Figure 1

(a) Measured (circles) imaginary part of the DF of undoped GaN and fit (thick solid line). Lines denoted by X, BB, and EPC show contributions of discrete excitons, band-to-band transitions, and transitions into exciton-phonon complexes, respectively. The inset presents the absorption coefficient determined from the measured DF. (b) Measured (solid lines) imaginary part of the DF for different electron concentrations. Curves are vertically displaced, for clarity. Numbers on the right indicate the electron concentration in units of ${10}^{18}{\text{cm}}^{-3}$. The X and EPC bands of undoped GaN (solid arrows) are transformed into broader X-like and EPC-like bands for high electron concentrations (open arrows). For the meaning of dashed and dotted lines, see the text. In the inset, ${\epsilon }_2$ spectra of $3.7\times {10}^{18}$ (dotted) and $2.3\times {10}^{19}{\text{cm}}^{-3}$ (circles) samples are compared to the spectrum of undoped GaN (thin solid line).Reuse & Permissions

Figure 2

Band structure of wurtzite GaN. The $k_t$ $\left(k_z\right)$ axis corresponds to wave vectors perpendicular (parallel) to the optic axis. Upper and lower valence subbands (Ref. 25) are shown by solid and dotted lines, respectively. Short open and filled arrows indicate wave vectors of free electrons at the Fermi level for electron concentrations of $3.7\times {10}^{18}$ and $2.3\times {10}^{19}{\text{cm}}^{-3}$, respectively. Long open arrows denote direct optical transitions from the valence band into the conduction-band Fermi-level states for the electron concentration of $3.7\times {10}^{18}{\text{cm}}^{-3}$. The inset shows that, for each valence subband, the absorbed photon energy is a function of the angle between the wave vector and the optic axis.Reuse & Permissions

Figure 3

Relative probability of direct optical transitions from $A$ (top), $B$ (middle), and $C$ (bottom) valence bands into the conduction band for the ordinary wave as a function of the wave-vector length for three angles between the optic axis and the wave vector: squares for $0°$, circles for $45°$, and triangles for $90°$. Solid lines superimposed on the symbols refer to upper valence subbands, while dotted and dashed lines stand for lower valence subbands (Ref. 25).Reuse & Permissions

Figure 4

(a) Contributions to the imaginary part of the DF due to band-to-band optical transitions from $A$, $B$, and $C$ valence bands (thin solid lines), their sum without broadening (dotted line) and with incorporated broadening (thick solid line). The electron concentration is $3.7\times {10}^{18}{\text{cm}}^{-3}$. Filled and open arrows indicate the band-gap energy $E_{gA}$ and an average photon energy for transitions from the VB $A$ to the CB states at the Fermi level. For comparison, experimental data are shown by circles. (b) Fit (thick solid line) to the experimental data (circles). Three contributing mechanisms are caused by band-to-band (dashed line), X-like (thin solid line), and EPC-like (dotted line) optical transitions.Reuse & Permissions

Figure 5

(a) Band-gap energy (squares) and peak positions of X-like (triangles) and EPC-like (circles) bands as a function of electron concentration. The solid line is a fitting curve for the observed band-gap narrowing. The dotted line represents the expected doping-dependent one-particle absorption edge (see the text). (b) Electron-concentration dependence of the normalized spectrally integrated strength of X-like (triangles) and EPC-like (circles) bands. Solid lines are guide for the eyes. The inset shows two branches (solid lines) due to the plasmon-phonon coupling. Horizontal dotted lines indicate the energy of LO and TO phonons for undoped wurtzite GaN. Circles are the determined average energies of phonons that participate in optical transitions into exciton-phonon complexes. (c) Calculated screening length as a function of free-electron concentration for $n$-type wurtzite GaN at room temperature (solid line). Two commonly used approximations, Debye-Hückel and Thomas-Fermi screening lengths, are shown by dotted and dashed lines, respectively. The inset presents the temperature dependence of the Mott density calculated by applying criterion (1).Reuse & Permissions