Analytical Formula of Wavelength-Dependent Transparent Current and Its Implications for Designing Wavelength Sensors and WDM Lasers

The wavelength dependency of transparent current is investigated theoretically and empirically for bulk and quantum-well (QW) materials. A new analytical formula is presented for obtaining accurate Fermi levels of QW structures under current injection. The transparent current can be described with an exponential function of the wavelength using two fitting parameters. The simple expression can clearly indicate the fundamental limit of the wavelength resolution when the wavelength dependency is applied for wavelength sensing. The formula was also exploited to obtain the condition of achieving uniform threshold current for wavelength division multiplexing (WDM) lasers that may cover a wide range of wavelength.