DOI 10.1007/s00340-008-3331-9
Numerical study of optical properties of InGaN
multi-quantum-well laser diodes with polarization-matched
AlInGaN barrier layers
J.-R. Chen· S.-C. Ling · H.-M. Huang · P.-Y. Su · T.-S. Ko· T.-C. Lu · H.-C. Kuo · Y.-K. Kuo · S.-C. Wang
Received: 30 September 2008 / Published online: 12 December 2008 © Springer-Verlag 2008
Abstract The optical properties of InGaN multi-quantum-well laser diodes with different polarization-matched AlIn-GaN barrier layers have been investigated numerically by employing an advanced device simulation program. The use of quaternary polarization-matched AlInGaN barrier layers enhances the electron–hole wave function overlap due to the compensation of polarization charges between InGaN quantum well and AlInGaN barrier layer. According to the simulation results, it is found that, among the polarization-matched quantum-well structures under study, lower thresh-old current and higher slope efficiency can be achieved si-multaneously when the aluminum composition in AlInGaN barrier layers is about 10–15%. The optimal polarization-matched InGaN/AlInGaN laser diode shows lower thresh-old current and higher slope efficiency compared to conven-tional InGaN/InGaN laser diodes.
PACS 42.55.Px· 78.20.-e · 78.20.Bh · 78.30.Fs
1 Introduction
Gallium nitride (GaN)-based light-emitting diodes (LEDs) and laser diodes (LDs) have received much attention in the
J.-R. Chen (
)· S.-C. Ling · H.-M. Huang · P.-Y. Su · T.-S. Ko · T.-C. Lu· H.-C. Kuo · S.-C. WangDepartment of Photonics & Institute of Electro-Optical Engineering, National Chiao Tung University, Hsinchu 300, Taiwan
e-mail:[email protected]
Fax: +886-3-571-6631 Y.-K. Kuo
Department of Physics, National Changhua University of Education, Changhua 500, Taiwan
past few years due to their promising applications such as solid-state lighting, high-density optical storage systems, and laser projection displays [1–4]. In order to develop these expected productions, many research groups are de-voted to the study of high-performance LEDs and LDs. Al-though InGaN/GaN laser diodes with an emission wave-length near 405 nm have been commercialized as light sources of the blu-ray disk system and the high-definition digital versatile disk (HD-DVD), superior operation per-formance and shorter emission wavelength are expected as challenges for the next-generation devices. Recently, sev-eral high-performance InGaN-based laser diodes have been achieved. Asano et al. demonstrated 100-mW kink-free blue–violet laser diodes in 2003 [5]. Ultraviolet laser diodes with 350.9-nm lasing wavelength were also realized by Kamiyama et al. in 2005 [6]. Moreover, Ryu et al. demon-strated single-mode blue–violet laser diodes with low beam divergence and high catastrophic optical damage (COD) level in 2006 [7]. They also reported high-performance blue laser diodes with an emission wavelength of 448 nm and a maximum output power of >300 mW in 2007 [8]. Although these high-performance laser diodes were reported, the in-herent problem of piezoelectric and spontaneous polariza-tion in c-plane GaN-based alloys is one of the most impor-tant properties which limit the development of GaN-based optoelectronic devices [9].
Several approaches have been proposed to eliminate, or reduce, the polarization effect in nitride-based heterostruc-tures. Franssen et al. demonstrated that the polarization-induced electric fields can be fully screened by employing heavy 1× 1019 cm−3 Si doping in quantum barriers [10]. Nevertheless, heavy Si doping in quantum barriers will duce severe free-carrier absorption, which results in the in-crease of laser threshold current. Besides, non-polar (a and
to this problem [11–14]. However, high dislocation density caused by large lattice mismatch and stacking faults inhibits the related development [15–17]. Recently, the concept of employing polarization-matched quaternary AlInGaN bar-rier layers has been proposed to control the electrostatic field in the quantum wells, which could be an attractive ap-proach to the problem of the electrostatic field in c-plane GaN-based heterostructures. By using quaternary AlInGaN barrier layers, we could control both spontaneous and piezo-electric polarization in the quantum wells as the appropriate aluminum and indium compositions are chosen [18–22].
In order to further investigate the GaN-based laser diodes with polarization-matched AlInGaN barrier layers, system-atic and compact theoretical modeling is a necessary ap-proach to improve existing laser structures and understand internal physical processes, which provides timely and ef-ficient guidance toward the optimal structure design and device parameters. In this study, the InGaN laser diodes with different polarization-matched AlInGaN barrier layers are systematically studied in detail by using an advanced laser technology integrated program (LASTIP), which self-consistently combines quantum well band structure calcula-tions by 6× 6 k · p theory, radiative and non-radiative car-rier recombination, carcar-rier drift and diffusion, and optical mode computation [23]. By appropriately designing the alu-minum and indium compositions in AlInGaN barrier layers, the built-in charge density at the interface between InGaN well and AlInGaN barrier layer can be compensated. Un-der this circumstance, the electron–hole wave function over-lap in the InGaN/AlInGaN quantum well increases as com-pared with the conventional InGaN/GaN or InGaN/InGaN quantum well and thus the performance of the polarization-matched InGaN/AlInGaN quantum-well lasers can be en-hanced. Furthermore, how the different physical mecha-nisms influence the threshold properties is investigated in this study as well.
2 Theoretical method and device structure
The self-consistent LASTIP simulation program combines band-structure and gain calculations with two-dimensional (2-D) simulations of wave guiding, carrier transport, and heat flux. The carrier-transport model includes drift and diffusion of electrons and holes in devices. Built-in polar-ization induced by spontaneous and piezoelectric polariza-tion is considered at hetero-interfaces of nitrirelated de-vices. In the quantum wells, self-consistent Poisson and Schrödinger equations are recomputed at every bias point for the states of quantum-well levels and carrier distrib-utions. In the optical mode model, a 2-D scalar complex wave equation is solved for the lateral modes. The phys-ical model of the InGaN quantum wells is considered in
such a way that the conduction bands are assumed to be de-coupled from valence subbands and have isotropic parabolic bands due to the larger band gap of nitride semiconductors and the valence band structures, which include the coupling of the heavy-hole (HH), the light-hole (LH), and the spin– orbit split-off bands, are calculated by the 6×6 Hamiltonian with envelope-function approximation [24,25]. The optical gain spectra of quantum-well structures, with the valence-band-mixing effect being taken into account, follow the ex-pression in [26], including a Lorentzian broadening function with 0.1-ps scattering time [26–28]. The calculations of car-rier capture and escape from the quantum wells are consid-ered in accordance with the model provided by Romero et al. [29]. More description about the physical models utilized in the LASTIP simulation program can be found in [30,31]. In this simulation, we first assume that the InGaN laser diodes are grown on a 3-µm n-type GaN layer. On top of this GaN layer is a 0.1-µm-thick n-type In0.1Ga0.9N
compliant layer and a 1.0-µm-thick n-type Al0.07Ga0.93N
cladding layer, followed by a 0.1-µm-thick n-type GaN guid-ing layer. The multiple-quantum-well active region consists of two 2-nm-thick In0.1Ga0.9N quantum wells and
5-nm-thick In0.035Ga0.965N or AlInGaN barrier layers. A
20-nm-thick p-type Al0.2Ga0.8N electronic blocking layer (EBL) is
grown on top of the active region to reduce electron leakage into the p-type GaN layer [32,33]. Furthermore, a 0.1-µm-thick p-type GaN guiding layer and a 1.0-µm-0.1-µm-thick p-type Al0.07Ga0.93N cladding layer are grown. Finally, a
0.1-µm-thick p-type GaN cap layer is grown to complete the struc-ture. The effective active region of the ridge geometry is 2 µm in width and 500 µm in length. The reflectivities of the two end mirrors are set at 20% and 50%, respectively. The doping concentrations in each layer and the detailed device structure are described in Table1.
3 Material parameters
In order to obtain reliable simulation results, proper material parameters are essential in the physical model. The material parameters of the binary semiconductors required for k· p calculations are taken from the paper by Vurgaftman and Meyer [34] and summarized in Table 2. As for AlInGaN materials, a linear interpolation between the parameters of the relevant binary semiconductors is utilized except for the band-gap energies. For the physical parameter P , the inter-polation formula is [35]
P (AlxInyGa1−x−yN)= P (AlN)x + P (InN)y
+ P (GaN)(1 − x − y). (1) The AlInGaN band-gap energies can be expressed as a weighted sum of the band-gap energies of relevant ternary
Table 1 Layer structure and room-temperature physical parameters of the InGaN quantum-well laser under study (d, layer thickness;
Ndop, doped carrier density; n, refractive index at wavelength 400 nm;
κ, thermal conductivity). The doped carrier density, Ndop, represents
the actual density of free carriers
Parameter (unit) d(nm) Ndop(1/cm3) n κ(W/cm K)
p-GaN (contact) 100 1× 1018 2.55 1.3
p-Al0.07Ga0.93N (cladding) 1000 5× 1017 2.519 0.8
p-GaN (waveguide) 100 5× 1017 2.55 1.3
p-Al0.2Ga0.8N (EBL) 20 5× 1017 2.489 0.8
i-In0.035Ga0.965N (barrier) 5 – 2.585 0.6
i-In0.1Ga0.9N (quantum well) 2 – 3.835 0.5
i-In0.035Ga0.965N (barrier) 5 – 2.585 0.6
i-In0.1Ga0.9N (quantum well) 2 – 3.835 0.5
i-In0.035Ga0.965N (barrier) 5 – 2.585 0.6
n-GaN (waveguide) 100 1× 1018 2.55 1.3
n-Al0.07Ga0.93N (cladding) 1000 1× 1018 2.519 0.8
n-In0.1Ga0.9N (compliance) 100 1× 1018 2.835 0.5
n-GaN (substrate) 3000 1× 1018 2.55 1.3
Table 2 Material parameters of the binary semiconductors GaN, AlN, and InN at room temperature (Δcr= Δ1, Δso= 3Δ2= 3Δ3)
Parameter Symbol (unit) GaN AlN InN
Lattice constant a0(Å) 3.189 3.112 3.545
Spin−orbit split energy Δso(eV) 0.017 0.019 0.005
Crystal-field split energy Δcr(eV) 0.010 −0.169 0.040
Hole effective mass parameter A1 −7.21 −3.86 −8.21
A2 −0.44 −0.25 −0.68
A3 6.68 3.58 7.57
A4 −3.46 −1.32 −5.23
A5 −3.40 −1.47 −5.11
A6 −4.90 −1.64 −5.96
Hydrost. deform. potential (c axis) az(eV) −4.9 −3.4 −3.5
Hydrost. deform. potential (transverse) at(eV) −11.3 −11.8 −3.5
Shear deform. potential D1(eV) −3.7 −17.1 −3.7
D2(eV) 4.5 7.9 4.5
D3(eV) 8.2 8.8 8.2
D4(eV) −4.1 −3.9 −4.1
Elastic stiffness constant C33(GPa) 398 373 224
Elastic stiffness constant C13(GPa) 106 108 92
Electron effective mass (c axis) mz
e/m0 0.2 0.32 0.07
Electron effective mass (transverse) mte/m0 0.2 0.30 0.07
semiconductors with appropriate band-gap bowing parame-ters. Specifically, the AlInGaN band-gap energies are calcu-lated by the following expressions [36]:
Eg(AlInGaN) =xyE
u
g(AlInN)+ yzEgv(InGaN)+ xzEgw(AlGaN)
xy+ yz + zx , (2)
Eug(AlInN)= uEg(InN)+ (1 − u)Eg(AlN)
− u(1 − u)B(AlInN), (3)
Evg(InGaN)= vEg(GaN)+ (1 − v)Eg(InN)
− v(1 − v)B(InGaN), (4)
Ewg(AlGaN)= wEg(GaN)+ (1 − w)Eg(AlN)
u=1− x + y 2 , v= 1− y + z 2 , (6) w=1− x + z 2 ,
where x, y, and z= 1 − x − y represent the compositions of aluminum, indium, and gallium in the AlInGaN mater-ial system, respectively. The band-gap bowing parameters of AlInN, InGaN, and AlGaN are 2.5 eV, 1.4 eV, and 0.7 eV, respectively [34].
Built-in polarization induced due to spontaneous and piezoelectric polarization is known to influence the perfor-mance of nitride devices. In order to consider the built-in po-larization within the interfaces of nitride devices, the method developed by Fiorentini et al. is employed to estimate the built-in polarization, which is represented by fixed inter-face charges at each hetero-interinter-face. They provided explicit rules to calculate the nonlinear polarization for nitride alloys of arbitrary composition [37]. Specifically, the spontaneous polarization of ternary nitride alloys can be expressed by
Psp(AlxGa1−xN)= −0.090x − 0.034(1 − x) + 0.019x(1 − x), (7) Psp(InxGa1−xN)= −0.042x − 0.034(1 − x) + 0.038x(1 − x), (8) Psp(AlxIn1−xN)= −0.090x − 0.042(1 − x) + 0.071x(1 − x). (9)
The spontaneous polarization of quaternary AlInGaN can be calculated in a similar way as that shown in expression (2). As for the piezoelectric polarization of AlInGaN, InGaN, and AlGaN, it can be calculated by the following expression:
Ppz(AlxInyGa1−x−yN)= Ppz(AlN)x+ Ppz(InN)y
+ Ppz(GaN)(1− x − y), (10) where Ppz(AlN)= −1.808ε + 5.624ε2 for ε < 0, (11) Ppz(AlN)= −1.808ε − 7.888ε2 for ε > 0, (12) Ppz(GaN)= −0.918ε + 9.541ε2, (13) Ppz(InN)= −1.373ε + 7.559ε2, (14) ε= (asubs− aL)/aL. (15)
Here asubs and aL are the lattice constants of the substrate
and epitaxial layer, respectively. The total built-in ization is the sum of spontaneous and piezoelectric polar-ization. At an abrupt interface of a top/bottom layer het-erostructure such as InGaN/GaN or AlGaN/GaN, the polar-ization can decrease or increase within a bilayer, causing a
Table 3 Net surface charge density at each interface of the InGaN laser diode
Interface Built-in charge density
Al0.07Ga0.93N/GaN +2.86 × 1012cm−2 GaN/Al0.2Ga0.8N −8.82 × 1012cm−2 Al0.2Ga0.8N/In0.035Ga0.965N +1.20 × 1013cm−2 In0.035Ga0.965N/In0.1Ga0.9N +6.46 × 1012cm−2 In0.1Ga0.9N/In0.035Ga0.965N −6.46 × 1012cm−2 In0.035Ga0.965N/GaN −3.19 × 1012cm−2 GaN/Al0.07Ga0.93N −2.86 × 1012cm−2
fixed polarization charge density σ defined by [38]
σ (Psp+ Ppz)= P (bottom) − P (top)
=Psp(bottom)+ Ppz(bottom)
−Psp(top)+ Ppz(top). (16) For the InGaN quantum-well lasers under study, the net sur-face charges at all intersur-faces are calculated and listed in Ta-ble 3. Although the interface charges can be obtained by this theoretical model, experimental investigations often find weaker built-in polarization than that predicted by theoret-ical calculation. It is mainly attributed to partial compen-sation of the built-in polarization by defect and interface charges [39]. Typical reported experimental values are 20%, 50%, or 80% smaller than the theoretically calculated val-ues [40–42]. As a result, 50% of the theoretical polarization values are used in our simulation from the average of the reported values.
The thermal conductivities of nitride compounds listed in Table 1 are obtained from the values of binary GaN, AlN, and InN by considering the impact of alloy and in-terface scattering of phonons. In our simulation, the ther-mal conductivities of GaN, AlN, and InN are 1.3 W/cm K, 2.85 W/cm K, and 0.45 W/cm K, respectively [30]. As for the refractive-index parameter, the Adachi model is em-ployed to calculate the refractive-index values in each layer listed in Table1as well [43]. The band-offset ratio, which is defined as the ratio between the conduction-band offset
Ecand the valence-band offset Ev, of an InGaN/InGaN
quantum well is assumed to be 0.7/0.3 based on the pub-lished literature [44,45].
4 Simulation results and discussion
The spontaneous and piezoelectric polarization charges as a function of Al or In composition for ternary AlGaN and InGaN alloys grown pseudomorphically on GaN templates are plotted in Fig. 1. Since the strains of AlGaN and In-GaN epitaxial layers are tensile and compressive respec-tively as compared with GaN templates, it can be found that
Fig. 1 Spontaneous (Psp) and piezoelectric (Ppz) polarization
charges as a function of Al or In composition for ternary AlGaN and InGaN alloys grown pseudomorphically on GaN templates
the variation of the piezoelectric polarization of AlGaN and InGaN is opposite with increasing Al or In composition. Although the spontaneous polarizations of AlGaN and In-GaN, and the piezoelectric polarization of AlIn-GaN, are all negative with increasing Al and In compositions, the ob-vious increase of the piezoelectric polarization of InGaN with increasing In compositions could compensate the to-tal polarizations. Therefore, by employing appropriate Al and In compositions in the AlInGaN barrier layers, it can be found that the polarizations at the interface between In-GaN quantum wells and AlInIn-GaN barrier layers can be matched according to the results of theoretical calculation [20,22,37]. The Al and In compositions are determined by fixing a specific Al composition and varying the In compo-sition to find the minimum interface charge density. When different Al compositions are chosen, there are correspond-ing In compositions which make the InGaN/AlInGaN in-terface charge density minimum. Therefore, several differ-ent Al and In compositions can reach this requiremdiffer-ent. For comparison purposes, Al0.25In0.226Ga0.524N is chosen to be
the polarization-matched quaternary barrier layer in our pre-liminary study because its energy band gap is nearly iden-tical to that of the original In0.035Ga0.965N barrier layer
after considering the strain-induced band-gap variation in both barrier layers. The interface charge density between the In0.1Ga0.9N quantum well and the Al0.25In0.226Ga0.524N
barrier layer is 3.12× 1010cm−2. This value is dramatically reduced as compared with that of the conventional InGaN barrier layer, as shown in Table 3. In Fig.2 we depict the potential profiles and the subband wave functions (C1 and HH1) for (a) conduction and (b) valence band in the ac-tive region of the conventional InGaN/InGaN laser diodes at the injection current of 120 mA. Data shown in Fig. 2
reveal that the built-in electric field causes a strong defor-mation of the quantum wells and induces a spatial separa-tion of the electron and hole wave funcsepara-tions, which leads to a reduction in the photon emission [9]. Figure3shows the potential profiles and the subband wave functions (C1
Fig. 2 Potential profiles and the subband wave functions (C1 and HH1) for (a) conduction and (b) valence band in the active region of the conventional InGaN/InGaN laser diodes at the injection current of 120 mA
Fig. 3 Potential profiles and the subband wave functions (C1 and HH1) for (a) conduction and (b) valence band in the active region of the laser diode with polarization-matched Al0.25In0.226Ga0.524N
barrier layers at the injection current of 120 mA
and HH1) for (a) conduction and (b) valence band in the active region of the laser diode with polarization-matched Al0.25In0.226Ga0.524N barrier layers at the injection current
of 120 mA. It is obvious that the relatively flat quantum-well band profiles enhance the electron–hole spatial overlap and consequently increase the oscillator strength and radiative efficiency. Furthermore, to compare the optical properties of these two laser diodes we illustrate the light-output power of the conventional InGaN/InGaN and polarization-matched InGaN/AlInGaN laser diodes as a function of the input cur-rent in Fig.4. It is found that although the threshold current of the laser diode with the quaternary barrier layer is lower than that of the conventional laser diode, the slope efficiency
Fig. 4 Light-output power of the conventional InGaN/InGaN and po-larization-matched InGaN/AlInGaN laser diodes as a function of the input current
of the polarization-matched laser diode is relatively lower than that of the InGaN/InGaN laser diode.
In order to further understand the internal physical mech-anisms which result in the lower slope efficiency in the polarization-matched laser diode, the vertical profiles of electron concentration distribution and conduction band edge in the active region at 120-mA injection current are shown in Fig.5 for laser structures with InGaN and AlIn-GaN barrier layers, respectively. In Fig.5a, it is noteworthy that the effective energy barrier height (i.e. the energy dif-ference between the quasi-Fermi level and the Al0.2Ga0.8N
EBL) created by the Al0.2Ga0.8N EBL is substantially
re-duced by the high density of positive polarization charges at the interface between the InGaN barrier layer and the Al0.2Ga0.8N EBL. Under this condition, the electrons are
attracted by Coulomb force and accumulate at this inter-face, which leads to strong band bending and decreases the effective energy barrier height. Consequently, the increase of laser threshold current will be expected due to the po-tential tilt in the quantum well and the enhanced electron carrier leakage from the active layer to the p-type cladding layer. On the other hand, we found that this band bend-ing is severer after replacbend-ing the InGaN barrier layer with the polarization-matched Al0.25In0.226Ga0.524N barrier layer
due to the increase of positive polarization charges. There-fore, the condition of electron accumulation is more obvi-ous and the effective energy barrier height also decreases, as shown in Fig.5b. Besides, the heterobarrier induced due to the increase of negative charges at the interface between GaN waveguide layer and AlInGaN barrier layer inhibits carrier injection. These factors lead to the strongly non-uniform carrier distribution in two quantum wells of the InGaN/AlInGaN laser diode.
Although the polarization-matched
Al0.25In0.226Ga0.524N barrier layer can provide lower
threshold current, the decrease of slope efficiency should be improved in the further study. Therefore, other
Fig. 5 Vertical profiles of electron concentration distribution and con-duction band edge in the active region of the laser structures with (a) InGaN and (b) AlInGaN barrier layers respectively at 120-mA in-jection current
Fig. 6 Light-output power of the conventional and polarization-matched laser diodes as a function of the input current
polarization-matched AlInGaN barrier layers which include Al0.20In0.207Ga0.593N, Al0.15In0.188Ga0.662N,
Al0.10In0.169Ga0.731N, and Al0.05In0.150Ga0.80N are
of the conventional and polarization-matched laser diodes as a function of the input current. The Al composition represents different polarization-matched AlInGaN barrier layers. According to the simulation results, the slope effi-ciency increases and the threshold current decreases with lower Al composition in AlInGaN barrier layers. However, when the Al composition decreases to 5%, the threshold current becomes higher. Therefore, the optimal Al composi-tion in the AlInGaN barrier layer is about 10–15%. In order to further understand the physical mechanism which leads to the increase of slope efficiency with lower Al composi-tion in AlInGaN barrier layers, the vertical profiles of elec-tron concentration distribution and conduction band edge in the active region at 120-mA injection current are shown in Fig. 7 for laser diodes with polarization-matched (a) Al0.15In0.188Ga0.662N and (b) Al0.05In0.150Ga0.80N barrier
layers, respectively. In Fig.7a, although the electron accu-mulation still can be found at the interface between bar-rier layer and EBL, the lower energy band gap resulting from the decreasing Al composition in the AlInGaN
bar-Fig. 7 Vertical profiles of electron concentration distribution and conduction band edge in the active region of the laser structures with polarization-matched (a) Al0.15In0.188Ga0.662N and
(b) Al0.05In0.150Ga0.80N barrier layers respectively at 120-mA
injec-tion current
rier layer makes the higher effective energy barrier height in the interface between barrier layer and EBL. Therefore, the electron carrier leakage can be suppressed, which en-hances carrier confinement in the active region and also im-proves the slope efficiency and threshold properties. More-over, as for the laser diode with the Al0.05In0.150Ga0.80N
barrier layer, although the low Al composition in the bar-rier layer can provide a higher effective energy barbar-rier, it is difficult to provide sufficient carrier confinement in the shallow quantum well, which leads to the electrons spread-ing into the barrier layer, as shown in Fig.7b. Lower car-rier concentration confined within the quantum well will result in the decrease of recombination efficiency. There-fore, the threshold current increases and the slope efficiency decreases for the laser diodes with the Al0.05In0.150Ga0.80N
barrier layer, as shown in Fig.6. In order to observe the condition of electron leakage current in the laser diodes with different polarization-matched barrier layers, we de-pict the vertical electron current density profiles within the active regions of laser structures with Al0.25In0.226Ga0.524N,
Al0.15In0.188Ga0.662N, and Al0.05In0.150Ga0.80N barrier
lay-ers respectively at 120-mA injection current in Fig.8a. This driving current is chosen to be above the threshold current values of the laser diodes under study. The positions of two quantum wells are marked with gray areas. The left-hand
Fig. 8 (a) Vertical electron current density profiles within the active regions of laser structures with Al0.25In0.226Ga0.524N,
Al0.15In0.188Ga0.662N, and Al0.05In0.150Ga0.80N barrier layers
re-spectively at 120-mA injection current. (b) Percentage of electronic leakage current as a function of the Al compositions in AlInGaN barrier layer at 120-mA injection current
side of the figure is the n-side of the device. The electron current is injected from n-type layers into quantum wells and recombines with holes in quantum wells. Therefore, the electron current density is reduced in the quantum wells. Electron current which overflows through quantum wells is viewed as leakage current. The problem of electron leak-age current plays an important role for the optical perfor-mance of III-nitride laser diodes [32,33]. In Fig.8a, elec-tron leakage current is severe for the laser diode with the Al0.25In0.226Ga0.524N barrier layer. Although the higher Al
composition in the barrier layer creates a deeper quantum well, the effective energy barrier provided by EBL is rel-atively lower. Therefore, the slope efficiency of the laser diode with the Al0.25In0.226Ga0.524N barrier layer is lower
than the conventional laser diodes due to the increase of electron leakage current. Lower Al composition in the AlIn-GaN barrier layer will create a higher effective energy bar-rier in the interface between EBL and barbar-rier layer, which can reduce the electron leakage current, as shown in Fig.8a. Figure8b depicts the percentage of electronic leakage cur-rent as a function of the Al compositions in the AlInGaN barrier layer at 120-mA injection current. The percentage of electron leakage current is defined as the ratio of the elec-tron current overflowed to the p-type layer to that injected into the active region of the laser diodes. It is found that the percentage of electron leakage current increases obviously with the Al composition in AlInGaN barrier layers.
Except for the effects of electron leakage current, the quantum-well optical confinement factor also plays an im-portant role for the laser threshold properties. As the Al and In compositions are changed in the AlInGaN barrier layers, the refractive index will be changed simultaneously. Figure9depicts the quantum-well optical confinement fac-tor as a function of the Al compositions in the AlInGaN barrier layers. As shown in Fig. 9, the quantum-well op-tical confinement factor decreases with the increasing alu-minum composition in the AlInGaN barrier layer due to the smaller difference of refractive index between barrier layer and waveguide layer. Therefore, the quantum-well optical
Fig. 9 Quantum-well optical confinement factor as a function of the Al compositions in the AlInGaN barrier layers
confinement factor is also one of the mechanisms which re-sult in the increase of the threshold current with increasing Al composition in the AlInGaN barrier layers.
5 Conclusion
We have carried out a theoretical simulation to investi-gate the properties of multi-quantum-well laser diodes with polarization-matched InGaN/AlInGaN quantum-well struc-tures rather than the conventional InGaN/InGaN strucstruc-tures. It is found that although the polarization-matched AlInGaN barrier layers enhance the electron–hole wave function over-lap, the strong band bending at the interface between barrier layer and EBL lowers the effective energy barrier height and then results in severe electron leakage current. Furthermore, we decrease the Al compositions in polarization-matched AlInGaN barrier layers. The lower Al composition in a bar-rier layer provides a higher effective energy barbar-rier height at the interface between barrier layer and EBL, which in-hibits the electron leakage current. Moreover, the quantum-well optical confinement factor decreases with the increas-ing aluminum composition in the AlInGaN barrier layer. The simulation results indicate that, among the polarization-matched quantum-well structures under study, lower thresh-old current and higher slope efficiency can be achieved si-multaneously when the aluminum composition in AlInGaN barrier layers is about 10–15%. The optimal polarization-matched InGaN/AlInGaN laser diode shows superior device performance compared to conventional InGaN/InGaN laser diodes.
Acknowledgements This work was supported in part by the MOE ATU program and in part by the National Science Council of the Re-public of China under Contracts NSC 96-2221-E009-092-MY3, NSC 96-2221-E009-093-MY3, NSC 96-2221-E009-094-MY3, and NSC 96-2112-M-018-007-MY3.
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