Effects of doping and free carriers on the refractive index of direct-gap semiconductors

Abstract

A model for the doping and current dependence of the refractive index of direct-gap semiconductors has been developed and applied to GaAs in order to explain certain properties of single heterostructure injection lasers. The model involves the concept of an effective energy gap which takes account of the effects of doping and free carriers via the Burstein shift, the exchange interaction, and the average screened Coulomb potential of the impurities. This effective gap, together with empirical results for the energy dependence of the refractive index, facilitates the calculation of refractive index changes with doping and current. Numerical results are given for GaAs, and the model is applied particularly to the substrate and active regions of single heterostructure injection lasers. In these devices the refractive index values are particularly important in determining the dielectric waveguide properties. With the aid of our model, this feature can be discussed in detail, with special reference to the breakdown of the waveguide effect which occurs (a) for substrate doping levels below a critical value, and (b) for currents well above threshold ('saturation').

The gain profile and time-delay effects in external-cavity-controlled GaAs lasers

“…A conventional diode will try to oscillate at a shorter wavelength which still can "fit" into the guide or which has the gain needed to overcome the additional diffraction loss; this has also been observed [ 1 11 , [ 171 as discussed above. There are at least two ways [26] - [28] in which the refractive index (and therefore the waveguiding) of the active region can change with drive level: 1) by the negative contribution to the index from injected minority carriers (plasma effect), and 2) through the Kramers-Kronig integral which relates the absorption coefficient a, or changes in a, to the index of refraction. These changes in the index with current are probably small (-0.1-1 percent) but are important in a SH or DJ diode because the waveguide is asymmetric and is, in fact, established by small index variations.…”

Gain-enhanced high-k transmission through metal-semiconductor hyperbolic metamaterials

“…At λ 0 =1500nm, the imaginary parts of these values are D,Abs "=Γg(N =1.0x16cm −3 )=+0.139 and D,Inv "=Γg(N =5.0x18cm −3 )=-0.143, where Γ=1/3 is the relative area of wells in the InGaAsP heterostructure. Using Kramers-Kronig relations 43 , the real parts at λ 0 =1500nm are D,Abs =11.997 and D,Inv =11.881, respectively. For the sake of simplicity, we used a carrierindependent but frequency dependent real permittivity, which is D =11.914 at λ 0 =1500nm, and justified because the transmission properties studied are dominated by loss and gain.…”