Figure 2. Illustration of the vertical LED energy band diagram including current flow and electron–hole recombination processes (A—defect-related recombination, B—photon emission, C—Auger recombination). Multiple quantum well (MQW) active regions typically consist of InGaN wells and GaN barriers. The electron blocker layer (EBL) is typically made of AlGaN.

The energy efficiency of the LED semiconductor chip is equivalent to the so-called wall-plug efficiency (WPE) which gives the ratio of light power P emitted from the chip to electrical power IV injected into the chip (I—injected electron–hole current, V—bias) as illustrated in Figure 1. Different energy loss mechanisms reduce the WPE, which are distinguished by splitting the WPE into separate components:

First, the injected electrons lose some energy on their way to the QWs, which is accounted for by the electrical efficiency ELE = hν/qV (hν—photon energy, q—electron charge). The remaining external quantum efficiency EQE = WPE/ELE is the ratio of emitted photon number to injected number of electron–hole pairs. The conversion of electron–hole pairs into emitted photons is accompanied by carrier losses and by photon losses: EQE = IQE × LEE. The light extraction efficiency LEE accounts for photon losses due to internal light reflection and absorption. The internal quantum efficiency IQE is the fraction of the total current that contributes to the desired photon generation inside the QWs. It can be further separated into the injection efficiency IE (current fraction that enters the QWs) and the radiative efficiency RE (fraction of QW carriers that recombines radiatively).

While WPE can be measured, the analysis of energy loss mechanisms depends mainly on modeling and simulation. For more than a decade, various models have been published for each GaN-LED efficiency component. These models can be separated into carrier transport models, QW recombination models, and light extraction models.

2. Carrier Transport Models

Drift-diffusion models based on the semiconductor transport equations are commonly employed for simulating the carrier movement of electrons and holes in GaN-LEDs. Carrier mobilities are crucial material properties in such models, besides recombination coefficients which are covered in the next section. Together with the free carrier density, the mobility determines the conductivity of each semiconductor layer. The low hole conductivity of Mg-doped III-nitride semiconductors typically dominates the LED bias. Due to the large Mg acceptor ionization energy, high Mg doping densities are required which in turn limit the free hole mobility by impurity scattering. Advanced models for carrier transport parameters have been developed; nevertheless, the material quality of fabricated devices is often best represented by experimental data, especially in the case of alloy layers.

Several groups employ Monte-Carlo transport models to track the path of individual carriers using tailored scattering models, partially in combination with drift-diffusion models. In particular, the movement of high-energy (hot) electrons has been investigated this way.

Quantum mechanical transport models based on the Non-Equilibrium Green’s Function (NEGF) method have been published more recently. Such models are especially valuable in the investigation of tunneling and carrier leakage processes. Simplified tunneling models have been implemented in drift-diffusion simulations to investigate multi-quantum barriers, trap-assisted interband tunneling, or LED structures with tunnel-junction cascaded active regions.

3. Quantum Well Carrier Recombination Models

Electrons and holes injected into the quantum wells of the LED can be consumed by different recombination mechanisms (cf. Figure 2):

1. Crystal defect related recombination

2. Radiative recombination

3. Auger recombination

Accordingly, the simple and popular ABC model adds up these different contributions to the total recombination rate R(n) = A·n + B·n² + C·n³ (n—QW carrier density; A, B, C—material parameters) and the net current density injected into the QWs j(n) = q·d·R(n)·(d—total active layer thickness). The radiative efficiency is then given by

However, the actual QW carrier density n is typically unknown so that different ABC parameter sets lead to identical efficiency characteristics RE(j). In fact, the QW carrier density is known to be non-uniform across a multi-quantum well active region and may even vary inside each QW due to current crowding and/or QW non-uniformities. Various groups proposed modified ABC models, e.g., to account for a reduced active volume, inhomogeneous carrier distribution, electron leakage, photon quenching, multi-level defects, trap-assisted Auger recombination, built-in fields, or temperature effects. In any case, ABC models serve as an important bridge between experiment and theory. More detailed models for each of the recombination mechanisms are discussed in  Reference [1]^[1].

4. Light Extraction Models