Long-range Spatial Correlations in the Exciton Energy Distribution in $\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}$ Quantum Wells

Variations in the width of a quantum well (QW) are known to be a source of broadening of the exciton line. Using low temperature near-field optical microscopy, we have exploited the dependence of exciton energy on well width to show that in GaAs QWs, these seemingly random well-width fluctuations actually exhibit well-defined order—strong long-range correlations appearing laterally, in the plane of the QW, as well as vertically, between QWs grown one on top of the other. We show that these fluctuations are correlated with the commonly found mound structure on the surface. This is an intrinsic property of molecular beam epitaxial growth.

Figure 1

(a),(b) Two-dimensional images of the exciton energy, $E_X(x,y)$, for samples 1 and 2, respectively. The energy ranges in (a) and (b) are 0.2 and 0.5 meV, respectively. (c),(d) The autocorrelation function $G_X(x,y)$ for the range $-10\mu \mathrm{m}\le x,y\le 10\mu \mathrm{m}$, of the exciton images of samples 1 and 2, respectively.

Figure 2

(a),(b) Surface topography images of samples 1 and 2, respectively. The full range is 20 nm. (c),(d) The autocorrelation function $G_h(x,y)$ for the range $-10\mu \mathrm{m}\le x,y\le 10\mu \mathrm{m}$, of the topography images of samples 1 and 2, respectively.

Figure 3

(a) The exciton energy fluctuations of three QWs grown one on top of the other along an $11\mu \mathrm{m}$ line. (b) The same line scan as in (a) translated to well-width fluctuations.

Figure 4

The standard deviation of the well-width fluctuations as a function of the well width. The inset shows a schematic drawing of the layers structure for narrow and wide QWs. Grey and white areas represent GaAs and AlGaAs layers, respectively.