br Numerical computations We present here
Numerical computations We present here the calculation data obtained for the structure prepared from ytterbium (Yb, eφ = 3.1 eV) and carbon (C, eφ = 4.7 eV) layers. Calculations necessary to optimize the layered field emitters and determine their emission characteristics have been carried out using the Comsol software. Electric fields, SBI-0206965 trajectories, current density distributions over the surface of the field emitter and emitter currents were found. The calculations took into account the existence of a transition zone between the layers of Yb and C, where the mixture of these materials exists . The current to the anode was determined by the Fowler–Nordheim equation (see for example ). Emission of the layered cathode is conditioned by the fields that exist due to the difference in work functions of contacted materials, as well as by the ‘external’ field associated with the supply of voltage between the cathode and the anode. The distribution of the potential U(x) in the transition zone due to the difference in the work functions of contacted materials was described by the function: where l is a width of the transition zone. The shape of this distribution can be varied by changing the coefficients A1 and A2. The coefficients were chosen so as to ensure the best possible agreement between the calculation and the experimental results on the emission characteristics of the layered cathode. Fig. 1, a schematically shows the contact region of adjacent Yb and C layers. The vertical dashed lines indicate the boundaries of the transition zone between the layers. Fig. 1, b demonstrates typical distributions (used in the calculations) of the potential U and the total electric field E in the contact area defined at = 6 kV and the given value Δeφ = 1.6 eV of the work function difference for these layers in the diode with a gap of 1 mm between the cathode and the anode. Typical electron trajectories (e) are shown in Fig. 1, a as well. As follows from the calculation results of electron trajectories, electrons emitted by the cathode region x ≤ reach the anode at a fixed voltage , whereas those from the region x > return to the cathode at the same voltage. The performed calculations revealed that the anode current of the layered cathodes depends on the thickness of the contacted layers. Typical calculated dependencies of the anode current upon the thickness values of the ytterbium (dYb) and the carbon (dC) layers are shown in Fig. 2. According to the information in literature (see for example [3,5]), the width of the transition zone is typically about 0.6–0.8 nm. Therefore, we can probably take dC = 1–2 nm as the optimal thickness of a carbon layer, as it is only a little more than the transition zone dimension. Thickness dYb of the ytterbium layers should be much more, and may be taken, for example, as about 5 nm. Two current-voltage characteristics of the cathodes including 20 pairs of Yb–C layers are shown in Fig. 3. The former was obtained for optimal thickness values dYb = 5 nm and dC = 2 nm, the latter was calculated for the cathode with different thickness values of the Yb and C layers: dYb = 2 nm and dC = 5 nm. It can be seen that the deviation from the optimal dimensions leads to a significant drop of current.
Experimental investigation Layered cathodes were made using magnetron sputtering. The carbon and ytterbium layers were sequentially deposited on a single crystal substrate of gallium arsenide. Two–three cathode systems, differing in the number N of pairs of layers (ytterbium-carbon) and/or in layer thicknesses, were located on a surface of a single substrate. After the procedure of the layers application was completed, cleavage of the single crystal and of the bottom part of the layered cathodes was accomplished. Thus, an atomically smooth emitting surface of the cathode was formed. The cathode surface morphology was examined with a scanning electron microscope Supra 45 WDXС.