Phonon pressure coefficients and deformation potentials of wurtzite AlN determined by uniaxial pressure-dependent Raman measurements

We studied bulk crystals of wurtzite AlN by means of uniaxial pressure-dependent Raman measurements. As a result, we derive the phonon pressure coefficients and deformation potentials for all zone center optical phonon modes. For the $A_1$ and $E_1$ modes, we further experimentally determined the uniaxial pressure dependence of their longitudinal optical–transverse optical (LO-TO) splittings. Our experimental approach delivers new insight into the large variance among previously reported phonon deformation potentials, which are predominantly based on heteroepitaxial growth of AlN and the ball-on-ring technique. Additionally, the measured phonon pressure coefficients are compared to their theoretical counterparts obtained by density functional theory implemented in the siesta package. Generally, we observe a good agreement between the calculated and measured phonon pressure coefficients but some particular Raman modes exhibit significant discrepancies similar to the case of wurtzite GaN and ZnO, clearly motivating the presented uniaxial pressure-dependent Raman measurements on bulk AlN crystals.

Figure 1

Scheme of the apparatus used for the uniaxial pressure-dependent Raman measurements. The helium gas pressure in the pressure transmission chamber pushes a steel piston onto the wurtzite AlN cube sample that situated on a movable steel hemisphere. Application of uniaxial pressure allows the hemisphere to slide into the ideal position where all pressure transmitting surfaces are aligned in parallel ensuring a homogenous strain distribution in the sample.

Figure 2

(a) The optically transparent AlN sample analyzed in this work was cut to a cube with a side length of 2.0 mm. All resulting facets were polished to an optical degree. (b) Corresponding Raman spectra for zero and maximal uniaxial pressure recorded in backscattering geometry from an $a$-plane surface of the AlN cube. The uniaxial pressure was applied along the $c$-axis of the crystal.

Figure 3

Raman mode shifts for all six first-order modes in wurtzite AlN induced by uniaxial pressure up to 0.57 GPa ($\vec{p} \parallel c$-axis). All mode positions were extracted from a manual peak fitting routine. The solid lines represent linear least-square fits to the data points yielding the phonon pressure coefficients (slopes) along with their errors as stated in parentheses.

Figure 4

Uniaxial pressure dependence for the LO-TO-splitting of the $A_1$ and $E_1$ phonon modes in wurtzite AlN ($\vec{p} \parallel c$-axis). The solid lines represent linear least-square fits of the data points yielding the LO-TO pressure coefficients and the errors stated in parentheses. Dashed lines show the corresponding theoretically derived uniaxial LO-TO pressure dependence from this work (red) or based on Ref. [44] (blue).