Spectral response of detectors can be modeled using a stack matrix approach. The different material layers that make up the detector form the optical stack. Light intensity is proportional to the square of the amplitude of the electromagnetic field’s electric field component. Using the electric component of light, the model takes into account the reflective and transmission coefficients at the interface between two adjacent layers and the phase difference during propagation within each layer. The transition from one optical layer to another and the propagation within an optical layer can be formulated as 2 × 2 matrices; their multiplication through every optical layer makes up the stack matrix that defines the optical properties of the detector. Knowing the complex index of refraction for each layer in the detector, the intensity of light can be calculated at any point in the detector structure, which can then be used to determine the response of the detector as a function of wavelength. This model shows fairly good agreement with the experimental data, even revealing fine structure and etalon effects. Using this model, the detector can be designed to meet specific spectral characteristics. The spectral response model was used on high-density vertically interconnected photodiode front-side-illuminated photodiodes.
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