GaN axial multiple quantum well nanowire for solar cell applications

Journal Pre-proof Development of Inx Ga1−x N/GaN Axial Multiple Quantum Well Nanowire for Solar Cell Applications A. Aissat, J.P. Vilcot

PII:

S0030-4026(19)31742-5

DOI:

https://doi.org/10.1016/j.ijleo.2019.163844

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IJLEO 163844

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Optik

Received Date:

8 September 2019

Accepted Date:

20 November 2019

Please cite this article as: Aissat A, Vilcot JP, Development of Inx Ga1−x N/GaN Axial Multiple Quantum Well Nanowire for Solar Cell Applications, Optik (2019), doi: https://doi.org/10.1016/j.ijleo.2019.163844

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Development of InxGa1-xN/GaN Axial Multiple Quantum Well Nanowire for Solar Cell Applications A.Aissat1,2 and J.P.Vilcot2 1

Faculty of Technology University of Blida.1, 09000 Blida, Algeria Institut d’Electronique, de Microe´lectronique et de Nanotechnologie (IEMN), UMR CNRS 8520, Universite´ des Sciences et Technologies de Lille 1, Avenue Poincare´, BP 60069, 59652 Villeneuve d’Ascq, France 2

e.mail : [email protected]

Abstract

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In this paper, we report a simulation and investigation of a single InxGa1-xN/GaN axial multiple quantum well nanowire (MQWNW) solar cell of radius r=190 nm and a length of L=1165nm. Our results have been shown that 15 In0.15Ga0.85N (QW) /GaN (barrier) periods is the maximum number that our structure can be supported

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with an optimal efficiency of about 1.65% achieved with ε=1.5%. The insertion of MQWs in nanowire permits the growth of InxGa1-xN MQWs with high indium concentration of about 50% and ε=5%. At this indium

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concentration, the optimal efficiency obtained was 1.70%. Moreover; the structure has been studied with respect to the nanowire radius. In this context, we have shown that the efficiency enhancement achieved through the

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increase of radius is attributed to the increase of photo-carriers. Study of polarization and proton irradiations has indicated the negative effect of polarization on structure performances and high resistance of III-N semiconductor materials against the radiations, respectively. From these novel structures we can improve solar

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cell performance for new applications.

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Keywords- Materials, Nanostructures, Nanowire, solar cells, optoelectronic.

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1. INTRODUCTION

Then a nowires have been appearing as emerging configurations to improve optical absorption and collection

efficiency in a planar solar cellin the recent years [1,2]. The surface/volume ratio of nanowires is advantageous to enhance the performances of optoelectronic devices via the variation of band structure parameters [3].In such nanostructure, the photocarriers are radially separated leading to reduce the collection distance of carriers [4]. Another advantage of nanowires is that they prevent the generation of dislocations during the combination of materials with large lattice mismatch (especially III-V-N materials) [5].

These superiorities make nanowires powerful configurations for developing nanowire photovoltaic (PV) devices. The insertion of multiple quantum wells (MQWs) absorption layers in axial or radial nanowires increases the carriers confinement and favorites the growth of III-V-N alloys with high indium composition [6,7]. III- N semiconductors and their alloys have many reasons making them attractive for optoelectronic devices, especially the solar cells, including the ability to tune the band gap energy from the ultraviolet to the near infrared [8] through variations in alloy composition, high resistance against radiations [9], and high absorption coefficient (~105 cm-1) [10]. This article focuses on simulation and investigation of InxGa1-xN/GaN axial MQWNW solar cell with a radius of 190 nm and L. Many effects are studied and discussed, such as the influence of insertion of InGaN/GaN MQW periods, indium composition of InxGa1-xN active layer, variation of nanowire radius,

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polarization created at the interfaces of our heterostructure, and proton irradiations on current density-voltage J-V characteristic and the important electrical parameters of our solar cell. Fig.1 represents the 3D structure of InxGa1-xN/GaN axial MQWNW solar cell with a radius of 190 nm and a length of L=1165nm. The structure

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consists of n-type Al0.1Ga0.9N called electron blocking layer EBL with doping concentration of about 5×1017 cm-3 and of 150nm thickness and n-type GaN with the same doping concentration of AlGaN and of 550 nm thick at the

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top [11,12], InxGa1-xN (3 nm)/GaN (8 nm) MQW periods inserted in the middle region, and a p-type GaN with doping concentration of 4×1016 cm-3and of 150 nm thickness at bottom. All are placed and grown axially on Si

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(111) substrate. The growth of thick active layers with a significant number of MQW InxGa1-xN/GaN for x>0.15 remains difficult, since it generally leads to a high density of defects which act as non-radiative recombination centers [13,14].

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2. Theoretical Model

The mobility of carriers dependent concentration described by Masetti model and the carrier recombination

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modeled by SRH recombination using concentration dependent lifetimes model is given in detail in [15]. We note here that we have neglected the radiative recombination and this is due that our simulations are done at room

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temperature [16].

The Drift-Diffusion model used to calculate the current density of electrons and holes in the core and shell

regions and Poisson equation are given in our previous works [17,18]. Calculations of absorption coefficient, band gap energy of ternary material structure, and the strain at the hetero-interfaces are detailed in [18-23]. In the absence of external polarization, the total polarization Pt in the InxGa1-xN wurizite structure is the sum of spontaneous polarization Psp and piezoelectric polarization Ppz (figure 2).

⃗⃗⃗⃗𝑇 = 𝑃 ⃗⃗⃗⃗⃗ ⃗⃗⃗⃗⃗ 𝑃 𝑠𝑝 + 𝑃𝑝𝑧

(1)

Total polarization can be positive or negative and its orientation depends on the strain type. Under tensile strain, the spontaneous polarization and the piezoelectric polarization have the same direction and the total polarization increases. Under the compressive strain, the two polarizations have opposite directions and the total polarization decreases. The spontaneous polarization Psp can also interact on the behavior of a component. The field associated to the material polarization spatially separates the electron and hole, thus reducing the probability of radiative recombination, the polarization will improve the component performances [24].

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In the InxGa1-xN material, the spontaneous polarization is described by a non-linear relation between the indium concentration and the Psp constants of the two binary materials GaN and InN, the third term corresponds to the quadratic correction curvature parameter b as shown by the following expression [24,25]. (𝐼𝑛𝐺𝑎𝑁)

= 𝑥𝑃𝑠𝑝 (𝐼𝑛𝑁) + (1 − 𝑥)𝑃𝑠𝑝 (𝐺𝑎𝑁) − 𝑏𝑥(1 − 𝑥)

(2)

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𝑃𝑠𝑝

Where b is the parameter of spontaneous polarization used for material InGaN. The parameters used in

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calculations are listed in Table 1 [23].

Piezoelectricity is the ability of some materials to produce an electric dipole proportional to mechanical strain

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that deforms them. Applying a certain pressure on the nitride materials, the structure is forced to accommodate the stresses by a variation of its lattice parameter with respect to those of the bulk material. It causes a piezoelectric polarization. This polarization is due to the non-centrosymmetry of the crystalline structure, the strongly ionic

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nature of the chemical bonds and deformations present in the crystal. A polarization P, whatever its origin, induces in the crystal a surface charge density.

(3)

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⃗⃗⃗⃗𝑡 . 𝑛⃗ 𝜎=𝑃

In the InGaN / GaN wurtzite quantum well, the polarization difference between the two nitride materials will

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induce a charge plane at each interface. 𝜎 = ∆𝑃⃗𝑡 ⃗⃗⃗ .𝑛

where 𝑛⃗ is unitary normal vector The piezoelectric field can be defined as:

(4)

𝑃𝑃𝑍

𝜀𝑥𝑥 𝜀𝑦𝑦 0 0 0 0 𝑒15 0 𝜀𝑧𝑧 0 0 0 𝑒15 0 0 =( ) 0 𝑒31 𝑒31 𝑒33 0 0 0 0 0 ( 0 ) εxx = εyy = εzz = −

C13 C33

(5)

as −ae

(6)

ae

. εxx

(7)

where as, ae are the lattice constants of substrate and epitaxial layer, respectively.

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Ppz is the piezoelectric polarization; it is given by the following relation:

  c Ppz  2 xx . e31  13 e33  c33  

(8)

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where e31 and e33 are piezoelectric constants, and C13 and C33 are elastic constants. The deformation of the interface between the layers is determined by:

(𝐼𝑛𝐺𝑎𝑁)

= 𝑥𝑃𝑝𝑧 (𝐼𝑛𝑁) + (1 − 𝑥)𝑃𝑝𝑧 (𝐺𝑎𝑁)

(9)

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𝑃𝑝𝑧

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The piezoelectric polarization Ppz is estimated with the linear relationship for the InGaN alloy.

It is essential that the active layer must be of excellent crystalline quality. This layer must be completely strained

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and does not have dislocations which constitute efficient recombination centers. The perfect growth of a heteroepitaxy is only possible if the epitaxial layer thickness does not exceed a certain limit called critical thickness Lc [26,27]. K. Koksal and B. Gonul [28] have proposed a model that allows the calculation of critical

as

1−(0.25.γ)

k.√2.π.εxx

(1+γ)

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Lc =

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thickness as a function of the alloy concentrations:

ln (

Lc .√2 as

+ 1)

(10)

𝑘 : Coefficient equal to 1 in the case of a superlattice; at 2 for a quantum well; 4 in the case of a single layer. 𝛾 : Poisson coefficient γ =

C12 (x) C11 (x)+C12 (x)

C11(x) , C12(x) are the elastic constants.

(11)

For the determination of the critical thickness we used the numerical method of Dichotomy. The current continuity of carriers along with Poisson equation is numerically coupled and solved using AM1.5G solar irradiance at intensity of one sun anda temperature of 300 K.

3. RESULTS AND DISCUSSION Fig 3 illustrates the variation of the critical thickness of the epitaxial layer and the deformation between the two materials as a function of the indium concentration. We note that the increase in the indium concentration causes a considerable decrease in the critical thickness Lc. On the other hand, the increase of the indium concentration induces the increase of the strain ε. For an indium concentration x = 0.50 a critical thickness Lc = 32.50Å and a

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strain of 5% are obtained. The quantum well thickness LW must not exceed the critical thickness Lc (Lw < Lc), otherwise the structure becomes dislocated. Calculation of the critical thickness and the strain allowed us to optimize the dimensions of the structure.

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Fig.4 represents the current density-voltage J-V characteristic of In0.15Ga0.85N/GaN axial MQWNW solar cell with a radius of 190 nm, strain equal 1.5% and L, for different number of MQW periods: 5, 10 and 15 periods.

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The characteristic parameters of the structure extracted from this figure are listed in table2. It is obvious that the short circuit current Jsc increases with the MQW periods increase. The open circuit voltage Voc keeps the same

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value of 0.70V when the number of MQW periods increases. Consequently, the efficiency η boosts with MQW periods insertion until 15 MQW periods, it reaches a maximum of about 1.65 %. This is the number for which the simulated structure gets saturated.Such optimization is due to the additional electron-hole pairs offered by MQW

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configuration. For the next simulation, we fixed the number of MQW periods at 15 periods. Fig. 5 shows the current density-voltage J-V characteristic of InxGa1-xN/GaN axial MQWNW solar cell with

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radius 190 nm and L for different indium concentration x of the active layer: 0.15, 0.25, 0.35 and 0.50. Characteristic parameters of the structure extracted from this figure are listed in table 3. It is clear that the short

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circuit current Jsc is slightly increased with the increase of indium concentration. Moreover, we can see that the open circuit voltage Voc is not influenced by the indium concentration because it depends only on the band gap energy of barrier material in MQW configurations. As a result, the efficiency is also slightly improved with the increase of indium concentration x until x=0.50, it takes a maximum of about 1.70% with a strain around 5%. This is clearer in figure.6 which shows the variation of short circuit current and efficiency with indium concentration x. This section of the study shows us the advantage of MQW insertion to allow the growth of InxGa1-xN with high indium concentration in axial InGaN/GaN nanowire [7]. For the next simulation, we set x at 0.50.

Fig.7 displays the current density voltage J-V characteristic of In0.5Ga0.5N/GaN axial MQW NW solar cell with 15 MQW periods for different radius 45 nm, 110 nm, and 190 nm. These selected values of the radius were calculated and extracted from [29], and are the optimal values for an efficient absorption in a nanowire. It can be viewed that with the increase of the radius, the short circuit current Jsc increases. Open circuit voltage decreases when we increase the radius until 110 nm, thereafter it keeps the same value 0.7 V. Fig. 8 shows the variation of short circuit current and efficiency with the nanowire radius. It was obvious that the efficiency is also raised when we increase the radius. Firstly, as reported in [3], the band gap energy of GaN and its alloys decreases as the radius decreases, leading to enhance the absorption of photons. Secondly, a thicker nanowire absorbs more photons and then much electron-hole pairs will be created. In our results, enhancement of efficiency achieved by

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the increase of radiusis attributed to the second report which dominates in this case.

Fig. 9 exhibits the current density voltage J-V characteristic of In0.5Ga0.5N/GaN axial MQW nanowire with a radius value of 190 nm and L, for various polarization scale ϕ: 0, 0.15, 0.25, 0.45, 0.65, and 0.85 which resultsin

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an interface total charge of about 0 C/cm2, 2.67×1013C/cm2, 4.43×1013C/cm2, 9.077×1013C/cm2, 9.17×1013C/cm2, and 11.7×1013C/cm2, respectively. All the characteristic parameters are summarized in table 4. It can be seen that

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the short circuit current is consistent (Jsc=3.29 mA/cm2) for low values of polarization scale. When ϕ=0.45, it starts to decline until a minimum of about 0.103 mA/cm2 for ϕ=0.85. The open circuit voltage Voc is slightly

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decreasing with the increase of polarization scale until ϕ=0.45. Thereafter, it drops strongly for higher polarization scale. The variation of efficiency with the polarization scale is shown in fig.10. It was clear that the efficiency follows the same behavior of short circuit current. For the strong polarization scale, there is an obvious

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degradation of the structure performances. This degradation is due to the spontaneous and piezoelectric polarizations generate negative and positive charges at the structure regions interfaces. By consequent, an electric

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field is created at interfaces. The polarization induced electric field prevents the diffusion of charge carriers photogenerated into the contacts, and therefore influences adversely on the solar cell performances [30]. Fig.11

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indicates the electric field profile along the depth of the simulated structure for various polarization scale ϕ: 0, 0.15, 0.25, 0.45, 0.65, and 0.85. It can be viewed that the electric field with the different polarization scales has approximately the same values at the top region n-GaN, thereafter is strongly increasing at GaN/AlGaN interfaces (0.52 µm-0.56 µm) where it reaches maximum values, then is decreasing from the depth 0.56 µm and returns to be consistent beyond the depth 0.58 µm. It is also obvious that the electric field with polarization scale ϕ=0.85 takes approximately higher values along the depth of the device with a maximum of about 7×105 V/cm at the depth of 0.55 µm. Fig. 12 shows the current density-voltage J-V characteristic of In0.5Ga0.5N/GaN axial MQW

nanowire solar cell with a radius of 190 nm and L exposed to different proton fluencies: 0 protons/cm-2, 1×1012 protons/cm-2, 3.9×1012 protons/cm-2, and 1.1×1013 protons/cm-2. These proton fluencies induce a deep level state located at Ec=-0.6 eV at room temperature T=300 K with trap concentrations of about : 2.8×1015 cm-3, 3×1015 cm-3, 3.7×1015 cm-3, and 3.6×1015 cm-3, respectively. All these values are extracted from [31]. As we can see, the short circuit current and open circuit voltage are not influenced by the proton irradiation. Fig.13 represents the evolution of efficiency as a function of proton fluency level. It was clear that there is a very small variation of efficiency with increasing proton fluency. These results reveal that In0.5Ga0.5N/GaN axial MQW nanowire solar cell is not affected by proton irradiations and prove high resistance to radiation damage of these configurations

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based on GaN material and their alloys, as reported in the literature [32].

4. CONCLUSION

In this work was investigated the InxGa1-xN/GaN axial MQWNW solar cell. 15 InGaN (MQW)/GaN

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(barrier) was the maximum number of periods that can be supported by the structure. With this number of MQW periods, the structure reached an efficiency of about 1.65 %. The insertion of MQW in the

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active region of the nanowire solar cell allowed the growth of InxGa1-xN with high indium concentration. With a composition of about 0.50, an efficiency of 1.70% was achieved. Radius

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simulation shaves shown that a good efficiency will be achieved with a radius of 190 nm. High polarization at the regions interfaces strongly degraded the performances of solar cell. Finally, we have

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shown how the structure based on III-N and their alloys are not affected by proton irradiations. This work will allow us in the future to improve the performance of the solar cell based on new technology

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for different applications.

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Figure captions Fig. 1. Structure of InxGa1-xN/GaN axial MQWNW solar cell with a radius r of 190 nm and L . Fig 2. Orientation of the piezoelectric polarization and spontaneous polarization of InGaN elaborated on a pseudo-substrate of GaN. a) compressive strain b) tensile strain Fig 3. Effect of indium concentration on the critical thickness and the deformation. Fig.4. J-V characteristic of In0.15Ga0.85N/GaN axial MQWNW solar cell with a radius r and L for different number of MQW periods inserted: 5, 10, and 15.

various x concentration.

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Fig.5. J-V characteristic of InxGa1-xN/GaN axial MQWNW solar cell with 15 InxGa1-xN MQW inserted for

Fig. 6. Variation of short circuit density current and efficiency of InxGa1-xN/GaN axial MQWNW solar cell with

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15 InxGa1-xN MQW inserted as a function of indium concentration.

different radius r=45 nm, 110 nm, and 190 nm.

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Fig. 7. J-V characteristic of In0.5Ga0.5N/GaN axial MQWNW solar cell with 15 MQW periods inserted for

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Fig. 8. Variation of short circuit density current and efficiency of In0.5Ga0.5N/GaN axial MQWNW solar cell with 15 MQW inserted as a function of radius.

Fig. 9. J-V characteristic of In0.5Ga0.5N/GaN axial MQWNW with a radius r and L for various polarization scales

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ϕ: 0, 0.15, 0.25, 0.45, 0.65, and 0.85.

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Fig. 10. Variation of short-circuit current and efficiency of In0.5Ga0.5N/GaN axial MQWNW solar cell with 15 MQW inserted as a function of polarization scale.

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Fig. 11. Electric field profile as a functionof depth of In0.5Ga0.5N/GaN axial MQWNW solar cell with 15 MQW inserted for various polarization scale ϕ: 0, 0.15, 0.25, 0.45, 0.65, and 0.85. Fig. 12. J-V characteristic of In0.5Ga0.5N/GaN axial MQW nanowire solar cell with a radius r of and L irradiated by 0 protons/cm-2, 1×1012 protons/cm-2, 3.9×1012 protons/cm-2, and 1.1×1013 protons/cm-2. Fig.13. Variation of efficiency as a function of protonfluencylevel.

L

AlGaN

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GaN p- type

-p

InGaN QWs

Jo

ur

na

Si

Fig.1

ro of

GaN n- type

InxGa1-xN Psp

InxGa1-xN

Compressive strain

Tensile strain

Psp

Ppz

GaN

GaN

substrate

substrate

Ppz

(b)

(a)

-p

0 -0.02

Inx Ga1-x N/GaN

4

-0.04 -0.06

3

Lc (Å)

10

lP

-0.1

1

0

na

10

2

Jo

0.1

0.2

0.3

0.4

0.5 In

0.6

0.7

0.8

0.9

1

0

0

0.1

ur

10

GaN

=aGaN-aInGaN/aInGaN

-0.08

10

InX Ga1-xN

compression strain



10

5

re

10

ro of

Fig 2

0.2

0.3

0.4

Fig 3

0.5 In

0.6

0.7

0.8

0.9

1

3,5 5 MQWs 10 MQWs 15 MQWs x=0.15 T=300K

Current density (mA/cm2)

3,0 2,5 2,0 1,5 1,0

ro of

0,5 0,0 0,0

0,1

0,2

0,3

0,4

0,5

0,6

Voltage (V)

re

3,35 3,30

lP

3,25 3,20 3,15

na

current density (mA/cm2)

0,8

-p

Fig.4

0,7

3,10 3,05

x=0.50 x=0.35 x=0.25 x=0.15

ur

3,00

Jo

0,0

0,1

0,2

0,3

voltage (V)

Fig.5

0,4

0,5

0,6

1,72

3,40

1,70

3,36

efficiency short circuit current

(%)

2

3,32

Jsc(mA/cm )

1,68 1,66 3,28 1,64 3,24

1,62 1,60 0,10

0,15

0,20

0,25

0,30

0,35

0,40

0,45

Fig.6

-p

3,5 3,0

re

2,5 2,0 1,5

lP

Current density (mA/cm2)

3,20 0,55

ro of

Indium content

0,50

r=45 nm r=110 nm r=190 nm

1,0

na

0,5 0,0

0,1

Jo

ur

0,0

0,2

0,3

0,4

Voltage (V)

Fig.7

0,5

0,6

0,7

0,8

3,50

1,8 1,7

short circuit current efficiency

1,6

3,00

1,5 1,4

2,75

(%)

Current density (mA/cm2)

3,25

1,3

2,50

1,2 2,25

1,1

2,00 20

40

60

80

100

120

140

Fig.8

1,0 200

-p

.

3,0 2,5

lP

=0 =0.15 =0.25 =0.45 =0.65 =0.85

re

3,5

2,0 1,5 1,0

na

Current density (mA/cm2)

180

ro of

Radius (nm)

160

0,5 0,0

0,1

Jo

ur

0,0

0,2

0,3

0,4

Voltage (V)

Fig.9

0,5

0,6

0,7

0,8

4,0

2,0 1,8

3,5

1,6

3,0

1,4 1,2

2,0

1,0 short circuit current efficiency

1,5

0,8

%)

2

Jsc(mA/cm )

2,5

0,6

1,0

0,4 0,5

0,2

0,0 0,1

0,2

0,3

0,4

0,5

0,6

0,7



5

7x10

5

6x10

5

5x10

5

4x10

5

3x10

5

2x10

5

1x10

5

-p

Fig.10

8x10

7,5x105

re

0.15 0.25 0.45 0.65 0.85

7,0x105

Electricfield(V/cm)

5,0x105 0,535

0,540

0,545

0,550

0,555

0,560

0,565

0,570

Depth(µm)

0,1

ur

0 0,0

Jo

0.15 0.25 0.45 0.65 0.85

lP

6,0x105

na

Electric field (V/cm)

6,5x105

5,5x105

0,0 0,9

0,8

ro of

0,0

0,2

0,3

0,4

0,5 0,6 Depth (µm)

Fig.11

0,7

0,8

0,9

1,0

4,0

2

Current density (mA/cm )

3,5 3,0 2,5 2

0 protons/cm 12 2 110 protons/cm 12 2 3.910 protons/cm 13 2 1.110 protons/cm

2,0 1,5 1,0 0,5 0,0 0,0

0,1

0,2

0,3

0,4

0,5

0,6

Fig.12 1,704 1,703

1,701

x=0.50,

=0.45, NQW=15, T=300K r=190nm

1,700 1,699 1,698

2,0x10

12

na

0,0

2.25 2.52 2.85 3.12 3.25

lP

(%)

1,702

2

Jsc (mA/cm )

Voc (V)

FF (%)

0.740 0.735 0.721 0.710 0.705

72.83 72.85 72.88 73.00 73.03

4,0x10

12

6,0x10 2

ur

Fluence Level (protons/cm )

Jo

n(%)

1.10 1.30 1.49 1.62 1.70

re

45 80 120 160 190

0,8

-p

R( nm)

0,7

ro of

Voltage (V)

Fig.13

12

8,0x10

12

Table captions

Table 1: Parameters used in calculations [23]. Table 2. The important parametres of InGaN/GaN axial MQWNW solar cell for different number of MQW periods inserted : 5, 10 and 15 QWs. Table 3 The important parameters of InGaN/GaN axial MQWNW solar cell with 15 MQW periods inserted for various x concentration : 0.15, 0.25, 0.35 and 0.50, dbarrier=8nm, LW=3nm. We compared the results with ref [14],

ro of

x=0.15, dbarrier=4.8nm, Lw=2.2nm.We note that MQW insertion in nanowires increases the efficiency of the solar cell.

Table 4 The important parameters of InGaN/GaN axial MQWNW solar cell with 15 MQW periods inserted for

Jo

ur

na

lP

re

-p

various polarizations scale ϕ : 0, 0.15, 0.25, 0.45, 0.65 and 0.85.

InN

AlN

a (Å)

3.189

3.545

3.112

Eg (eV)

3.510

0.78

6.25

α(meV/K)

0.909

0.245

1.799

β (K)

830

624

1462

0.20

0.07

0.32

C11 (GPa)

390

223

396

C12 (GPa)

145

115

137

C13 (GPa)

106

92

108

C33 (GPa)

398

224

373

C44 (GPa)

105

48

116

e13(C m−2)

-0.527

-0.484

-0.536

e33(C m−2)

0.895

1.058

1.561

Psp (C m )

-0.034

-0.042

-0.09

εr

8.9

10.5

8.5

Δso (eV)

0.017

0.005

0.019

ac (eV)

-6.71

-2.26

-4.5

av (eV)

-0.69

-0.7

-4.9

b (eV)

-2.0

-1.2

me

*

−2

-1.7

re

Table 1

ro of

GaN

-p

Parameter

10

Voc (V)

FF (%)

η (%)

2.74

0.70

69.29

1.33

2.99

0.70

73.90

1.56

3.21

0.70

72.89

1.65

ur

15

Jsc (mA/cm2)

na

Number of MQWs 5

lP

\

Table 2

Jsc (mA/cm2)

Voc (V)

FF (%)

η (%)

0.15

3.21

0.70

72.89

1.65

0.25

3.23

0.70

72.87

1.66

0.35

3.24

0.70

72.86

1.67

0.50

3.24

0.70

72.83

1.70

ref [14], x=0.15

0.65

1.66

49.60

0.52

Jo

Indium content

Table 3

Polarization scale ϕ 0

Jsc (mA/cm2)

Voc (V)

FF (%)

η (%)

3.289

0.736

75.06

1.82

0.15

3.289

0.736

75.06

1.82

0.25

3.290

0.734

74.37

1.79

0.45

3.2913

0.726

70.60

1.68

0.65

0.104

0.618

73.12

0.05

0.85

0.103

0.614

67.99

0.04

Jo

ur

na

lP

re

-p

ro of

Table 4