Influence of QW polarization field on carrier injection
Utilization of two TJs, each on every side of the active region, makes the BD LED structure symmetrical. However, there are some noticeable differences in the band alignment, evident even for unbiased structure in Fig. 2b. Indeed, the growth on (0001) GaN introduces an asymmetry in the arrangement of the built-in spontaneous and piezoelectric fields in the QW39. In the conduction band the left-hand side barrier of the QW is higher than the right-hand side, which can lead to electron escape from the QW to the right-hand side barrier. When it comes to the valence band it is the opposite: the right-hand side barrier is higher. Therefore, taking into account the direction of the carrier injection, the band alignment in the active region is more favorable for reverse bias (see Fig. 2f) and leads to high injection efficiency. In the case of positively biased BD LED, the barrier for electron escape from the QW is small (Fig. 2e) and the resulting injection efficiency is low. In addition, electrons, which overshoot the QW under forward bias, can recombine with holes outside of it giving rise to parasitic recombination. In this work, we decided to keep the structure symmetric, when it comes to the doping and composition of subsequent layers. This choice allows to directly link the differences in band alignment, due to existence of internal electric fields, with the electro-optical properties of BD LEDs under both DC biasing conditions. It should be emphasized that so far it has not been possible to study this effect for the same QW in the active region.
In fact, the positive and negative bias conditions of the BD LED can be directly compared to III-N LEDs grown on Ga-polar and N-polar GaN substrates, respectively. In such LEDs, the differences in the injection efficiencies for structures with various polarities have been widely discussed19–22, 40-42. In the case of Ga-polar structures, low injection efficiency and electron overflow above the QW is a commonly known issue. It occurs due to large difference in electron and hole mobility. This problem is obviated by introduction of an electron blocking layer (EBL) on the p-side right after the QW1. Heavily doped AlGaN:Mg layer is most commonly used as the EBL, which due to its higher bandgap, forms an energetic barrier for electrons. When the EBL is not present or is not working properly (e. g. under cryogenic temperatures) electrons that pass over the QW recombine in the p-type region. This leads to the parasitic recombination in the spectral range of λ = 420–430 nm22,42. In literature this peak is often identified as transition from the unknown deep donor down to Mg acceptor level43,44. In case of N-polar LEDs there is a favorable arrangement of built-in electric fields that provides high injection efficiency20–22, 40,41.
In view of these well-known properties of III-N LEDs, one can find that presented here electro-optical properties of BD LED under positive and negative biasing conditions correspond to Ga-polar and N-polar III-N LEDs, respectively. The injection efficiency is much higher for negatively biased BD LEDs, which leads to above 10 times higher optical power in this case. Moreover, for positively biased BD LED, electrons overflow above the QW and recombine with holes in the In0.02Ga0.98N:Mg layer (in between 235 nm and 270 nm in the band diagram shown in Fig. 2c) as evidenced by the registered parasitic peak at λ = 428 nm and λ = 419 nm for single and stack of two BD LEDs, respectively. The electron overflow problem, has been even more pronounced for pulse measurements presented in Fig. 4, where the intensity of parasitic luminesce follows current spikes, especially when BD LED was switched from negative to positive bias conditions. It is also possible that part of the electrons that overflow QW reaches the n-type layers through the top TJ, which could be the reason for lower operating voltages for positively biased BD LEDs. Considering the presented here BD LEDs as directly AC-driven light source, efforts should be made to increase the optical power obtained under positive bias. In principle, an AlGaN:Mg EBL placed on the right-hand side of the active region, should increase the injection efficiency and prevent electron overflow. However, under the negative bias, it could also provide a barrier for electrons that are injected into QW and thus disrupt this process. Therefore, in order to implement the EBL into the BD LED polar structure it is necessary to take a broader look at its band diagram.
It should be pointed out that the asymmetry in operation of presented here BD LEDs is solely due to the existence of built-in electric fields specific to III-N structures grown on polar substrates. Fabricating a BD LED on a non-polar GaN substrate or in a different material system, in which the issue of embedded piezoelectric fields does not exist, should give a symmetric light-current-voltage (LIV) characteristics, regardless of the current flow direction. Then, when powered directly by AC, one will get twice as much light from a single BD LED than from a single standard LED, which will be a step towards greater energy efficiency. It is worth to highlight the ability of stacking multiple BD LEDs during a single epitaxial process, in order to multiply the optical power obtained at the same current density. By growing a cascade of BD LEDs, high light output can be provided when operating at low peak current and high voltage, such as in an electrical grid25.
Electron transport through p-type layers in BD LEDs
For standard LEDs, electrons are injected into the active region directly from the n-type doped region. However, in the case of BD LED, electrons firstly have to pass through a thin p-type region placed below and above the active region for positive and negative biases, respectively. Electrons that flow though the p-type region, on the path to the QW, may cause the ionization of neutral magnesium acceptors (\({R}_{A}^{-}\)) following the formula \({e}^{-}+{N}_{A}^{0}\to {N}_{A}^{-}\), which is shown in Fig. 5. Additionally, there are two other processes that are always present in p-type region and occur between the acceptor level (NA) and the valence band (EV) (see Fig. 5). Neutral magnesium acceptors are thermally ionized that promotes holes to the valence band (\({R}_{T}\)), which is \({N}_{A}^{0}\to {N}_{A}^{-}+{h}^{+}\). In the opposite process ionized acceptors are neutralized by holes (\({R}_{A}^{0}\)). \({R}_{T}\) and \({R}_{A}^{0}\) are in thermal equilibrium under constant bias, providing a locally constant concentration of holes over time. However, if the rate of \({R}_{A}^{-}\) process is much larger than \({R}_{T}\) and \({R}_{A}^{0}\), then all of the incoming electrons will firstly ionize neutral acceptors and only then will reach the QW. Hence, it may be a source of unwanted loss of injected electrons and cause a delay in switching the device from negative to positive bias and vice versa.
The rates of \({R}_{A}^{-}\), \({R}_{T}\), \({R}_{A}^{0}\) processes can be determined form the following formulas43:
\({R}_{A}^{-}={C}_{nA}{N}_{A}^{0}n\) (1),
\({R}_{T}={N}_{A}^{0}{C}_{pA}{N}_{v}{g}^{-1}exp\left(-{E}_{A}/kT\right)\) (2),
\({R}_{A}^{0}={C}_{pA}{N}_{A}^{-}p\) (3),
where \({C}_{nA}\) is the electron capture coefficient (3.2x10-12 cm3/s)43, \({N}_{A}^{0}\) is the concentration of neutral magnesium acceptors, \(n\) is the concentration of electrons in the conduction band, \({C}_{pA}\) is the electron capture coefficient (5x10-7 cm3/s)43, \({N}_{v}\) is the effective density of states in the valence band, \(g\) is the degeneracy factor of acceptor level, \({E}_{A}\) is the ionization energy of magnesium acceptor, \(k\) is the Boltzmann constant, \(T\) is temperature, \({N}_{A}^{-}\) is the concentration of ionized magnesium acceptors and \(p\) is the concentration of holes in the valence band.
In general, considering all three processes, the kinetic equation describing the in-time changes of concentration of neutral acceptors can be written as:
\(\frac{d{N}_{A}^{0}}{dt}={R}_{A}^{0}-{R}_{T}-{R}_{A}^{-}\) (4).
However, while there is no electron in the p-type Eq. (4) reduces to:
\(\frac{d{N}_{A}^{0}}{dt}={R}_{A}^{0}-{R}_{T}\) (5).
We will now consider the situation, when a positive bias is suddenly applied to unbiased or negatively biased BD LED, following the experiment, to check if there is any significant delay of electroluminescence caused by \({R}_{A}^{-}\). In other words, the in-time stable Eq. (5) changes to Eq. (4). Now we need to check if the \({N}_{A}^{0}\) is still governed by thermodynamic processes \({R}_{T}\) and \({R}_{A}^{0}\). As an example, we will estimate their rates locally for a point in the middle of considered p-type region at 142.5 nm. We extract the carrier concentrations in the structure using One Dimensional Drift-diffusion Charge Control solver (1D DDCC) made by Y-R Wu45–47 and use constants in Eqs. (1–3) from Reshchikov et al.43.
Firstly, we calculate the rates of \({R}_{T}\) and \({R}_{A}^{0}\) for unbiased structure, in which no electron current is flowing through p-type region. Under these conditions \(p\), \({N}_{A}^{0}\) and \({N}_{A}^{-}\) were locally 1.0x1018 cm-3, 6.5x1019 cm-3 and 1.0x1018 cm-3, respectively, which gives the rates of \({R}_{T}\) and \({R}_{A}^{0}\) equal to 2.8x1029 cm-3s-1 and 5.3x1029 cm-3s-1, respectively. The order of magnitude of both process is the same, whereas small inequality of \({R}_{A}^{-}\) and \({R}_{T}\) values might results from the different carrier ionization energies assumed in the simulations (0.178 eV) and in article of Reshchikov et al (0.15 eV)43, which affects the calculated concentration of holes. Then, with applying the forward bias of 100 A/cm2 we get \(n\) of 1.94x1014 cm-3, which gives the rate of \({R}_{A}^{-}\) equal to 4.06x1022 cm-3s-1.
The above calculations show that the rate of \({R}_{A}^{-}\) is seven orders of magnitude smaller than \({R}_{A}^{0}\) and \({R}_{T}\). This means that the \({R}_{A}^{-}\) process is too weak to effectively ionize the neutral magnesium acceptors. \({N}_{A}^{0}\) does not change even if electrons are passing through p-type. Therefore, we do not observe any significant time delay, due to the electron-acceptor ionization process \({R}_{A}^{-}\), from switching the current direction of BD LED to the emission from QW. Otherwise, if the \({R}_{A}^{-}\) process were dominant, we should observe delays of hundreds of nanoseconds, which is the time needed to supply a matching number of electrons equal to the total number of neutral magnesium acceptors in the p-type region in between 120 nm and 165 nm.
Nevertheless, the relatively small value of \({R}_{A}^{-}\) process does not mean that it can be completely ignored, when it comes to the loss of electron current (\({j}_{loss}\)) passing through Mg-doped layers. Current losses can be estimated from the equation:
\({j}_{loss}=q{\int }_{{x}_{1}}^{{x}_{2}}{R}_{A}^{-}\left(x\right)dx\) (6),
where \(q\) is elementary charge, \({x}_{1}\) and \({x}_{2}\) are start and end point of considered p-type region (120 nm and 165 nm) and \({R}_{A}^{-}\left(x\right)\) is the rate of space depend electron-acceptor ionization process. From Eq. (6) we get \({j}_{loss}\) equal to 0.03 A/cm2, which is, however, negligibly small comparing to the total current of 100 A/cm2. From the above discussion, it is clear that the presence of p-type layers surrounding the active region has no significant impact on electron transport to the QW, which has been also confirmed by the time-resolved electroluminescence experiment. This makes BD LEDs feasible even in applications requiring fast switching times on the order of tens of nanoseconds.