Kramers-Kronig analysis of the optical linearity and nonlinearity of nanostructured Ga-doped ZnO thin films

Pure zinc oxide and gallium-doped ZnO films have been deposited on a glass substrate using a sol-gel assisted spin coating technique. The prepared films were characterized by structural, morphological, optical, and the effect of doping is studied. XRD analyses of the films confirm amorphous nature. Raman studies give support to XRD and confirm secondary phases are absent in the film. The AFM images give the grain size, which decreases with an increase in doping concentration from 116 nm to 81 nm. Roughness, Skewness, and Kurtosis factor are varying from 45.694 nm to 29.153 nm 1.085 to 0.453, 3.583 to 2.605, respectively. Kramers-Kronig equations are the most accurate methodology for optical thin-film technology for the calculations of optical linearity and nonlinearity parameters. The bandgap values are decreasing with increasing thickness from 2.97 to 2.79, respectively. The doped films are more transparent compared to the pure ZnO films. The enhancement in the linear optical properties such as refractive index, absorption index, and dielectric constant are also observed with an increase in the doping concentration. The nonlinear optical properties such as χ⁽¹⁾, χ⁽³⁾ and n⁽²⁾ are varying in the range of 0.288 esu to 0.252 esu, 1.1 × 10⁻¹² esu to 7 × 10⁻¹³ esu, 1.92 × 10⁻¹¹ esu to 1.30 × 10⁻¹¹ esu, respectively. The enhancement in optical properties with increasing the doping concentration suggests the present films are useful for various optical device applications.