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Determining Material Properties under Lasing Conditions from Low Excitation Luminescence

Here is an example of a closed-loop wafer growth to photo luminescence and gain-measurement of processed sample.

The idea is explained in more detail in Refs.[15] and [16].

The structure is an MBE grown electrically pumped p-i-n doped multi quantum-well structure. The active region consists nominally of three 5 nm wide In0.2Ga0.8As quantum wells between GaAs barriers. In the absence of external pump voltage and pump carriers the doping profile has been calculated to result in an internal electric field across the active region of 34 kV/cm.

STEP 1: Nominal Spontaneous Emission (PL)

In the first step the spontaneous emission (PL) for several densities in the low density regime is calculated using the semiconductor luminescence equations for the nominal structural parameters (layer widths and compositions). Here, as in typical PL experiments, optical pumping is assumed, i.e. the dopant related electric fields are present. The spectra are only homogenbeously broadenend (due to electron-electron and electron-phonon scattering), there is no inhomogeneous broadening.
Comparing the results to experimental spectra shows that the theoretical spectra are 6 nm off the experimental peak positions. This shift can here be either due to an actual Indium concentration of 19% instead of the nominal 20%, or a well width which is 4.5 nm instead of the nominal 5 nm.

The above picture shows the theoretical PL spectra in the absence of inhomogeneous broadening and for the nominal structural parameters (red lines) and the measured PL spectra (blue lines). The theoretical results are for carrier densities of 0.1, 0.17, 0.23, 0.3, 0.4, 0.53, 0.68 and 0.86x10¹²/cm². The experimental results are for optical pump powers of 12, 16, 18, 21 and 24mW.

STEP 2: Comparison to the Experimental PL

A match to the experimental spectra can only be found for an inhomogeneous broadening of 9.8 meV (Gaussian broadening; half width at 1/e amplitude) and when associating the rather uncertain experimental pump powers with the theoretical densities as shown in the picture. This broadening corresponds to well width fluctuations of rather implausibly high 0.5 nm, and/or a more probable fluctuation of the Indium-composition of 1%.

The above picture shows the theoretical PL spectra for the determined material parameters (19% Indium) and inhomogeneous broadening (9.8 meV) (red lines) and the measured PL spectra as already shown under Step 1 (blue lines). The theoretical results are for carrier densities of 0.1, 0.17, 0.23, 0.3, 0.4, 0.53, 0.68 and 0.86x10¹²/cm².

STEP 3: Actual Gain and Absorption

Using the actual material parameters and inhomogeneous broadening determined in Step 2 the absorption and gain spectra for the device under lasing conditions are calculated. The doping related electric fields across the active region are absent when using electrical pumping.

The above picture shows resulting gain/absorption spectra for densities of between 0.5 and 4.5x10¹²/cm² with density steps of 0.25x10¹²/cm² between neighbouring spectra.

STEP 4: Testing the Resulting Gain

For this device the gain spectra have actually been measured in order to test the approach. The theoretical spectra are for the actual material parameters and inhomogeneous broadening as determined from the PL-analysis. No additional spectral shifting, broadening or amplitude-scaling has been used to modify the theoretical results.

The above picture shows theoretical spectra for densities of 1.0, 1.125, 1.25, 1.375, 1.5, 1.625, 1.75 and 1.875x10¹²/cm² (red lines). The experimental pump currents are 6.0, 6.5, 7.0, 7.5, 8.3, and 9.0 mA. The experimental spectra have been measured using the Hakki-Paoli method.

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