Electron emission contributions to dark current and its relation to microscopic field enhancement and heating in accelerator structures

Abstract

Analytically tractable models of thermal-field emission, field enhancement, and heating mechanisms (Nottingham and resistive) are developed and combined to make estimates of the fields and temperatures that accompany the development and growth of asperities. The relation of asperity dimensions to dark current is discussed in two experimentally motivated examples. The hypothetical relation of microscopic sources of dark current and heating to breakdown is discussed in the context of Nottingham and resistive heating. The latter are estimated using a general thermal-field methodology. A point-charge model is used to find field enhancement factors. Last, a thermal model is used to estimate the temperature dependence of the resistivity and thermal conductivity. Together, these models suggest that conditions can arise in which the temperature at the apex of an asperity can experience growth and contribute to melting or fracture (or both), and that Nottingham heating generally dominates the resistive heating term.

Space charge effects in field emission: One dimensional theory

“…As is well-known in electrostatics (and explicitly utilized by the Point Charge Model [20,21]), conducting surfaces can be replaced by equipotential surfaces at the same potential, and the converse holds as well: the equipotential surface signifying "anode" in the point charge model becomes the "cathode" of the 1D region, as schematically illustrated in Figure 8. How far from the plane of charges the "anode" in the point charge model must be before the discrete nature of the PCM is sufficiently smoothed to approximate the planar "cathode" in the 1D approach is now investigated.…”

“…Thus, the degenerate root in the FN case is given by f = 2/3 and j = 2/9 (half of the CL limit). In MKSA units, this will occur when: (20) which can be solved iteratively. The departure from linearity on such plots indicates the impact of space-charge forces.…”

“…Here, a methodology for the analysis of space charge forces on the emission process is described, and a manner in which 1D methods may be brought to bear on arrays of emitters operating together is presented (the second, and separate, study concerns the impact of space charge on individual 3D structures, and builds on methods introduced in the analysis of dark current [20] and emittance [21]. The objective is to provide a framework to investigate field emitters without intensive numerical efforts in a manner amenable to PIC codes for when space charge is an issue and the cathode area is but a small region of the simulation.…”

2D/3D image charge for modeling field emission

“…We shall describe a model that may be adapted to be used with a line charge model appropriate for CNT and carbon fiber field emitters, 9-12 itself a generalization of point and line segment charge models that can be used to model field emitters. [13][14][15] The elongation of the emitter will be seen to affect quite strongly the simple form of the spherical image charge, but as emission is concentrated on axis, the form developed herein is expected to provide a reasonable account of the nonplanar image charge effects. The model is developed by analogy to a common model of the image charge for an electron outside a spherical surface.…”

Electromagnetic power absorption due to bumps and trenches on flat surfaces

“…14, 15 The enhanced power loss due to surface and interface roughness exerts significant effects on signal integrity of microelectronic circuits. [16][17][18][19][20] Other effects due to surface roughness, such as local electric and magnetic field enhancements, may trigger RF-breakdown 5,8,11,[19][20][21][22][23] and abrupt quenching 2,7,9 (i.e., rapid loss of superconductivity) of a superconducting cavity.…”