Simulation of Carrier Injection Efficiency in AlGaN-Based UV-Light-Emitting Diodes

Numerical simulations of carrier transport in aluminium gallium nitride based ultraviolet light emitting diodes (UV-LED) are performed in order to understand injection efficiency for light sources in the deep ultraviolet. With our simulator, calibrated with experimental data from a 265 nm UV-LED, quantum efficiencies have been analyzed. The maximum internal quantum efficiency (IQE) of 30% consists of the product from radiative recombination efficiency (RRE) of 60% and carrier injection efficiency (CIE) of 50%. It is found that poor hole injection into the active region and a surplus of electrons limit both efficiencies, and leads to significant electron leakage into the p-side. This leakage is bias dependent, and has a minimum at maximum IQE. Further simulations show that distributed polarization doping (DPD) could improve carrier injection efficiency.


Simulation of Carrier Injection Efficiency in
AlGaN-Based UV-Light-Emitting Diodes Gregor Hofmann, Anton Muhin , Norman Susilo , Friedhard Römer , Tim Wernicke, Michael Kneissl , Fellow, IEEE, and Bernd Witzigmann , Senior Member, IEEE Abstract-Numerical simulations of carrier transport in aluminium gallium nitride based ultraviolet light emitting diodes (UV-LED) are performed in order to understand injection efficiency for light sources in the deep ultraviolet.With our simulator, calibrated with experimental data from a 265 nm UV-LED, quantum efficiencies have been analyzed.The maximum internal quantum efficiency (IQE) of 30% consists of the product from radiative recombination efficiency (RRE) of 60% and carrier injection efficiency (CIE) of 50%.It is found that poor hole injection into the active region and a surplus of electrons limit both efficiencies, and leads to significant electron leakage into the p-side.This leakage is bias dependent, and has a minimum at maximum IQE.Further simulations show that distributed polarization doping (DPD) could improve carrier injection efficiency.Index Terms-Efficiency, gallium nitride, LED, light emitting diode, light source, modeling.

I. INTRODUCTION
L IGHT emitting diodes (LEDs) provide an efficient way to convert electrical to optical power.Aluminium gallium nitride (AlGaN) LEDs produce ultraviolet (UV) radiation with wavelengths as short as 210 nm [1].UV emitters will improve environmental, medical and industrial application with their compactness and efficiency.Those applications include curing, sterilization and water purification [2].Despite the recent advancements in AlGaN research, the external quantum efficiency (EQE) of UV-C LEDs is not comparable to visible LEDs yet [3].The EQE, calculated by the product of carrier injection efficiency (CIE), the radiative recombination efficiency (RRE) and the light extraction efficiency (LEE) can be improved by increasing any of these efficiency factors.With the recent experimental evaluation of the CIE and RRE [4], simulations can complement the improvement of the efficiency not only by theoretical understanding but by developing models towards a predictive character.The investigation of the CIE from low to high current densities and the relation between the CIE and the

II. OUTLINE
We first calibrate our simulation model to experimental data from a UV-LED emitting at 265 nm [4].These data include electroluminescence (EL) spectra and the optical power at different current densities.From those, the iIQE, the CIE and the RRE can be extracted.With the calibration, several parameters in the model can be determined, which are the carrier recombination times, the inhomogeneous broadening parameter [5], the carrier mobility and an effective polarization.Subsequently, the quantum efficiencies and losses will be discussed.

III. SIMULATION SETUP
The geometry of the UV-LED is modelled in the TCAD environment Sentaurus Workbench by SYNOPSYS [6].The calculations are carried out using a carrier transport model developed in [7].It solves the drift and diffusion equations and the recombination processes in the quantum wells (QWs), with a special treatment of carrier transport in the QWs.They act as scattering centers for the continuum carriers [8].The system of equations can be solved in 1-to 3-dimensions.For the simulations presented here, a 1-dimensional setup is used.Radiative recombination and spectral luminescence is computed only in the QWs by solving the Schrödinger equation based on a 6-band k • p theory for wurtzite structured semiconductors [9], [10].Luminescence is calculated by spectral integration of transitions, with homogeneous and inhomogeneous broadening models as described in [5].
In Fig. 1, the device structure is shown.The layer sequence follows the LED heterostructure grown by metalorganic vapourphase epitaxy.Starting from the n-side contact, a 100 nm thick n-type Al 0.68 Ga 0.32 layer doped to 4 × 10 18 cm −3 is followed by the active region (AR) containing three 1.4 nm thick Al 0.53 Ga 0.47 QWs with adjacent Al 0.65 Ga 0.35 quantum barriers (QB) of 5 nm thickness.The QB are n-doped to 4 × 10 18 cm −3 as well.The AR contains an intentionally undoped 10 nm thick electron blocking layer (EBL) with an Al fraction of 86% between the last QB and the Al 0.76 Ga 0.24 hole injection layer (HIL).The device structure is completed by a p-GaN layer doped to 6 × 10 19 cm −3 .The first, bottom n-layer of the device model is thinner compared to the UV-LED in the experiment.This doesn't change the outcome of the calculations.The layers are considered to be strained and lattice matched to AlN.The aluminium contents, the thicknesses and the doping concentration can also be taken from the block diagram in Fig. 1.In order to simulate light emission at 265 nm, the aluminium content in the QWs is fine-tuned to match the experimental data.
The doping profile in Fig. 1 follows data from secondary ion mass spectrometry (SIMS) of the device.The doping concentrations N D and N A describe the donor and acceptor density, respectively.Si acts as the main donor and Mg as the main acceptor species.The dopants are incorporated with an alloy dependent ionization rate, using an activation model [11].Activation depends on the local carrier density following a Shockley model, and the activation rate includes enhancement due to proximity and field effects [12].The energy level of Si is 30 meV in GaN and 65.1 meV in Al 0.68 Ga 0.32 N. The energy level of Mg is 245 meV in GaN and 630 meV in AlN [1], [13], [14], [15].For the ternary alloys, the energy levels are interpolated linearly.Also, for the Mg doping we take into account that residue hydrogen atoms deactivate the capability of Mg to provide holes [16].
Basic material parameters are taken from literature [17], unless noted otherwise.At room temperature, the bandgap energy for GaN is 3.437 eV and the bandgap energy for AlN is 6.1 eV.We choose a global bandgap bowing parameter of b = 1.1 eV [18], [19].The electron mobility μ e is modelled by the Arora model [20].The hole mobility μ h is assumed to be constant across the device heterostructure.The simulation temperature is 300 K. Recent pyroelectric material parameters for wurtzite materials are used [21].The spontaneous and piezoelectric polarization value is scaled with an effective polarization parameter p eff to account for alloy fluctuations and surface states [22].
The threading dislocation density (TDD) is set to N T DD = 1 × 10 9 cm −2 in the device [4] and acts as non-radiative recombination term [23].Another non-radiative recombination terms is the Shockley-Read-Hall (SRH) recombination at point defects.Hereby, we use recombination times τ SRH e for electrons and τ SRH h for holes, which are independent of the aluminium content.Additionally, we assume non-radiative Auger-Meitner recombination [24], [25], [26] using calibrated data from a previous work [7].The scattering parameters for the carrier capture model into the QWs [7] have been set to τ e/h = 5/1 ps for electrons and holes, respectively.

IV. COMPARISON TO EXPERIMENT
For the calibration of the parameters, the carrier recombination times τ SRH e and τ SRH h , the inhomogeneous broadening parameter σ IHB , and the hole mobility μ h are adjusted to match the experimental data.Experimental data for the electroluminescence (EL) spectra and optical power versus current density are available, from the devices published in [4].The measurements have been taken in pulsed mode, and the efficiencies taken from mounted LEDs.The parameters have been chosen as follows in order to calculate the results in this paper: the defect related SRH carrier recombination times are set to τ SRH e = 3 ns and τ SRH h = 5 ns, which is the inverse of the A-parameter in a rate equation model.These values are close to PL characterization of similar structures, where a non-radiative lifetime of τ nr = 3 ns has been extracted at room temperature [27].The inhomogeneous broadening parameter is chosen as σ IHB = 100 meV, and the hole mobility set to μ h = 2 cm 2 /V/s.The effective polarization at the hetero interfaces has been set to p ef f = 50%, which accounts for alloy fluctuations and charged impurities within this model.

A. EL Spectrum
The EL spectra in Fig. 2 shows the simulated (lines) compared to the measured data (dots) for a variation of current densities.The main parameter is the inhomogeneous broadening which is set to σ IHB = 100 meV, close to the values obtained in [5].Compared to the device sample sheet, the aluminium content in the active region is increased by 3% in order to match the peak wavelength.The low energy side of the spectrum shows some deviation, and requires future refinement of the model.The simulated spectra are normalized to the peak of the experimental spectrum, measured at J = 100 Acm −2 .In the simulation, only the TE polarization of the emission is plotted, which represents the measured data.The simulated degree of polarization (DoP), which consists of the ratio (I T E − I T M )/(I T E + I T M ) has been calculated to 82%, which is in good agreement to experiment [28].The simulations replicate the negligible peak shift with increasing current density showing that neither band filling nor screening of polarization fields affect the emission wavelength in the investigated current density range.Due to the n-doping in the barriers the electron concentration in the quantum wells is almost constant and ten times larger than the hole density for the investigated current densities.As the electrons govern band filling and screening the emission wavelength Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.Fig. 2. Simulated spectra (line) compared to a EL measurements (dots, [4]) for the current densities shown in the legend.The simulated intensity is normalized to the peak of the J = 100 Acm −2 spectrum, and the simulated DoP is 82%.
stays constant.The hole densities govern the recombination rates causing the increasing emission intensities.

B. Electro-Optical Efficiency
The device EQE η EQE associates the optical power density P to the current density J.The EQE can be expressed as follows: Here q is the electron charge, E ph is the photon energy averaged over the LED emission spectrum, and η LEE is the light extraction efficiency (LEE).The LEE η LEE was calculated by calibrated ray tracing simulations as described in [29] and [4], and is used in our simulation as well.Additionally η RRE exp was determined by a modified ABC-model fit in [4] allowing to calculate the peak RRE and subsequently the peak CIE.Therefore we can compare the calculated efficiencies to the experimentally derived efficiencies Our simulator calculates the quantum efficiencies η CIE and η RRE directly from the microscopic model.The CIE is defined by the fraction of carriers that recombine inside the QW, and is obtained from where J QW the current density injected into the QWs of the LED.The RRE is evaluated by Here, J rad is the current density from radiative recombination in the QW.The IQE is calculated by The IQE is then Equation ( 6) can be compared to the experimental efficiency data in (2).In Fig. 3, the simulated measured efficiencies are shown for current densities up to 100 mA/cm 2 .At J = 25 Acm −2 , the IQE maximum reaches 30%, and drops for higher values.
This efficiency drop at higher optical power is still being investigated [4], [7], [30], [31].analysis purpose, the EQE η EQE can also be plotted versus the normalized optical power p, where p = P P max,IQE (7) is calculated by the optical power P divided by the optical power at peak IQE P max,IQE .This transfer characteristic is shown in Fig. 4. The peak IQE is reached at p = 1, corresponding to J = 25 Acm −2 for both the experiment and the simulation, as seen in Fig. 3.We assume η LEE to be independent from the optical power density p and we use (1) to calculate the EQE.In summary, good agreement between experiment and simulation has been obtained by with our model.

V. CARRIER TRANSPORT IN SIMULATION
Based on the calibration of the simulation model to experimental quantities in Figs. 2, 3 and 4, internal device physics such as the carrier distributions can now be analyzed.Comparing the simulation data (blue) to experimental data (green) [4].Fig. 5. Simulation of band structure and carrier densities at different current densities J = 1, 25, 100 Acm −2 .The background color represents the layers, (see Fig. 1).The thick black lines are the conduction/valence band energies, and the blue/red lines the electron/hole densities.

A. Carrier Distribution
In the QWs, a strong imbalance of the carrier species is present.At the IQE maximum, the electron density reaches n e = 1.8 ± 0.2 × 10 19 cm −3 while the hole density only reaches n h = 8.2 ± 0.9 × 10 17 cm −3 .Also, with rising current, the QW electron density stays nearly constant, and only the hole density rises: from J = 1 Acm −2 to J = 100 Acm −2 the hole density rises from n h = 1.7 ± 0.8 × 10 16 cm −3 to n h = 2.7 ± 1.0 × 10 18 cm −3 .Clearly, a lack of holes in the active region prevents efficient UV-LED operation.
A major factor for the lack of holes in the QWs is the high ionization energy of Mg acceptors in AlGaN.Fig. 6 shows the ionized dopant density in the device for donor N * D and acceptor N * A densities.At the n-side, the donors are ionized to at 45% of the impurity density.The n-layers therefore possess a low resistance and good electron injection in the active region.At the p-side, despite a high doping concentration of acceptors, only a tiny fraction < 5% of the acceptors provide free holes and contribute to the overall carrier transport.The HIL with an Al content of 76% and Mg concentration of 1 × 10 19 cm −3 is ionized by 0.03%, which leads to the low density shown in Fig. 5. Achieving a high density of mobile holes in AlGaN devices is ongoing research and still a technological challenge [32], [33].Another issue is the hetero interface between the last thick barrier layer and the EBL with a high Al content of 86%.The positive polarization charge attracts electrons (similar to the channel in a HEMT structure), pulling down the energy bands.This leads to a high barrier for the injection of holes, and to strong recombination close to this interface due to the high electron density.
Within the three QWs, the carrier distribution is relatively homogeneous.At each QW interface, polarization charges create an electric field in the barriers and wells, which tilts the bands.In the barriers, this field introduces an additional electrostatic potential spike of approx.60 meV between the wells.In the current design, the barriers are doped with Si (n-type), and at LED operation, the ionized immobile donors have a positive charge.As a consequence, the bands in the barriers are curved, which facilitates electron transport through the MQW structure.

B. Quantum Efficiencies
The maximum IQE at 30% consists of the product of the RRE η RRE ≈ 60% and the CIE η CIE ≈ 50%, with the latter being strongly current dependent (see Fig. 3).Both contributions are now described in more detail.

1) Radiative Recombination Efficiency:
The RRE describes the ratio of radiative recombination to total recombination for the carriers in the QWs.In Fig. 3 the RRE versus current starts at 58% and drops to 50% at current densities of 200 A/cm 2 (not shown).In the low current regime, the SRH rate R SRH e,h is the main contributor of non-radiative recombination.The large Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.imbalance of electron to hole density leads to a high electron SRH rate, as many electrons can recombine non-radiatively.They lack a corresponding hole state for radiative bi-molecular recombination.The SRH rate at lowest current densities is also influenced by trap assisted tunneling, as shown in [34].Additional calculations (not included here) show that the overall RRE has strongly depends on the hole SRH rate, as it limits the bimolecular radiative recombination.In Fig. 7 effective B-and C-coefficients are extracted from the simulations (with QW1 on the n-side and QW3 on the p-side).The extraction of the coefficients is done by taking the respective recombination rate, calculated from the microscopic simulation, and, in the case of the B-coefficient, dividing the rate by the product of electron and hole density.The same procedure is applied for the Auger-Meitner C-coefficient.In a rate equation model, the coefficients would be constant at all densities or currents.In our simulation, they are dependent on current density due to phase space filling effects [35] and change of wave function overlap between the QW states.In Fig. 7, the B-coefficient decreases and the C-coefficient increases at high current densities.The latter is due to the increased wave function overlap in the QWs.The decrease of B is from phase space filling, a combination of non-parabolic band dispersion and use of Fermi-Dirac carrier distributions.The decrease of the RRE with current follows the decrease of the B-coefficient.In general, the values of B-and C-coefficient are in good agreement with atomistic calculations in [25].On the other hand, fitting the measured efficiencies to ABC-models result in larger coefficients for B and C (see e.g.[4]), which can be explained by the unipolar approximation and missing CIE in the ABC model.

2) Carrier Injection Efficiency (CIE):
The CIE determines how many carriers injected into the semiconductor enter the QWs.For the calibrated UV-LED structure, the CIE can be Fig. 8. Simulation of the electron current density J e reaching the p-contact, the hole current density J h reaching the n-contact and the overall CIE for a variation of the total current density J = J e + J h .
extracted by measuring the minority currents close to the AR, which represent the leakage currents from the QWs.Even in an ideal case, the leakage is not zero, as any pn-diode with finite thickness exhibits minority currents.Fig. 8 plots the CIE and the respective leakage currents in the LED for electrons and holes versus current density.At low currents, the electron leakage is almost 100%.This is due to high barriers at the p-side between the GaN, HIL and EBL, and the low conductivity of these layers, which prevent any significant hole injection into the device (see also Fig. 5).The UV-LED is almost unipolar, with electron current flowing from the n-to the p-contact.At these low currents, there is however a small hole current leading to electron and hole density in the QWs, and it is possible to generate RRE of close to 60%.
Increasing the potential difference between the contacts results in a larger hole current through the p-doped AlGaN layers, and the hole density in the QWs leads to higher radiative recombination.Hence, the CIE rises to a maximum of 51%.At higher currents, electron leakage sets in again, as the QWs are saturated with electrons, resulting in the IQE efficiency droop.Parameter variations in the simulations show that the CIE can be increased by increasing the hole mobility or the p-dopant levels in the HIL to values of p dop = 1 × 10 20 cm −3 .Both measures are difficult to realize technologically, in addition to being contradictory, as higher impurity density harms the mobility in general.These results underline the importance of improving hole injection into the active region.

VI. DISTRIBUTED POLARIZATION DOPING (DPD)
One way to improve the hole injection into the active region is to employ layers with graded aluminium fractions, which leads to immobile volume charges due to the polarization gradient in the polar crystal.Details can be found in [36], [37], [38].
Here, the HIL is replaced by a nominally undoped layer with aluminium grading from x = 86% to x = 65%, creating an immobile polarization charge density of n pol = 2.5 × 10 18 cm −3 within the thickness of 25 nm, and a mobile hole density of the same magnitude.In the simulation, this is calculated by taking the divergence of the local polarization as preprocessing step.
For comparison, the reference structure possesses an HIL with Mg doping of p dop = 1 × 10 19 cm −3 , and Al content of 76%.Fig. 9 shows the band structure and carrier densities at a current density of J = 25 Acm −2 , with solid lines being the DPD case and dashed lines the calibrated reference structure.For the DPD structure, the hole density in the HIL reaches the charge density induced by the polarization gradient, which leads to a layer with low resistance.As a consequence, the active QW hole density rises from p = 1.5 ± 4.0 × 10 17 cm −3 (Mg doped) to p = 1.5 ± 0.5 × 10 18 cm −3 (DPD).The DPD layer leads to a doubling of the hole density and a much reduced inhomogeneity of the carrier distribution in the MQW structure.
The improved hole injection modifies the efficiencies of the UV-LED structure.In Fig. 10 the current dependent CIE, RRE and IQE are plotted, again comparing the calibrated structure (red curves) versus the DPD structure (blue curves).Due to the improved conductivity at the p-side, the CIE is almost constant between 90% at low current densities to 70% at current densities above J = 10 Acm −2 .This leads to a substantial improvement of the IQE, which is around 40% at typical operating current densities.RRE decreases more strongly at high currents due to phase space filling.At low currents, the hole injection bottleneck disappeared, as much less voltage is necessary to supply holes to the active region.

VII. CONCLUSION
Analysis of the carrier injection efficiency (CIE) in AlGaNbased UV-LEDs using a carrier transport simulation has been presented.The model has been calibrated with experimental data from a UV-LED emitting at 265 nm.It has been found that a low hole density in the p-doped layers by Mg doping with high activation energies is the main challenge.Lack of holes in the active region and n-doping of the barriers leads to a surplus of electrons, and their non-radiative recombination reduces the radiative recombination efficiency.In addition, high barriers in the valence band at the p-side prevent hole injection at low current densities, leading to high minority currents of electrons at the p-contact, resembling a unipolar device.This is the main reason for the strong current dependence of the IQE observed in experiments.As a solution, distributed polarization doping can increase the IQE maximum from 30% to above 40%, which should be considered in further designs.
Conflict of Interest: The authors declare no conflict of interest.
Data Availability Statement: The data that support the findings of this study are available from the corresponding author upon reasonable request.

Fig. 1 .
Fig. 1.Simulation model of the device.The alloy composition, thickness and the doping concentration of each layer is shown.The active region is modelled with a background doping concentration of N A = 1 × 10 16 cm −3 and N D = 4 × 10 16 cm −3 − if not stated otherwise in the diagram.

Fig. 5
Fig.5shows calculated electron and hole density distribution for the current densities at J = 1, 25, 100 Acm −2 , with J = 25 Acm −2 being the IQE maximum.In the figure, the device layers are indicated by the shading of the background.

Fig. 4 .
Fig. 4. Dependency of the EQE on the normalized optical power parameter p.Comparing the simulation data (blue) to experimental data (green)[4].

Fig. 6 .
Fig. 6.Simulation of ionized donor and acceptor density at a current density J = 25 Acm −2 .The blue line indicates the ionized donor N * D and red the ionized acceptor density N * A .The percentages show relative magnitude of ionized dopants in the respective layers.

Fig. 7 .
Fig. 7. Effective B-and C-coefficient as calculated from the microscopic simulation (left axes), and RRE for the 3 QWs (QW1-3 from n-side to p-side).

Fig. 9 .Fig. 10 .
Fig. 9. Band energy plot and carrier densities for an LED with with DPD standard doped design.

)
Fig. 3. Efficiency diagram of a simulated 265 nm LED for varying current densities.The yellow curve is the average RRE from the QWs.Red is the CIE.Blue is the IQE.Black and grey circles indicate experimental values [4].