Improvement of blue InGaN light-emitting diodes with gradually increased barrier heights from n- to p-layers

Abstract

The advantages of blue InGaN light-emitting diodes (LED) with the active region of gradually increased barrier heights from n- to p-layers are studied. The energy band diagram, hole concentration, electrostatic field near the electron blocking layer (EBL), and the internal quantum efficiency (IQE) are investigated by Crosslight simulation program. The simulation results show that the structure with gradually increased barrier heights has better performance over the equal one, which can be attributed to the mitigated polarization effect near the interface of the last barrier/EBL due to less interface polarization charges. Moreover, reduced barrier height toward the n-layers is beneficial for holes injection and transportation in the active region. As a result, holes are injected into the active region more efficiently and distributed uniformly in the quantum wells, with which both the IQE and the total lighting power are increased. Although it can lead to the broadening of the spontaneous emission spectrum, the increase is slight such that it has little effect on the application in solid-state lighting.

Key words： InGaN; light-emitting diodes (LED); polarization effect; gradual barrier height

Introduction

In recent years, the III-nitride light-emitting diodes (LEDs) have received much attention because of their potential usages in ultraviolet and blue lighting and detection [1], high density optical storage systems, full-color displays, chemical sensors, and medical applications [2,3]. Specially, the InGaN LEDs are widely studied due to the advantages of wide spectrum coverage, low power consumption, compact size, and long lifetime over conventional incandescent and florescent lamps [4,5]. However, the quenching of current injection efficiency at high injection level is still a challenge to fabricating high-efficiency LED devices. This problem becomes especially prominent for InGaN LEDs, which limits their high power application. The mechanisms determining the current injection efficiency in general semiconductor LED and laser devices have been widely studied [6-8]. Various factors are proved to affect the injection process, such as carrier transport (mainly limited by hole transport), thermionic carrier escape processes [9,10], and recombinations in both quantum wells (QWs) and barrier layers. Thermionic carrier escape processes under high current injection are revealed to cause the current injection efficiency quenching in InGaN-based LEDs [11-13], which is consistent with recent experimental works [14,15].

On the other hand, III-nitride LEDs suffer from low hole injection efficiency. In a typical LED structure, a large number of holes remain at the interface of the electron blocking layer (EBL) and p-GaN, which attract electrons to flow over the EBL and thus reduce the radiative recombination rate. Therefore, to enhance the quantum efficiency and suppress the current injection quenching of InGaN LEDs, it is important to design a new structure which has high electron blocking and hole injection efficiency.

Several recent works have proposed the design of novel barrier structure for suppression of quantum efficiency droop in nitride-based LEDs, such as using large bandgap AlInN [7,9,11,12] or AlGaN [16] barrier materials, and gradually changing single barrier height [17]. Interband Auger process is also proved to have important contributions to efficiency droop [18]. A potential solution to this issue is using new active region materials instead of traditional QW materials [19]. Furthermore, other approaches have been proposed to improve the hole injection efficiency, such as grading barrier design for the EBL [20], using polarization matched AlInGaN EBL [21], specially designed AlGaN/GaN superlattice EBL [22], and Mg doped multi-quantum wells (MQWs) for the active region [23]. Nonetheless, there are still drawbacks in these approaches, such as non-uniform distribution of holes in quantum wells and poor crystalline quality caused by dopant, which bring new challenges to the device performance.

In this work, the structure with gradually increased barrier heights from the n-layers to p-layers is proposed to overcome those drawbacks in current InGaN LEDs design. Crosslight APSYS (Advance Physical Model of Semiconductor Devices) programs, which solve the Schrödinger equation, Poisson’s equation, the carrier transport equations, and the current continuity equation self-consistently [24], are used to simulate the band diagram, and the optical and electrical properties of the structure in details.

Sample structure and parameters

The LEDs labeled as structure A with equal barrier heights, shown in Fig. 1, is used as a reference. The proposed sample is labeled as structure B. Two-dimension finite element analysis is used for the simulation, and the device width is set to be 200 μm. These two structures are designed to be grown on a c-plane sapphire substrate, followed by a 1-μm-thick undoped GaN layer, and a 3-μm-thick n-type GaN layer (n doping= 5×10¹⁸ cm^-3). The active region of structure A includes three 2-nm-thick In_0.21Ga_0.79N QWs separated by four 15-nm-thick GaN barriers, while the barrier heights of structure B are increased from n-type to p-type layers by varying the mole fraction of In and Al. A 20-nm-thick p-type Al_0.15Ga_0.85N EBL (p doping= 5×10¹⁷ cm^-3) is on top of the active region, followed by a 500-nm-thick p-type GaN contact layer (p doping= 1.2×10¹⁸ cm^-3). The background doping levels for the undoped i-GaN, i-InGaN, and i-AlGaN layer used in the simulation are set to be 5×10¹⁶, 1×10¹⁷, and 1×10¹⁶ cm^-3 [25], respectively. The main advantages of the proposed sample are expected to not only reduce polarization field near the interface between the last barrier and the EBL, but also change the distribution of electrons and holes in each QW. With the improvements, the carriers injection efficiency quenching can be mitigated. The Shockley-Read-Hall (SRH) recombination time is set to be 0.8 ns, and the internal loss is 2000 m^-1 [26].

In general, the band gap energies of InGaN and AlGaN are governed by the following formulas [27]:

$$\begin{gathered} E_g(I{n}_{x}G{a}_{\mathrm{1}-x}N)=x{E}_{g,InN}+(\mathrm{1}-x)E{\mathrm{1}}_{g,GaN}-b_{\mathrm{1}}x(\mathrm{1}-x), \\ {E}_g(A{l}_{x}G{a}_{\mathrm{1}-x}N)=x{E}_{g,AlN}+(\mathrm{1}-x)E_{g,GaN}-b_{\mathrm{2}}x(\mathrm{1}-x), \end{gathered}$$

where Eg,InN, Eg,GaN, and Eg,AlN are the band gap energies of InN, GaN and AlN, which equal to 0.77, 3.42 and 6.25 eV, respectively [27]. The bowing parameters b₁ and b₂ of InGaN and AlGaN are 3 and 1 eV respectively, and the band-offset ratio is assumed to be 0.7/0.3 for InGaN and AlGaN materials.

Fig.1 Schematic diagrams of structures A and B. In structure A the three pairs of InGaN/GaN quantum wells are of uniform composition, while in structure B barrier heights are gradually increased toward p-AlGaN layer

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It is well known that AlN, GaN, InN and their crystal alloys crystallize are in the wurtzite structure with space group {\mathrm{C}}_{6\mathrm{v}}^4, which means that there are strong spontaneous polarization and piezoelectric polarization in the InGaN and AlGaN materials [25]. The highly polar nature yields a large amount of fixed charge at interfaces, which can induce a big electrostatic field in the LED. The total macroscopic polarization P of InGaN (AlGaN) is defined as the sum of the spontaneous polarization P_{SP} in the equilibrium lattice and the strain-induced piezoelectric polarizationP_{PE}. The spontaneous polarization P_{SP\_InGaN} (P_{SP\_AlGaN}) can be obtained by numeric interpolations between the physical properties of GaN and InN (AlN) [28]:

P_{SP\_I{n}_{x}G{a}_{\mathrm{1}-x}N}=P_{SP}^{InN}x+P_{SP}^{GaN}(\mathrm{1}-x)-{\beta }_{\mathrm{1}}x(\mathrm{1}-x),

P_{SP\_A{l}_{x}G{a}_{\mathrm{1}-x}N}=P_{SP}^{AlN}x+P_{SP}^{GaN}(\mathrm{1}-x)-{\beta }_{\mathrm{2}}x(\mathrm{1}-x),

where {\beta }_{\mathrm{1}} and {\beta }_{\mathrm{2}} are the bowing parameters, defined as -0.038 C/m² for InGaN and -0.019 C/m² for AlGaN. Piezoelectric polarizations of InGaN and AlGaN are dependent on the strains in the materials, which can be expressed as [29,30]:

P_{PE}=\mathrm{2}{\displaystyle \frac{a(x)-a_{\mathrm{0}}}{a_{\mathrm{0}}}}(e_{\mathrm{31}}-e_{\mathrm{33}}{\displaystyle \frac{C_{\mathrm{13}}}{C_{\mathrm{33}}}}),

where a(x) and a_{\mathrm{0}} are the lattice constants of relaxed and pseudomorphically strained In_xGa_1-xN (Al_xGa_1-xN), respectively; e_{\mathrm{31}} and e_{\mathrm{33}} are piezoelectric constants; and C_{\mathrm{13}} and C_{\mathrm{33}} are elastic constants of the In_xGa_1-xN (Al_xGa_1-xN), which can also be obtained by the linear interpolation between the physical properties of GaN and InN (AlN). The related parameters used in the programs are listed in Table 1, which can be found in Refs. [31,32]. Under polarization, the sheet charge density \sigma can be obtained by the following equation:

\sigma ={(P_{SP}+P_{PE})}_{top}-{(P_{SP}+P_{PE})}_{bottom}.

Tab.1 Important parameters of AlN, GaN and InN used in the programs

parameters	GaN	AlN	InN
a/Å	3.189	3.112	3.545
c/Å	5.185	4.982	5.703
m_{\mathit{\parallel }e}	0.2	0.32	0.07
m_{\perp e}	0.2	0.3	0.07
C13/GPa	106	108	92
C33/GPa	398	373	224
e13/(C∙m-2)	-0.35	-0.5	-0.57
e3/(C∙m-2)	1.27	1.79	0.97
PSP/(C∙m-2)	-0.034	-0.09	-0.042

Taking into account the screening by defects, the surface charge densities are assumed to be 40% of the calculated values [33]. In structure A, the surface charge density is 7.8×10¹⁶ m^-2 at the InGaN/GaN interface, and is 2.5×10¹⁶ m^-2 at the interface between the last barrier and EBL. The fixed charge densities of structure B used in this program are shown in Table 2.

Tab.2 Surface fixed charge densities at interfaces of structure B

Interface	surface charge density/m-2
i-In0. 1Ga0.9N/i-GaN	-3.4 × 1016
i-In0.21Ga0.79N/i-In0.1Ga0.9N	-4.4 × 1016
i-In0.05Ga0.95N/i-In0.21Ga0.79N	6.1 × 1016
i-In0.21Ga0.79N/i-In0.05Ga0.95N	-6.1 × 1016
i-GaN/i-In0.21Ga0.79N	7.8 × 1016
i-In0.21Ga0.79N/i-GaN	-7.8 × 1016
i-Al0.05Ga0.95N/i-In0.21Ga0.79N	8.6 × 1016
p-Al0.15Ga0.85N/i-Al0.05Ga0.95N	1.7 × 1016
p-GaN/p-Al0.15Ga0.85N	-2.5 × 1016

Simulation results and discussion

The energy band of structure A at forward voltage of 3.4 V is plotted in Fig. 2(a), which uses the interface between the last barrier and EBL as the reference point and so are other figures shown below. It is observed that the quasi-Fermi level of holes around the active region is far away from the valence band edge, indicating that the population of holes injected into the active region is small. This is due to the large effective barrier height for holes injection (~0.423 eV) caused by valence band downward bending which results from large polarization field at the interface. Furthermore, because of large effective mass of holes, it is hard for holes to pass through the GaN barriers, resulting in fewer holes in the quantum wells near the n-type layers, which can be seen from Fig. 2(b). As addressed in our approach, the structure with gradually increased barrier heights exhibits better performance in this aspect, which is shown in Fig. 3.

Fig.2 (a) Energy band diagram of structure A at forward voltage of 3.4 V. The red dash lines indicate the quasi-Fermi levels; (b) distribution of hole concentration P_h in structure A at 3.4 V forward voltage in log scale

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Figure 3(a) shows the energy band diagram of structure B at forward voltage of 3.4 V. Obviously, the polarization at the interface between the last barrier and EBL is decreased, resulting in less downward band bending. As a result, the effective potential height for holes injection is lowered (from 0.423 to 0.312 eV). From this diagram, it is also evident that the hole quasi-Fermi level is nearer to the valence band than that of structure A, resulting in larger hole concentration in QWs. As shown in Fig. 3(b), holes are distributed uniformly in the active region to the concentration of ~10¹⁹ cm^-3, about three orders of magnitude higher than structure A. There are two factors contributing to this improvement. First, due to gradually decreased barrier heights from p-layers to n-layers, holes can be transported from p-type layers to the wells near n-type layers more easily, which contributes to a large number of holes resided in the wells near n-type layers at low voltage. Secondly, because of different composition of In(Al)GaN materials used as barriers, the degree of abrupt change of polarization is lowered, which leads to less fixed charges at the interface between the last barrier and the EBL. It reduces the interface electrostatic field in structure B in comparison with structure A, and so is the field in the last well as dictated by zero-bias boundary condition. As a result, the effective barrier height for hole transport is reduced.

Fig.3 (a) Energy band diagram of structure B at forward voltage of 3.4 V. The red dash lines indicate the quasi-Fermi levels; (b) distribution of hole concentration P_h in structure B at forward voltage of 3.4 V in log scale

Full size|PPT slide

To examine this aspect, we calculate the electrostatic field across the last barrier/EBL interface, and the result is shown in Fig. 4. It can be clearly seen that the electrostatic field at the interface is decreased, and thus the downward band bending is mitigated. Therefore, holes are injected to the active region in structure B with much higher efficiency. The result suggests the importance of minimizing the polarization field in improving the performance of LEDs. It is worth noticing that an effective way of minimizing the electrostatic field in the QW layer is by applying non/semi-polar InGaN QWs [34,35], or polar QWs with large wavefunction overlap design [36,37]. Further investigations will be conducted on the function of gradually increased barrier heights in non-polar InGaN LED devices.

Fig.4 Electrostatic field in structure A (black dash line) and structure B (red solid line) near the EBL at forward voltage of 3.4 V

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Regarding the influence of gradually increased barrier height for MQWs in the active region, we probe into the internal quantum efficiency of both structures. As shown in Fig. 5, the IQE of structure B is also higher than structure A. Since the interface electrostatic field in structure B is smaller than that of structure A, the conduction band bending is mitigated, which means the effective barrier height for electron escape is increased. Because fewer electrons pass through the EBL, it leads to higher IQE of structure B. As a result, the total output light power of structure B also becomes higher. At the current density of 250 A/m, the total power of structure B is about 27% larger than structure A, which suggests that radiative recombination is more efficient in structure B.

Fig.5 Total light power and IQE as function of current for structure A (black dash line) and structure B (red solid line)

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In addition, the total rates of spontaneous emission of these two structures are investigated. As shown in Fig. 6, the spontaneous emission rate of structure B is almost three orders of magnitude higher than structure A, which is resulted from the higher hole concentration in structure B. Furthermore, the full width at half maximum (FHWM) of the emission peak for structure B is 22 nm, slightly larger than that of structure A (18 nm). This can be attributed to the fact that the barrier heights of the QWs in structure B are not uniform, which leads to different transition wavelength in each well. However, the broadening of emission peak is minor such that it does not undermine the application of the proposed structure in blue and white lighting devices.

Fig.6 Total spontaneous emission rate for structure A (black dash line) and structure B (red solid line)

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From the above discussion, it is clear that structure B performs better than structure A in both optical and electrical aspects. Compared with the method of Mg doping in the MQWs [23] used for higher hole injection efficiency, the dopant can introduce thread dislocations and stacking dislocations in the active region. In this sense, the approach of gradually-increasing barrier height instead of Mg-doping can not only enhance the hole injection efficiency, but also avoid the problem of poor crystalline quality caused by doping. Therefore, the design of variable barrier height in the active region is preferable for high power and high efficiency light emitting applications. However, this approach requires further growth optimization in realizing the potential advantages.

Conclusions

In summary, the effects of barrier height variation on the performance of InGaN LED structure are studied by designing a sample with the active region of gradually increased barrier heights from n- to p-layers. The simulation results show that, when the GaN barriers are replaced by In(Al)GaN materials with increased barrier heights, the degree of abrupt change of polarization at the EBL/last barrier interface is mitigated due to lower lattice mismatch, and holes are injected more efficiently. Furthermore, decreased barrier heights from p-type to n-type layers enhance holes flow in the active region and distribute uniformly. As a result, the designed LED structure shows higher light output power and IQE, which is promising for high efficiency solid-state lighting and other optoelectronic applications.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 60976042 and 10990103), the National Basic Research Program of China (Nos. 2010CB923204 and 2012CB619302), and the China Postdoctoral Science Foundation (No. 20100480064). The authors are also grateful to Mr. M. Yang from Crosslight Software Inc. for technical assistance.

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