Light emission at photon energies higher than the injected energy, qV, was first observed in semiconductor materials more than 60 years ago [1–3]. This phenomenon is the result of thermoelectric pumping of the carriers by heat supplied from the crystal lattice at finite temperatures. The possibility of using the thermoelectric pumping effect to achieve net cooling, i.e. > 100% wall-plug efficiency (WPE), by the conversion of heat energy to light emission was recognized and subsequent thermodynamic analyses supported its validity [4,5]. In 2012, the first demonstration of an LED exhibiting ≥ 100% WPE was published for a mid-IR device operating at extremely low bias voltage, V [6]. The observation of > 100% WPE is even more remarkable considering the poor efficiency of these devices at operating conditions near the onset voltage [6]. Although a breakthrough for the field of LED physics, the technological application of this approach is limited due to the inappreciable light output powers (picowatt levels) that can be emitted at such low voltage.

A different operating point using wide band gap III-nitride LEDs may enable ≥ 100% WPE while maintaining technologically relevant light output powers. Violet and blue-emitting III-nitride LEDs are the basis for solid-state white lighting and already exhibit high peak WPE (> 70%) at current densities in the range of 1 A/cm² – 5 A/cm². Light output powers at milliwatt levels or higher (depending on the chip area) are easily produced at these current densities.

This work summarizes the requirements and prospects for operating nitride LEDs at ≥ 100% WPE based on an assessment of the electrical and optical performance of several commercial and state-of-the-art nitride devices and in the context of the recent literature. We propose operating current densities of a few A/cm², which is near the peak EQE, to capitalize on the high efficiencies and useful output powers that are already obtainable there. We provide suggestions for redesign of the LED epitaxy and package considering those operating conditions.

The wall-plug efficiency (WPE) of an LED is defined as the fraction of the input power (IV) that is converted to optical output power and can be expressed per injected electron-hole pair as the product of three terms:

The IQE is defined as the fraction of the injected electrons in the LED that generate photons in the active region, and the LEE is defined as the fraction of photons emitted from the active region that escape to free space. The product of the IQE and LEE is the external quantum efficiency (EQE), which is defined as the fraction of photons produced in the LED active region that escape to free space. All three of these efficiencies have maximum values of 1.

The voltage ratio V_p/V is typically less than unity at operating conditions because it accounts for series and spreading resistance, which increase V compared to V_p. However, V also accounts for the thermal promotion of carriers to energies greater than their electrical injection energy (thermoelectric pumping), which decreases V compared to V_p. Thus, it is possible for V_p/V to exceed unity at finite lattice temperatures. Indeed, this phenomenon is readily observed when operating conventional nitride LEDs at low bias. It is also a necessary condition for operating an LED at > 100% WPE.

In nitride LEDs operated at room temperature, the applied voltage V often remains below the photon voltage V_p until current densities in the magnitude of several A/cm². Figure 1 shows the room temperature V_p/V vs. current density curves for several nitride devices including UCSB-processed commercial epitaxial material (“UCSB + Vendor A” and “UCSB + Vendor B”) as well as a fully packaged commercial device measured at UCSB (“Vendor C”). Two high performance commercial LEDs from Nichia Corporation [7] (Narukawa et al. 2010) and Soraa [8] (David et al. 2016) that were described in the literature are also included in Fig. 1. The value for V_p for each curve was calculated from the peak wavelength at 1 A/cm² or from the reported peak wavelength for the literature results. See Appendix for further details on the materials, processing, and packaging for the devices in this figure.

 

Fig. 1 Dependence of the room temperature V_p/V on current density for several InGaN-based devices. UCSB + Vendor A and UCSB + Vendor B devices are commercial blue material emitting at 448 nm and 449 nm respectively, processed and packaged at UCSB and tested at 22 °C. Vendor C is a fully packaged commercial device emitting at 460 nm tested at UCSB at 20 °C. David et al. 2016 is a 435 nm emitting device measured at 27 °C [8], and Narukawa et al. 2010 is a 444 nm emitting device measured at an unspecified room temperature [10].

Download Full Size | PDF

The devices in Fig. 1 have similar room temperature voltage at ~1 A/cm². The shaded area indicates the region for V_p/V >1 and where $\ge$ 100% WPE could occur if the EQE is sufficiently high. It has been proposed that the characteristic polarization-induced electric fields, which create triangular potential barriers in multi-quantum well structures of basal plane nitride devices, may enhance the thermoelectric pumping [9] which is observed at low current densities.

The region where V_p/V crosses unity in Fig. 1 corresponds to current densities in the range of 3 A/cm² - 20 A/cm². Peak room-temperature EQE values for blue-emitting nitride LEDs often occur at 1 A/cm² - 10 A/cm² [7,11–13], which means that the peak EQE often falls at a point where V_p/V > 1. In those cases, the peak WPE exceeds the peak EQE.

Substituting $EQE=IQE\times LEE$ into Eq. (1), it can be shown that the WPE can equal or exceed 100% only when the gains in the voltage term are large enough to compensate for the losses in the EQE. This condition is shown in Eq. (2). Practically, this could be achieved in a device by targeting either or both of the following characteristics: (i) Ultra-low V, (ii) Ultra-high EQE.

In the first demonstration of > 100% WPE LED operation in 2012, Santhanam et al. achieved the requirement in Eq. (2) by operating an In_0.15Ga_0.85As_0.13Sb_0.87 mid-IR LED ($\lambda$ = 2.42 μm) at extremely low voltage V = 70 μV [6], and thus at vanishingly low current from the diode equation:

At decreasing bias, the IQE diminishes as the SRH non-radiative recombination mechanism dominates progressively more over the radiative term. However, at extremely low bias such that V < kT/q, the active region excess electron and hole concentrations Δn and Δp become negligible compared with the equilibrium electron and hole concentrations (i.e., those given for the unbiased diode). Thus, the net recombination rate is constant and finite in this regime, and the IQE becomes constant and independent of further diminishing bias [6]. This effect has a strong band gap dependence because equilibrium carrier density falls exponentially with increasing band gap. The LEE is also approximately independent of current at low bias (i.e. no current crowding effects), thus EQE also becomes approximately constant in the region where V < kT/q. Further reducing the voltage enables the WPE to increase proportionally with the voltage ratio, V_p/V.

Operation at elevated temperatures can also further decrease V, while increasing the equilibrium carrier concentration. A temperature of 135 °C enabled the demonstration in [6]. The highest reported WPE to date is 8000 ± 1700% for an infrared In_0.15Ga_0.85As_0.13Sb_0.87 LED emitting at 2.4 μm, that produced just under 8 pW of output power when heated to 167 °C [14]. The electroluminescent cooling phenomenon has been achieved at room temperature in the near-equilibrium low-bias regime by utilizing narrower bandgap InAs and InAsSb-based LEDs, emitting at 3.4 μm and 4.7 μm, respectively [15]. The highest room temperature output power achieved for 100% WPE LEDs was approximately 10 pW for a 3.4 μm-emitter [15].

Figure 2 contrasts the relationships among the WPE, EQE, V_p/V and the measured optical output power between the 135 °C mid-IR device in [6] and a room temperature blue-emitting nitride device in [16]. In both LEDs, the EQE has a single peak corresponding to the point at which the radiative recombination dominates in the IQE equation (Eq. (4)). The mid-IR device has two peaks in the WPE over a wide span of output powers. The local maximum in WPE near the milliwatt range is at overall poor efficiency (< 1%), however at extremely low bias, the WPE exceeds 100% and continues to rise as the EQE saturates at a value of only 0.03%, while the voltage continues to drop. This high WPE is at the expense of output power, which becomes nearly negligible (69 pW).

 

Fig. 2 Relationship among EQE, WPE, V_p/V, and emitted optical power for the 135 °C mid-IR LED measurement data reported in [6] compared with the room temperature blue LED measurement reported in [16]. The mid-IR WPE curve has two peaks, the conventional peak near the EQE peak at moderate power, and the other at extremely low power where the EQE saturates as V_p/V continues to rise.

Download Full Size | PDF

For the nitride LED, the peaks in EQE and WPE in the milliwatt range are already very high, near 80%. The wide band gap of the III-nitrides precludes their useful operation at extremely low bias due to their much lower equilibrium carrier concentrations, even considering high temperatures. Thus, for both technical and technological reasons, the optimal operation point for high WPE in nitride LEDs will be near the peak EQE at injection levels of a few A/cm². A tradeoff between efficiency and output power will still exist, although much more minor in the nitride case, because typical operating conditions for general illumination applications target ~35 A/cm² at the expense of a few percent loss resulting from efficiency droop [17].

The nitride voltage ratio in the milliwatt range is also very close to unity, which limits the amount of efficiency boost that can be captured from thermoelectric pumping to a few percent. Thus, at room temperature, an EQE > 90% would likely be required even for a device with negligible parasitic voltages.

It is possible, as in the narrow band gap case, that higher operating temperatures could be leveraged to improve the performance. This is possible only if the rise in V_p/V is at least as fast as the decline in the EQE resulting from increased SRH recombination at higher temperatures. A recent experiment has demonstrated thermoelectric pumping at 3 A/cm² for an unpackaged$(20\overline{2}\overline{1})$InGaN/GaN single quantum well LED emitting at 450 nm [18]. Upon heating up to 615 K, the device exhibited negligible drop in peak WPE, while the peak moved to higher current densities, resulting in a nearly fourfold increase in output power compared with the room temperature performance.

A similar phenomenon was also demonstrated at Soraa, Inc. in 2015 for a packaged violet (415 nm) LED measured at 25 °C and 85 °C. This device achieved a very high WPE of 84% at both temperatures [19]. These results demonstrate that thermoelectric pumping in nitride devices can be used to mitigate the effects of thermal droop for a heated package. However, WPE of 100% or higher for nitride LEDs, or for any LED near the onset bias voltage has yet to be achieved. It has been pointed out that the thermoelectric pumping effect is limited for bias voltages near V_p and is also reduced for wider band gap semiconductors [8,20,21]. This is because the thermal pumping per carriers is of the order of kT and it leads to a relative increase of V_p/V or kT/V, which diminishes with increasing bandgap.

An analysis by David et al. [8] evaluated the limit of V_p/V based on an analytical injection model for an idealized LED with uniform carrier injection and no carrier leakage. They calculated that for nitride LEDs, the maximum V_p/V for current densities of a few A/cm² is ~108%, meaning that the minimum EQE to reach 100% WPE must be ~92%. This represents an outstanding challenge for the field. A recent analysis by Xue et al. 2017 gives similar values for the efficiency limit of visible light emission intensities in the few W/cm², which is approximately the minimum power density that would be required for practical applications [20].

Figure 3 illustrates the performance space in EQE vs. V/V_p that would lead to the observation of > 100% WPE and electroluminescent cooling. The dashed diagonal line where EQE = V/V_p is the threshold where WPE = 100%, and above that line is where operation would occur at WPE > 100%. The same nitride devices from Fig. 1 are also shown here. The UCSB-processed devices used our recent low loss designs for high LEE to maximize the peak EQE [16], which occurred at current densities of 3 A/cm² – 6 A/cm².

 

Fig. 3 (a) Dependence of EQE on V/V_p for several state-of-the-art devices. The dashed black line indicates the threshold for > 100% WPE operation. (b) Temperature-dependent behavior for the Vendor C device between 22 °C and 80 °C stage temperature. Increasing stage temperature results in a decrease in the LED operating voltage as well as a decrease in peak EQE.

Download Full Size | PDF

The LEDs in Fig. 3(a) are blue-emitting multi-quantum well nitride devices on sapphire substrates with the following peak emission wavelengths: Vendor A (448 nm), Vendor B (449 nm), Vendor C (460 nm), Narukawa et al. 2010 (444 nm), except for David et al. 2016 (435 nm), which was grown on a freestanding bulk GaN substrate. The implicit variables are the current and carrier densities, which both increase with applied voltage. This figure illustrates that top performing devices are still far from the threshold for > 100% WPE. To reach this threshold, the efficiency curves must move upward (increasing EQE), leftward (decreasing voltage) or both. In the case of the > 100% WPE mid-IR and IR devices demonstrated at MIT, operation was in the extreme lower left corner of the graph in Fig. 3(a)-3(b) at such infinitesimal V/V_p and EQE that it would not be visible on the same scale as these nitride devices [6,15]. The objective for nitride devices destined for solid-state lighting applications is to operate much closer to the upper right limit of the graph, where useful output powers can be achieved.

Figure 3(b) illustrates the effect of increasing the temperature of operation for the Vendor C commercial device. With increasing temperature, the curves move leftward as the voltage drops, but they also move downward due to decreasing EQE as SRH non-radiative centers activate. This represents a fundamental tradeoff. The drop in voltage with increasing temperature can be largely attributed to the strong temperature dependence of the hole concentration in the Mg-doped p-layers [22], which are only ~1% ionized at room temperature as well as the temperature-dependence of the pn junction properties [23].

A line can be drawn connecting the peak EQEs vs. temperature in Fig. 3(b). If the slope of the line is greater than 1, as it is in the case of this device, then cooling the device, rather than heating it may present the best opportunity to maximize the WPE. In some cases, such as in the two thermal-droop free literature reports already discussed, the WPE remains constant as the operation temperature is increased from room temperature [18,19]. In these cases, the devices could be depicted in an EQE vs. V/V_p graph as moving along an iso-WPE line with slope = 1. Both these LED reports involved materials grown on bulk GaN substrates, which have reduced epitaxial defect density. This growth platform may result in fewer temperature-activated SRH centers compared with conventional heteroepitaxy on patterned sapphire substrates (PSS). In devices where this type of EQE vs. V/V_p behavior is observed, the output power may be maximized by heating the device. Finally, in a case in which the slope of the line connecting the peak EQEs is < 1, the WPE would increase upon heating. This was the situation observed in the near-equilibrium low bias regime for the mid IR LEDs in [6,15], however, this behavior has yet to be observed near conventional operating conditions for any LED.

Future efforts in achieving ≥100% WPE must focus on specific optimization of the epitaxial structure and device design targeting operation at relatively low current densities in the range of 1 A/cm²– 5 A/cm². The comparative features of today’s LED designs with the target designs for WPE ≥ 100% are given in Table 1. Operation at relatively low current density eliminates efficiency droop effects and opens the LEE design space compared with typical illumination current densities (~35 A/cm²) by enabling designs with thin current spreading layers, aggressive contact designs and elimination of the heat sink. A separate publication describes the effects of these modifications on LED LEE and WPE considering this expanded design space [16]. Tunnel-junction designs may also provide a path to ultra-high LEE that could be useful for high WPE if further developments can reduce the parasitic voltage [24].

Table 1. Comparison among typical commercial device, record device, and target performance for LEDs emitting at 450 nm (corresponding to V_p = 2.75 V). The voltage boost in V_p/V, that is required to make up for the LED EQE losses for WPE = 100% is approximately 205 mV.

View Table

New epitaxial designs targeted toward high IQE, low voltage performance at low current densities (and possibly elevated temperatures) can eliminate or modify certain typical components of nitride LED design. For example, lower bias and reduced carrier overflow concerns may obviate the need for highly Mg-doped electron blocking layers (EBL). Removal of the EBL offers an opportunity to increase the IQE and LEE while reducing the operating voltage. Lower carrier densities and reduced contribution of efficiency droop at relatively small current density may also enable shorter-period multiple quantum well structures and/or lower barrier heights, further reducing the voltage. Growth on bulk GaN substrates may offer opportunities to increase the peak IQE and to improve high temperature efficiency, despite tradeoffs for LEE due to higher substrate absorption than conventional PSS [25].

These opportunities to tune the epitaxial design, processing, and packaging for operation at relatively low current density (and potentially high temperature) may allow nitride devices to approach the 100% WPE threshold while producing output powers high enough to be useful in solid-state lighting applications.

Conclusion

The standing possibility of a nitride LED with 100% or greater wall-plug efficiency is examined considering recent observations of the phenomenon for smaller bandgap mid-IR LEDs under extreme low-bias operation. While achieving 100% or greater WPE is more challenging in nitride LEDs, assessments of state-of-the-art nitride device electrical and optical performance are summarized here with suggestions for approaching the regime of > 100% WPE at technologically relevant current densities of 1 A/cm²– 5 A/cm² leading to emission intensities in the few W/cm².