependence of function \(I/W^{2}\) on the inverse value of field strength 1/W. Qualitative matching to experimental results of emission current is obtained when the voltage was kept less than the threshold value of 260 V and the distance between cathode and anode was kept constant, \(\approx 5 {\text{mm}}\).