Spectral Analysis of Field Emission Flicker (1/F) Noise.
Spectral analysis of field emission noise induced by emitter surface equilibrium density fluctuations is developed. The noise spectrum factors as S((omega)) = S(,(INFIN))((omega)) + S(,B)((omega)) for a canonical ensemble, which characterizes adsorbate covered emitters. S(,(INFIN))((omega)) and S(,B)((omega)) correspond to unbounded diffusion and the boundary effect respectively. Chemical diffusivity D(,c) is defined by Fick's first law. Its equilibrium limit, termed hydrodynamic D(,h), is derived from S((omega)) and related to the adsorbate fluctuations. These diffusivities are compared using irreversible thermodynamic and Kubo relations. Their equality is ensured by evaluation of the excess entropy production only when the density gradient is small and no phase change occurs. Two dimensional adsorbate phase transitions are identified by correlating incipient nonlinearity in the Arrhenius plot of diffusivity with the onset of a temperature dependent total noise power, which is proportional to adsorbate isothermal compressibility. Examples using K/W, Xe/W, and H/W are given. Thermal field emission noise is characterized by a grand canonical ensemble (GCE). Here the diffusive fluctuation mechanism includes adatom creation and defect vacancy formation resulting from surface free energy minimization. Adatom dynamics are governed by a stochastic diffusion equation. A multidimensional version of Carson's theorem is formulated, which leads to S((omega)) (DBLTURN) C(x = 0,(omega))N(,c)('-1)((omega)), where (hkl) geometry affects C(x = 0,(omega)) and N(,c)((omega)) accounts for probe spatial averaging. From this factorization of S((omega)) an outstanding noise power divergence problem for diffusive equilibrium fluctuations within a GCE is solved. The solution requires finite fluctuation lifetime, which is also proved to be a necessary equilibrium condition. The other part of the solution leads to a new method of measuring the resolution of the microscope. Derived values agree well with a calculation that considers the transverse momentum distribution of the field emitted electrons. The S((omega)) characteristics of tungsten thermal field emission from W(112), W(310), and W(100) planes are explained in detail. Diffusivity values, their corresponding activation energies, and the defect vacancy formation activation energy agree well with other experimental data. Conditions for the broadest band S((omega)) (PROPORTIONAL) (omega)('-1) are given and a hypothesis is proposed explaining its frequent occurrence for diffusive equilibrium systems.
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- Physics: Condensed Matter