Identification of pristine and defective graphene nanoribbons by phonon signatures in the electron transport characteristics

Inspired by recent experiments where electron transport was measured across graphene nanoribbons (GNRs) suspended between a metal surface and the tip of a scanning tunneling microscope [Koch et al., Nat. Nanotechnol. 7, 713 (2012)], we present detailed first-principles simulations of inelastic electron tunneling spectroscopy (IETS) of long pristine and defective armchair and zigzag nanoribbons under a range of charge carrier conditions. For the armchair ribbons we find two robust IETS signals around 169 and 196 mV corresponding to the $D$ and $G$ modes of Raman spectroscopy as well as additional fingerprints due to various types of defects in the edge passivation. For the zigzag ribbons we show that the spin state strongly influences the spectrum and thus propose IETS as an indirect proof of spin polarization.

Figure 1

(a) Computational setup for a pristine AGNR showing electrode, device, and dynamical regions. (b) Electronic band structure $(k_x$ is in units of inverse unit cell length). The different bands are colored according to symmetry of the electronic states. Red: symmetric, corresponding to Figs. 2 and 2. Blue: antisymmetric, corresponding to Figs. 2 and 2. (c) Electronic transmission for varying electrode broadening describing the coupling to the metal contacts, $\eta =0,0.1,1$ eV, see text. (d) Electronic DOS projected onto the dynamical region. (e)–(h) Similar entities for the pristine ZGNR case.

Figure 2

(a)–(d) Electron transmission eigenchannels for the clean AGNR for the valence bands at $E-E_F=-1$ eV and for the conduction bands at $E-E_F=1$ eV. (e)–(h) Electron transmission eigenchannels for the clean ZGNR in the valence bands at $E-E_F=-0.4$ eV and in the conduction bands at $E-E_F=0.4$ eV for one spin component. The eigenchannels for the other spin component are simply mirror images around the middle of the ZGNR (not shown). The red/blue (pink/gray) isosurfaces represent the real (imaginary) part and sign of the scattering state wave function. For all eigenchannel calculations the electrode broadening was set to zero $(\eta =0$ eV).

Figure 3

Convergence of the intrinsic IETS for pristine (a) AGNR and (b) ZGNR as a function of the size of the dynamical region (stated in the legends). The results (offset for clarity) are normalized with respect to the number of vibrating unit cells, i.e., we show the IETS amplitude per ${\mathrm{H}}_4{\mathrm{C}}_{14}$ segment for AGNR and per ${\mathrm{H}}_2{\mathrm{C}}_8$ segment for ZGNR. No gate voltage is applied $(V_G=0.0$ V).

Figure 4

IETS signals as a function of gate voltage for (a) pristine AGNR (four vibrating unit cells) and (b) pristine ZGNR (six vibrating unit cells). Vertical dashed lines are guides to the eye indicating the energy of the most contributing vibrational modes. Specific IETS signals (offset for clarity) for the (c) AGNR and (d) ZGNR at selected gate voltages marked with horizontal dashed lines in (a) and (b). Broadening originates from temperature $T=4.2$ K and a lock-in modulation voltage $V_{\mathrm{rms}}=5$ mV (except for the thin red lines in the lower panels with $V_{\mathrm{rms}}=0$ mV).

Figure 5

(a) Computed phonon band structure for the pristine, infinite AGNR $(k_x$ is in units of inverse unit cell length). The magnitude of the red, green, and blue bands [corresponding to the three vertical lines in Fig. 4], is proportional to the signal size weighted overlap [$F_{nk}(V_G=0\mathrm{V})$ in Eq. (8)], between the repeated band vector and modes with frequencies $\hslash \omega >180$ meV, $180>\hslash \omega >162$ meV, and $\hslash \omega <162$ meV for red, green, and blue, respectively. The red band is scaled by $0.2$ compared to blue and green. (b)–(e) Selected phonon band modes at $\Gamma$ for the infinite structure which, according to the projection, characterize the active IETS modes.

Figure 6

(a) IETS signals with $V_G=0.0$ and 0.5 V (offset for clarity) for the pristine ZGNR (six vibrating unit cells). The black lines correspond to spin-degenerate calculations while the red lines are the spin-up components of spin-polarized calculations. Broadening originates from temperature $T=4.2$ K and modulation voltage $V_{\mathrm{rms}}=5$ mV (full lines) or $V_{\mathrm{rms}}=0$ mV (dashed lines). (b) Electronic transmission from spin-degenerate calculations with varying electrode broadening describing the coupling to the metal contacts, $\eta =0,0.1,1$ eV [see also Fig. 1 for the corresponding spin-polarized case].

Figure 7

The phonon band structure of the ZGNR $(k_x$ is in units of inverse unit cell length), together with the $\Gamma$-point modes. The widths of the red bands are proportional to the weight function $F\left(0\mathrm{V}\right)$ [Eq. (8)], while the widths of the blue bands are proportional to $F\left(0\mathrm{V}\right)+F\left(0.5\mathrm{V}\right)$.

Figure 8

Top and side views of the dynamical region describing the various AGNR defect structures. The dashed red ellipses are guides to the eye highlighting the defect position. (a) Pristine AGNR. (b) One extra H atom on one of the edges. (c) Two extra H atoms on one of the edges. (d) One H atom replaced by a F atom. (e) Dehydrogenated edge where 4 H atoms have been removed from each side. (f) One broken C-C bond. (g) Two broken C-C bonds. (h) Four broken C-C bonds. (i) Cu adatom in a hollow site on the edge.

Figure 9

Electronic properties of the AGNR structures shown in Fig. 8. The total transmission is shown with black lines. The ratio $T/T_1$, where $T_1$ is the transmission originating from the most transmitting eigenchannel, is shown with green dashed lines (this ratio gives a lower bound to the number of contributing eigenchannels). The DOS (arb. units) for the C atoms in the dynamical region is shown with red lines (offset by three units).

Figure 10

(a)–(i) IETS as a function of gate voltage $V_G$ for the pristine and defective AGNR structures shown in Fig. 8. (j)–(o) IETS for six selected structures at three specific gate values [dashed horizontal lines in (a)–(i)]. The curves are offset with the most negative gate value at the bottom (black curves) and the most positive at the top (green curves). (j) Clean AGNR at gate values $V_G=-0.3$, 0.0, and 0.8 V. (k) 1H-edge at $V_G=-0.3$, 0.0, and 0.2 V. (l) 8H-free at $V_G=-0.3$, 0.0, and 0.6 V. (m) 1C-broken at $V_G=-0.3$, 0.0, and 0.3 V. (n) 4C-broken at $V_G=-0.3$, 0.0, and 0.3 V. (o) Cu-adatom at $V_G=-0.3$, 0.0, and 0.3 V. Dotted vertical lines are guides to the eye of characteristic IETS signals corresponding to the modes in Fig. 11.

Figure 11

Visualization of the most contributing defect-induced vibrational modes to the IETS signals indicated by vertical lines in Figs. 10–10. (a) and (b) The two hydrogen signals for 1H-edge. (c) Localized edge mode at the carbon dimers for the 8H-free. (d) Delocalized edge mode for the 8H-free. (e) Hydrogen mode from the zigzag edge of 4C-broken. (f) and (g) Defect modes for 4C-broken.

Figure 12

Top and side views of the dynamical region describing the various ZGNR defect structures. The dashed red ellipses are guides to the eye highlighting the defect position. (a) Pristine ZGNR. (b) One extra H atom on one of the edges. (c) One H atom replaced by a F atom. (d) Cu adatom in a hollow site on the edge. (e) Li adatom in a hollow site on the edge. (f) One H replaced by a OH group. (g) One H replaced by a ${\mathrm{NO}}_2$ group. (h) Structural defect (R57). (i) Substitutional Si defect next to the edge.

Figure 13

Electronic properties of the ZGNR structures shown in Fig. 12 with the spin-up/down components in the left/right panel. The spin-resolved total transmission is shown with black lines while spin-averaged total transmission is shown with thin blue lines. The ratio $T^{\sigma }/T_1^{\sigma }$, where $T_1^{\sigma }$ is the transmission originating from the most transmitting spin eigenchannel, is shown with green dashed lines (this ratio gives a lower bound to the number of contributing eigenchannels with spin $\sigma )$. The spin-resolved DOS (arb. units) for the C atoms in the dynamical region is shown with red lines (offset by three units).

Figure 14

(a)–(i) Spin-averaged IETS as a function of gate voltage $V_G$ for the pristine and defective ZGNR structures shown in Fig. 12. (j)–(o) IETS for six selected structures at three specific gate values [dashed horizontal lines in (a)–(i)]. The curves are offset with the most negative gate value at the bottom (black curves) and the most positive at the top (green curves). (j) Clean ZGNR for gate values $V_G=0.0$, 0.4, and 0.8 V. (k) 1H-edge at $V_G=-0.6$, 0.0, and 0.4 V. (l) Cu-adatom at $V_G=-0.2$, 0.0, and 0.8 V. (m) 1OH-edge at $V_G=-0.2$, 0.0, and 0.8 V. (n) R57 at $V_G=-0.8$, 0.0, and 0.2 V. (o) Si-substitute at $V_G=-0.3$, 0.0, and 0.3 V. Dotted vertical lines are guides to the eye of characteristic IETS signals corresponding to the modes shown in Fig. 15.

Figure 15

Visualization of the most contributing modes to the IETS signals indicated by vertical lines in Figs. 14–14. (a) Edge mode at the edge with the extra hydrogen in 1H-edge. (b) Mode contributing to the asymmetric signal in Fig. 14 for the 1OH-edge. (c) Out-of-plane mode for Cu-adatom. (d) Localized mode for R57. (e) Out-of-plane mode for Si-substitute.