Figure 1

(Color) (a) Impact ionization rates and (b) impact excitation rates for a (25,0) nanotube $(d=2.0\mathrm{nm})$ as a function of energy (measured from the bottom of the first conduction band ${\Delta }_1$), for the first seven conduction bands shown in red, blue, green, cyan, magenta, light red, and black in increasing order of the band index. The vertical dashed lines correspond to the bottoms of the conduction bands ${\Delta }_i$ $(i=2,3,\dots ,7)$ relative to ${\Delta }_1$. (c) The vertical lines are allowed $k$ points of zigzag tube with $\mathrm{mod}(n,3)=1$ for the first four doubly degenerate bands $e_i^{L_i}$ $\left({e_i^{\prime }}^{L_i}\right)$. The angular momenta $L_i$, in units of $2∕\left(3d\right)$, measures a minimum distance from the $K$ $\left(K^{\prime }\right)$ point of graphene to the 1D lines of allowed $k$ points of a nanotube. Note that the hole momentum has the opposite sign to that of the electron momentum.Reuse & Permissions

Figure 2

(Color) Electron distribution function in a (25,0) nanotube at applied electric field of $F$=(a) 0.1 and (b) $0.05\mathrm{MV}∕\mathrm{cm}$ as a function of energy in the first six conduction bands shown in red, blue, green, cyan, magenta, and light red, respectively. Black curves are the total distributions. In (a) solid curves use impact excitation and dotted curves impact ionization scattering rates with phonons at $T=300\mathrm{K}$. In (b) we use impact excitation scattering, solid curves use phonon scattering at $T=300\mathrm{K}$, and dotted curves use acoustic phonon scattering at $T_{ac}=300\mathrm{K}$ and optical phonon scattering, at $T_{op}=1500\mathrm{K}$.Reuse & Permissions

Figure 3

(Color) Exciton production rate $P$ per unit carrier in a (25,0) tube as function of the electric field for acoustic phonon scattering at $T_{ac}=300\mathrm{K}$ and different optical phonon temperatures (from bottom to top) $T_{op}=300$ (red), 900 (blue), 1200 (green), 1500 (cyan), 1800 (magenta), and $2100\mathrm{K}$ (light red) along with the best fit to Eq. (5) for ${\lambda }_{op}=25\mathrm{nm}$, $E_t=0.57\mathrm{eV}$, and $P_0=18{\mathrm{ps}}^{-1}$. The inset shows scaling of all the calculations with the effective temperature in accord with Eq. (5).Reuse & Permissions

Figure 4

(Color) Energy distribution $I_{\omega }$ of excitons produced in the impact excitation process in (a) a (25,0) tube and (b) a (26,0) tube with phonons at $T=300\mathrm{K}$ and different applied electric fields $F$ in MV/cm: 0.03, red; 0.06, blue; 0.09, green; 0.12, cyan; 0.15, magenta; and normalized to the total production rate $P=\int I_{\omega }d\omega$.Reuse & Permissions