## 1 Introduction  
GaN and AlN alloys have attracted more and more attention as candidate materials for realizing ultraviolet (UV) optoelectronics [1; 2; 3; 4; 5]. As potential substitutes for the traditional mercury UV light source, AlGaN-based deep UV light-emitting diodes (DUV-LEDs) have attracted more and more attention due to their potential applications in many fields, such as solid-state lighting, medicine, and biochemistry. In the past few decades, the significant research efforts into the development of III-nitride UV LEDs have resulted in LED operation over a wide range of UV wavelengths from 210 nm to 400 nm. Recently, [PERSON] et al. summarized the recent advances in UV materials and devices and gave guidance to further development and applications [1]. Nevertheless, the external quantum efficiency (EQE) of such a device decreased significantly as the wavelength decreased. Particularly when the wavelength was less than 300 nm, the EQE and output power were far lower than those of their visible counterparts. There are several factors responsible for the lower EQE and power, such as the lack of high-quality AlN substrate or an AlGaN template with low threading dislocation density, the difficulty in obtaining high conductivity in p-type layers [6; 7; 8], and the excessive self-heating effect of these devices under direct current operation [2; 3]. In addition, the large spontaneous and piezoelectric fields in group III nitrides will result in the tilted band structure diagrams of multiple quantum wells (MQWs) [9; 10] and reduce overlap of electron and hole wave functions, which will decrease the internal quantum efficiency of DUV-LEDs. Due to the lack of high-quality AlN substrate, a high-quality AlN template on sapphire is usually used for DUV-LEDs. It is well known that the weak surface migration of Al adatoms on the growth front limited the improvement of crystal quality. Therefore, many growth techniques have been developed for high quality AlN growth [11; 12; 13; 14; 15]. It has been demonstrated that high temperature annealing could significantly improve the AlN crystal quality [11]. By increasing the growth temperature, high-quality AlN thick films were obtained by homemade high temperature hydride vapor phase epitaxy [12]. [PERSON] et al. revealed the mechanism of different initial conditions on the quality of AlN and got high quality AlN on sapphire substrate by a \"two-step\" method [13]. In addition, nano-patterned sapphire and AlN/sapphire templates were used for high-quality AlN growth [14; 15]. As the crystal quality increased, the efficiency can be increased effectively [16]. Besides the increase in crystal quality, the use of core-shell-type AlGaN/AlN MQWs on AlN nanorods can also significantly increase the photoluminescence efficiency due to the decrease in dislocation density, the large active volume and the increase of light extraction efficiency [17]. In addition to the above-mentioned factors, electron overflow also exists in these devices. The electron overflow not only decreases the EQE and forward-voltage characteristics [18; 19], but also results in a sub-band parasitic peak [20; 21]. Therefore, the suppression of electron overflow is absolutely favorable for the optical property of the devices. Generally, an electron blocking layer (EBL) between the active region and the p-type layers was used to suppress the electron overflow. There are seldom works to study the effect of quantum well (QW) number on the electron overflow in DUV-LEDs. It has been reported that with the increase in InGaN QW number from 5 to 7, the external quantum efficiency (EQE) was increased by 30.4% [22]. However, when the QW number increased to more than 15, the photoluminescence intensity of InGaN/GaN MQWs decreased significantly due to the relaxation of an accumulated strain through the dislocations induced by an increase in the total thickness of the MQWs [23].