Introduction

GaN is widely used in the study of ultraviolet detectors, microwave devices, LED chips, and laser [1–4]. GaN-based LED is an environmental, energy saving, and long lived of the blue light-emitting devices. But these devices have not absolutely replaced other lighting devices for their low light extraction efficiency (LEE). Only a small percentage of photons escape from the LEDs and much of them eventually converts to heat. On the other hand, their light extraction efficiency is still limited by the total internal reflection at the interface. Furthermore, poor directional emission profiles of LEDs limit their application because of the broad radiation pattern from the surface and sidewalls.

Although InGaN/GaN LEDs are commercially available, the LEE is still needed for further improvement. The limitation of LEE is mainly attributed to the low internal quantum efficiency (IQE) and light extraction efficiency [5]. The low IQE results from the high threading dislocation (TD) density of GaN films grown on a hetero-substrate [6]. The TD creates a diffusion pathway for metals that electrons injected into the active layer can leak through [7].

In order to further enhance the performance of LEDs, it needed to improve the IQE and to increase their light output power. Predecessors have done a lot of work, such as the research of multiple quantum well [8], phosphors [9], fluorescence crystals [10], and flip LED [11], etc. Now many researchers have focused their study on how to obtain better crystalline quality of GaN films on the sapphire substrates [12] and how to improve the quantum efficiency [13, 14].

Low-dislocation-density GaN from single cantilever overgrowth on deep trenched sapphire substrates has been reported earlier [15]. Enhancement of the external efficiency in GaN-based LEDs grown on patterned sapphire substrates has been achieved based on the effect of the optical reflection from the side edge of the etched sapphire [16]. Chang et al. also reported that it can enhance the intensity of electroluminescence (EL) when LEDs are grown on a shallow-trenched sapphire substrate [17].

In this paper, the substrates (PSS) and flat sapphire substrates (FSS) were researched to enhance LEE. GaN thin films and multi-quantum wells (MQWs) were grown on PSS and FSS by metal organic chemical vapor deposition (MOCVD). The stress of GaN thin films and the special reflection of PSS were systematically studied.

Materials and methods

The sapphire substrates’ diameter is 2 inches and the thickness is 430 μm, respectively. GaN thin films and MQWs were grown on the c-axis PSS and c-axis FSS by MOCVD. Trimethylgallium (TMGa), trimethylindium (TMIn), ammonia (NH3), bis-cyclopentadienyl (Cp2Mg), and silane (SiH4) were used as sources of Ga, In, N, Mg, and Si.

At first, the process of GaN thin films is as follows: firstly, the GaN buffer layer were grown at a low temperature of 566 °C and the thickness is 30 nm; then the undoped GaN films were grown at a higher temperature of 1020 °C and the thickness is 2.74 μm which is the second step. Schematic diagram of GaN thin films’ structure is shown in Fig. 1.

Fig. 1
figure 1

Schematic diagram of GaN thin films’ structure

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Then, the MQWs would be grown on the GaN thin films. At first, Si-doped GaN as N-type junction would be grown on undoped GaN thin films at the temperature of 995 °C, and the thickness is 2.95 μm. Secondly, GaN as the barrier with the thickness of 3 nm and InGaN as the well with the thickness of 12.7 nm would be grown on n-GaN successively at the temperature of 834 and 750 °C, respectively. This second process was repeated seven times; multi-quantum well had been created. At last, Mg-doped GaN as P-type junction would be grown. The growth process of Mg-doped GaN as P-type junction consists of two steps: Mg-doped GaN would be grown at 795 °C with the thickness of 25 nm, then Mg-doped GaN would be grown at 908.5 °C with the thickness of 70 nm. The schematic diagram of GaN-based light-emitting diodes’ structure is show in Fig. 2.

Fig. 2
figure 2

Schematic diagram of GaN-based light-emitting diodes’ structure

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PSS’s surface morphology was studied by SEM (VEGA\\TESCAN type scanning electron microscope produced by TESAN company in Czech). The crystal structure of GaN thin films and MQWs was characterized by X-ray diffraction. The optical properties of LED were measured by photoluminescence (PL) (FSL920).

Results and discussion

The surface morphology of FSS and PSS are shown in Fig. 3. The shape of PSS with the character of the pyramid is different from Wuu [18]. The Fig. 3a, c are the planforms of FSS and PSS, respectively. From the Fig. 3b, FSS has a good flatness and doesn't have any impurity. The pyramid has the similar height and bottom diameter. The average height and bottom diameter are 1.71 and 2.57 μm, respectively.

Fig. 3
figure 3

SEM image of FSS and PSS

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The crystal structure of GaN thin films was characterized by X-ray diffraction rocking curves. Figure 4 shows the (002) and (102) orientation’s X-ray rocking curves of GaN thin films on c-axis FSS and PSS. As shown in Fig. 4a, the full width at half maximum (FWHM) of GaN (002) plane on PSS and FSS are 0.101° and 0.102°, respectively, and the resolution of PSS and FSS are 2.3395 × 10−7 and 2.3211 × 10−7°/a.u, respectively. While the FWHM of (102) plane are 0.103° and 0.226°, respectively, and the resolution of PSS and FSS are 5.0920 × 10−6 and 2.4210 × 10−5°/a.u, respectively. No matter from the (002) or (102) plane, the films on PSS were better than FSS.

Fig. 4
figure 4

The double crystal X-ray rocking curves for symmetric (002) and (102) plane of GaN thin films on PSS and FSS

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Kaganner et al. [19] have recently published a model to correlate the dislocation density from the FWHM of the peak in X-ray diffraction using reciprocal space maps. In his work, it is shown that the FWHM is proportional to \( \sqrt {{\raise0.7ex\hbox{$\rho $} \!\mathord{\left/ {\vphantom {\rho d}}\right.\kern-0pt} \!\lower0.7ex\hbox{$d$}}} \). It is given in Eq. (1).

$$ \Delta q \propto \sqrt {{\raise0.7ex\hbox{$\rho $} \!\mathord{\left/ {\vphantom {\rho d}}\right.\kern-0pt} \!\lower0.7ex\hbox{$d$}}} {\text{or }}\Delta q = k\sqrt {{\raise0.7ex\hbox{$\rho $} \!\mathord{\left/ {\vphantom {\rho d}}\right.\kern-0pt} \!\lower0.7ex\hbox{$d$}}}, $$
(1)

where \( \Delta q \) is value of FWHM, ρ is the dislocation density (cm−2), and d is the total thickness (cm−2) of the thin films on the substrate. The rough equivalent of FWHM in Fig. 4a indicates that the dislocation density of GaN thin film on both PSS and FSS is all so roughly equivalent. But the peak diffraction angle of GaN thin films on FSS is 17.048°, which is closer to the standard value 17.281° than that of films on PSS (16.902°).

As shown in Fig. 4b, it can be known that the GaN thin film’s dislocation density of PSS is less than that of the FSS. But from the peak diffraction angle, the FWHM of MQWs on the PSS is 0.103° which is smaller than that on FSS (0.226°). So the MQWs on PSS has a better crystalline quality in the [102] direction than that on FSS.

The crystal structure of MQWs was studied by high-resolution X-ray diffraction (HRXRD). Figure 5 shows the HRXRD curves of MQWs on c-axis flat substrate and PSS. The strongest peak comes from the GaN. The peaks on the left side of the GaN peak come from the In0.1Ga0.9N/GaN MQWs with -1st, -2nd, -3rd, and -4th orders. The peaks on the right side of the GaN peak come from the n-AlN/n-GaN multilayer fringes of +1st, +2nd, and +3rd orders. The fourth satellite peak can be clearly observed for two samples, which indicated that the two samples have the similar smooth interface [20], so the quality of MQWs is wonderful on both substrates. It can be known that the IQE of MQWs is not very clearly improved after using PSS.

Fig. 5
figure 5

Measured HRXRD curves and simulation for c flat plane and PSS substrates

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According to the Bragg equation and Hoffman [21] formula, the relationship between the stress and the diffraction angle is shown in Eqs. (2)–(9):

$$ 2d_{hkl} \sin \theta = n\lambda $$
(2)
$$ \frac{1}{{d_{hkl}^{2} }} = \frac{4}{3}\frac{{h^{2} + hk + k^{2} }}{{a^{2} }} + \frac{{l^{2} }}{{c^{2} }} $$
(3)
$$ \varepsilon_{xx} = \frac{{a_{\text{epi}} - a_{0} }}{{a_{0} }} $$
(4)
$$ \varepsilon_{yy} = \frac{{m_{\text{epi}} - m_{0} }}{{m_{0} }} $$
(5)
$$ \varepsilon_{zz} = \frac{{c_{\text{epi}} - c_{0} }}{{c_{0} }} $$
(6)
$$ \delta_{xx} = c_{11 } . \varepsilon_{xx} + c_{12} .\varepsilon_{yy} + c_{13} .\varepsilon_{zz} $$
(7)
$$ \delta_{yy} = c_{12 } . \varepsilon_{xx} + c_{11} .\varepsilon_{yy} + c_{13} .\varepsilon_{zz} $$
(8)
$$ \delta_{zz} = c_{13 } . \varepsilon_{xx} + c_{13} .\varepsilon_{yy} + c_{33} .\varepsilon_{zz}, $$
(9)

where X‖[11\( \bar{2} \)0] GaN, Y‖[1\( \bar{1} \)00] GaN, Z‖[0001] GaN, ε xx represents X direction’s strain epsilon, ε yy represents Y direction’s strain epsilon, ε zz represents Z direction’s strain epsilon. δ xx represents X direction’s residual stress, δ yy represents Y direction’s residual stress, δ zz represents Z direction’s residual stress. In the Eqs. (7)–(9): c 11 = 3.9 × 1011 N/m2, c 12 = 1.45 × 1011 N/m2, c 13 = 1.06 × 1011 N/m2, c 33 = 3.98 × 1011 N/m2, and the [0001] plane δ zz  = 0.

According to the above equations, the residual stress of GaN thin films can be calculated which is shown in Table 1.

Table 1 The residual stress of GaN thin films
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In the Table 1, the negative value represents residual stress. So the residual stress of GaN thin films on PSS and FSS are compressive stress. Meanwhile, the stress in GaN thin films on PSS is larger than that on FSS. The cell volume of the GaN is: V = a2·c·sin120°, the values of PSS and FSS are 45.407 and 45.473 Å3, respectively. The values of FSS are larger than PSS, so the LED on the PSS would have higher density of electrons and holes. The stress in the GaN films on the PSS: δ xx  = −1.098 GPa, δ yy  = −0.132 GPa; FSS: δ xx  = −0.827 GPa, δ yy  = −0.100 GPa. The films on PSS had subjected to larger stress in the X and Y direction than FSS.

Therefore the density of electrons and holes in GaN thin films on PSS is higher too, the intensity of carrier diffusion becomes powerful, and thus the depletion layer becomes broad, so the band gap becomes larger. All of these maybe resulted in MQWs on PSS having a shorter wavelength and stronger luminous intensity compared to that on FSS. It can be confirmed by PL spectra of MQWs.

Table 2 gives the data of PL spectra to measure the optical performance of MQWs on PSS and FSS. In the Table 2, AVR represents the average, and STD represents the standard deviation. As we all know, the higher the luminous intensity, the better is the quality of MQWs, and also the higher is the light extraction efficiency. It is observed that the light intensity of MQWs on PSS is 4836.96 and that on FSS is 718.60 from Table 2; the light intensity of MQWs on PSS is almost seven times of that on FSS. Therefore the light extraction efficiency of MQWs is improved after using PSS. On the other hand, the peak wavelength and dominant wave of GaN-based light-emitting diodes on PSS are 447.22 and 452.47 nm, respectively while the peak wavelength and dominant wave of GaN-based light-emitting diodes on FSS are 466.58 and 469.79 nm, respectively. It means that the wavelength of GaN-based light-emitting diodes on PSS appeals blue shift compared to that on the FSS, which is consistent to XRD results in Fig. 4a.

Table 2 The data of PL spectra of MQWs
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On one hand, compressive stress is contributed to increase the luminous intensity on PSS, because higher density of electrons and holes would lead to larger amount of photons as a result of the recombination of electrons and holes. On the other hand, the increase of luminous intensity is also related with the special reflection system of PSS. Figure 6 is the reflection system of PSS and FSS.

Fig. 6
figure 6

The reflection system of PSS and FSS

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The refractive index of GaN layer, sapphire, and air are about 2.4, 1.7, and 1.0, respectively. From Fig. 6, the light easily occurs because the GaN surface is paralleled to the substrates (FSS), and the angle of total reflection is smaller than 25° (sinθ = n 1/n 2). Much of the light can’t reflect out from GaN surface, so the luminous intensity is lower. While the light propagation direction is changed uncertain for the GaN surface, it isn’t parallel to the substrates on the PSS obviously. So more photons would reflect out to the air, and it improved the light extracting efficiency of GaN-based LED on PSS.

Conclusion

GaN thin films and InGaN/GaN MQWs LEDs were grown by MOCVD. The residual stress of GaN thin films on PSS is δ xx  = −1.098 GPa, δ yy  = −0.132 GPa, the residual stress of GaN thin films on FSS is δ xx  = −0.827 GPa, δ yy  = −0.100 GPa. The residual stress is compressive stress, it results in the wavelength on PSS appeals blue shift compared the FSS, and IQE haven’t improved after used PSS. The compressive stress, special reflection system, and the better crystalline quality in the (102) plane of MQWs on PSS are contributed to its higher luminous intensity.