Critical Size of Temperature-Dependent Band Shift in Colloidal PbSe Quantum Dots

The temperature-dependent property of band gap in colloidal PbSe quantum dots has been investigated from both experiment and theory above room temperature. When the particle size increases, the temperature coefficient evolves from negative values to zero and then to positive value following the trend to its bulk material value. The calculated critical size of 4.88 nm for the temperature coefficient dE/dT = 0 is consistent with the experimental result. When the particle size is smaller than the critical size, the temperature coefficient dE/dT is also dependent on the temperature, which has not been observed before. However, this phenomenon is not obvious at large particle sizes. The functions of size-and temperature-depended band gap E and temperature coefficient dE/dT are achieved through theoretical calculation and experimental calibration. Temperature-induced variations of quantum confinement energy and exciton-phonon coupling are the key factors for the temperature coefficient. The balance between the variations of confined effect and exciton-phonon coupling causes the critical size of temperature coefficient in colloidal PbSe quantum dots.