Excitonic recombination dynamics in shallow quantum wells

We report a comprehensive study of carrier-recombination dynamics in shallow AlxGa1-xAs/GaAs quantum wells. At low crystal temperature (2 K), the excitonic radiative recombination time is shown to be strongly enhanced in shallow quantum wells with x>0.01, consistently with a model that takes into account the thermal equilibrium between the three-dimensional exciton gas of the barrier and the two-dimensional exciton gas, which are closer in energy as x decreases. Furthermore, we demonstrate the existence of a thermally activated escape mechanism due to the low effective barrier height in these structures. The nonradiative recombination is shown to dominate the carrier dynamics for temperatures as low as 10 K for x≈0.01. Our experimental observations are analyzed using three different variational exciton calculations. In particular, we study the crossover from the two-dimensional to the three-dimensional behavior of the exciton, which occurs for x as low as 0.01 and affects mainly the oscillator strength, whereas the transition energies in shallow quantum wells can be calculated, to a large extent, using the same approximations as for conventional quantum wells. The peculiar behavior of the oscillator strength at the crossover to the weak confinement regime is obtained by expansion in a large basis

Mathematics Motivation in Students with Low Cognitive Ability: A Longitudinal Study of Motivation and Relations with Effort, Self-Regulation, and Grades

Expectancy-value theory (EVT) is a popular framework to understand and improve students’ motivation. Unfortunately, limited research has verified whether EVT predictions generalize to students with low levels of cognitive ability. This study relies on Grade 5 and 8 data from 177 students with low levels of cognitive ability and a matched sample of 177 students with average to high cognitive ability from the German ‘Project for the Analysis of Learning and Achievement in Mathematics’. Results showed that students with low levels of cognitive ability were able to differentiate EVT components. Both groups demonstrated a similar downward developmental trend in motivation from early to middle adolescence, and similar relations between EVT components and levels of efforts, self-regulation, and mathematics class grades