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The performance of the InGaN multi-quantum wells (MQWs) laser diode structures has been numerically investigated by using ISE TCAD software. We investigated the effect of well numbers, barrier thickness and barrier doping on the output power, threshold current, and slope efficiency. All material parameters used in the model are evaluated based on the recent literature values. We observed the maximum output power and lower threshold current when the well number was two. Effective change in the output power and threshold current was observed with the variations in barriers thickness and doping level. Our results are in agreement with the experimental results observed by [S. Nakamura et al. Jpn. J. Appl. Phys. Part 2 37, L1020 (1998) and S. Nakamura et al. Appl. Phys. Lett. 76, 22 (2000)].
©2007 Optical Society of America
1. Introduction
Major developments in wide-gap III–V nitride semiconductors have recently led to the commercial production of high-brightness blue-green light-emitting diodes (LEDs) and to the demonstration of room-temperature (RT) violet laser light emission in InGaN: GaN:AlGaN based heterostructures under pulsed and continuous-wave (CW) operations [1]. These developments are the outcome of the realization of high-quality crystals of AlGaN and InGaN, and p-type conduction in AlGaN.
The radiative recombination of the spontaneous and stimulated emissions of the InGaN MQW LEDs and laser diodes (LDs) were attributed to the carriers localized at deep traps (250meV) which originated from the In-rich region in the InGaN wells [2–4]. Further improvements and studies of the LD characteristics are required to enable commercialization of short-wavelength InGaN MQW LDs. The emission mechanisms are not fully understood due to complex material physics and engineering of the InGaN alloy, such as phase separation [5,6] due to large lattice mismatch, large effective masses [7], and polarization due to the wurtzite crystal lattice.
Several groups have assigned the spontaneous emission from InGaN quantum wells (QWs) to the recombination of excitons localized at certain potential minima [8–14]. On the other hand, enormous progress has been made in the development of short-wavelength AlGaInN laser diodes in the past couple of years driven by a broad range of applications, particularly high-density optical data storage. Today’s most advanced devices are operating with lifetimes greater than 10 000 h [15, 16] for the commercialization of blue/violet laser. Several other groups have meanwhile demonstrated room-temperature continuous wave (CW) operation of InGaAlN laser diodes [17–20] on the path to the commercialization. Nevertheless, relatively little is known about the physics of the optical gain and the origin of the lasing mechanisms in such devices. For example, one of the still ongoing discussions is the effect of band-gap inhomogeneities on the optical properties of InGaN multi-quantum wells (MQWs) [21, 22].
Some of the previous studies have indicated that localized states originating from indium composition fluctuations in the InGaN MQW active region may enhance the optical gain in laser structures [21]. However, there have also been experimental and theoretical investigations showing that random alloy fluctuations result in broadening of the spontaneous emission and gain spectra which would lead to a reduced peak gain [22] and therefore higher threshold current densities. InGaN composition fluctuations are certainly present in all laser devices and one may expect that alloy fluctuations would become more dominant with the increasing indium content.
Nakamura et al. [20, 21] studied the laser performance of several LDs with an emission wavelength of 390–450 nm as a function of the number of InGaN well layers. They found that the lowest threshold current density was obtained when the number of InGaN well layers was two. However, in another study, it was observed that in LDs with emission wavelengths longer than 435 nm, when the number of InGaN well layers varied from one to three, the threshold current density was the lowest at one, and increased with the number of InGaN well layers . This phenomenon was attributed to the dissociation of the high indium content InGaN well layer at a high growth temperature of 750 °C due to a high InGaN dissociation pressure [23].
In this paper, the laser performance of the blue InGaN LD structures are numerically investigated with a laser technology integrated program ISETCAD simulation program. It was observed that the inhomogeneous hole distribution in the quantum wells also plays an important role in the laser performance as a function of the number of InGaN well layers. Furthermore, the effects of barriers thickness and doping level on the InGaN laser performance are also investigated.
2. Laser structure and parameters used in the numerical simulations
The laser simulation program solved the Poisson equation, the current continuity equations, the photon rate equation and the scalar wave equation using the two-dimensional (2-D) simulator. The carrier drift-diffusion model which includes Fermi statistics and incomplete ionization were included in our simulation models.
The Shockley Read-Hall (SRH) recombination lifetime of electrons and holes is assumed to be 1 ns; however, this is a rough estimate since the type and density of recombination centers are sensitive to the technological process. From its band gap dependence in other materials, a very small Auger parameter of C = 1×10-34 cm6 s-1 is estimated for GaN. Thus, even with large carrier densities, Auger recombination in nitride materials is negligible. In our strained InGaN quantum wells GaN values are used for the deformation potentials.
We have started with a simple free carrier gain model, including a hyperbolic-cosine broadening function with 0.1ps scattering time. Optical reflection and waveguiding mainly depend on the refractive index profile inside the device and for photon energies close to the bandgap; the refractive index is a strong function of wavelength. The refractive indices of ternary alloys are extracted from GaN waveguide measurements [24, 25] using bandgap variations (x<0.3) and are given by Eq. (1) and Eq. (2) respectively as:
The band gap energies of the InxGa1-xN and AlxGa1-xN ternary alloys at room temperature are governed by the following equations:
Where Eg,InN, Eg,GaN and Eg,AlN are the bandgap energies of InN, GaN and AlN at room temperature, respectively. The bandgap energies of InN, GaN and AlN used in our simulation are 0.77, 3.42 and 6.2 eV, respectively [26].
The effective masses of electron and holes for InxGa1-x N active layer used in our laser simulation were calculated using Eq. (5), Eq. (6) and Eq. (7) below:
Where me,InxGa1-x N is the effective mass of electrons in InxGa1-xN material, mhh,InxGa1-xN and mlh,InxGa1-xN are the effective masses of heavy holes and light holes in InxGa1-xN respectively me,InN for InN is 0.1m0 and me,GaN for GaN is 0.151m0. While mhh,InN and mlh,InN for InN are 1.44m0 and 0.157m0 respectively, and for GaN mhh,InN and mlh,InN are 1.595m0, 0.261m0 respectively, and m0 is the electron mass in free space.
A schematic diagram of the laser diode structure is shown in Fig. 1. n-type GaN layer that is 3μm in thickness is assumed to grow first then followed by 0.4 μm n-type Al0.07Ga0.93N cladding layer, followed by a 0.1μm n-type GaN guiding layer. The active region of the preliminary laser diode structure under study consists of a 3 nm In0.13Ga0.87N well that is sandwiched between two 5 nm In0.01Ga0.99N barriers. 0.02 μm p-Al0.15Ga0.85N stopper layer is assumed to be grown on the top of the active region, followed by 0.1μm p-type GaN guiding layer, 0.4 μm p-Al0.07Ga0.93N cladding layer and 0.1μm p-GaN contact layer.
The doping concentration of n-type and p-type are 5× 1017 cm-3 and 5× 1018 cm-3 respectively. The laser cavity length is 800 μm and width 1μm. The reflectivities of the two ends of left and right facets are set at 30% and 90% respectively.
3. Simulation results and discussion
For the preliminary LD structure under study, the energy band diagram, electrostatic potential and refractive index of the double quantum wells (DQWs) InGaN LD are shown in Fig. 2. The right side of the diagram is the n-side and the left side is the p-side of the laser diode. The horizontal axis is the distance along the crystal growth direction.
Fig. 2. Energy band digram of the double quantum -well InGaN LD together with refractive index profile.
The optical material gain inside the quantum wells are shown in Fig. 3. The quantum well in the left side (p-side) has a higher optical material gain due to the use of an Al0.15Ga0.85N blocking layer in the p-side of which the electrons tend to accumulate in the left quantum well. The holes have difficulty moving from the left quantum well to the right quantum well due to the relatively large effective mass, low mobility, and high band offset in the valence band, more holes are expected in the left quantum well. Since the left quantum well possesses more electrons and holes as compared with the right quantum well, it has higher population inversion and hence higher stimulated recombination rate.
The carrier (hole, electron) distribution inside the quantum wells determines the optical performance of the laser diode. From Fig. 4 we can observe that the carrier distributions are inhomogeneous and are increasing towards the p-side. When the laser oscillation takes place, the hole injection becomes inhomogeneous among wells. This is ascribed to the poor hole injection due to the low mobility and thermal velocity of the hole. Thus the hole density becomes higher on the p-side and the electrons are attracted to the p-side.
Optical reflection and waveguiding mainly depend on the refractive index profile inside the device. Fig. 5 shows the optical intensity together with the refractive index profile. The maximum optical intensity was observed in the active region due to the optical confinement achieved by the refractive index profile provided by the GaN waveguide and Al0.07Ga0.93N cladding layer. Fig. 6 shows the build up in the electrical field in the double quantum well. The internal field causes the QW to be skewed, so that it is no longer square causing the electron and hole distribution to be spatially separated. This reduces the wave function overlap integral, and thereby at a given injected carrier density both the gain and the spontaneous recombination rate are reduced. Hence the optical properties of this structure are determined by the interaction of band filling, band gap renormalization and screening of internal field. The internal field in InGaN quantum wells causes separation of the electron and hole wave functions thus reducing the wave function overlap integral [27,28].Consequently, when the carrier lifetime increases the oscillator strength reduces. As the carrier density in the quantum well increases, screening of the internal field occurs, hence a blue shift of the emission is observed.
Most electrons confined in the active region due to the presence of the Al0.15Ga0.85N stopper layer, which is preventing electronic overflow to the p-side as shown in Fig. 7. The electron current density increases rapidly at the quantum wells due to electrons confinement with the presence of the stopper layer.
The output power curve and slope efficiency of the DQW laser diode are shown in Fig. 8. Output power of 27.0 mW at a threshold current of 26.3 mA was obtained with an emission wavelength of 416.1 nm. Slope value of 1.8 W/A was recorded at the laser threshold current. We observed small blue shift of the emission wavelength from 417 nm to 416.1 nm with an increase in the forward current as shown in Fig. 9. The spectral blue shifting of the InGaN QW emission with the current injection resembles the competition processes between the bandgap renormalization and band filling effects that are known to conventional III–V QW laser. This is due to the fact that the bandgap renormalization scales with the reduced dimensionality. The spectral blue shifting observed in piezostrained InGaN QW emission represents an interesting fundamental phenomenon and it was observed in our study.
The differential external quantum efficiency (DQE) ηd is one of the key performance parameters of laser diodes. It can be obtained from the slope of the light output power versus current (ΔP/ΔI) characteristic above the threshold current. We extract the external differential quantum efficiency using Eq. (8).
Where: h = 6.6262×10-34 J.sec, q = 1.6022 × 10-19 C, c = 2.99×108 m/sec, λ = output wavelength, in our case (416.1 nm)
Fig. 8. Laser output power and slope efficiency as a function of the forward current for the double quantum well InGaN LD.
Fig. 9. The emission wavelength and differential external quantum efficiency as a function of the forward current for the double quantum well InGaN LD.
A maximum value for DQE of 0.44 was obtained in the DQW laser diode as shown in Fig. 9. The laser threshold current, slope efficiency, output power and DQE at various well numbers are shown in Fig. 10. We observed maximum output power and lowest threshold current when the well number is two. These results are in agreement with the experimental results observed previously by Nakamura et al. [20, 21] in which they studied the laser performance of several laser diodes with an emission wavelength of 390–450 nm as a function of the number of InGaN well layers and found that the lowest threshold current was obtained when the number of InGaN well layers was two. Moreover, in another work they observed that when the number of InGaN well layers of the laser diodes with emission wavelengths longer than 435 nm was varied from one to three, the lowest threshold current was obtained when the number of well layers was one and the threshold current increased when the number of InGaN well layers was increased. This phenomenon was attributed to the dissociation of the high indium content InGaN well layer at a high growth temperature of 750 C due to a high InGaN dissociation pressure. We observed the deterioration in laser performance with increased quantum wells number in our simulation results, and attributed it to the non-uniform carrier distribution in the quantum wells. We did not take Nakamura et al. assumption (the indium dissociation) in our simulation process.
Fig. 10. Laser output power, slope efficiency, threshold current and differential quantum efficiency (DQE) as a function of well number of the MQWs InGaN LD.
Fig. 11. Threshold current density (J th) as a function of quantum wells number obtained by Nakamura et al. experimental work and our simulation work.
From Fig. 11 we observed relatively close results for the threshold current density to that obtained by Nakamura et al. [20] as a function of well numbers. Nakamura et al. obtained an output power of 30 mW from DQWs laser diode. In our laser structure we obtained an output power of 27 mW from our DQWs laser diode which it is close to Nakamura et al. result. However the threshold current and output power values depend also on the laser geometry and mirror facets reflectivity.
Fig. 12. Laser output power, slope efficiency, and threshold current as a function of barrier doping concentration.
Figure 12 shows the effect of barrier doping on the output power and threshold current. We observed an increase in output power with the increasing barrier doping concentration up to 30 m W for 1×10-19 cm-3 doing concentration. This may be attributed to the lowering of barrier heights in the active region with increase doping level. Low barrier heights lead to higher injection of carriers into the active region hence generating higher radiative recombinations. Also we investigated the effect of barrier thickness on the optical power and threshold current of InGaN MQWs laser. It was found that the In0.01Ga0.99N barrier thickness also plays a key role in determining the optical characteristics of the InGaN MQWs laser diode.
Figure 13 shows that as the thickness of the In0.01Ga0.99N barrier layer is increased, the output power decreases. This may be attributed to the abruptness of the interface between well and barrier layers probably due to the generation of defects that limits the radiative recombination process inside the quantum well and increases the non-radiative recombination as heat inside the structure.
Figure 14 shows the current dependence of the model gain at a specified wavelength of 416.1 nm. The specified wavelength was selected to be the peak of stimulated emission.
4. Conclusion
We have numerically investigated the effect of the well number, barrier thickness and doping on the laser performance of InGaN QW Laser with ISE TCAD simulation program. The problem of inhomogeneous carrier distribution in InGaN laser diode structures deteriorates with the increase of QW number for the spectral range under study. The inhomogeneous carrier distributions in the QWs play an important role in the laser performance. The lowest threshold current is obtained when the number of InGaN well layers is two at our laser emission wavelength. We also concluded that the barrier thickness and doping play important roles to determine the laser diode performance. Our simulation results in this study are in agreement with the experimental result observed by Nakamura et al. [20, 21].
Acknowledgment
This work was conducted under IRPA RMK-8 Strategic Research grant. The support from Universiti Sains Malaysia and Ministry of Science Technology and Innovation are gratefully acknowledged
References and links
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