## 3 Results and Discussion
The enhancement factors are increased with an increase in the thickness of the spacing layer in the condition of a thickness of spacing \(\leq\)6 nm because the Forster energy transfer efficiency is decreased with an increase in thickness of the spacing layer. Moreover, the nonradiative decay of excitons is decreased when the thickness of the spacing between the EML and the GNPs is increased. In addition, the maximum enhancement factor is obtained when the Forster energy transfer efficiency is 50%. The relationship between the Forster energy transfer efficiency and the spacing distance can be expressed as follows [23]:  
\[E=\frac{1}{1+\left(\frac{R}{R_{0}}\right)^{6}} \tag{1}\]  
Where the \(E\) is the Forster energy transfer efficiency, \(R\) is the spacing distance between the EML and GNPs, and \(R_{0}\) is the Forster radius. The Forster energy transfer efficiency of can be obtained when the spacing distance between the EML and GNPs is equal to the Forster radius. The Forster radius can be expressed as follows [24; 25; 26]:  
\[R_{0}=0.0211\left(\varphi_{0}n^{-4}Jk^{2}\right)^{\frac{1}{6}} \tag{2}\]  
where \(R_{0}\) is the Forster radius, \(\varphi_{0}\) is the quantum yield of the donor, \(n\) is the refractive index of the medium, \(J\) is the normalized overlap integral of the donor and the acceptor spectra, and \(k\) is the orientation of the dipoles. We have investigated the values for the variables in Equation (2). Both the \(\varphi_{0}\) and the \(J\) are 0.22 and 1.16 \(\times\) 10\({}^{16}\), respectively, with an \(n\) of 1.35 and \(k^{2}\) of 0.667 to calculate the optimized value of \(R_{0}\). Therefore, the Forster radius is calculated as 6 nm by using Equation (2). Furthermore, the enhancement factor of the device with a thickness of spacing \(\leq\)4 nm is quite low because the Forster energy transfer efficiency of devices with a thickness of spacing \(\leq\)4 nm is nearly 100%. Figure 4: Enhancement factor and Forster energy transfer efficiency for different spacing between emission layer and GNPs. According to the relative studies [27], which are clearly researched for the important role of the buffer layer, the nonradiative decay process of the excitons in the device can be avoided by the addition of the NPB between the hole-transport layer and the emitting layer. We also find that the power efficiency of the device with the NPB buffer layer is higher than that of the device without the NPB buffer layer. At the same time, the devices with and without GNPs have a significant difference in luminance characteristics under different applied voltages [27]. In order to further research how strong the influence of the GNPs is, we conducted a proper comparison with pure PEDOT:PSS and NPB at the optimized thickness of 6 nm in Figure 5. Both Figure 5 and its inserted image show the difference with GNPs in the PEDOT:PSS layer and without by the luminance-voltage and power efficiencies-voltage curves, respectively. It is clear that the device with GNPs has higher luminance and power efficiencies than that of device without GNPs. When the applied voltage is below 5 V, the results for the luminance of the device under two conditions are not different. Additionally, there is a slight increase of the luminance of the device when we enhance the applied voltage from 5 to 6 V. Finally, we have found a surprising consequence that the luminance of the device is largely increased when the voltage reaches more than 6 V. In the insert in Figure 5, the results show that the device with GNPs is excellent for power efficiency. According to the investigation of polymer effects by time-resolved PL [28; 29], at the same time, the decay rate from the nonradiative process of excitons is about 4 ns, which is same as the result of doped Alq\({}_{3}\) organic semiconductors.