Strain-related phenomena in GaN thin films

Abstract

Photoluminescence ͑PL͒, Raman spectroscopy, and x-ray diffraction are employed to demonstrate the coexistence of a biaxial and a hydrostatic strain that can be present in GaN thin films. The biaxial strain originates from growth on lattice-mismatched substrates and from post-growth cooling. An additional hydrostatic strain is shown to be introduced by the presence of point defects. A consistent description of the experimental results is derived within the limits of the linear and isotropic elastic theory using a Poisson ratio ϭ0.23Ϯ0.06 and a bulk modulus Bϭ200Ϯ20 GPa. These isotropic elastic constants help to judge the validity of published anisotropic elastic constants that vary greatly. Calibration constants for strain-induced shifts of the near-bandedge PL lines with respect to the E 2 Raman mode are given for strain-free, biaxially strained, and hydrostatically contracted or expanded thin films. They allow us to extract differences between hydrostatic and biaxial stress components if present. In particular, we determine that a biaxial stress of one GPa would shift the near-band-edge PL lines by 27Ϯ2 meV and the E 2 Raman mode by 4.2Ϯ0.3 cm Ϫ1 by use of the listed isotropic elastic constants. It is expected from the analyses that stoichiometric variations in the GaN thin films together with the design of specific buffer layers can be utilized to strain engineer the material to an extent that greatly exceeds the possibilities known from other semiconductor systems because of the largely different covalent radii of the Ga and the N atom. ͓S0163-1829͑96͒03148-7͔

Strain-Induced Band Gap Engineering in Selectively Grown GaN–(Al,Ga)N Core–Shell Nanowire Heterostructures

“…In particular, the E 2 high mode of GaN is known to be sensitive to strain within the crystal lattice. 20 Thus, the energetic shift of the E 2 high mode, i.e., Δk = k(E 2 high,ex ) − k(E 2 high,0 ), of the respective core−shell NW arrays is plotted in Figure 3b as a function of the core diameter. As a reference for unstrained GaN a value of k(E 2 high,0 ) = 572.5 cm −1 has been obtained from sample A ( Table 1).…”

“…20 In a good approximation, it can be assumed that Δk = −2a·ε xx − b·ε zz where a and b are the socalled phonon deformation potential constants. 29 In the present case this can be simplified to Δk ≈ −b·ε zz where lateral strain contributions ε xx can be neglected.…”

Optical and structural characterisation of epitaxial nanoporous GaN grown by CVD

“…As the deposition time increases, the NBE band shifts towards the high energy side, from 3.432 eV (361 nm) for a deposition time of 15 min, to 3.467 eV (357 nm) for a deposition time of 60 min. As previously discussed, the energy gap of a semiconductor is affected by the residual strain [7]. When GaN is under tensile strain, the NBE emission is shifted towards lower energies, while compressive strain leads to a blue-shift of the NBE.…”

“…The strain tensor components (ε) are similar on the c-plane and different along the perpendicular component, corresponding to the hexagonal symmetry of wurtzite GaN (ε xx =ε yy ≠0, ε zz ≠0) [7]. Not only the built-in biaxial strain plays a role in the resulting strain of the layers, but also the point defects can induce local hydrostatic strain for which all the strain tensor components are equal (ε xx =ε yy =ε zz ) [7]. The hydrostatic strain is related to the difference between the atomic radius of the impurity or defect and the host atom replaced, it can be compressive or tensile [8].…”

“…As a consequence of the different strain contributions, the band structure, and, in particular, the band gap of GaN is modified, inducing a red-shift of the band-edge luminescence emission for tensile strain and a blue-shift when compressive strain prevails [9,10]. Therefore, luminescence spectroscopy can be used to measure the strain in the GaN layers by means of the energy shift of the near band edge (NBE) emission [7]. Raman scattering is also a powerful and direct technique to monitor the residual strain in epitaxial GaN layers [11,12].…”