A method of characterizing a semiconductor structure, the method comprising: providing a semiconductor structure comprising a semiconductor and a high-k dielectric layer formed over the semiconductor, wherein the high-k dielectric layer has electron traps formed therein; at least partially transmitting an incident light having an incident energy through the high-k dielectric layer and at least partially absorbing the incident light in the semiconductor, wherein the incident energy is sufficient to cause electrons to be transported from the semiconductor to the electron traps such that some of the electrons are temporarily trapped by the electron traps, and wherein the incident energy is sufficient for the electron traps filled with temporarily trapped electrons to cause generation of light having an energy different from the incident energy resulting from nonlinear optical effects; obtaining a nonlinear spectrum resulting from the light having the energy different from the incident energy, energy, the spectrum being a measurement of intensity over time, the nonlinear spectrum having a first region (404a, 604a, 608a, 704a, 712a) and a second region (404b, 604b, 608b, 704b, 712b) subsequent to the first region, wherein an intensity in the first region increases at a faster rate compared to the second region; determining from the spectrum a first time constant from the first region and optionally a second time constant from the second region; characterized in that the method further comprises determining an electron trap density in the high-k dielectric layer based on the first time constant or both of the first time constant and the second time constant. providing a semiconductor structure comprising a semiconductor and a high-k dielectric layer formed over the semiconductor, wherein the high-k dielectric layer has electron traps formed therein; at least partially transmitting an incident light having an incident energy through the high-k dielectric layer and at least partially absorbing the incident light in the semiconductor, wherein the incident energy is sufficient to cause electrons to be transported from the semiconductor to the electron traps such that some of the electrons are temporarily trapped by the electron traps, and wherein the incident energy is sufficient for the electron traps filled with temporarily trapped electrons to cause generation of light having an energy different from the incident energy resulting from nonlinear optical effects; obtaining a nonlinear spectrum resulting from the light having the energy different from the incident energy, energy, the spectrum being a measurement of intensity over time, the nonlinear spectrum having a first region (404a, 604a, 608a, 704a, 712a) and a second region (404b, 604b, 608b, 704b, 712b) subsequent to the first region, wherein an intensity in the first region increases at a faster rate compared to the second region; determining from the spectrum a first time constant from the first region and optionally a second time constant from the second region; characterized in that the method further comprises determining an electron trap density in the high-k dielectric layer based on the first time constant or both of the first time constant and the second time constant.