Nano Express | Open | Published:
Dominant Influence of Interface Roughness Scattering on the Performance of GaN Terahertz Quantum Cascade Lasers
Nanoscale Research Lettersvolume 14, Article number: 206 (2019)
Effect of interface roughness of quantum wells, non-intentional doping, and alloy disorder on performance of GaN-based terahertz quantum cascade lasers (QCL) has been investigated by the formalism of nonequilibrium Green’s functions. It was found that influence of alloy disorder on optical gain is negligible and non-intentional doping should stay below a reasonable concentration of 1017 cm−3 in order to prevent electron-impurities scattering degradation and free carrier absorption. More importantly, interface roughness scattering is found the dominating factor in optical gain degradation. Therefore, its precise control during the fabrication is critical. Finally, a gain of 60 cm−1 can be obtained at 300 K, showing the possibility of fabricating room temperature GaN Terahertz QCL.
Terahertz (THz) spectral region is a subject of intensive research because of its potential applications in quality and security control, medical diagnosis, and telecommunication. However, its development has been hindered by the lack of available compact devices. Quantum cascade laser (QCL) is a promising candidate for developing powerful THz solid state sources [1, 2]. Up until now, the best THz QCL is based on GaAs, whose maximum operating temperature is about 200 K due to the low LO-phonon energy (36 meV) of GaAs [3, 4]. With the assistance of a magnetic field, this temperature can be raised up to 225 K. However, this method is unsuitable for wide-spread applications [5, 6]. When the temperature increases, electrons in the upper-level state can acquire enough thermal energy for activating non-radiative relaxations via LO-phonon emission towards the lower level state, hence destroying the population inversion. In comparison to GaAs, GaN has much higher LO-phonon energy (92 meV) and thus provides the possibility of producing THz QCL operating at room temperature [7,8,9]. Furthermore, GaAs-based QCLs cannot be operated in the 4.6–12 THz frequency range because of their Reststrahlen band, the spectral region where the material is completely opaque due to the absorption by optical phonons. The larger energy of optical phonons in GaN opens prospects for THz quantum cascade devices, which can operate in a much broader spectral range between 1 and 15 THz.
The first step study in GaN THz QCLs was the tuning of the intersubband (ISB) transition to the far-infrared domain. ISB absorption at THz frequencies has been observed in polar [10, 11] and nonpolar nitride-based quantum wells (QWs) [12,13,14,15,16,17]. THz operating ISB GaN-based detectors were demonstrated at 13 THz  and 10 THz , respectively. No electroluminescence demonstration in this range has been achieved so far, except for some controversial report from Hirayama group on the spontaneous electroluminescence from a QCL structure [20, 21]. Several theoretical studies have been published [7, 9, 22,23,24,25,26], among them, some investigate limiting factors of GaN THz QCL performances such as gain spectrum broadening due to very strong interactions between electrons and LO phonons in GaN .
In this article, we propose to complete these studies by analyzing other factors that can damage THz GaN QCL optical gain such as interface roughness of quantum wells, non-intentional doping, and alloy disorder. It was found that influence of alloy disorder on optical gain is negligible, and non-intentional doping should stay below a reasonable concentration of 1017 cm−3 in order to prevent electron-impurities scattering degradation and free carrier absorption . Finally, we found that interface roughness scattering is the dominating factor in optical gain degradation. And a gain of 60 cm−1 can be obtained at 300 K, which is well above the theoretical loss of a double metal waveguide, showing the possibility of fabricating room temperature GaN THz QCL.
It is known that fabrication of GaN THz QCL devices needs to grow thick active regions with low dislocation densities. This task is challenging because of the lattice mismatch between GaN and AlGaN . Other unwanted factors coming from epitaxy can also appear: interface roughness (IFR) depending on growth condition, n-type non-intentional doping (n.i.d) coming from impurities (mostly oxygen) incorporation during growth and alloy disorder (AD) originating from Ga surface segregation and Al adatom low mobility. To investigate how these phenomena influence THz GaN QCL performance, we use the formalism of nonequilibrium Green’s functions (NEGF). Calculations are performed using Nextnano QCL software [29,30,31]. This model includes relaxation induced by interface roughness, ionized impurities, alloy disorder, LO phonon, acoustic phonon, or electron-electron interaction. We employed a three-quantum-well QCL with a resonant-phonon depopulation scheme since that THz QCL design provides the highest operating temperature till now [3, 32]. Figure 1a shows the designed active region structure. The layer sequence for one AlGaN quantum structure/AlGaN quantum structure is 1.6/6.2/1.6/3.4/1.0/3.4 nm, where the italics ones show thickness of barriers. Figure 1b shows the conduction band diagram of the designed QCL structure at a bias of − 84.5 kV/cm. From the previous period on the right, electrons are injected by resonant tunneling in the upper lasing state, labeled by 1. Then, they undergo a radiative transition to the lower lasing state 2. This lower lasing state is depopulated through tunneling to state 3. Finally, electrons relax through into state 4 by LO-phonon emission. The process is repeated for each period.
In the calculation, we use the parameters usually found in GaN/AlGaN grown structure with plasma-assisted molecular beam epitaxy (PAMBE): an interface roughness of 0.25 nm  with a correlation length of 1 nm and a non-intentionally n-doping with a carrier concentration of 1017 cm−3. Alloy disorder scattering is also included in the simulation.
Results and Discussion
Figure 1c shows the calculated carrier densities of this structure at the operating bias of − 84.5 kV/cm. We observed the anti-crossing between the previous period and the upper lasing state 1. We also see that the lower lasing state 2 is depopulated by resonant phonon in state 3 and 4. In order to analyze and compare the influence of IFR, n.i.d, and AD, we calculated our GaN THz QCL optical gain and current characteristics for several configurations: the reference configuration taking IFR, n.i.d, and AD into account, a configuration without IFR, another one without n.i.d, and a last one without AD. Figure 2 shows the maximum optical gain vs frequency (a) and current densities vs applied electric field (b) for each configuration calculated at a temperature of 10 K. The reference structure shows a peak gain of 142 cm−1 at 8.7 THz, frequency unreachable for arsenides material. Let us see how n.i.d influences our QCL performance. Without n.i.d, the peak gain is 127 cm−1 at 8.46 THz. The gain drop is due to that carrier concentration decreases in the upper lasing state after taking away electrons coming from n.i.d. Indeed, in the reference configuration, electron concentration of the upper and lower lasing state is ∆N = N1 – N2 = 5.43 ×1012cm−2, while without n.i.d it becomes ∆N = N1 – N2 = 5.06 ×1012cm−2. Applied electric field shifts from − 84.5 to − 81.6 kV/cm. Current threshold drops and shifts from 25.11 kA/cm2 at − 84.49 kV/cm to 17.11 kA/cm2 at − 93.24 kV/cm. Current density drop can be attributed to the reduction of electron-impurities scattering which increases electrons transport in the calculation without n.i.d. Another hint of this hypothesis is the peak at − 64 kV/cm that we see in the case without n.i.d current densities characteristics. This is an inter-period resonant tunnel between 4’ and 3 (not shown here). This phenomenon is hidden by electron-impurities scattering in the current characteristics taking account of n.i.d. The current threshold and applied electric field shift are attributed to conduction band misalignment between the configuration with or without n.i.d. Interestingly, even though the gain peak is larger in the n.i.d case, we observe a gain spectrum broadening, the signature of charged impurities influence  Non-intentional doping should stay at a reasonable concentration of 1017 cm−3 to prevent electron-impurities scattering degradation and free carrier absorption. In the configuration without AD scattering, peak gain is 147 cm−1 at 8.7 THz. We observe that peak gain is at the same frequency with or without AD scattering. Optical gain only gets a marginal increase of 3% when AD scattering is not included in the calculation. Current characteristics are also almost identical. Since our design uses a low aluminum content of 15% and fairly thin barriers (1–1.5 nm), AD scattering influence in this QCL is negligible.
On the contrary, IFR scattering influence in the device’s performance is important. Without IFR scattering, we observe a peak gain of 191 cm−1 at 8.7 THz. Current density threshold is 24.08 kA/cm2. This gain increase of 34% and the current density threshold drop reflects the fact that a lot of electrons are transported through IFR scattering. The more IFR scattering, the less radiative scattering there is for lasing. When comparing the reference configuration electrons population of the upper and lower lasing state ∆N = N1 – N2 = 6.6 ×1012 – 1.27 ×1012 = 5.43 ×1012cm−2 to the one without IFR ∆N = N1 – N2 = 7.4 ×1012 – 1.17 ×1012 = 6.23 ×1012cm−2, one can see that the upper state electrons population is higher. This is due to the upper lasing state lifetime which increases due to the absence of IFR scattering. In comparison to the case without n.i.d, in the current densities characteristics of the device without IFR scattering, we observe a peak at − 67 kV/cm, signature of the inter-period resonant tunnel between 4’ and 3. This phenomenon is more visible in the case without taking IFR scattering process taken into account. This is a proof of its predominance over resonant tunneling. With those observations, we highlight the predominance of IFR scattering influence in the performance of THz GaN QCL.
After noticing the importance of IFR scattering in THz performance. We investigated further by varying IFR size. We added to our study the case of IFR = 0.5 nm and 0.75 nm. Correlation length is kept at 1 nm. In figure 3, we showed the maximum gain vs frequency (a) and current densities vs applied electric field characteristics (b). First, we observed that for IFR = 0.5 nm, maximum optical gain decreases to 47.9 cm−1 and even dramatically drops to − 8.8 cm−1 losing optical gain for IFR = 0.75 nm. The gain broadening as a function of IFR length is also evident. As we can see in I-V characteristics, as IFR size increase, its role in electrons scattering increases, increasing current densities and diminishing resonant tunnel and radiative scattering process in the devices. This effect becomes evident when comparing the reference configuration of IFR = 0.25 nm to the extreme case of IFR = 0.75 nm, electrons population of the upper and lower lasing state dropping from ∆N = 5.43 ×1012cm−2 to ∆N = N1 – N2 = 3.71 ×1012cm−2.
The latter decreases to the point that we cannot see lasing in the devices anymore. As already pointed out in previous studies using GaAs-based THz QCL [25, 34,35,36], we highlight the importance of considering IFR size during epitaxy and of keeping it smaller than 0.5 nm for fabrication of GaN THz QCL to be able to provide positive optical gain.
An advantage for GaN THz QCL is its potential to operate at a higher temperature than GaAs-based THz QCL. In this part, we analyzed our device performance as a function of operating temperature. We continued using our reference devices with IFR = 0.25 nm, n.i.d, and AD included in the calculation. Figure 4 shows the maximum optical gain for different lattice temperatures. The gain value is stable from 10 to 150 K at around 142 cm−1, it begins to decrease between 150 and 250 K, for dropping to 61 cm−1 at 300 K. Indeed, as temperature increases, population inversion decreases due to thermal backfilling and LO-phonon scattering increase induces gain broadening. This optical gain value of 61 cm−1 is still higher than the loss of a GaN THz QCL double metal waveguide (30 cm−1), showing that this GaN THz QCL design should be able to operate at room temperature. We also mention that besides being able to operate at room temperature, GaN-based THz QCL has another advantage: because of their higher doping concentration, lower refractive index, and thinner period length, they have the potential to provide much higher optical gain than in their GaAs counterpart. Our design provides a fairly high optical gain value of 142 cm−1 at 10 K, which is a good example.
In conclusion, we report a GaN THz QCLs design operating at 8.7 THz. The simulation shows an optical gain of 142 cm−1 at 10 K and 60 cm−1 at room temperature. Among unwanted phenomena originating from epitaxy, we have calculated the influence of interface roughness, non-intentional doping, and alloy disorder in the performance of GaN THz QCL gain. Alloy disorder influence is neglectable: optical gain only drops from 147 to 142 cm−1 when adding alloy disorder scattering in the simulation. Non-intentional doping should be taken into account in the design to prevent conduction band misalignment. We did observe applied electric field shift from − 84.5 to − 81.6 kV/cm induced by n.i.d in our study. Finally, we observed a great disparity in optical gain for different interface roughness values: 191, 142, 47.9, and − 8.8 cm−1 for interface roughness equal to 0, 0.25, 0.5, and 0.75 nm, respectively. That is why we identify the dominant influence of interface roughness scattering in the degradation of optical gain. This work provides routes for performance optimization of eventually future GaN THz QCL fabrication.
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.
Nonequilibrium Green’s functions
Quantum cascade laser
Faist J, Capasso F, Sivco DL et al (1994) Quantum cascade laser. Science (80- ) 264:553–556. https://doi.org/10.1126/science.264.5158.553
Kohler R, Tredicucci a BF et al (2003) Terahertz semiconductor heterostructure laser. Phys Semicond 2002. Proc 171:145–152. https://doi.org/10.1038/417156a
Fathololoumi S, Dupont E, Chan CWI et al (2012) Terahertz quantum cascade lasers operating up to ∼ 200 K with optimized oscillator strength and improved injection tunneling. Opt Express 20:3866. https://doi.org/10.1364/OE.20.003866
Kumar S, Hu Q, Reno JL (2009) 186 K operation of terahertz quantum-cascade lasers based on a diagonal design. Appl Phys Lett 94:2–4. https://doi.org/10.1063/1.3114418
Wade A, Fedorov G, Smirnov D et al (2009) Magnetic-field-assisted terahertz quantum cascade laser operating up to 225K. Nat Photonics 3:41–45. https://doi.org/10.1038/nphoton.2008.251
Telenkov MP, Mityagin YA, Kartsev PF (2012) Intersubband terahertz transitions in Landau level system of cascade GaAs/AlGaAs quantum well structures in strong tilted magnetic field. Nanoscale Res Lett 7:1–5. https://doi.org/10.1186/1556-276X-7-491
Bellotti E, Driscoll K, Moustakas TD, Paiella R (2008) Monte Carlo study of GaN versus GaAs terahertz quantum cascade structures. Appl Phys Lett 92:101112. https://doi.org/10.1063/1.2894508
Bellotti E, Driscoll K, Moustakas TD, Paiella R (2009) Monte Carlo simulation of terahertz quantum cascade laser structures based on wide-bandgap semiconductors. J Appl Phys 105. https://doi.org/10.1063/1.3137203
Jovanović VD, Indjin D, Ikonić Z, Harrison P (2004) Simulation and design of GaN/AlGaN far-infrared (λ∼34 μm) quantum-cascade laser. Appl Phys Lett 84:2995–2997. https://doi.org/10.1063/1.1707219
Machhadani H, Kotsar Y, Sakr S et al (2010) Terahertz intersubband absorption in GaN/AlGaN step quantum wells. Appl Phys Lett 97:1–4. https://doi.org/10.1063/1.3515423
Beeler M, Bougerol C, Bellet-Amalric E, Monroy E (2013) Terahertz absorbing AlGaN/GaN multi-quantum-wells: demonstration of a robust 4-layer design. Appl Phys Lett 103:10–14. https://doi.org/10.1063/1.4819950
Machhadani H, Tchernycheva M, Sakr S et al (2011) Intersubband absorption of cubic GaN/Al(Ga)N quantum wells in the near-infrared to terahertz spectral range. Phys Rev B - Condens Matter Mater Phys 83:1–5. https://doi.org/10.1103/PhysRevB.83.075313
Lim CB, Ajay A, Bougerol C et al (2015) Nonpolar m-plane GaN/AlGaN heterostructures with intersubband transitions in the 5-10 THz band. Nanotechnology 26:435201. https://doi.org/10.1088/0957-4484/26/43/435201
Lim CB, Ajay A, Bougerol C et al (2016) Effect of doping on the far-infrared intersubband transitions in nonpolar m-plane GaN/AlGaN heterostructures. Nanotechnology 27:145201. https://doi.org/10.1088/0957-4484/27/14/145201
Lim CB, Ajay A, Bougerol C, et al Short-wavelength , mid- and far-infrared intersubband absorption in nonpolar GaN / Al ( Ga ) N heterostructures. 1–5
Lim CB, Ajay A, Lähnemann J et al (2017) Effect of Ge-doping on the short-wave, mid- and far-infrared intersubband transitions in GaN/AlGaN heterostructures. Semicond Sci Technol 32:125002. https://doi.org/10.1088/1361-6641/aa919c
Edmunds C, Shao J, Shirazi-HD M, et al (2014) Terahertz intersubband absorption in non-polar m-plane AlGaN/GaN quantum wells. 3–6. https://doi.org/10.1063/1.4890611
Sudradjat FF, Zhang W, Woodward J et al (2012) Far-infrared intersubband photodetectors based on double-step III-nitride quantum wells. Appl Phys Lett 100. https://doi.org/10.1063/1.4729470
Durmaz H, Nothern D, Brummer G et al (2016) Terahertz intersubband photodetectors based on semi-polar GaN/AlGaN heterostructures. Appl Phys Lett 108:201102. https://doi.org/10.1063/1.4950852
Terashima W, Hirayama H (2009) Design and fabrication of terahertz quantum cascade laser structure based on III-nitride semiconductors. Phys Status Solidi Curr Top Solid State Phys 6:615–618. https://doi.org/10.1002/pssc.200880772
Terashima W, Hirayama H (2011) Spontaneous emission from GaN/AlGaN terahertz quantum cascade laser grown on GaN substrate. Phys Status Solidi 8:2302–2304. https://doi.org/10.1002/pssc.201000878
Sun G, Soref RA, Khurgin JB (2005) Active region design of a terahertz GaN/Al0.15Ga0.85N quantum cascade laser. Superlattices Microstruct 37:107–113. https://doi.org/10.1016/j.spmi.2004.09.046
Yasuda H, Kubis T, Hosako I, Hirakawa K (2012) Non-equilibrium Green’s function calculation for GaN-based terahertz-quantum cascade laser structures. J Appl Phys 111:0–4. https://doi.org/10.1063/1.4704389
Freeman W, Karunasiri G (2013) Nonresonant tunneling phonon depopulated GaN based terahertz quantum cascade structures. Appl Phys Lett 102:0–4. https://doi.org/10.1063/1.4801947
Grier A, Valavanis A, Edmunds C et al (2015) Coherent vertical electron transport and interface roughness effects in AlGaN/GaN intersubband devices. J Appl Phys 118. https://doi.org/10.1063/1.4936962
Ive T, Berland K, Stattin M et al (2012) Design and fabrication of AlN/GaN heterostructures for intersubband technology. Jpn J Appl Phys 51(1–4). https://doi.org/10.1143/JJAP.51.01AG07
Jasnot FR, Péré-Laperne N, de Vaulchier LA et al (2011) Magnetotransport in quantum cascade detectors: analyzing the current under illumination. Nanoscale Res Lett 6(2–5). https://doi.org/10.1186/1556-276X-6-206
Kladko V, Kuchuk A, Lytvyn P et al (2012) Substrate effects on the strain relaxation in GaN/AlN short-period superlattices. Nanoscale Res Lett 7:1–9. https://doi.org/10.1186/1556-276X-7-289
Grange T (2014) Nanowire terahertz quantum cascade lasers. Appl Phys Lett 105. https://doi.org/10.1063/1.4897543
Grange T (2014) Electron transport in quantum wire superlattices. Phys Rev B 89:165310. https://doi.org/10.1103/PhysRevB.89.165310
Grange T (2015) Contrasting influence of charged impurities on transport and gain in terahertz quantum cascade lasers. Phys Rev B - Condens Matter Mater Phys 92:1–5. https://doi.org/10.1103/PhysRevB.92.241306
Luo H, Laframboise SR, Wasilewski ZR et al (2007) Terahertz quantum-cascade lasers based on a three-well active module. Appl Phys Lett 90. https://doi.org/10.1063/1.2437071
Sarigiannidou E, Monroy E, Gogneau N et al (2006) Comparison of the structural quality in Ga-face and N-face polarity GaN/AlN multiple-quantum-well structures. Semicond Sci Technol 21:612–618. https://doi.org/10.1088/0268-1242/21/5/008
Franckié M, Winge DO, Wolf J et al (2015) Impact of interface roughness distributions on the operation of quantum cascade lasers. Opt Express 23:5201. https://doi.org/10.1364/oe.23.005201
Krivas KA, Winge DO, Franckié M, Wacker A (2015) Influence of interface roughness in quantum cascade lasers. J Appl Phys 118. https://doi.org/10.1063/1.4930572
Flores YV, Albo A (2017) Impact of interface roughness scattering on the performance of GaAs/AlxGa1-xAs terahertz quantum cascade lasers. IEEE J Quantum Electron 53. https://doi.org/10.1109/JQE.2017.2689743
The authors would like to thank F. H. Julien and T. Grange for fruitful discussions.
The authors declare that they have no competing interests.
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