Blue LED Simulation

 

1. Introduction

It is very important to understand the operation and underlying physics of InGaN/GaN materials based electronic device in modern display industry such as flat-panel-display for back-light illumination and high efficiency light bulbs. For these reasons, the numerical device simulation is adapted to study the improvement of LED efficiency and to understand the basic operation of multiple quantum well LEDs.

But the main problem in device simulation is that there are so many unknown physical parameters which cannot be easily measured and is also still in debate regarding the actual polarization in the layer after screening by defects(dislocation or V-defect) and uncertain polarity which depends on substrate condition and growth condition.

The basic simulation study for GaN LEDs utilizes the conventional InGaN/GaN MQW (multiple quantum well) LED structure and then extends the efficiency limit of this conventional LED structure to further incorporate n+SPS (short-period-superlattice) for pure ohmic contact and current spreading layer for both n-side and p-side layers. Regarding active emission regions, we may consider various techniques to improve LED efficiency such as band-gap engineered cascade quantum well design or tunneling junction which will dramatically improve carrier injection into the quantum well regions and to increase efficiency by above 100%.

Despite the fact that all of these LED structure are basically based on the conventional LED structure, it is still not known about the correct simulation models and how to take into account experimental observation such as trap-assisted tunneling through trap states in the quantum well region, the amount of actual polarization, and polarity.

These motivate this article to study more details about basic forward characteristic of current injection and various effects on the forward voltage shift.

We will briefly explain the new capture-escape model for an accurate description of carrier distribution in the barrier, quantum well region and importance of polarity in AlN/GaN/InN material growth, and finally how to simulate the forward characteristic of LED operation.

 

2. Simulation Models

Practical approach to simulate LED device is to use the classical drift-diffusion solver with the self-consistent Schrodinger-Poisson solver for the quantum well bound state energy and then use this result to calculate spontaneous emission rate by developing effective mass approximation from k.p theory. We need to know that this approach is only valid in parabolic band approximation. With this assumption we simulated a conventional led with the following structure.

 

(1) Simulation LED Structure

0.4um pGaN – acceptor: 12x1018 / cm3

0.045um thick EBL (Alxsub>GaN(1-x) x=0.15) acceptor: 12x1018 / cm3

0.015um thick GaN spacer

8 pairs of InxGaN(1-x)/GaN well(x=0.17)

3um nGaN donor-5x1018 / cm3

* spacer and well/barrier have unintentionally doped donor level~2x1018 / cm3

 

(2) Band-offset Ratio

We studied band-offset effect on the carrier profile with drift-diffusion solution.

The default hetero junction band-offset ratio is 70% in ATLAS but in this case it shows very low electron carrier concentration in the first few quantum well/barrier regions (top in Figure 1.) even though the injected current density is 200mA/cm2. When we used 50% band-offset ratio it showed reasonable electron concentration and radiative rate in the wells (bottom in Figure 1.) within the drift-diffusion solution.

Figure 1. Carrier density profile with different band-offset ratio(left: 70% band-offet, right:50% band-offet) red color is electron concentration and blue color is hole concentration.

 

(3) Limitation of Drift-diffusion Simulation

From previous simulation results, even though we adjusted the band-offset to a lower value to get high electron concentration in the first few quantum well regions, the hole and electron profile in barrier regions is very low and abrupt at the interface. This is related to lower carrier penetration to barrier from well regions. We will discuss this in more details in section 2-4.

We studied the forward current behavior depending on the number of quantum well with drift-diffusion without capture-escape model. It shows that the IV shifts to higher forward voltage when the number of quantum well increases at fixed positive polarization and is related to increased series resistance of quantum well/barrier regions caused by low carrier density in the barrier regions. Also when we increase the polarization charge from 0 to 50% then it will also increase the forward voltage (Figure 2). This is unrealistic behavior as we can see in a real LED operation. So we can conclude that the drift-diffusion solution cannot alone explains current behavior very well.

Figure 2. Polarization effect on IV shift by polarization(left) and by the number of quantum well(right).

 

At this point, we need to take into account of more general carrier transport models to describe the accurate carrier dynamics in both the quantum well and barrier regions.

 

(4) Capture-Escape Model

It is well known fact that the conventional LED simulation can be easily done by classical drift diffusion with self-consistent quantum well Schrodinger-Poisson solver and spontaneous emission rate from multiple band kp theory. But the classical drift-diffusion approach have shown very high forward voltage even at low polarization, low series resistance(high doping), and show unrealistic carrier profile between barrier and quantum well. It is worse in case of multiple quantum well in that when the number of quantum well is increased then the IV curve tends to shift to higher forward voltage.

For these reasons, we recently developed a new capture-escape model which calculates the exact 2D bound carrier density in the well regions with detailed carrier capture from the bulk barrier and escape from the well into the barrier by adding probability of carrier capture-escape mechanism into the carrier rate equation.

The purpose of this article is to show the validation of new capture-escape model through comparison with experimental data and to give some guidelines for optimizing new models for real LED simulation.

General 3D carrier density rate equations are now modified into the following form.

n3D is bulk carrier density and Cn3D->2D is capture-escape rate from this bulk carrier to 2D carrier in the well.

(1)

(2)

2D carrier density rate equations in the well regions become

(3)

(4)

In the 2D in-plane quantum well regions, net recombination rate is the sum of spontaneous emission rate and total capture-escape rate.

Here, x,z plane is in quantum well in-plane and y is assumed to be normal growth direction.

The 2D bound carrier density becomes

(5)

The bulk carrier density which is used to calculate the current density in the drift-diffusion formalism is modified to consider this confined 2D carrier in the quantum well regions.

(6)

The capture-escape rate is calculated by the following equation.

(7)

Here, tn is capture time in the well. ( material well.taun=1e-12 s well.taup=1e-12 s )

To consider this additional 2D bound carriers, we also have to consider SRH recombination as well as Auger recombination in the well region. Atlas takes into account these recombinations in the quantum well regions including surface and interface trap recombinations.

material capt.augern=1e-31 capt.augerp=1e-31 ;Auger in the well

material capt.srh.n=1e-9 capt.srh.p=1e-9 ;SRH in the well

inttrap qwell s.i donor e.level=0.2 density=1e12 ;interface trap

interface s.i s.well.n=1e3 s.well.p=1e3 ;surface recombination

To activate the above recombinations we need to turn on the following model flags.

model capt.srh capt.auger well.capt well.inplane well.selfcon

In the above model, well.inplane consider 2D in-plane current density equation.

In the effective mass and parabolic approximation, the radiative recombination in quantum well is

(8)

where

r2D = mr/h2L2 is the two-dimensional density of states.

mr is a reduced electron-hole mass.

• nr is a material refractive index.

Im,n = (m|n) in a overlap integral of electron and hole wavefunctions.

Now, when we consider this new capture-escape model to the forward current dependence on number of quantum well as in section 2-3, the forward voltage shift is less pronounced as compared to Figure 2.

If polarization is further decreased by taking into account of more defect screening effect or is zero then, forward voltage change is less pronounced with increasing quantum well or no further forward voltage shift in 4QW case (Figure 3). The carrier-profile by capture-escape model well explain why forward voltage is lower than by drift-diffusion solution. The carrier has some probability to penetrate into barrier regions which is much higher than in the case of non-capture-escape model (Figure 4).

Figure 3. Forward current behavior by capture-escape model(left figure shows IV shift by the number of quantum well with +50%polarization of theoretical value and right figure shows less IV shift plot by the number of quantum well without polarization).

 

Figure 4. carrier distribution at 200A/cm2 ( left is without capture-escape model and right figure shows carrier distribution with capture-escape model).

 

The carrier profile without capture-escape model shows that electron concentration in the barrier region is far below 1x1010/cm3 in 1st barrier and hole concentration is decreased to below 1x10/cm3 at the 3rd barrier region. But the carrier concentrations in the barrier by capture-escape model are smoothly decayed from quantum well region and have 1x1014/cm3 in the first two quantum well/barrier pairs. We can conclude from this result that the capture-escape model accurately describes the exact carrier profile and so explains why drift-diffusion solution always produces high forward voltage when the number of quantum well is increased.

 

3. Material Growth and Trap-Assisted Tunneling (TAT)

So far we have used the positive polarization scheme, in which polarization is directed toward to bottom interface as in Ga-face growth condition. But polarity is still uncertain because it is very dependent on which substrate buffer layer is used and also on growth condition.

Figure 5. Polarity inversion by substrate and buffer layer.

The default polarity in Atlas uses the positive convention which is positive charge at the bottom interface and negative charge at the top interface. So direction of polarization is downward and built-in electric field is opposite direction. Figure 6. shows that polarity inversion significantly affects the forward voltage. The actual amount of polarization by screening effect from various defects(dislocation or V-defect) is very hard to estimate and optimize to fit the experimental forward current. Most simulation tasks so far normally use polarization between 20% and 80% from the theoretical value but it is a very broad range to adjust to fit forward current.

Figure 6. Forward current behavior by polarity (red: minus polarity, blue: positive polarity).

When we use polarization we should keep in mind that the polarization is globally scaled from theoretical calculation which is not true in actual polarization of each layer. To simulate more accurate polar-GaN LEDs it is very important to understand underlying polarization in each layer.

Also, if non-negligible traps in the quantum well exist, there are some possibilities that electron can tunnel from n-side to p-side region via trap-assisted tunneling mechanisms.

For this purpose, we simulated trap-assisted tunneling to see the effect on forward tunneling current in a single quantum well case.

Figure 7 shows forward current behavior caused by existence of traps in quantum well regions and trap-assisted tunneling effects in low bias regions. In a positive polarity case, we can see the conventional trap-assisted tunneling current at low bias range.

Figure 7. forward current behavior by donor trap and trap-assisted tunneling (red: without traps and TAT, blue: with trap only, light blue: traps + TAT). Top plot is negative polarization case and bottom plot is positive polarization case.

 

 

4. Band-gap Reduction by Ambient Temperature

We studied the ambient temperature effect on forward current because LED performance is significantly affected by the operation temperature. Normally, high efficiency and high power LED operates in fairly high temperature above 300K and band-gap reduction by temperature is very important to analyze forward current behavior. The default band-gap reduction model by temperature is Varshini model and model parameters are listed in Piprek’s book[5].

(9)

In negative polarity, low bias region is much more affected by temperature but in positive polarity whole region is increased by evaluated ambient device temperature.

Figure 8. Ambient temperature effect on forward current (top: negative polarity, bottom: positive polarity).

 

5. Validation

(1) Capture-escape Model

The new capture-escape model in Atlas was validated through experimental data from reference[1].

 

Figure 9. Simulation of forward current using capture-escape model (top figure is linear plot and bottom is log plot).

 

The forward voltage is 3.24V at 20mA and it is very close to the reported value in the reference.

The ~V/Rs region(ohmic) is well reproduced and at medium bias range it shows very close to the experimental data. Thereafter, red color is the experimental data and blue color is the fitted simulation data.

The power curve is fitted by assuming 80% extraction efficiency and effective mass is adjusted to fit luminious power from spontaneous emission spectrum (Figure 10).

 

Figure 10. IL curve fitting result to experimental data.

Figure 11 shows apparent Auger droop efficiency curve and Auger coefficient value of 2.4e-30 is adjusted to fit high current regions.

Figure 11. EQE plot (left is linear scale and right is log scale).

 

To fit the low and medium bias range SRH life time is most dominant fitting parameters which are well explained in ABC model and Auger coefficient is the most important to fit the efficiency droop curve in the high injection range. The external quantum efficiency (EQE) is defined as the ratio of the emitted number of photons to the number of injected carriers. From the simulation results, the total EQE ratio is obtained through dividing the total radiative rate in the quantum wells by injection current.

The internal quantum efficiency (IQE) is defined as Rrad /( Rrad + Rnon_rad).

The radiative rate (Rrad) is the total radiative rate which is mostly coming from quantum well regions and the non-radiative rate (Rnon_rad) is the sum of each SRH and Auger recombination rate.

Figure 12. carrier distribution (left) and each recombination rate in the quantum well by the capture-escape model.

 

Figure 13. Wall-Plug-Efficiency.

 

As we can see from Figure 13, the carrier profile is very different with drift-diffusion solution (Figure 1.)

The carrier concentration is much higher in barrier regions than the profile by the drift-diffusion solution.

Because the standard LED has AlGaN EBL layer to block electron current from n-side, there is small leakage current and most current flows into the quantum well and then recombines to give spontaneous or non-radiative rate. Some references define the external quantum efficiency as the following equation.

(10)

The injection efficiency() is the ratio of the total injected current into the quantum well to the total current. In this conventional LED example, the injection efficiency is assumed to be 1.0 and EQE equals to internal quantum efficiency.()

The wall-plug-efficiency(WPE) in Figure 13 is defined as ratio of the total output power(W) to the input power(I*V). There are many unknown physical parameters like SRH life time, Auger coefficients, and capture-escape time. The SRH life time and Auger coefficients are adjusted to fit the experimental data. The overall simulation results are quite well reproduced with the capture-escape model and physical parameters from the reference[1].

 

(2) Trap-assist tunneling(TAT)

Because trap-assisted tunneling is very important mechanism in low and medium bias ranges, we fitted to the experimental data[6] through Atlas trap-assisted tunneling model with the capture-escape approach. For this purpose, we took into account of mid-gap traps states in quantum well region where is the most probable path for tunneling via trap site. Because field enhancement term of TAT is strongly dependent on local field in SRH recombination rate, the most important fitting parameter is actual polarization charge which is also affected by well Indium composition, defects, and well thickness.

We used tunneling effective mass to fit the experimental data and Figure 14 shows reproducing the experimental forward current behavior except below 2.0V. According to the paper, difference below 2.0V could be due to heavy-hole tunneling. We need to study more about this another trap-assisted tunneling mechanism.

Figure 14. Simulation of Trap-assisted tunneling.

 

6. Summary

We can conclude that the new capture-escape model is a very accurate description model for exact carrier distribution on both barrier and quantum well . We developed a self-consistent solution from Schrodinger-Poisson solver for 2D bound carrier density in quantum well and bulk carrier density equation is linked by proper capture-escape rate equation to simulate the GaN based LED device. To simulate correctly EQE(or IQE) curve and efficiency droop, we have to consider the exact carrier density which will affect the radiative and non-radiative recombination rate in quantum well region through the capture-escape model. Theoretical approaches using k.p and capture-escape model are well incorporated into the recent ATLAS device simulation and it is a very accurate model for carrier dynamics in multiple quantum well design.

 

References.

  1. Blue light emitting diode exceeding 100% quantum efficiency, Joachim Piprek, Phys. Status Solidi RRL 8, No. 5, 424-426(2014)
  2. Simulation of light-emitting diodes for new physics understanding and device design, K. A. Bulashevich et al., Proc. Of SPIE, vol. 8278(2012)
  3. Consistent set of band parameters for the group-III nitrides AlN, GaN, and InN, Patrick Rinke et al. Physical Review B 77. (2008)
  4. Atlas User’s Manual, Silvaco , 2015
  5. Semiconductor Optoelectronic Devices, Introduction to Physics and Simulation, Joachim Piprek, University of California at Santa Barbara, Academic Press
  6. Trap- tunneling in InGaN/GaN LEDs: experiments and physics-based simulation, NUSOD 2014
  7. Trap-assisted tunneling in InGaN/GaN single quantum well light emitting diodes, M. Auf der Maur, et al., Applied Physics Letters. 105 (2014)