Device Simulation on GaN‐LED Operating in Noncarrier Injection Mode for Performance Improvement by Enhancing the Tunneling Effect in Multiquantum Wells

Noncarrier injection (NCI) operation mode is an emerging driving mode for nanoscale light‐emitting diodes (LEDs) for application in nanopixel light‐emitting displays. However, the luminescence intensity of the NCI‐LED with traditional epitaxial structure is relatively low because of the absence of external carrier injection. Therefore, improving the luminescence intensity by optimizing the epitaxial structure of the LED is an important technical measure. In this work, the tunneling behavior of the NCI‐LED under reverse bias, which plays a key role in increasing the luminescence intensity, is studied through modeling and simulation. The dynamic variation of carrier concentration in each voltage cycle is studied to explore the working process of the NCI‐LED. Results show that the luminescence output of the NCI‐LED is highly sensitive to doping concentrations, and reducing the number of multiquantum wells can increase the probability of interband tunneling so as to improve dramatically the carrier number contributing to luminescence. This simulation work can deepen the understanding of the NCI mode and serve as an important guidance for the rational design of the NCI‐LEDs.


Introduction
Expanding from a simple display to a wider range of intelligent applications is the future development trend of display technology. [1][2][3][4][5] For this trend, nanopixel light-emitting display (NLED) is an emerging display technology to close the gap between display images and the real world; it has broad prospects for light field displays, eye computer interfaces, implantable displays, and other fields. [6] The core component of NLED is the nanoscale light-emitting diodes (nano-LED). [7][8][9][10][11][12] However, effective electrical connection between the electrode array and the nano-LED array is challenging. [13][14][15][16][17] Recently, an operation mode for nano-LEDs, namely, noncarrier injection (NCI) mode, [18][19][20][21][22][23][24] has been demonstrated. For LEDs operating in the NCI mode, the LED chips are sandwiched between insulating layers, and the periodic electroluminescence (EL) can be obtained under an alternating current (AC). Given the existence of insulating layers between the electrodes and the LED chip, external carriers cannot be injected into the LED chip, and only the inherent holes and electrons contribute to radiative recombination. Therefore, the nano-LED operating in the NCI mode has an ultrasimple structure without the requirement of precisely designed electrode bonding, which proposes a new technical route for the development of NLED.
Given that no carrier is injected from the external electrode, the working mechanism of NCI-LED differs from that of conventional LED. [25][26][27][28][29][30][31][32] How the inherent carriers in the device are transmitted under an AC electric field is unclear, and the direct physical pictures of the dynamic variation of carrier concentration are lacking. Additionally, given the existence of insulating layers, the device could only be operated under AC voltage with high voltage amplitude and high frequency. Given that only a small portion of the voltage is applied to the LED in the EL process, the luminescence intensity of the NCI-LED with traditional epitaxial structure is relatively low. [18,19] Therefore, the working mechanisms of NCI-LED must be understood, and the device's performance must be improved by optimizing the epitaxial structure. The increasing of reverse current can highly increase the EL intensity. [33][34][35] Although the introduction of an "electron pump" can be used to increase the reverse current, another strategy for EL enhancement must be developed. According to a previous simulation work, [23] the variation value of the energy band in the barrier region under the reverse bias is much larger than that of under the forward bias. It comes to us whether the interband tunneling behavior will occur in a strong reverse-biased state. Therefore, it is crucial to study the behavior of interband tunneling to improve the performance of NCI-LED.
In this work, modeling and simulation are used to explore the behavior of interband tunneling in NCI-LEDs first. Then, the dynamic distributions of carrier concentration in each voltage cycle are quantitatively presented, which is beneficial to understand the working mechanism of the NCI mode. The effect of doping concentration, which plays a key role on EL performance, is demonstrated. In addition, a structural optimization method to improve EL intensity is proposed, i.e., reducing the number of multiquantum wells (MQWs) to increase the reverse current. This work can deepen the understanding of the NCI mode and provide guidance for promoting NCI-LED performance.

Model Details
The NCI-LED model is established, as schematically shown in Figure 1a. In this model, the Al 2 O 3 layer/LED/Al 2 O 3 layer is sandwiched between two electrodes and the AC voltage is applied to the electrodes. The diameter of the LED is 500 nm with the conventional epitaxial structure ( Table 1). The device structure from top to bottom is composed of 100-nm-thick Al 2 O 3 insulating layer, 200-nm-thick p-GaN layer, 20-nm-thick Al 0.15 Ga 0.85 N electron blocking layer, 117-nm-thick multiquantum wells (MQWs) region, 1000-nm-thick n-GaN layer, and 100-nm-thick Al 2 O 3 insulating layer. The MQWs' structure is composed of seven 3-nmthick In 0.15 Ga 0.85 N quantum wells which are embedded in eight 12-nm-thick In x Ga 1−x N barriers. The indium content of the top three barriers is 0 and that of the last five barriers is gradual (x = 0.01-0.05). The detailed device epitaxial structure is demonstrated in Table 1.
Given the existence of insulating layers, the radiative recombination is attributed to the inherent carriers in the NCI-LED. Thus, the finite element model of the NCI-LED is different from that of conventional LED. The device model is constructed by an electrostatic induction module and a semiconductor module (Figure 1b). The function of the electrostatic induction module is to transfer the applied voltage to the semiconductor terminal through the Al 2 O 3 insulating layer. The normal electric displacement field at the insulator-semiconductor interface can be given as where V g is the potential at the electrode-insulator interface, V is the potential at the insulator-semiconductor interface, d ins is the thickness of the insulator, ins is the relative dielectric permittivity of the insulator, 0 is the permittivity of free space, and ⃗ n is the outward normal of the semiconductor domain. V g with applied potential V 0 is given by where Φ m is the work function of the metal, and E f is the offset in the Fermi level. The condition of charge conservation is necessary for the Al 2 O 3 layer, which can effectively prevent external carriers from being injected into the device. Therefore, the electron and hole currents flowing into the insulator must be zero where ⃖⃖ ⃗ J p and ⃖⃖ ⃗ J n are the current densities of the hole and the electron, respectively. For the semiconductor module, different from the conventional LED, the boundary condition at the p/n-GaN terminal of NCI-LED is electrostatic induction instead of ohmic contact. A detailed introduction to the semiconductor part is presented in the Text S1 in the Supporting Information. Its function is to receive the electric signal transferred by the electrostatic induction module, and the induced potential at the LED terminals (V LED ) is defined as An experience model of NCI-LED working mechanism is proposed (Figure 1c,d). As shown in Figure 1c, the forward bias causes inherent electron diffusion from n-GaN to MQWs. [18][19][20][21] A similar process is performed on the hole in the p-GaN. The amount of electron movements in the positive half cycle is defined as N e-forward . N e-forward is divided into two parts, namely, diffusion electrons without recombination (N e-diff ) and recombination electrons (N e-recon ). The electrons (defined as N e-reverse ) moving in the negative half cycle can be divided into two cases, as shown in Figure 1d. In the case of small reverse bias, the reverse bias drifts the electrons from p-GaN to n-GaN (N e-drift ). Thus, N e-reverse is attributed to the electric-induced drift process. In the case of large reverse bias, the interband tunneling occurs in NCI-LED. It should be noted that the interband tunneling refers to the electrons in the valence band of p-GaN can tunnel into the conduction band of n-GaN. Consequently, N e-reverse contains not only N e-drift but also the number of tunneling electrons (N e-tunnel ). To increase the EL intensity, N e-tunnel under the reverse bias should be increased to increase the number of electrons for radiative recombination.

Behavior of Interband Tunneling
As a result, studying the tunneling behavior in MQWs under reverse voltage is crucial to improving the device performance. The working state of the NCI-LED in a voltage cycle is shown in Figure 2a. The forward field causes the diffusion of majority of carriers and the subsequent radiative recombination in MQWs. Given the small forward resistance of LED, the applied voltage is almost distributed to the insulating layers. The reverse field drifts the carriers to their original state. LED presents a highimpedance state due to unidirectional characteristics. [36] Thus, the voltage applied to the LED under the reverse bias increases, which is different from the conventional LED. The behavior of interband tunneling occurs in MQWs with the increase in the reverse voltage, which affects EL. A detailed introduction to the interband tunneling effect is presented in Text S2 in the Supporting Information.
Therefore, the detailed energy band variation of the MQWs (△E MQW , inset of Figure 2b) under different voltage amplitudes is studied, as shown in Figure 2b. In the positive half cycle (0.0-0.5 μs), the value of △E MQW shows a trend of decreasing initially and then increasing. In the negative half cycle (0.5-1.0 μs), the value of △E MQW increases initially, followed by a decrease. The △E MQW variation under the reverse voltage is much larger than that of the forward voltage, which is different from the LED operating in injection mode. Furthermore, the value of △E MQW is further increased with the increase in applied voltage. Thus, the number of electrons for recombination can be increased by introducing the tunnel effect.
On the basis of the analysis of △E MQW , the tunnel generation rate of the NCI-LED is presented in Figure 2c. The tunnel generation rate increases with the increase in the applied voltage, and its value reaches the maximum at the peak voltage. Quantitatively, the maximum values of tunnel generation rate at 25, 50, 75, and 100 V are 1.6 × 10 −13 , 7.4 × 10 14 , 2.5 × 10 22 , and 1.1 × 10 24 cm −3 s −1 , respectively. Thus, the tunneling probability of the device increases with the increase in the applied voltage. The maximum emission rates (MER) and peak currents (I peak ) of the devices with and without tunneling effect at different applied voltages are demonstrated, as shown in Figure 2d. As the applied voltage increases, the MER and I peak show an upward trend. The initial voltage of the tunneling behavior affecting the EL intensity is 75 V. Compared with the model without the tunneling effect, the MER and I peak are amplified by 0.008 and 0.023 times, respectively, at 75 V and are amplified by 0.079 and 0.112 times, respectively, at 100 V.
To study further the effect of interband tunneling on the NCI-LED, the simulated time-resolved EL when a sinusoidal voltage with an amplitude of 100 V is presented, as shown in Figure 2e.  Figure 2f. When considering interband tunneling, the electron concentration in the n-GaN is increased. Thus, more carriers can be injected into the MQWs, maximizing the probability of radiative recombination.

The Mechanism of Carrier Transport
Giving a quantitative changing process of electron concentration within one cycle is of great value for revealing the working mechanisms of the device and further optimizing the device's performance. Given that the movement of electrons and holes is similar, only electrons are considered to simplify the discussion. As shown in Figure 3a, when the forward voltage is increasing, electrons in the n-GaN layer diffuse to MQWs and combine with holes. Thus, the electron concentration in the n-GaN terminal decreases to form a depletion region, and an induced electric field from n-GaN to p-GaN is generated, which is different from the conventional LED. [37][38][39] The consumption of electrons in the n-GaN terminal is the largest at the peak voltage. The minimum electron concentration at the terminal boundary is about 2 × 10 12 cm −3 . When the forward voltage is decreasing (Figure 3b), due to the existence of the induced electric field, the electrons gradually move to the n-GaN terminal. Thus, the electron concentration in the n-GaN terminal is increased.
As the reverse voltage increases (Figure 3c), electrons continue to be drifted to n-GaN. Therefore, the electron concentration in the n-GaN terminal is continuously increased. Finally, the depletion region in the n-GaN terminal disappears, and the accumulation region is formed, resulting in an induced electric field from p-GaN to n-GaN being formed again. The maximum electron concentration accumulated at the terminal boundary is about 1.2 × 10 19 cm −3 . As the reverse voltage decreases (Figure 3d), the electrons in the accumulation region gradually move far away When the applied voltage reduces to 0 V, the state of the electron concentration varies from the initial state. This is because the carrier inside the device cannot completely restore the initial state based on the unidirectional characteristics of LED.
To have an in-depth understanding of the working status of the device, the charge variation of the electrode on the n-GaN side within one cycle is quantitatively demonstrated, as shown in Figure 3e. In the positive half cycle, the number of electrons decreases initially, followed by an increase. The maximum value of the charge at the peak voltage is −1.15 × 10 −15 C (the minus means that the number of electrons in the n-GaN region is decreased), that is, the depletion region at the n-GaN terminal is maximized. The number of electrons shows a trend of increasing initially and then decreasing under the reverse bias, as shown in Figure 3e-II region. This process corresponds to the accumulation of electrons in the device. The maximum value of the positive charge is +5.22 × 10 −16 C (the plus means that the number of electrons in the n-GaN region is increased).
The current through the NCI-LED with and without the tunneling model in one cycle is further presented in Figure 3f. The amount of carrier movements is a critical parameter that affects the luminous characteristics of the device, which is quantitatively reflected by the amount of total charge (N c ). The peak current with the tunneling model is slightly larger than that without the tunneling model. Additionally, the total number of charge (N c+ ) flowing through MQWs is equal to the total number of charge (N c− ) in the negative half cycle. In the tunneling model, the value of N c+ and N c− is 5.3 × 10 −9 C. In the nontunneling model, the value of N c+ and N c− is 5.1 × 10 −9 C. Therefore, the tunneling electrons contribute to the recovery of the initial state, which is beneficial to the EL process of the next voltage cycle. Given the long length of the MQWs, the tunneling probability of the device remains relatively low. In other words, the performance gain caused by the interband tunneling effect in LED with traditional structure is small.

Effect of Doping Concentration on Device Performance
On the basis of the simulation results of the NCI-LED, luminescence intensity is determined by the inherent carrier concentration, that is, how many carriers can be provided for the next cycle. Figure 4a shows the operating characteristics of devices with different doping concentrations. With the increase in the doping concentration of p/n-GaN, the number of carriers generated by tunneling behavior gradually increases. [40] However, the number of carriers diffused into MQW in the positive half cycle first increases and then tends to be constant. Given that the NCI-LED is equivalent to an electronic system with a capacitor-LED-capacitor structure, [41,42] the total number of carriers that can be driven remains constant with the same applied voltage. In other words, with the increase in p/n-GaN doping concentration, an extreme value for the amount of charge induced by the insulator (equivalent to capacitor) is achieved. To understand clearly the influence of drift electrons on device performance in a negative half cycle, the relationship between MER/N c and the carrier generation rate in the space charge region is studied, as presented in Figure 4b. The MER increases rapidly with the carrier generation rate increasing from 0 to 1 × 10 24 cm −3 s −1 , and then the increasing rate decreases gradually. The N c+ and N c− increase linearly with the carrier generation rate. The carriers generated in the space charge region contribute to the accumulation of carriers at the device terminals. Additionally, the appropriate doping concentration is crucial to device performance because the generation of electrons in the space charge region is determined by the doping concentration of p/n-GaN.
As shown in Figure 4c, the MER and N c at different doping concentrations of p-GaN are presented. MER and N c first increase as the hole concentration of the p-GaN increases from 1 × 10 17 to 7 × 10 18 cm −3 and then remains unchanged as the hole concentration of the p-GaN further increases from 7 × 10 18 to 1 × 10 23 cm −3 . The maximum value of MER is 5.6 × 10 9 s −1 . When the doping concentration of p-GaN reaches 1 × 10 19 cm −3 , a dynamic equilibrium of carrier movement is achieved. Thus, the carrier utilization rate is maximized. Additionally, the ratio of N c− to N c+ decreases as the hole concentration of the p-GaN increases from 1 × 10 17 to 7 × 10 18 cm −3 . The reason for this phenomenon is that the induced electrical field is enhanced with the increase in doping concentration, resulting in a slower increase rate of N c− . Figure 4d shows MER and N c at different doping concentrations of n-GaN when the p-GaN doping concentration is 7 × 10 17 cm −3 . MER and N c first increase as the electron concentration increases from 1 × 10 17 to 1 × 10 19 cm −3 , and then the stable state can be obtained as the hole concentration of the n-GaN increases from 1 × 10 19 to 1 × 10 23 cm −3 . The maximum value of the MER is 5.2 × 10 9 s −1 when the n-GaN concentration is 1 × 10 19 cm −3 . Comparing the two doping methods reveals that the hole concentration has a greater influence on the performance of the device.
Based on the simulation results, the doping concentration of p/n-GaN is one of the important factors affecting the NCI-LED performance. First, due to the existence of the insulating layer, the EL intensity is limited by the number of internal carriers. With the increase in p/n-GaN doping concentration, the number of carriers moving into the MQW can be increased, which makes the probability of radiation recombination increase. In addition, the increase in doping concentration of p/n-GaN can narrow the width of band gap based on Zener tunneling theory. Thus, the electron interband tunneling can be realized by finely adjusting the doping concentration of p/n-GaN.

Effect of Different Numbers of QWs on Device Performance
The optimal doping concentration is a key parameter for improving the performance of NCI-LED. However, the performance gain brought by changing the doping concentration is not great, and the disadvantage of low power efficiency is inevitable. At high doping concentrations, the quality of LED might be degraded as a result of the increased dopant diffusion. [43][44][45] Moreover, the increase in defect-related nonradiative recombination with increasing doping concentration. According to the dynamic change of △E MQW (Figure 2b), the device structure optimization based on the interband tunneling effect is feasible, as shown in Figure 5a. In NCI mode, the gain brought by the tunneling behavior of LED with traditional epitaxial structure is also small because the complex functional layer structure makes the length of the band gap in the energy band longer. Thus, on the basis of However, the values of MER and I peak further decrease with the increase in doping concentration, as shown in Figure 5d,e. The MER of LED-C and LED-D show a trend of decreasing initially and then increasing with the decrease in the number of QWs, which is different from LED-A and LED-B. The reason for this trend is that no tunneling behavior occurs in NCI-LEDs with more than four QWs. Then, as the number of QWs further increases from five to seven, the electrons and holes can be effectively confined in the luminescent layer so that the number of carriers participating in radiative recombination is increased. As the number of QWs decreases from four to one, the MER values of LED-C increased by 0.13, 0.53, 1.35, and 2.48 times, respectively, in comparison with the NCI-LED with seven QWs, as shown in Figure 5d. The I peak values of LED-C increase by 0.12, 0.19, 0.28, and 0.40 times, respectively. As shown in Figure 5e, with the number of QWs decreasing from four to one, the MER values of LED-D increase by 0.03, 0.20, 0.33, and 0.45 times, respectively, in comparison with the NCI-LED with seven QWs. The I peak values of LED-D increase by 0.12, 0.18, 0.24, and 0.29 times, respectively.
According to the simulation results, the performance of NCI-LED can be improved by reducing the number of QWs to improve the tunneling probability. In addition, the probability of interband tunneling should be highly sensitive to the doping concentration of p/n-GaN in NCI-LED. As the doping concentrations increase, MER shows a trend of increasing initially and then decreasing in the same device structure because the impedance of the device decreases with higher doping concentrations so that the voltage applied to the LED decreases under the reverse bias. Therefore, two conditions of a thinner active layer and proper doping concentration are essential for the design of NCI-LED.

Conclusion
In summary, the detailed dynamic variation of carriers and the structure optimization method for NCI mode are successfully demonstrated by using finite element simulation. The interband tunneling behavior occurs in NCI-LED under reverse bias due to the considerable energy bending near the PN junction, which contributes to the intensity of EL. In addition, EL is found to increase with doping concentration due to the enhancement of interband tunneling, and especially, the maximum intensity of EL increases by 9.8% and 8.4% by increasing the doping concentration of p-GaN or n-GaN, respectively. Finally, the tunneling probability can also be improved by reducing the number of QWs. The stronger luminescence intensity occurs in the device with a single QW layer, and the performance gain caused by the interband tunneling behavior in the device with the doping concentrations of p-GaN and n-GaN are 7 × 10 18 and 5 × 10 19 cm −3 respectively is largest. This work can serve as important guidance for the rational design of NCI-LEDs.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.