Physical models and parameter setting

To explore theoretically this study, the numerical simulation software, APSYS (Advanced Physical Models of Semiconductor Devices), was used to preview and optimize our LEDs design, and it is based on 2D/3D finite element analysis of electrical, optical and thermal properties of compound semiconductor devices. Emphasis is placed on band structure engineering and quantum mechanical effects. Inclusion of various optical modules also makes this simulation package attractive for applications involving photosensitive or light emitting devices. The APSYS simulator solves the Poisson’s equation, the current continuity equations, the carrier transport equations, the quantum mechanical wave equation,

and the heat transfer equations, via self-consistent manner. Built-in polarization induced by spontaneous and piezoelectric polarization is considered at hetero-interfaces of nitride related devices. We put commonly accepted physical parameters to perform the simulations.

Usually, for performing a simulation, the used material parameters had been set as default data from former research results. However, we also can modify and update these values to be similar to real device. Therefore, setting suitable parameters for simulation is an important point.

3.2.1 Theoretical model

The physical model of the InGaN MQWs is considered in such a way that the conduction bands are assumed to be decoupled from valence subbands and have isotropic parabolic bands due to the larger bandgap of nitride semiconductor and the valence band structures, which includes 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 envelop function approximation. By using the basis transformation, the 6×6 Hamiltonian can be transformed

into a block-diagonalized Hamiltonian [35],

𝐹 = Δ1+ Δ2 + λ + θ , 𝐺 = Δ1 − Δ2+ λ + θ λ = ℏ²

2m0�𝐴1𝑘z2+ 𝐴2𝑘t2� + λℇ , λℇ = 𝐷1ℇzz+ 𝐷1�ℇxx+ ℇyy� 𝐾t = ℏ²

2m0𝐴5𝑘t2 , 𝐻t = ℏ²

2m0𝐴6𝑘z𝑘t

∆= √2∆3 , and 𝑘_t² = 𝑘_x² + 𝑘_y²

where m0 is the free electron mass. The Ai parameters are related to the hole effective

masses. The crystal-field split energy is Δcr = Δ1 and the spin-orbit splitting is Δso = 3Δ2 = 3Δ3. The Di parameters are deformation potential constants.

To obtain the numerical parameters required for calculations for the nitrogen-containing semiconductors, a linear interpolation between the parameters of the relevant binary semiconductors is utilized except for the unstrained bandgap energies. The material parameters of the binary semiconductors are taken from the paper by Vurgaftman and Meyer [36] and summarized in Table 3.1.

Table 3.1 Material parameters of the binary semiconductors Hole effective mass (transverse) met

/m0 0.2 0.30 0.07

3.2.2 Bandgap energy of Ⅲ-nitride Alloys

As being mentioned before, nitride-based materials are mainly made up of three binary compounds (GaN, AlN, and InN), so the bandgap energy of these nitride-based compounds is also made up of these binary materials. Besides, the bandgap energy of these three binary materials is related to the temperature. Therefore, we will extend this discussion to ternary and quaternary nitride-based compound in the next paragraph.

The bandgap energy of GaN, AlN, and InN at temperature T can be expressed by the

Varshni formula (3.2.1) [37]

𝐸g(𝑇) = 𝐸g(0) − 𝛼𝑇² 𝑇 + β

where Eg(T) is the bandgap energy at temperature T, Eg(0) is the bandgap energy at 0 K, α and β are material-related constant,of the binary alloys are listed in Table 3.2.[36]

The bandgap energy of InxGa1-xN and AlxGa1-xN ternary alloys measured by Osamura et

al. [38] at room temperature (RT) is treated as

𝐸g(In𝑥Ga1−𝑥N) = 𝑥 ∙ 𝐸g(InN) + (1 − 𝑥) ∙ 𝐸g(GaN) − bowing ∙ 𝑥 ∙ (1 − 𝑥)

Where “bowing” is the so-called bowing parameter (also called bowing vector), which is 7.0 eV for AlInN, 3.0 eV for InGaN, and 1.0 eV for AlGaN in our calculation, and the suffix 1, 2, and 3 is taken for AlN, InN, and GaN, respectively.

Table 3.2 Bandgap energy of GaN, AlN and InN related-temperature parameters

Parameter unit GaN AlN InN

Eg(0 K) eV 3.507 6.23 0.735

α meV/K 0.909 1.799 0.245

β K 830 1462 624

3.2.3 Band-offset ratio of Ⅲ-nitride Alloys

The value of band-offset, which plays a very important role in the analysis of energy band diagram, is quite significant for the design of heterostructure devices. In some other textbooks, band-offset is also called band discontinuity, and it is obvious that when two different materials are grown next to each other, the conduction and the valence bands of the two materials will become discontinuous at the interface. However, the devotion of the determination of the band-offset values in semiconductor hetero-junction from experimental measurements and theoretical calculations exists large discrepancy which may be related to different factors in the following.

(B) Possible dependence of band discontinuity on detailed, conditions of interface preparation,

(C) Strain dependence of band discontinuity.

And they may be related to the difficulty of obtaining high equality epitaxial films.

The conduction band offset ratio (∆E c/∆Eg) for the AlN/GaN interface is between 0.66 and 0.81 according to the recent calculations [40]. In our study, a band offset ratio of 67/33 for the all interface is assumed principally.

3.2.4 Carrier transportaion of Ⅲ-nitride Alloys

The physical model of carrier transport is the traditional drift-diffusion model for semiconductors. The specific equations can be expressed as

𝐽_𝑛 relation 𝐷 = 𝜇𝑘𝐵𝑇/q. The equations used to describe the semiconductor device behavior are Poisson’s equation,

∇ ∙ �ε₀ε𝐹⃑� = q�𝑝 − 𝑛 + 𝑝_𝐷 − 𝑛_𝐴 ± 𝑁_𝑓�

and the current continuity equations for electrons and holes,

1 respectively. The electric field is affected by the charge distribution, including the electron and hole concentrations, dopant ions 𝑝_𝐷 and 𝑛_𝐴, and other fixed charges 𝑁_𝑓 that are of special importance in nitride-based devices due to the effect of built-in polarization.

Built-in polarization induced due to spontaneous and piezoelectric polarization is known to influence the performance of nitride devices. In order to consider the built-in polarization 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 interface charges at each hetero interface. They provided explicit rules to calculate the nonlinear polarization for nitride alloys of arbitrary composition. [41]

Although the interface charges can be obtained by this theoretical model, experimental investigations often find weaker built-in polarization than that predicted by theoretical calculation. It is mainly attributed to partial compensation of the built-in polarization by

80% smaller than the theoretically calculated values. [43] As a result, 50% of the theoretical polarization values are used in our simulation from the average of the reported values.

A widely used empirical expression for modeling the mobility of electrons and holes is the Caughey Thomas approximation, which is employed in our calculation and can be expressed as [44]

𝜇(𝑁) = 𝜇_min+ 𝜇max− 𝜇min

1 + (𝑁/𝑁_ref)^𝛼

where 𝜇max, 𝜇min, 𝑁ref and 𝛼 are fitting parameters. The parameter 𝜇max represents the mobility of undoped or unintentionally doped samples, where lattice scattering is the main scattering mechanism, while 𝜇min is the mobility in highly doped material, where impurity scattering is dominant. The parameter 𝛼 is a measure of how quickly the mobility changes from 𝜇min to 𝜇max and 𝑁ref is the carrier concentration at which the mobility is half way between 𝜇min and 𝜇max. The electron mobility of Ga1-x-yAlxInyN in our simulation can be expressed as

𝜇_min (Ga_1−x−yAl_xIn_yN) = (1 − x − y) ∗ 𝜇_min (GaN) + x ∗ 𝜇_min (AlN) + y ∗ 𝜇_min (InN) 𝜇_max (Ga_1−x−yAl_xIn_yN) = (1 − x − y) ∗ 𝜇_max (GaN) + x ∗ 𝜇_max (AlN) + y ∗ 𝜇_max (InN)

The relative parameters are summarized in Table 3.3.

Table 3.3 Mobility parameters of GaN, AlN and InN [29]

Parameter (unit) Electrons 𝑁ref (cm⁻³) 1.0*10¹⁷

𝜶 1.37

GaN ; InN

𝜇_max (cm²V⁻¹s⁻¹) 684 𝜇min (cm²V⁻¹s⁻¹) 386

AlN

𝜇_max (cm²V⁻¹s⁻¹) 306 𝜇min (cm²V⁻¹s⁻¹) 132

Chapter 4 Study of Graded-composition electron blocking layer

4.1 Introduction

As the conception of inserting EBL mentioned before (Section 2.4), to reduce the carrier overflow in active region, an AlxGa_1−xN EBL was usually used in common InGaN-basded LED structures. However, For the band structure of the LED with EBL, as illustration of Fig.

4.1(a), the raised barrier height of the conduction band (CB) can hold electrons back. In the same way, the EBL moreover acts on holes. As well as the condition of CB, the larger band gap also brings the higher barrier height to the valence band (VB) and results holes inject more difficultly. Further, due to the spontaneous and piezoelectric polarization at the heterojunction interfaces for c-plane LEDs, the severe band bending leads the blocking layer to be a sloped triangular barrier and results in the higher potential barrier for holes, besides electrons. Furthermore, under a high driving current, the forward bias could make the n-side CB energy level higher then p-side, and the active region confinement of the EBL would be affected unsuccessfully.

In this chapter, the concept of band-engineering started from the observation on the band diagram of InGaN/GaN LEDs. If the composition of aluminum in EBL increases from the n-GaN side toward the p-GaN side, the band-gap broadens gradually. As a result, the barrier in the VB could be level down and even overturn, while the slope of the CB could be enhanced, as illustration of Fig. 4.1(b). Then, the improvement in capability of hole

transportation across the EBL as well as the electron confinement could be expected. To overcome the problem of the conventional EBL, we designed a linearly graded-composition of the p-AlxGa1-xN to replace the constant composition structure. For the gradual change of the band gap, it is expected to flatten the slope of VB edge and make the slope of CB edge cliffy simultaneously. As increasing the holes injection and preventing the electrons escape, the region of MQWs will collect more carriers and obtain more luminous intensity.

Fig.4.1 (a) The influence of inserting EBL between MQWs and p-GaN.

(b)Schematic diagram of the concept of band engineering at EBL.

4.2 Simulationstructure and parameter setting

To prove the feasibility of the hypothesis above, the band diagrams and carrier distributions in LED with GEBL were investigated first by APSYS simulation program. The simulation LED structures were composed of 4- μ m-thick n-type GaN layer (n-doping=2×10¹⁸ cm⁻³), six pairs of In_0.15Ga_0.85N/GaN multiple-quantum wells (MQWs) with

2.5-nm-thick wells and 10-nm-thick barriers, 20-nm-thick p-AlxGa_1−xN EBL or GEBL (p-doping=5×10¹⁷ cm⁻³), and 200-nm-thick p-type GaN layer (p-doping=1×10¹⁸ cm⁻³) For the

LEDs with GEBL, three types of GEBLs with compositions of aluminum graded along the (0 0 0 1) direction from 0% to 15%, 25%, and 35%, respectively, were simulated and denoted as LEDs A, B, and C. Furthermore for the conventional LED, the composition of aluminum was a constant of 15%.

Then, we put commonly accepted physical parameters to perform the simulations. The percentage of screening effect is 50% , the conduction-valence band offset ratio is 67:33 at all interfaces, the Shockley-Read-Hall recombination lifetime is 1ns, the Auger recombination coefficient in QWs is 2×10^-30 cm⁶/s, and the internal loss is 2000m^-1, respectively.

Fig. 4.2.1 The simulation structure of GEBL LEDs with material, thickness, and doping concentration.

Fig. 4.2.2 The simulation structure of conventional LED, LED A, LED B, and LED C.

4.3 Calculated band diagrams and carrier distribution analysis

The calculated energy band diagrams of LEDs A, B, and C at current density of 100 A/cm² is illustrated in Figure 4.3.1. According to our concept of band-engineering, the degree of gradation had the decisive influence on the capability of holes injection.

Fig. 4.3.1 Calculated energy band diagrams of (a) Al0GaN to Al0.15Ga0.85N,

(b) Al0GaN to Al0.25Ga0.75N, and (c) Al0GaN to Al0.35Ga0.65N graded-composition EBLs at a current density of 100 A/cm².

Even with small degree of gradation as LED A, the slope of the VB can be leveled.

Then the slope starts to overturn when the composition of aluminum at the p-side increases up to 25%. Moreover, it is worth noting that the valence band offset (∆Ev) between the last GaN barrier and the EBL is diminished in all three LEDs with GEBL. Therefore, the hole injection can be improved effectively by using the GEBL. In the meantime, as the degree of gradation increased, the conduction band offset at the interface of p-GaN and EBL increases as well, so does the confinement capability of electrons. But correspondingly, the ∆Ev between EBL and

p-GaN increases as the composition of aluminum rises, which might retard the transportation of holes.

Then, for further analysis of band changes under different current injection, we list the band diagrams at EBL region (20, 100, and 300 A/cm²) in Figure 4.3.2.

Fig. 4.3.2 The calculated band diagram of GEBL LEDs at 20, 100, and 300 A/cm²

For conduction bands, although all GEBL LEDs show upward band edge in EBL region, the slopes of EBL band edge are flatter as current increasing. The lessened effective barrier height causes the electron overflow severer under high injection, as shown in Fig. 4.3.3. From

LED always exist at 20 A/cm² to 300 A/cm². On the contrary, for all GEBL LEDs, this overflow phenomenon can be suppressed drastically at 20 A/cm². However, as injection current rising to 300 A/cm², electron leakage of LED A and LED C come alive. The leakage reason of LED A is its smaller barrier height limits. One the other hand, for LED C with the largest grading composition of aluminum (0~30%), the energy band of EBL is bent down under high forward bias (high current injection, 300 A/cm²) and lead to electron overflow.

Therefore, from current injection of 20A/cm² to 300 A/cm², only LED B stands out above the GEBL LEDs and suppress electron overflow successfully. Of cause the most important reason is that holes injection are improved for LED B all the while, under high injection current especially, as shown in Fig. 4.3.4.

Fig. 4.3.3 Simulated electron current density for conventional LEDs and GEBL LEDs

Fig. 4.3.4 Distribution of hole concentration of conventional LEDs and GEBL LEDs

In addition, high aluminum composition EBL is not practical for actual application due to the low acceptor-activation efficiency and the low crystal quality in epitaxy. Consequently, only LED B with aluminum graded from 0% to 25% is discussed in detail in the following paragraph.

The profiles of hole and electron concentration distribution at a current density of 100 A/cm² are illustrated in Figs. 4.3.5(a) and 4.3.5(b), respectively. It can clearly be seen that with GEBL, injected holes uniformly distribute along the EBL region compared to conventional one, demonstrating that the flat valence band indeed favored the hole transportation across EBL. Meanwhile, the hole concentration in MQWs is significantly increased as expected. Moreover, the electron concentration in MQWs is also enhanced, while the electron distribution within the GEBL region and p-GaN is enormously decreased over two orders. This result indicates that GEBL can suppress the electron overflow out of active region more effectively than conventional EBL, even though the conduction band offset between the last GaN barrier and the GEBL is diminished.

Fig. 4.3.5 Calculated (a)hole concentration distribution and (b)electron concentration

4.4 Sample structure and Fabrication

The LED structures with EBL and GEBL were grown on c-plane sapphire substrates by MOCVD. After depositing a low temperature GaN nucleation layer, a 4 μm n-type GaN

layer, and a ten-pair InGaN/GaN superlattice prestrain layer, the rest of the LED structures were grown based on our simulation design. The epitaxial recipe for the GEBL is worth noting. Generally, the graded-composition ternary III-nitride semiconductors can be grown by two methods: growth temperature ramping and III/III ratio ramping. [45, 46] Here we adopted the Al/Ga ratio ramping because the temperature ramping would change the growth rate, and the higher temperature might damage the quality of QWs. The growth temperature of conventional EBL and GEBL was the same (870 °C), and the aluminum composition profile of the GEBL was approximately graded from 0% to 25%. Finally, the LED chips were fabricated by regular chip process with ITO current spreading layer and Ni/Au contact metal, and the size of mesa is 300×300μm². The sample structure is shown in Fig. 4.4.1. The

fabrication processes of sample LED are shown in Fig. 4.4.2.

Fig.4.4.1 The schematic drawing of sample structure (GEBL LED).

Fig.4.4.2 The schematic drawing of fabrication processes of LED.

4.5 Analysis of carrier-dependence EL efficiency and efficiency droop behavior

Fig. 4.5.1 shows the L-I-V curves of the conventional and GEBL LED. The output powers were measured with a calibrated integrating sphere. The forward voltages (Vf) at 22 A/cm² and series resistances (Rs) of GEBL LED are 3.28 V and 7 Ω, respectively, which are lower than that of 3.4 V and 8 Ω for conventional LED. The reduced V f and Rs can be attributed to the improvement in hole injection and the higher-efficiency p-type doping in GEBL. [47] In the case of L-I curves in Fig. 4.5.1, although the output power of GEBL LED is a little lower at low current density (below 30 A/cm²), it increases more rapidly as the injection current increases as compared to the conventional one. The output powers were enhanced by 40% and 69% at 100 and 200 A/cm², respectively. This phenomenon can be explained as follows: at low current density, it is more difficult for holes to tunnel across the barrier at the interface of p-GaN and EBL in GEBL LED because the ∆Ev is larger than that in conventional LED. While at high current density, the tunneling process of holes can be negligible, and the diffusion process is dominated for the hole transportation into the MQW.[32] As discussed above, the diffusion process in GEBL is much easier than that in conventional one due to the flat valence band and much lower ∆Ev at the interface of the last GaN barrier and EBL. In conjunction with the superior electron confinement, much stronger light output was achieved in GEBL LED at high current density.

Fig. 4.5.1 Forward voltage and output power as a function of current density for conventional and GEBL LEDs.

Finally, the normalized efficiency of conventional and GEBL LEDs as a function of current density was investigated, as shown in Fig. 4.5.2. The maximum efficiency (ηpeak) of GEBL LED appears at an injection current density of 80 A/cm², which was much higher than that for conventional LED (at 20 A/cm²). More interestingly, the efficiency droop, defined as (ηpeak− η200 A cm−2) / ηpeak, was reduced from 34% in conventional LED to only 4% in GEBL LED. This significant improvement in efficiency can be mainly attributed to the enhancement of hole injection as well as electron confinement, especially at high current density.

Fig. 4.5.2Normalized efficiency as a function of current density for conventional and GEBL LEDs

4.6 Summary

In conclusion, we have designed a graded-composition electron blocking layer for InGaN/GaN LED by employing the band-engineering. The simulation results showed that the triangular barrier of conventional EBL at the valence band could be balanced, while the slope of the conduction band could be increased by increasing the band-gap of AlxGa_1−xN along the (0001) direction. As a result, the hole concentration in MQWs was significantly increased, while the electron distribution within the GEBL region and p-GaN was enormously decreased over two orders, indicating that the GEBL can effectively improve the capability of hole transportation across the EBL as well as the electron confinement. Furthermore, the LED structure with GEBL was realized by MOCVD. The L-I-V characteristics of GEBL LED

higher-efficiency p-type doping in GEBL as compared to the conventional LED. More importantly, the efficiency droop was reduced from 34% in conventional LED to only 4% in GEBL LED. This work implies that carrier transportation behavior could be appropriately modified by employing the concept of band-engineering.

Chapter 5 Study of InGaN-Based UV LED with InAlGaN Barrier

5.1 Introduction

GaN-based ultraviolet (UV) LEDs have attracted great attention in last few years due to its potential applications in photo-catalytic deodorizing such as air conditioner,[48] and there have been interests in solid-state lighting by using near-UV LEDs light for the phosphor-converting source.[49, 50] However, it is difficult to fabricate near-UV LEDs with high efficiency, because the external quantum efficiency (EQE) decreases drastically below the wavelength of 400 nm.[51] This is due to the smaller InN mole fluctuation with reduced indium composition in the near-UV quantum wells (QWs), and thus less localized energy states lead to lower efficiency of the near-UV LEDs.[52, 53] Moreover, crystalline quality and light absorption of GaN are significant for short wavelength near-UV LEDs.[54, 55] It’s well

GaN-based ultraviolet (UV) LEDs have attracted great attention in last few years due to its potential applications in photo-catalytic deodorizing such as air conditioner,[48] and there have been interests in solid-state lighting by using near-UV LEDs light for the phosphor-converting source.[49, 50] However, it is difficult to fabricate near-UV LEDs with high efficiency, because the external quantum efficiency (EQE) decreases drastically below the wavelength of 400 nm.[51] This is due to the smaller InN mole fluctuation with reduced indium composition in the near-UV quantum wells (QWs), and thus less localized energy states lead to lower efficiency of the near-UV LEDs.[52, 53] Moreover, crystalline quality and light absorption of GaN are significant for short wavelength near-UV LEDs.[54, 55] It’s well