Thermal-equilibrium relation between the optical emission and absorption spectra of a doped semiconductor quantum well

We report experimental demonstration of the Kennard-Stepanov (KS) relation, a fundamental equilibrium relation determined by absolute temperature, between photoluminescence (PL) and PL-excitation spectra of a doped quantum well. With the resonant excitation PL measurement technique, the KS relation has been fulfilled at 5–220 K, thanks to the thermal bath provided by the resident carriers introduced with the doping. Crossover to quasi thermal or nonthermal carrier distributions has also been characterized quantitatively via systematic off-resonant excitations.

Figure 1

Normalized PL (solid curve), PLE (dotted curve), and $F\left(\omega \right)$ (vertical line segments) measured at the environmental temperature $T$ of $33\pm 1\text{K}$.

Figure 2

(a) $F\left(\omega \right)$ measured at various temperatures plotted on each offset. Filled triangles indicate excitation energies set to be resonant to the PL peak energies. Values inside and outside the parentheses indicate $T$ and $T^{\ast }$, respectively. (b) Plots of estimated temperatures $T^{\ast }$ as a function of environmental temperatures $T$. The solid line indicates $T^{\ast }=T$.

Figure 3

Normalized PLE, PL spectra, and $F\left(\omega \right)$ measured at 33 K (left a–c) and 5.6 K (right d–f), respectively. We set different excitation energies for the PL in (b) and (c) and for the PL in (e) and (f).

Figure 4

Plots of $T^{\ast }$ as a function of excitation energy measured at 5–50 K. The indices of (b), (c), (e), and (f) correspond to the measurements shown in Fig. 3.