High-temperature Mott transition in wide-band-gap semiconductor quantum wells

The crossover from an exciton gas to an electron-hole plasma is studied in a GaN/(Al,Ga)N single quantum well by means of combined time-resolved and continuous-wave photoluminescence measurements. The two-dimensional Mott transition is found to be of continuous type and to be accompanied by a characteristic modification of the quantum well emission spectrum. Beyond the critical density, the latter is strongly influenced by band-gap renormalization and Fermi filling of continuum states. Owing to the large binding energy of excitons in III-nitride heterostructures, their injection-induced dissociation could be tracked over a wide range of temperatures, i.e., from 4 to $150\mathrm{K}$. Various criteria defining the Mott transition are examined, which, however, do not lead to any clear trend with rising temperature: the critical carrier density remains invariant around ${10}^{12}{\mathrm{cm}}^{-2}$.

Figure 1

(a) PLE spectrum (black dots) of the QW recorded at $4\mathrm{K}$ revealing two fundamental excitons ${\mathrm{X}}_{\mathrm{A}}$ and ${\mathrm{X}}_{\mathrm{B}}$ and the BB absorption at higher energies. A PL spectrum (red, excitation energy $3.627\mathrm{eV}$) is shown for comparison. (b) SP simulations: normalized wave-function overlap (black) and QW ground-state energy shift for excitons (red solid, accounting for $E_{\mathrm{X}}^{\mathrm{b}}\left(n\right)$) and free carriers (red dashed) as a function of $n$.

Figure 2

(a) Streak camera image recorded at $4\mathrm{K}$. (b) Fingerprint of the MT at $4\mathrm{K}$: evolution of peak energy, upper and lower half-maximum energy (red dots), $E_{\mathrm{m}}$, $\Delta E_{\mathrm{QCSE}}^{\mathrm{X}}$, $\Delta E_{\mathrm{F}}$ (blue dashed line), and $E_{\mathrm{BGR}}$ (black dashed line, the result of cw-PL is shown for comparison as a dotted line, cf. Fig. 3) as a function of $n$. The MT range is shaded in red. (c) and (d) Spectral profiles at different time delays: comparison of experimental data (dots) and modeling (lines) at 4 (steps of $60\mathrm{ps}$) and $150\mathrm{K}$ (steps of $180\mathrm{ps}$), respectively.

Figure 3

MT in cw-PL: (a) and (b) injection-dependent PL spectra measured at 4 and $150\mathrm{K}$, respectively. In (b), exponential fits of the high-energy tail are shown with green lines. The red spectrum marks the transition from a monoexponential tail to an excitonic line shape. (c) and (d) MT at 4 and $150\mathrm{K}$ by analogy with Fig. 2, respectively. The MT range is highlighted with a red background and the red arrow in (d) marks the position of the red spectrum in (b). The inset in (c) shows $I_{\mathrm{PL}}$ as a function of excitation power density $P_{\mathrm{exc}}$ at $4\mathrm{K}$.

Figure 4

(a) Schematic of the MT-defining criteria $E_{\mathrm{X}}=E_{\mathrm{BGR}}$ and $\Delta E_{\mathrm{F}}=E_{\mathrm{BGR}}$ (based on cw-PL values taken at $4\mathrm{K}$). The MT range is shaded in red, $E_{\mathrm{X}}$ is given by the black solid line, and the gray dashed lines mark upper and lower QW half maximum energies. (b) $n_{\mathrm{crit}}$ values deduced from various criteria: $\Delta E_{\mathrm{F}}=E_{\mathrm{BGR}}$ (blue), disappearance of an excitonic line shape [red, cf. Fig. 3], and $E_{\mathrm{X}}=E_{\mathrm{BGR}}$ (black). Results of tr-PL at $4\mathrm{K}$ are shown with open circles. The red background marks the confidence interval.