Periodic Field Emission from an Isolated Nanoscale Electron Island

We observe field emission from an isolated nanomachined gold island. The island is able to mechanically oscillate between two facing electrodes, which provide recharging and detection of the emission current. We are able to trace and reproduce the transition from current flow through a rectangular tunneling barrier to the regime of field emission. A theoretical model via a master equation reproduces the experimental data and shows deviation from the Fowler-Nordheim description due to the island’s electric isolation.

Figure 1

(a) Scanning electron microscopy micrograph and experimental setup of the device: the electron shuttle consists of a gold island I situated at the end of a nanomachined silicon cantilever. Free suspension outside the area marked by the dotted lines is $\sim 200\mathrm{n}\mathrm{m}$. The island oscillates between source S and drain D, where the current $I_{\mathrm{D}}$ is detected via a current amplifier. ac excitation is applied at frequency $f$ at gate A with a voltage amplitude of ${\overline{V}}_{\mathrm{a}\mathrm{c}}\approx 500\mathrm{m}\mathrm{V}$. The dc bias $V$ is superimposed on gate S. (b)  Finite element simulation of the local electric field strength $|\mathbf{E}(\mathbf{r})|$, ranging from zero (white) to $1.5\times {10}^8\mathrm{V}/\mathrm{m}$ (black) for an instantaneous external bias of $V_{\mathrm{a}\mathrm{c}}=-500\mathrm{m}\mathrm{V}$ at gate A, and a neutral island charge. In (i) the shuttle is deflected parallel toward the drain, whereas in (ii) the same deflection of the center of mass is assumed with an edge facing the gate. The inset magnifies the facing tip with the absolute field maximum of $6.9\times {10}^9\mathrm{V}/\mathrm{m}$. This explains the manifestation of field emission only for specific modes of excitation.

Figure 2

Spectral drain current $-I_{\mathrm{D}}$ vs excitation frequency $f$ for bands in which field emission occurs first (dc bias $V$ ranges from 0 to $-200\mathrm{m}\mathrm{V}$). These three modes are denoted by M100, M200, and M201. The inset shows the transition from tunneling to field emission in a magnified current scale. The current differs roughly by 2 orders of magnitude. The dotted line is a tunneling fit for a set of superimposed resonances, according to the standard theory of a single electron shuttle of Equations (1, 2). The double-headed arrow corresponds to the respective scope given in the main figure.

Figure 3

Peak current $I_{\mathrm{D}}^{\mathrm{p}\mathrm{e}\mathrm{a}\mathrm{k}}$ vs dc bias voltage $V$ for the first three modes, which show transition to field emission. Error bars correspond to maximum variation during the averaged recording of the spectral current. The data have been fitted according to Eq. (5). Inset: If $n_I$ electrons are on the island after field emission, a Monte Carlo integration of the tunneling at the other electrode (points) yields a current $I=g{n}_{I}ef$ with $g<1$ (solid line) and thus justifying the analytic curve of Eq. (5). The latter describes well the experimental results.