The electron beam technique of the Scanning Electron Microscopy (SEM) has been widely used for the characterization of bipolar devices and photodiode materials. The resolution of an electron beam technique is affected by the interaction of the beam and the specimen. The size of this interaction volume, commonly termed the generation volume, is usually characterized by what is called the electron penetration range and is measured from the surface. Since there is currently no consensus on the expressions to use in the calculation of the electron range, this paper provides an analysis of the three most commonly used semiempirical expressions. They are the Gruen range, the universal curve of Everhart and Hoff, and the maximum range of Kanaya and Okayama. This analysis is done using data from the statistical method of Monte Carlo simulations. It was found that the Everhart and Hoff universal curve performs better at low beam energies than the equation of Kanaya and Okayama. However, the validity of all the three expressions is questionable below 5 keV. In order to overcome this, fitted expressions based on the extrapolated range are provided for beam energies below 5 keV in the case of Si and GaN materials. The accuracy of these expressions is affected by the physical parameters used in the Monte Carlo simulations.
The spatial distribution of the electron-hole pairs generated by the electron beam is commonly called the generation volume or interaction volume. The generation volume affects the electron beam-induced current (EBIC) profile. This effect of the generation volume on the EBIC profile is particularly true for regions near to the semiconductor junctions. Mathematical models have been proposed for use in the computation of EBIC profiles. Three pear-shaped generation volume distributions were analyzed by comparing the resulting EBIC profiles to the profile obtained from the data using the Monte Carlo simulations. The result shows that the Bonard model gives an EBIC profile that is closest to the one computed using the Monte Carlo simulation. This result is easily observed in the first and the second derivatives of the semilogarithmic EBIC profiles.
A ballistic calculation of a full quantum mechanical system is presented to study 2D nanoscale devices. The simulation uses the nonequilibrium Green's function (NEGF) approach to calculate the transport properties of the devices. While most available software uses the finite difference discretization technique, our work opts to formulate the NEGF calculation using the finite element method (FEM). In calculating a ballistic device, the FEM gives some advantages. In the FEM, the floating boundary condition for ballistic devices is satisfied naturally. This paper gives a detailed finite element formulation of the NEGF calculation applied to a double-gate MOSFET device with a channel length of 10 nm and a body thickness of 3 nm. The potential, electron density, Fermi functions integrated over the transverse energy, local density of states and the transmission coefficient of the device have been studied. We found that the transmission coefficient is significantly affected by the top of the barrier between the source and the channel, which in turn depends on the gate control. This supports the claim that ballistic devices can be modelled by the transport properties at the top of the barrier. Hence, the full quantum mechanical calculation presented here confirms the theory of ballistic transport in nanoscale devices.
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