# On the Thermoelectrically Pumped LED

## Suhas Kumar June 11, 2012

### Submitted as coursework for PH250, Stanford University, Spring 2012

 Fig. 1: ηEQE as a function of current. Note the two known regions of forward bias. [2]

When a light emitting diode (LED) is biased with a potential below its bandgap energy, we still see photons coming out of it with the bandgap energy of the active region. It is known that the extra energy comes from the thermal heat in the lattice of the material, known as Peltier heat, which originates from its temperature. [1]

## Background

The two interesting effects as a result of this are 1) Electroluminescent cooling of the LED; i.e., when the LED is thermally isolated, the Peltier heat exchange must bring down the temperature of the LED and 2) Above unity wall-plug-efficiency; i.e.: the total optical power coming out is more than the total electrical power being pumped in. A direct observation of either of these had been elusive, until recently when Rajeev Ram's group at MIT demonstrated an LED operating above unitywall-plug-efficiency. [2] This document explains the idea of this work and comments on it, without using much math.

If V is the applied voltage, then qV is the supplied energy per excitation. If the probability of the excitation undergoing a radiative recombination is ηEQE (the external quantum efficiency), the wall plug efficiency is η = ħωηEQE/qV. To maximize η, we could maximize ηEQE by trying to make sure most recombinations are radiative, which can be approached by several materials science tricks like photon recycling, getting rid of all deep level defects, etc. [3] Most efforts had focused on the regime where qV ~ Eg. The regime where qV << Eg had been dismissed since the Fermi-Dirac distribution would exponentially reduce the excited carrier concentration as we linearly scaled down the voltage applied, which would approach the defect concentration, in turn ruining ηEQE. [4]

## The Approach

Let us take a look at what these guys did differently.

1. They used a smaller Eg material in the active region in its intrinsic form (intrinsic GaInAsSb) and slightly larger Eg one sandwiching it (n and p GaSb). This means that there are lot more free carriers and hence lot more 'dark' current; all you need is a tiny potential to drive this 'dark' current. The way the hetero-junction is made suggests that there is better confinement of carriers in active region.

2. They increased the temperature to 135 °C. Now, even more free carriers, but about the same defect concentration as before. More random excitations and recombinations. More Peltier heat. A tiny potential will drive a far larger 'dark' current now.

 Fig. 2: Wall-plug efficiency as a function of current. Note the two known regions of forward bias. Inset is ηEQE as a function of temperature. [2]

As seen in Fig. 1, the ηEQE flattens out for all currents (or voltages) below a certain threshold, which is a known diode behavior. Also, recall that a diode forward bias behavior has 4 important regions: (1) Recombination dominated below and around threshold voltage, (2) Low level injection dominated above threshold voltage, (3) High level injection dominated at high bias and (4) Series resistance dominated at very high bias. So recombination dominates when we considerably reduce bias! If we reduce qV further, we are gaining on η, without affecting anything else in the efficiency equation. This is mainly because a greater portion of the output is driven by Peltier heat. We could reduce qV all the way to thermal noise limits. Of course, ηEQE is compromised a bit by increasing the temperature in this experiment.

This simple analysis lets us predict that very tiny voltage can be used to drive the diode. They used about 70 μV and observed above unity η. Their results shown in Fig. 2 are called here by a qualitative analysis. Other efforts have focused on the local maxima seen in Fig. 2, which is dominated by low-level injection.

## The Missing Cooling

The authors did not directly observe cooling, mostly because they did not thermally isolate the diode, instead they chose to keep the temperature fixed! They calculate the net cooling. In simple terms, one would not observe cooling in the recombination dominated region. At the local maxima in Fig. 2, with sufficiently low temperatures, one must be able to see cooling or a sustained transient of it. In our case, The rate of recombination dominates the rate of thermal generation so that there is little chance of sustaining a transient of cooling since it diverges from the required parameters to keep η > 1.

In conclusion, the result is an important reminder that in several solid state devices, we can use thermal energy and Fermi-Dirac statistics to do 'efficient work' at very low biases. But it is also a reminder of the physical limitations of such a method, as in here, where we cannot sustain continuous cooling and ηEQE is very low. Also, in the region of the local maxima in Fig. 2, as cooling happens, there is an interesting competition between the changing properties of the solid, like its increasing bandgap, changing effective mass of carriers and the reducing probability of excitation for a fixed voltage below Eg, and the required bias to sustain cooling.

© Suhas Kumar. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.

## References

[1] S.-Q. Yu et al., "Fundamental Mechanisms of Electroluminescence Refrigeration in Heterostructure Light-Emitting Diodes," Proc. SPIE Int. Soc. Opt. Eng. 6486, 648604 (2007).

[2] P. Santhanam et al., "Thermoelectrically Pumped Light-Emitting Diodes Operating Above Unity Efficiency," Phys. Rev. Lett. 108, 097403 (2012).

[3] O. Heikkila, J. Oksanen, and J. Tulkki, "The Challenge of Unity Wall Plug Efficiency: The Effects of Internal Heating on the Efficiency of Light Emitting Diodes," J. Appl. Phys. 107, 033105 (2010).

[4] S.-T. Yen and K.-C. Lee, "Analysis of Heterostructures for Electroluminescent Refrigeration and Light Emitting Without Heat Generation" J. Appl. Phys. 107, 054513 (2010).