Measurement of the volume plasmon energy from strained GaN quantum wells
Monochromated valence electron energy-loss spectroscopy (VEELS) is used to study the plasmon energy (Ep) from strained GaN quantum wells (QWs) embedded in an AlN matrix . The primary specimen is a set of three wells with 4 nm, 3 nm, and 2 nm widths, separated by 30 nm thick AlN layers. The SESAM microscope is used to record EFTEM data and then a Gaussian function is fitted to the volume plasmon peak at each image pixel. After integration parallel to the QWs the plasmon energy profile is obtained (see figure). A distinct blue-shift of the plasmon peak position with decreasing QW width is observed. To take into account the influence of the AlN/GaN interfaces, we solve the relativistic expressions for the begrenzungs effect given by Bolton et al.  and Moreau et al. . The interfaces induce an apparent blue-shift of the plasmon with decreasing layer width. However, after correction of this shift the dependence of Ep on QW width is still marked. We also consider the influence of the compressive strain of the GaN layers, which is known to cause a blue-shift of the plasmon . Because the critical thickness is about 3 nm, the 2-nm- and 3-nm-QWs are completely strained whereas the strain relaxation in the 4-nm-QW is about 0.12 % . Assuming a square-root dependence of the plasmon energy on unit-cell volume, the adjusted data show a reasonably linear trend, which is consistent with the concept of quantum confinement.
The use of high-resolution valence electron imaging offers the possibility to distinguish the different confinement behaviours of strained GaN QWs, which is important for understanding and exploiting bandgap engineering in today’s sophisticated devices.
 M. Benaissa, W. Sigle, M. Korytov, J. Brault, P. Vénneguès, P. A. van Aken, Appl. Phys. Lett. 103 (2013) 021901
 J. P. R. Bolton, M. Chen, J. Phys.: Cond. Matter 7 (1995) 3389
 P. Moreau, N. Brun, C. A. Walsh, C. Colliex, A. Howie, Phys. Rev. B 56 (1997) 6774
 J. Palisaitis, C.-L. Hsiao, M. Junaid, J. Birch, L. Hultman, P. O. A. Persson, Phys. Rev. B 84 (2011) 245301
 B. Damilano, N. Grandjean, F. Semond, J. Massies, M. Leroux, Appl. Phys. Lett. 75 (1999) 962
This research has received funding from the European Union Seventh Framework Programme [FP7/2007-2013] under grant no. 312483 (ESTEEM2).