Illustrating field emission theory by using Lauritsen plots of transmission probability and barrier strength
Comparison of barrier-strength dependences on inverse scaled barrier field, for the exact triangular (ET) and Schottky–Nordheim (SN) barrier models. Line PL is drawn parallel to line ET, a distance η above it. Curve SN starts at the reference point "R," at (1,0).
To illustrate the relationships between the SN-barrier correction functions (f), s(f) and r 2012(ϕ,f), for the specific values ϕ = 4.50 eV (η ≈ 4.637), f = 0.2. The line T(5) is the tangent to curve SN at point "P," at which f −1 = 5. The slopes of lines ET, V, and T(5) are, respectively, −η, −η· (0.2), and −η·s(0.2), and G F ET = 5η.
To show how the barrier-form correction factor for the Coulomb barrier (ν F CL) varies with Edgcombe's parameter υ ("upsilon"), defined by Eq. (18) .
To show how, for a Coulomb barrier, the barrier strength for state F varies with inverse barrier field, for the work-function value 4.50 eV, and the emitter radii shown. For sufficiently small model radii, the curvature in the Lauritsen plot is detectable.
To show how the transmission probability D F varies with inverse barrier field. (a) and (b) show results for an exact triangular barrier of height 4.50 eV, as predicted by the original Fowler–Nordheim formula (FN) and by an exact treatment (FD). (c) and (d) show results for a Schottky–Nordheim barrier of zero-field height 4.50 eV, as predicted by the usual simple-JWKB treatment (JWKB) and by the Kemble approximation (Kem). For each barrier, the left-hand figure shows the high-field (low F L −1) region in greater detail.
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