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Principal physical properties of GaN/AlN multiquantum well systems determined by density functional theory calculations
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10.1063/1.4805057
/content/aip/journal/jap/113/19/10.1063/1.4805057
http://aip.metastore.ingenta.com/content/aip/journal/jap/113/19/10.1063/1.4805057

Figures

Image of FIG. 1.
FIG. 1.

Band structure and density of states obtained from VAPS for PBE exchange-correlation functional and LDA-1/2 method of (a) left—AlN and (b) right—GaN.

Image of FIG. 2.
FIG. 2.

DFT results of 16 Ga/16 Al layers periodic QW system: (a) total electric potential (i.e., electron energy) averaged over the surface perpendicular to c-axis (blue line); c-axis smoothed values obtained by an adjacent averaging procedure (red line); (b) averaged smoothed potential, obtained from LDA-1/2 (red line) and PBE (blue line) formulations; (d) derivation of a dipole layer localization by Gaussian fit; (c) dipole moment magnitude at the GaN/AlN heterointerface and the electric field determination in well/barrier interior in the 16 GaN/16 AlN MQWs system.

Image of FIG. 3.
FIG. 3.

Band energy obtained from projection of the band wavefunctions on theatom centered harmonics (shading) and the electric potential distribution surface averaged (dashed line) and c-axis smoothed (solid line) potential profiles. Left diagram—c-smoothing profiles were adjusted to AlN-33 points used and the energy band difference shift equal to 5.95 eV; right diagram—c-smoothing profiles were adjusted to GaN-34 points used and the energy band difference shift equal to 3.5 eV.

Image of FIG. 4.
FIG. 4.

Electric field in (left) AlN barrier and (right) GaN well for systems having a different thickness of an AlN barrier (top) and GaN well (bottom).

Image of FIG. 5.
FIG. 5.

Plane averaged and c double smoothed electric potential, obtained within LDA-1/2 approximation for systems with a different thickness of a GaN well. The barrier is 32 AlN atomic layers wide.

Image of FIG. 6.
FIG. 6.

DFT LDA-1/2 results: Dispersion relation (left) and the DOS projected on the atomic wavefunction, presented in function of the positions of the atoms (right) for systems of the well having 1, 2, 4, 8, 16, and 32 GaN layers and the same barrier having 16 AlN layers. The black lines are plane averaged double c-smoothed potential profiles presented as electron energy. The lines are separated by 5.96 eV in accordance to AlN conduction and valence bands energy difference.

Image of FIG. 7.
FIG. 7.

Spatial overlap of electron and hole wavefunction densities obtained in LDA-1/2 approximation: (a) for different well width, i.e., 1 GaN, 4 GaN, 8 GaN, and 16 AlN layers wide barrier; (b) for different barrier width, i.e., 8 AlN, 4 AlN, 1 AlN, and 16 GaN layers wide well; (c) —short period equal width superlattices: 2 GaN/AlN, 4 GaN/AlN, and 8 GaN/AlN layers. The densities were integrated in the x-y plane; therefore, c-axis dependence is shown in the horizontal axis.

Image of FIG. 8.
FIG. 8.

Characteristics of the principal optical transitions in the equal width AlN/GaN MQWs system: (a) energy and (b) oscillator strength. The c parallel polarized transition, i.e., the electric field vector parallel to c-axis, is denoted by red circles; the c perpendicular polarized transitions (two degenerate modes), having electric field vector perpendicular to c-axis, are denoted by blue squares.

Image of FIG. 9.
FIG. 9.

Characteristics of the principal optical transitions in an AlN/GaN MQWs system having a 32 ALs thick AlN barrier: (a) energy and (b) oscillator strength. The parallel polarized transition is denoted by red circles; the perpendicular transitions are denoted by blue squares.

Image of FIG. 10.
FIG. 10.

Characteristics of the principal optical transitions in AlN/GaN MQWs system having 16 ALs thick AlN barrier: (a) energy and (b) oscillator strength. The c parallel and perpendicular polarized transitions are denoted by red circles and blue squares, respectively.

Image of FIG. 11.
FIG. 11.

Characteristics of the principal optical transitions in AlN/GaN MQWs system having 4 ALs thick AlN barrier: (a) energy and (b) oscillator strength. The c parallel polarized transition is denoted by red circles, the pairs of perpendicular transitions (degenerate) are denoted by blue, green, and cyan polygons.

Image of FIG. 12.
FIG. 12.

Characteristics of the principal optical transitions in AlN/GaN MQWs system having 32 ALs thick GaN wells: (a) energy and (b) oscillator strength. The c parallel polarized transition is denoted by red circles, the perpendicular ones by blue, green, cyan, and blue-navy polygons.

Image of FIG. 13.
FIG. 13.

Characteristics of the principal optical transitions in AlN/GaN MQWs system having 16 ALs thick GaN wells: (a) energy and (b) oscillator strength. The c parallel polarized transition is denoted by red circles, the perpendicular ones by blue and green polygons.

Image of FIG. 14.
FIG. 14.

Characteristics of the principal optical transition in AlN/GaN MQWs system having 4 ALs thick GaN wells: (a) energy and (b) oscillator strength. The c parallel and perpendicular polarized transitions are denoted by red circles and blue squares, respectively.

Image of FIG. 15.
FIG. 15.

Spatial dependence of the different symmetry band states in 32 AlN, 16 GaN ALs system obtained by their projection on the atom centered: (a) ; (b) ; (c) orbitals (VASP LDA-1/2 approximation). The top diagrams present three dimensional plot in which the vertical axis is the magnitude of the projection. The bottom plots contain color maps in the logarithmic color scale.

Tables

Generic image for table
Table I.

Electric fields in the wells and barriers in (×10 V/Å), potential jumps in V at AlN/GaN heterojunctions. For the fields calculated from Ref. , we have used dielectric permittivity and . We have assumed no zero strain for , i.e., .

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/content/aip/journal/jap/113/19/10.1063/1.4805057
2013-05-17
2014-04-24
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Principal physical properties of GaN/AlN multiquantum well systems determined by density functional theory calculations
http://aip.metastore.ingenta.com/content/aip/journal/jap/113/19/10.1063/1.4805057
10.1063/1.4805057
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