Quantitative models for excess carrier diffusion and recombination in STEM-EBIC experiments on semiconductor nanostructures

Abstract

The increased complexity and reduced size of (opto-)electronic devices demands for quantitative descriptions of excess carrier transport and recombination via various mechanisms. In addition, experimental methods capable of resolving carrier dynamics on the nanometer scale are required. In this paper, we present a quantitative model of a confined geometry including recombination at two surfaces, which is very generic for electron beam induced current measurements in a scanning transmission electron microscope - a method which offers atomic scale spatial resolution. The model is based on analytical considerations as well as finite element simulations and underlying assumptions are subjected to an in-depth discussion. Finally, the successfull application to experimental data obtained on the complex oxide SrTi0.995Nb0.005O3 demonstrates the practicality and robustness of the approach, which enables the precise determination of its bulk diffusion length of L = 10.2 +- 0.1 nm.

Figures (8)

• Figure 1: Overview of modeled geometries: (a) A neutral n-type semiconductor of finite thickness $t$ is excited by a high-energy electron beam causing a stripe shaped generation of excess charge carriers. The material consists of an active interior area with thickness $t_\text{a}$ and dead surface layers with thickness $t_\text{d}$ and surface recombination occurs at the edges of the active layer. (b) Resulting profile of the excess hole concentration $\Delta p$ integrated along the $z$ axis. Deviations from an exponential decay at the sample edges are caused by the boundary condition $\Delta p=0$. (c) Extended geometry including a junction to a p-type semiconductor (with possibly different dead layer thickness) and metallic contacts to probe the short-circuit current caused by the electron beam, i.e., the STEM-EBIC signal. (d) Resulting STEM-EBIC profile with beam positions located in the neutral and space charge region of the n-type material.
• Figure 2: Comparison between numerical simulation results and model equations for different values of the surface recombination velocity $s$ as a function of active thickness $t_\text{a}$: (a) shows the total number of excess holes $\Delta p^\text{tot}$ obtained via FEM for the geometry in Figure \ref{['fig:geometry']}a (points) and the analytical prediction by Equation (\ref{['eq:delta_p_finite']}) (lines). (b) shows the decay lengths $L_{\Delta p}$ and $L_{I}$ obtained from exponential fits of the excess hole concentration integrated along $z$ (points, model shown in Figure \ref{['fig:geometry']}a) as well as the STEM-EBIC profiles (crosses, model shown in Figure \ref{['fig:geometry']}c). In addition, the predictions by Equations (\ref{['eq:L_tau']}) and (\ref{['eq:L_empirical']}) are shown as dashed and solid lines.
• Figure 3: (a) SEM overview of the lamella extracted from an RP-PCMO-STNO junction and mounted on a MEMS chip. Vertical cuts were applied to prevent short circuits across the junction. (b) Comparison of the current-voltage characteristics of the lamella (black points) and the macroscopic sample (red line).
• Figure 4: (a) Annular dark-field STEM image showing all layers of the junction and the front contact. The region marked by the yellow rectangle was analyzed with vertical STEM-EBIC scans and contains an intentional thickness gradient in the horizontal direction. The three arrows indicate the profiles along which the current is shown in (b). (c) and (d) show the thickness dependence of the line profiles' maximal STEM-EBIC signal and decay length in the n-type STNO substrate (points). While (c) includes a linear regression of the data points, a model fit to Equation (\ref{['eq:L_empirical']}) is given in (d) (lines).
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