“Plasmonic” GaN substrates and their use for lasers
As we have shown earlier (Section 2.3), the crystals of GaN grown by the HNPS method can be strongly n-type doped with free electron concentration as high as 1019-1020 cm-3, depending on growth temperature. This can be used as an element of the refractive index engineering in InGaN-based laser diodes (i.e. Perlin et al., 2009; Perlin et al., 2011a; Perlin et al., 2012) to achieve efficient transversal confinement of the optical mode. Typically, in nitride-based LDs a wider band gap AlGaN alloys are used as cladding layers providing optical confinement. However in contrast to the lattice-matched GaAs-AlGaAs system, the lattice mismatch between the GaN waveguide and AlGaN cladding makes the AlGaN layer suffer from tensile strain which leads to its cracking and generation of defects. Additionally, the refractive index contrast between GaN and AlGaN decreases with emission wavelength. This limits the possibility of creating a sufficiently strong optical confinement in the device, and causes a significant leakage of the optical mode to the substrate (Smolyakov et al., 2005; Laino et al., 2007), increasing the internal losses in the laser, especially for longer wavelengths. To suppress the mode leakage the AlGaN claddings as thick as 2 pm (Laino et al., 2007) or even 5 pm (Nagahama et al., 2000) are used.
Fig. 2.31. Penetration of light into the substrate of LD: (a) carbon deposit on the LD mirror due to light-induced chemical reactions, (b) near-field image of the beam of LD deposited on a low-conductivity substrate.
The effect of mode penetration into the substrate is sometimes visualized by the formation of a carbon deposit (Package Induced Failure) being the result of light-induced reactions on the facet of the laser. This effect is shown in Fig. 2.31(a).
Perlin et al. (2009, 2011a, 2012) have shown that the use of a highly conductive HNPS GaN substrate allows suppressing the mode leakage completely in laser diodes with AlGaN lower cladding as thin as 0.5-0.8 pm. This was possible because of a significant decrease of dielectric constant, and consequently a reduction of the refractive index of GaN at frequencies closer to the plasma frequency. This dependence can be well described by the following equation (Perlin et al, 1995):
where is the plasma frequency given by the expression:
Figure 2.32 shows the dependence of refractive index contrast between strongly n-type and undoped GaN on the wavelength for various electron concentrations. For the blue spectral range (450 nm) the refractive index contrast reaches 0.5% for an electron concentration of 5 x 1019 cm~3 and 1% for 1 x 1020 cm~3. This provides the possibility of constructing the laser diode using such a type of substrate as a part of its optical waveguide.
The results of the calculations (Perlin et al., 2009) of the transversal mode distribution in two identical laser structures with 0.6-pm thick 8% AlGaN lower
Fig. 2.32. Refractive index contrast versus wavelength for various electron concentrations. Solid line: theoretical curves derived from eq. (2.8); squares and circles: experiment, after Perlin et al. (2012).
cladding layers deposited on two different substrates are presented in Fig. 2.33. It is clear that the refractive index contrast induced by free electrons at a concentration of 5 x 1019 cm~3 is sufficient to suppress the leakage of the optical mode to the substrate in contrast to the conventional HVPE-grown substrate with an electron concentration of 1018 cm~3.
The results of the calculations were confirmed by experimental near-field distributions for laser diodes corresponding to the structures used for modeling. Figure 2.34 presents the result of this experiment. For the conventional
Fig. 2.33. Plane-wave expansion method (Schwarz and Witzigmann, 2007) calculation of the transversal mode distribution in LD: (a) for a standard HVPE-based structure, (b) for the plasmonic substrate.
Fig. 2.34. The comparison of the near-field distribution for two structures—the upper one grown on a plasmonic substrate, and the lower one on a standard HVPE substrate.
structure the optical mode extends deep into the substrate, while in the case of the plasmonic substrate the mode is well confined around the active area.
An important and quite obvious effect is a significant reduction in the threshold current density. For considered cases it was from 5.2 kA/cm2 to 2.3 kA/cm2 (Perlin et al., 2009).
The threshold current density of the laser structure with an AlGaN cladding of thickness 0.5 pm has been simulated (Perlin et al., 2012) as a dependence on the refractive index contrast of the substrate compared to the undoped GaN. For around 0.5% the threshold current density suddenly dropped. This 0.5% index change corresponds roughly to the electron concentration of 5 x 1019 cm~3, in agreement with the results mentioned previously.
It is therefore shown that the concept of using plasmonic substrates is a way of improving and simplifying the design of blue and green InGaN laser diodes. It can help to design optimum laser structures with minimized strain, and can fully profit from the advantages provided by plasmonic substrates.