Dynamic characteristics of 410 nm semipolar $(202¯1¯)$ III-nitride laser diodes with a modulation bandwidth of over 5 GHz

III-nitride laser diodes (LDs) were first demonstrated in 1996 and have been developed for high-power applications such as optical storage, medical, and solid-state lighting.¹ However, the performance of LDs grown on conventional polar (0001) c-plane GaN has been hindered due to polarization-induced electric fields, leading to a reduction of wave-function overlap.^2,3 Recent progress on semipolar and nonpolar planes has shown significant improvement in high-power performance of light emitting diodes (LEDs) and LDs by reducing the polarization-induced electric field.^4–12 In addition, semipolar and nonpolar LDs are expected to have higher optical gain than c-plane LDs due to a higher wave-function overlap and a reduction in the density of states.^13–15 

While conventional III-nitride LEDs have typical bandwidth limits in the MHz range,^16,17 recent studies on LDs for light fidelity (LiFi) applications have demonstrated more than 2.6 GHz bandwidth and 4 Gbit/s data transmission rate using a blue LD alone as well as 2 Gbit/s data transmission rate using a blue LD with a phosphor by on-off keying (OOK).^18,19 Higher order modulation schemes could have improved data rates.^20–23 Future LiFi applications will require high-power and high-efficiency solid-state light sources with a capacity for high-speed data transmission.²⁴ Since semipolar and nonpolar LDs are expected to have higher differential gain than c-plane LDs, they also have the potential for improvements in modulation bandwidth. Although blue LEDs and LDs are typically used as the excitation source for solid-state lighting systems, violet LEDs and LDs have potential candidates in high quality white lighting with red-green-blue phosphors. In addition, violet LDs may have advantages in terms of LiFi system performance due to potential challenges with creating high-speed photodetectors (PDs) that absorb light in the blue region of the spectrum.^25–27 In this letter, we study the dynamic characteristics and high-speed performance of violet semipolar III-nitride LDs for LiFi applications.

Violet LDs were grown on free standing bulk GaN semipolar $(202¯1¯)$ substrates by metalorganic chemical vapor deposition (MOCVD). As shown in Fig. 1(a), the epitaxial structure consisted of a 1 μm Si-doped n-GaN cladding layer, a 500 nm n⁺-GaN topside contact layer ([Si] = 5.2 × 10¹⁹ cm⁻³), a 350 nm n-GaN buffer layer ([Si] = 6.2 × 10¹⁸ cm⁻³) to minimize the absorption loss, and a 60 nm composition graded n-In_0.025Ga_0.975N waveguiding layer. The active region consisted of a 4 period undoped In_0.1Ga_0.9N/GaN (3.5 nm/7 nm) multiple quantum well (MQW) structure, followed by a 16 nm p-Al_0.18Ga_0.82N electron blocking layer (EBL) linearly graded in composition and doping down to GaN at the topside. Then, a 60 nm composition graded p-In_0.025Ga_0.975N waveguiding layer and a 600 nm thick Mg-doped p-GaN cladding layer were grown followed by a 10 nm highly Mg-doped p⁺-GaN contact layer.²⁸ The doping level of the n-GaN contact layer was optimized to obtain a low resistance topside n-type contact, which is essential for reducing the resistance of the device as well as enabling radio frequency (RF) measurements with ground-signal (GS) or ground-signal-ground (GSG) probe configurations.

After the MOCVD growth, the samples were fabricated into ridge waveguide LDs. Ridges with widths of 2 μm and 3 μm were formed by reactive ion etching (RIE). A commercial 2-D mode solver FIMMWAVE²⁹ was used to model the waveguide of the 2 μm and 3 μm LD and calculate a confinement factor of 0.0230 and 0.0234, respectively, as shown in Fig. 1(b). 200 nm of SiO₂ was deposited as a passivation layer onto the field and ridge sidewalls via sputtering and was lifted off of the laser ridges using a self-aligned process.⁸ After wet etching a portion of the SiO₂ layer, the window for n-via contact area was etched via RIE down to the center of a 500-nm n⁺-GaN layer to form the topside n-type contact. Ti/Al/Ni/Au (15/100/100/100 nm) n-contacts were deposited by electron beam evaporation, followed by rapid thermal annealing (RTA) with N₂ ambient at 450 °C to lower the contact resistance. Pd/Au (30/100 nm) p-contacts were deposited on top of the ridges, followed by common pad metals of Ti/Au (15/1000 nm) for both p- and n-pads. Mirror facets were formed by RIE and were left uncoated. The cavity lengths of the LDs ranged from 900 μm to 1800 μm. Figure 1(c) shows a scanning electron microscopy image of a 2 μm LD with a topside n-contact.

The light-current-voltage (L-I-V) characteristics of the LD with the highest bandwidth (2 μm wide and 1200 μm long) were measured under continuous wave (CW) operation at 15 °C, as shown in Fig. 2(a). The threshold current (I_th) and threshold current density (J_th) were 150 mA and 6.25 kA/cm², respectively, with a corresponding threshold voltage (V_th) of 5.1 V using a four-probe measurement. The slope efficiency and differential efficiency were 0.35 W/A and 23%, respectively, with etched facets before high-reflection coating. An injection efficiency of 80% was extracted by analyzing the dependence of differential efficiency on cavity length for a number of different LDs, which is in a good agreement with the data reported by Becerra et al.¹¹ The internal loss was estimated to be 16.9 cm⁻¹ by considering the lowered reflectivity of the RIE-etched facet.³⁰ The lasing wavelength was around 410 nm, as shown in Fig. 2(b).

The small signal modulation characteristics can be derived from the carrier and photon density rate equations³¹ 

where n and s are the carrier and photon densities in the active region, respectively, $ηi$ is the injection efficiency, I is the drive current, q is the electron charge, V is the volume of the active layer, τ and τ_p are the carrier and photon (or cavity) lifetimes, respectively, $υg$ is the group velocity, Γ is the optical confinement factor, and $gth$ is the threshold material gain. Under small signal conditions, a small fluctuation of gain is added onto the threshold gain by multiplying the differential gain, $dg/dn$⁠, by the fluctuation in carrier density, Δn. The spontaneous emission that is coupled into the lasing mode is ignored far above the threshold for this modulation condition. The small signal modulation for both carriers and photons is proportional to a second-order transfer function³¹ 

where $ωR$ is the relaxation resonance frequency (or $fR=ωR/2π$⁠) and $γ$ is the damping factor.

The sinusoidal small signal modulation was performed with an Agilent E8361A PNA network analyzer and received at an ALPHALAS UPD-50-UP high-speed Si p-i-n photodetector (PD). The bandwidth of the PD was measured with a 410 nm pulse train by frequency doubling a mode locked Ti-Sapphire laser emitting at 820 nm.³² The measured bandwidth of the PD was 3.76 GHz as shown in Fig. 3(a). As shown in Fig. 3(b), the small-signal frequency response of the 2 μm wide by 1200 μm long LD was recovered by subtracting the fitted PD response, although the resonance peaks were still saturated near 4 GHz. The highest measured 3-dB bandwidth of the LD was 5 GHz at 220 mA of drive current, which was limited by the bandwidth of the PD. This can be concluded because the data before subtracting the PD response hit the noise floor near 4.8 GHz. It should be possible to obtain higher 3-dB bandwidths with a higher speed PD that covers the UV-violet spectrum because the LD bandwidth is not the limiting component in the experimental setup.

Large signal modulation was performed to evaluate the capability of the LD for data transmission. The LD was driven by using a 2³¹ – 1 non return-to-zero (NRZ) OOK pseudorandom bit sequence (PRBS) with a peak-peak 1.5 V drive input signal. The best optimized open eye diagram was obtained at 280 mA of drive current up to 4 Gbit/s with a 4.76 of signal-to-noise (SNR) ratio, as shown in Fig. 3(c). The highest data rate with a clearly open eye diagram was 5 Gbit/s, while 6 Gbit/s was limited by the bandwidth of PD.

To investigate the intrinsic modulation capability of the LDs, the differential gain, $∂g/∂n$⁠, can be derived by the following equation for f_R:

Figure 4(a) shows the dependence of relaxation resonance frequency on the drive current for different cavity sizes. The slopes of the curves were highly dependent on each cavity size, resulting in similar differential gains as expected. The slopes ranged from 0.5543 GHz/mA^1/2 for the largest cavity to 0.2646 GHz/mA^1/2 for the smallest cavity. The differential gains ranged from 1.94 × 10⁻¹⁶ cm² for the largest cavity to 2.84 × 10⁻¹⁶ cm² for the smallest cavity, as shown in Fig. 4(b). These values are in a good agreement with the reported differential gains of other III-nitride QW LDs and even comparable with those of quantum dot (QD) and nanowire (NW) LDs.^33–37 Compared to conventional polar c-plane LDs, the differential gain of semipolar $(202¯1¯)$ LDs is expected to be higher due to the higher electron-hole wave-function overlap in the lower density of states.^13,38,39 At low power operation, where gain compression is not significant, high differential gain leads to a higher f_R, resulting in a higher modulation bandwidth.⁴⁰ 

For high power operation, where gain compression is significant, the modulation bandwidth depends more on the damping factor (or K-factor) than f_R.³¹ As shown in Fig. 5, the K-factors were obtained by fitting the measured damping factor and f_R with the following relationship:

where $γ0$ is the damping factor offset. Since parasitic roll-off of larger cavities occurs at lower frequencies, the smallest three cavities were analyzed at low injection levels and found to be in a good agreement. The lowest K-factor and the corresponding damping factor offset were 0.33 ns and 5.69 GHz for the 2 μm wide by 900 μm long LD, respectively. The gain compression factor was calculated to be 7.4 × 10⁻¹⁷ cm³ by $K=4π2τp(1+εΓgth/(dg/dn))$⁠, where $ε$ is the gain compression factor.³¹ The intrinsic maximum bandwidth can be also obtained by the K-factor, which is the bandwidth limit due to the photon lifetime of the cavity. The maximum bandwidth occurs when the 3-dB bandwidth is at the resonance frequency. Hence, the calculated intrinsic maximum bandwidth was 27 GHz by $f3dBmax=2(2π/K)$⁠, where $(γ/ωR)2=−3 dB$⁠, in Eq. (3).

In summary, the dynamic characteristics of CW violet III-nitride LDs grown on the semipolar $(202¯1¯)$ plane were studied. A 3-dB bandwidth of 5 GHz was achieved giving an open eye diagram for a data rate of 5 Gbit/s. The differential gain of the LDs was determined to be 2.5 ± 0.5 × 10⁻¹⁶ cm² by comparing the slope efficiency for different cavity lengths. The calculated K-factor, the gain compression factor, and the intrinsic maximum bandwidth were 0.33 ns, 7.4 × 10⁻¹⁷ cm³, and 27 GHz, respectively. Although the measured bandwidth was limited by the PD, these results show the potential of III-nitride semipolar LDs for high-speed visible light communication.

This work was funded by the KACST-KAUST-UCSB Solid State Lighting Program (SSLP) and by the Solid State Lighting and Energy Electronics Center (SSLEEC) at University of California, Santa Barbara (UCSB). A portion of this work was done in the UCSB nanofabrication facility, part of the National Science Foundation (NSF) funded Nanotechnology Infrastructure Network (NNIN) (ECS-0335765). This work also made use of UCSB Materials Research Laboratory (MRL) central facilities supported by the NSF MRSEC Program (DMR05-20415). The authors thank Professor L. A. Coldren for fruitful discussions.