Interface Roughness Scattering: Key Determinant of GaN Terahertz Quantum Cascade Laser Performance

Introduction

The terahertz (THz) spectral window holds promise for security screening, medical imaging, and high‑speed communications, yet practical, compact sources remain scarce. Quantum cascade lasers (QCLs) are the leading candidate for solid‑state THz emitters. While GaAs‑based QCLs reach a maximum operating temperature of ~200 K, the high longitudinal optical (LO) phonon energy of GaN (92 meV) offers a pathway to room‑temperature operation and a broader accessible frequency range (1–15 THz). Recent advances in GaN THz QCLs have demonstrated intersubband (ISB) absorption at 10–13 THz and theoretical models have highlighted LO‑phonon interactions as a key limitation. However, the influence of growth‑related defects—interface roughness (IFR), non‑intentional doping (n.i.d.), and alloy disorder (AD)—has not been fully quantified. This work extends existing studies by quantifying how these scattering mechanisms impact optical gain and by identifying IFR as the dominant degradation factor.

Methods

High‑quality GaN THz QCLs require thick active regions with low dislocation densities, a challenge due to the GaN/AlGaN lattice mismatch. Epitaxial growth introduces additional scattering sources: IFR from surface roughness, n.i.d. from residual impurities (notably oxygen), and AD from Ga surface segregation and Al adatom mobility. We employed the NEGF formalism, implemented in the Nextnano QCL suite, to model a three‑quantum‑well resonant‑phonon design—currently the highest‑temperature configuration for GaN THz QCLs. The layer sequence (in nm) for one period is 1.6/6.2/1.6/3.4/1.0/3.4, with the 6.2 nm well n‑doped at 5×10¹⁷ cm^-3. Figure 1 illustrates the designed structure, conduction band profile, envelope functions, and carrier densities under a bias of –84.5 kV cm^-1 at 10 K.

Designed active region structure, conduction band profile, squared envelope functions, and carrier densities. a The layer sequence for one period is 1.6/6.2/1.6/3.4/1.0/3.4 nm. Barriers are indicated in italics. The 6.2 nm‑thick well is n‑doped with n = 5×10¹⁷ cm^-3. b Conduction band profile and squared envelope functions of the GaN/Al_0.15Ga_0.85N QCL considered in this study. An electric field of –84.5 kV cm^-1 is applied. c Carrier densities and conduction band of the QCL calculated in the NEGF model. The electric field applied is –84.5 kV cm^-1. Temperature is set at 10 K.

In the simulations we used the following realistic parameters for PAMBE‑grown GaN/AlGaN: IFR amplitude 0.25 nm, correlation length 1 nm; n.i.d. concentration 1×10¹⁷ cm^-3; AD scattering was also included. These values reflect typical experimental conditions.

Results and Discussion

Figure 2(a) shows the calculated optical gain spectra for four configurations: the full reference model (IFR, n.i.d., AD), and three models each omitting one scattering mechanism. At 10 K, the reference structure delivers a peak gain of 142 cm^-1 at 8.7 THz. Removing n.i.d. reduces the peak to 127 cm^-1 (8.46 THz) because the upper‑state electron population declines when the additional donor electrons are removed. However, the current density threshold also drops, indicating that impurity scattering hampers carrier transport. Eliminating AD has a negligible effect: the peak gain increases only 3 % to 147 cm^-1 at the same frequency, reflecting the modest role of alloy disorder in our low‑Al‑content (15 %) design. In contrast, removing IFR boosts the peak to 191 cm^-1 (8.7 THz) and lowers the threshold current, a 34 % gain enhancement. IFR therefore dominates the loss of optical gain by scattering electrons out of the lasing transition.

Simulated maximum optical gain vs frequency and current–electric field for different scattering mechanisms. a Optical gain spectra. b Current–electric field characteristics. Temperature: 10 K.

To explore IFR sensitivity, we varied the roughness amplitude to 0.5 nm and 0.75 nm while keeping the correlation length at 1 nm. Figure 3 shows a dramatic reduction: the peak gain falls to 47.9 cm^-1 at 0.5 nm and becomes negative (–8.8 cm^-1) at 0.75 nm, effectively suppressing lasing. The current–voltage curves reveal increased current densities and diminished resonant tunneling as IFR grows, confirming that IFR scattering outweighs resonant tunneling under realistic conditions. These results align with previous GaAs studies and underscore the necessity of keeping IFR below 0.5 nm during epitaxy.

Simulated maximum optical gain vs frequency and current–electric field for different IFR amplitudes. a Gain spectra. b Current–electric field. Temperature: 10 K.

Finally, we assessed temperature dependence for the reference model (IFR = 0.25 nm, n.i.d., AD). Figure 4 indicates that the peak gain remains stable (~142 cm^-1) up to 150 K, then decreases to 61 cm^-1 at 300 K. The decline is driven by thermal back‑filling and enhanced LO‑phonon scattering, yet the gain remains above the 30 cm^-1 loss of a GaN double‑metal waveguide, confirming that the device can operate at room temperature. Compared to GaAs THz QCLs, the higher doping, lower refractive index, and thinner period of GaN afford higher optical gain, as evidenced by the 142 cm^-1 peak at 10 K.

Characteristics of the calculated maximum gain vs lattice temperature.

Conclusions

We present a comprehensive NEGF study of a GaN THz QCL operating at 8.7 THz. The design yields 142 cm^-1 gain at 10 K and 60 cm^-1 at 300 K, confirming room‑temperature feasibility. Alloy disorder has a negligible effect (<5 % gain change). Non‑intentional doping must be limited to ≤1×10¹⁷ cm^-3 to avoid band‑misalignment and excessive impurity scattering. Interface roughness dominates optical‑gain degradation; keeping IFR below 0.5 nm is essential for positive gain. These insights provide concrete guidelines for optimizing GaN THz QCL fabrication toward practical, high‑temperature devices.

Availability of Data and Materials

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

Abbreviations

AD

Alloy disorder

IFR

Interface roughness

ISB

Intersubband

n.i.d.

Non‑intentional doping

NEGF

Nonequilibrium Green’s functions

QCL

Quantum cascade laser