The lateral spontaneous emission intensities of 850-nm proton-implanted and 780-nm oxidized vertical-cavity surface-emitting lasers(VCSEL) were measured and characterized. The spontaneous emission intensity was not proportional to the injected current in the low current range below threshold showing the effect of nonradiative recombinations. A simple phenomenological relation between the spontaneous emission and the current was modeled and used to fit the measured data. The extracted nonradiative recombination coefficients ($A_{nr}'s$) through the fitting process are $2.5 \times 10^8$, $1.7 \times 10^8$, $1.3 \times 10^{8} s^{-1}$ for the 10, 15, and 20-㎛ proton- implanted VCSELs, respectively. The larger value of $A_{nr}$ for the smaller device is related to the induced damages from the proton implantation.
Very small 780-nm VCSELs ranging 2 to 10 ㎛ were fabricated by selective oxidation. The below-threshold spontaneous emission intensities were measured in lateral direction. The spontaneous emission intensity was not proportional to the injected current in the low current range showing the effect of carrier diffusion as well as nonradiative recombination. A simplified below-threshold diffusion equation with $A_{nr}$ as a parameter was modeled and used to fit the measured data. It turns out that the ambipolar diffusion coefficient of 5.4㎠/s gives almost same values of $A_{nr}$ regardless of device sizes. Therefore, in the assumption of size-independent $A_{nr}$, the diffusion coefficient of 5.4㎠/s and the nonradiative recombination coefficient of $0.79 \times 10^8s^{-1}$ were obtained experimentally. Further analysis through the diffusion equation shows that there exists a certain optical loss increasing the threshold current significantly for the sizes less than 4 ㎛. It might be the optical scattering at the edge of oxidized layer.
The spontaneous emission factors (β's) were measured for the very small 780-nm oxidized VCSELs. To extract β, a new experimental method was proposed and demonstrated. The proposed method uses the below-threshold power and linewidth of the fundamental mode. The experimentally determined β's were $1.33 \times 10^{-3}$, $1.00 \times 10^{-3}$, $6.32 \times 10^{-4}$ for the 2, 3, 4-㎛ oxidized VCSELs, respectively. The somewhat small value of 2-㎛ VCSEL is due to the carrier diffusion. The measured β's agree well with theoretical values within ±30% if the effect of carrier diffusion is considered. It is pointed that the effect of carrier diffusion would reduce the β significantly for sub-㎛ oxidized VCSELs.
