Negative Differential Resistance in Transport through Organic Molecules on Silicon

Recent scanning tunneling microscopy studies of individual organic molecules on Si(001) reported negative differential resistance (NDR) above a critical applied field, observations explained by a resonant tunneling model proposed prior to the experiments. Here we use both density functional theory and a many-electron $GW$ self-energy approach to quantitatively assess the viability of this mechanism in hybrid junctions with organic molecules on Si. For cyclopentene on $p$-type Si(001), the frontier energy levels are calculated to be independent of applied electric fields, ruling out the proposed mechanism for NDR. Guidelines for achieving NDR are developed and illustrated with two related molecules, aminocyclopentene and pyrroline.

Figure 1

Schematic depiction of resonant tunneling mechanism for NDR. (a) zero bias, (b) molecular level at resonance with $E_F$ ($V\uparrow$, $I\uparrow$), (c) molecular level driven into Si band gap ($V\uparrow$, $I\downarrow$).

Figure 2

Atomic structure of 0.5 ML (a) cyclopentene (${\mathrm{C}}_5{\mathrm{H}}_8$) on clean Si(001), (b) $\mathrm{\text{amino}}\mathrm{\text{−}}{\mathrm{C}}_5{\mathrm{H}}_8$ on $\mathrm{H}$-terminated Si(001), and (c) pyrroline on $\mathrm{H}$-terminated Si(001). Orange (medium dark gray), green (medium gray), light blue (light gray), and dark blue (dark gray) circles represent Si, $\mathrm{C}$, $\mathrm{H}$, and $\mathrm{N}$, respectively.

Figure 3

LDA PDOS on the molecule for 0.5 ML ${\mathrm{C}}_5{\mathrm{H}}_8$ on clean Si(001) (a), (d), $\mathrm{\text{amino}}\mathrm{\text{−}}{\mathrm{C}}_5{\mathrm{H}}_8$ on $\mathrm{H}$-terminated Si(001) (b), (e), and pyrroline on $\mathrm{H}$-terminated Si(001) (c), (f). The insets show the orbitals associated with the leading states in each system. Pink (medium gray) and purple (dark gray) indicate positive and negative isocontours taken at the same value across all systems.

Figure 4

DFT $E_m$ as a function of the effective electric field. (a) ‘$\mathrm{\text{dimer}}+\mathrm{\text{molecule}}$’ state in ${\mathrm{C}}_5{\mathrm{H}}_8/\mathrm{Si}$ (black circles), (b) lone pair state in $\mathrm{\text{amino}}\mathrm{\text{−}}{\mathrm{C}}_5{\mathrm{H}}_8/\mathrm{Si}$ (red triangles), and (c) lone pair derived level in pyrroline/Si (blue squares). Straight lines of best fit are plotted in each case.