2.2 Graphene is a single layer honeycomb lattice of carbon atoms. Graphite can be viewed as a stack of graphene layers.
2.3 Schematic of (a) zigzag and (b) armchair edge configurations of GNRs. The position of the edge is indicated by the pink line. (c) An armchair edge graphene superlattice structure.
2.4 Honeycomb lattice and its Brillouin zone. (a) Lattice structure of graphene, composed of two interpenetrating triangular lattices (a1 and a2 are the lattice unit vectors, and δi, i = 1, 2, 3 are the nearest-neighbor vectors). (b) Corresponding Brillouin zone. The Dirac cones are located at the K and K′ points.
2.5 The energy dispersion relations for graphene are shown through the whole region of the Brillouin zone. The lower and the upper surfaces denote the valence π and the conduction π* energy bands, respectively. The coordinates of high symmetry points are Γ = (0, 0), K = (2π∕3a, 2π∕3
a), and M = (2π∕3a, 0). The energy values
at the K, M, and Γ points are 0, t, and 3t, respectively.2.6 Schematic of a graphene photodetector.
2.7 Subbands in a quantum well. The potential well caused by the AlGaAs/GaAs layer structure gives rise to bound states localized in the well. In k-space, there exist continuous subbands as the electrons are not confined in the plane of the well.
2.8 Schematic conduction band energy diagram of two QCL active regions with the intermediate injector region and the moduli squared of the wave functions involved in the laser transition (labelled 1, 2, and 3). The laser transition is indicated by the vertical arrow, the electron flow by the horizontal arrow.
2.9 Conduction-band structure of the original SL-QCL. Two active region SLs with the preceding injector regions are shown. The minibands are indicated by gray regions. Laser action, as denoted by the wavy arrows, takes place across the first minigap 2-1.
3.1 Schematic view of the sp2 hybridization. The orbitals form angles of 120∘.
3.2 The structure of an AGNRn ccBNmbn. The incident light is assumed to be polarized along the x-direction. CA∕B,NA∕B, and BA∕B represent a carbon, a nitrogen, and a boron atom at the sublattice A or B.
3.3 The wavefunctions of a AGNR20BN40 at CA (red circles), NA (red squares), CB (black circles), and BB (black squares). nc = 1 (nv = 1) represents the lowest conduction (highest valence) subband.
3.4 (a) The dielectric function of an AGNR20BN40 based on TB (solid line) and first principle calculations (dashed line). The inset shows the related JDOS using the TB model. (b) The electronic band-structure of an AGNR20BN40 from TB (solid line) and first principle calculations (red dotted line).
3.5 The quantum efficiency of an (a) AGNR8BN30, (b) AGNR16BN30, and (c) AGNR33BN30 compared to a H-AGNRs with the same indices.
4.1 The structure of a GNR with zigzag edges along the x direction. Each unit cell consists of N atomes at the sublattice A or B. A hard wall boundary condition is imposed on the both edges.
4.2 Numerically evaluated the wavenumber θ as a function of kx for 6-ZGNR, 19-ZGNR, and 30-ZGNR.
4.3 The wavenumber θ as a function of the ribbon index, N, for different subband numbers, q. Dashed lines show the first approximation (Eq. 4.25) and circles show the second approximation (Eq. 4.28).
4.4 The electronic band structure of 6-ZGNR ((a), (b), and (c)) and 19-ZGNR ((d), (e), and (f)). The analytical model (black dashed lines) is compared against the numerical results (red solid lines).
4.5 The wave functions of 6-ZGNR and 19-ZGNR. Red(Blue) symbols denote the wave functions in sublattice B(A). The analytical model (squares) are compared against the numerical results (circles).
4.6 The wave functions of 125-ZGNR. Red(Blue) symbols denote the wave functions at the sublattice B(A). The analytical model (squares) and curve fitted model (diamonds), are compared against the numerical results (circles) for different subbands.
4.7 The electronic band structure of 125-ZGNR. The analytical model (red symbols) and the curve fitted (blue symbols) are compared with the numerical results (black symbols).
4.8 Dielectric function of (a) 6-ZGNR and (b) 19-ZGNR. The peaks are related to electronic band structure of (c) 6-ZGNR and (d) 19-ZGNR.
5.1 The structure of (a) a hydrogen-passivated superlattice, and (b) a boron nitride-confined superlattice. Both superlattices have the same index for the graphene nanoribbon part. CA∕B represents a carbon, NA∕B a nitrogen, and BA∕B a boron atom at the sublattice A or B. nw and nb denote the well and barrier indices respectively.
5.2 The electronic bandstructure for (a) a HSL(11), and (b) a BNSL(11) based on the TB model and first principles calculations. (c) The geometrical parameters of the structure. (d) Energy gap as a function of nw for a HSL and a BNSL.
5.3 The dielectric response of a HSL(11) and a BNSL(11) based on the TB (solid lines) and first principles calculations (dashed lines). The optical power density is 100kW∕cm2 and the photon flux is assumed to be normal to the HSL/BNSL plane.
5.4 The local density of states for (a) an HSL(11) and (b) a BNSL(11). (c) normalized LDOS for a unit cell of an ultrathin HSL. The optical power density of 102 kW/cm2 and the photon flux normal to the HSL/BNSL plane are assumed.
5.5 (a) Photocurrent and (b) quantum efficiency for a HSL(11) and a BNSL(11). The optical power density is 100kW∕cm2 and the photon flux is assumed to be normal to the HSL/BNSL plane.
5.6 The structure of (a) HSL(13) and (b) HSL(17). (c,d) Superlattices with different well/barrier lengths. The quantum efficiency and local density of states of each structure are depicted.
5.7 (Dashed-black line) The average photocurrent spectrum over different samples and (gray lines) the photocurrent spectrum of each sample as a function of the incident photon energy.(a,c) HSL and (b,d) BNSL.
5.8 The ideal and average photocurrent spectra for (a) HSL(11) and (b) BNSL(11) at various roughness amplitudes.
5.9 Local density of states for (a) an ideal and (b,c,d) rough HSL(11) at various roughness amplitudes. The optical power density is 100kW∕cm2 and the photon flux is assumed to be normal to the HSL/BNSL plane.
6.1 The algorithm of the developed optimization framework.
6.2 (a) The PSO results for different particles in the search space and (b) gain spectra and instability thresholds for the reference and optimized structures.
6.3 The conduction band diagram and the wavefunctions of (a) the reference design and (b) the optimized structure. The lasing subbands are indicated with bold solid/bold dashed lines.
6.4 The parametric gain g(Ω) as a function of the resonance frequency Ω at various (a) SA coefficients and (b) pumping strengths.
6.5 (a) The parametric gain g(Ω) as a function of the resonance frequency Ω. (b) The pumping ratio pf at which the RNGH instability sets in as a function of the SA coefficient. Inset: Optical gain spectra obtained for two optimized active-region QCLs.
6.6 The parametric gain g(Ω) as a function of the resonance frequency Ω at various (a) SA coefficients (γ =0,3, and 6 m/V2) and (b) pumping strengths (2, 2.4, 2.8) for a mid infrared QCL (solid red line) and a terahertz QCL (dashed black line).
6.7 The m×n mesh points for the finite difference approximation. Here m = 8 and n = 6. The boundary conditions are shown by green dots and initial condition by pink dots. E(m,n+1), a sample step in time domain, is shown with blue dot and its value is dependent on the previous steps, the orange dots.
6.8 Intensity as a function of time. In this graph, pf = 16,L = 6×10-3m,k = 1∕(10T 2), and T1 = 2T2. After a few round trips, the variables saturate to the approximate continuous wave solution in which the intensity is transformed from the initial Gaussian to a the stable operation mode.
6.9 The spectra of the optical intensity in logarithmic scale for (a) no SA coefficient (b) SA coefficient at the instability threshold, and (c) SA coefficient at the instability threshold and a larger pumping factor.
6.10 Schematic conduction-band diagram of a QCD. Ground-level electrons are excited to the active QW’s upper level by absorbing a photon. Due to the asymmetric band profile between two active QWs, the cascade excited electrons relax mostly in one direction (in this case to the right), resulting in a net photocurrent.
6.11 Responsivity of the ISB transition at room temperature. The responsivity values of 3.07, 2.39, 2.12, 2.71, 3.51, and 4.45 mA/W are obtained for the optimized QCDs from number 1 to 6, respectively.