Temperature dependent gain characteristics

Figure 5.8 shows the normalized photoluminescence spectra of the GaN-based

VCSEL under different pumping power levels at 300K. The PL spectra indicate that there are about six axial cavity modes. Above the threshold condition, only one lasing mode at 419 nm dominates. The optical gain can be therefore estimated using the Hakki-Paoli [5.14] method to analyze these multiple cavity modes from the photoluminescence spectra below the threshold condition. By applying the Hakki-Paoli method, the gain in a VCSEL structure can be expressed as

( )

where λ is the wavelength at which the cavity modes are being measured.

Confinement factor of the laser structure is estimated as Γ = 0.05 by calculating the spatial overlap between the optical field and MQWs layers in the VCSEL cavity, da is

the thickness of ten quantum wells, I⁺ and I⁻ are the maximum and minimum PL intensities for each cavity mode obtained from the measured PL spectra, R1 and R2 are DBRs reflectivities which are 99% and 98%, respectively, αι is the average internal loss of the cavity, which is dominated by the absorption of thick GaN layer and was set to be 30 cm^-1 [5.15] and L is the cavity length. Under different pumping levels, the

obtained from the Eq. (1). The gain spectra of the VCSEL under different pumping power levels at 300K are shown in Fig. 5.9. Each data point was calculated from the corresponding cavity mode in Fig. 5.8. The gain curves show an increasing trend as the pumping intensity increases and the gain bandwidth keeps broadening. In addition, the mode peaks blue shift due to the increase of the optical gain. At room temperature, the peak gain of 2.9×10³ cm^-1 was obtained at threshold condition. The gain spectra under different temperature (at 220K, 150K and 80K) were also obtained with the same measurement and calculation method, respectively.

The pumping carrier density dependence of the peak gain of the lasing mode (at

~420 nm) is plotted in Fig. 5.10 for different measurement temperature. Here the carrier density in QWs was estimated from the power density of the pumping laser assuming that the pumping light with the emission wavelength of 355 nm has experienced a 60% transmission through the SiO2/Ta2O5 DBR layers and undergone a 98% absorption in the thick GaN layer with a absorption coefficient of 10⁴ cm^-1 [5.16].

At room temperature, the threshold carrier density was estimated to be about 6.5×10¹⁹ cm^-3. The figure shows that the carrier density required to reach a given gain increases with increasing temperature. We use the logarithmic law to express the relation between gain and carrier density in QWs as g N

( )

(

)

density. The solid curves in Fig. 5.10 were fitted to the data for different measurement temperature respectively. The g0 as a function of temperature is shown as Fig. 5.11.

Increasing of g0 was observed as the temperature decreased. It implies that the gain increase more rapidly as a function of the injected carrier density at lower temperature, which could be resulted from several reasons. Firstly, the ratio of radiative to nonradiative recombination is higher at low temperature than that at high temperature.

Secondly, carrier overflow becomes pronounced at higher temperatures resulting in less radiative recombination in the MQWs and consequently a lower gain [5.17].

Another main cause is the broadening of Fermi occupation probability function which spreads carriers over a larger energy range for a given overall carrier density. The result is a lower spectral concentration of inverted carriers, which leads to a broadening and flattening of the gain spectrum.

The linewidth enhancement factor can be measured from the amplified spontaneous emission spectra below the threshold condition [5.18]. The α-factor is the ratio of the change of the refractive index (n) with carrier density (N) respect to the change in optical gain with carrier density and can be expressed by

2 d

L dg π λ α ⁼ Δλ ,

where λ is the wavelength of each mode peak, Δλ is the cavity mode spacing, L is the cavity length, dλ is the wavelength shift when the carrier density is varied by dN, and

dg is the change in optical gain as the carrier is changed by dN. Using Eq. (2), the

α-factor can be calculated from the emission spectra under different pumping power levels below the threshold.

The calculated α-factors as a function of wavelength for different measurement temperature are shown in Fig. 5.12. The α-factor shows dependence on wavelength and is smaller at shorter wavelength. As temperature varied, taking the lasing mode for example, the α-factors decrease with the decreasing temperature. However, the increase or decrease of α-factor with respect to the temperature could be due to two different mechanisms in VCSEL operations. As the temperature increased, the lasing wavelength is detuned to the shorter wavelength side of the gain peak, thus the α is reduced as the laser operates closer to the differential gain maximum, whereas the lasing operation away from the gain maximum could increase the carrier density required to the threshold condition, and thus increase the α value [5.19]. In our case, the decrease of α values as the temperature goes down could be mainly due to the reduction of carrier density in the QWs. For the lasing mode, the α-factors varied from 2.8 to 0.6 as the temperature varied from 300K to 80K. In comparison to the InGaN/GaN edge emitting laser structure that the α value varies between 2.5 and 10 [5.20], the linewidth enhancement factor in the GaN-based VCSEL structure is smaller.