Tag Archives: Shockley-Queisser limit

Exceeding the Shockley-Quisser limit

After carefully reviewing the assumptions made in deriving the SQ limit (previous post), we can begin to list opportunities for exceeding the limit. All these efforts of overcoming the limit are classified as ‘third-generation’ PV cells.

1) Each incoming photon excites only one electron-hole pair: When a photon successfully excites an electron across the band-gap and into a certain region of the conduction band, the electron loses the excess energy through thermalization and falls down to the lowest energy level in the conduction band. When this lost energy is equal to or more than the band-gap energy, we are losing energy that is theoretically sufficient to excite a second electron. There are two ways to prevent this loss:

a) Multiple exciton generation: In certain materials, the phonons from the lost energy can be re-absorbed to excite another electron across the bandgap. MEG can also take place through other mechanisms. This behaviour was first exhibited in PbSe quantum dots[1] (2004). It was later also observed in quantum dots of lead, cadmium and indium compounds, silicon, single-walled carbon nanotubes, graphene, and organic pentacene derivatives[2]. Such materials show a quantum yield > 100% and upto 300%. The biggest challenge in quantum dots is the collection of these carriers before they recombine. During excitation, the electron-hole pair exists as ‘excitons’ and are bounded by coloumbic forces. Excitons have to be split into free charges to do useful work.

b) Down conversion: Certain luminescent materials can absorb high energy photons and emit a higher number of lower energy photons. These emitted photons can be energetic enough to excite electrons and thus, quantum yield > 100% can be achieved. The process is often through auger recombination and de-excitation of all excited electrons. Such luminescence has been famously exhibited in quantum dots and even has applications in ligh-emitting technologies[3]. The size of quantum-dots/nanocrystals can be tuned to obtained desired wavelengths of emitted light. Generally, smaller quantum-dots have larger band-gaps and emit light of shorter wavelengths. The drawback of using QDs is that they lead to many interfaces and hence recombinations.


Colloidal quatum dots produced in a kg scale at PlasmaChem GmbH

Image courtesy: commons.wikimedia.org, user: antipof

2) Photovoltaic material consists of a single band gap energy: This restriction leads to either thermalization losses (if band-gap is too low) or absorption losses (if band-gap is too high) as shown in the illustration below.


Image courtesy: commons.wikimedia.org, user:  Sbyrnes321

The solution to this problem is the use of multi-junction cells incorporating 2 or more different band-gap materials which can together, absorb the solar spectrum more efficiently. Multi-junction cells (upto 4 layers) are often made with III-V group elements (tunable band-gap) or amorphous silicon-microcrystalline silicon junctions (high and low band-gap respectively).


Spectral utilization of multi-junction solar cells

Image courtesy: commons.wikimedia.org, Fraunhofer ISE

3) Photons with energy lower than band gap energy are not absorbed: This limit can also be addressed in two ways:

a)Intermediate band gap: Materials can be added which provide an energy level in the forbidden band-gap. Thus, electrons do not necessarily need photons of band-gap energy but can also be excited to the intermediate state with lower energy photons. From this state, they can be further excited to the conduction band with low energy photons. This behaviour has been demonstrate in InAs quantum dots embedded in a InGaAs matrix.[4]
The severe draw-back of this method is that it is similar to having defects/impurities in a materials and leads to high rates of SRH recombination.

b) Upconversion: Certain rare-earth ions can absorb low energy radiation and emit light with lesser photons, but more energy.[5] Thus, low-energy photons undergo ‘up-conversion’ and can excite electrons across a band-gap, which they otherwise could not do.

4) Illumination of the solar cell is by unconcentrated sunlight: Concentrators can be used to greatly increase the amount of incident light. This often leads to higher efficiency in a solar cell but can make the module setup more expensive.

It’s best to conclude with some perspective on this topic. While solar cells have a bad reputation for low efficiency, and the best solar cells have been pegged at 46% (4-junction cell at Fraunhofer ISE), it is also important to remember that most thermal power stations have an operating efficiency of 33% to 48%!


[1] Schaller, R.; Klimov, V. (2004). “High Efficiency Carrier Multiplication in PbSe Nanocrystals: Implications for Solar Energy Conversion”. Physical Review Letters 92 (18): 186601
[2] https://en.wikipedia.org/wiki/Multiple_exciton_generation
[3] X D Pi et al 2008 Nanotechnology 19 245603
[4]Ramiro, I. et al., “Wide-Bandgap InAs/InGaP Quantum-Dot Intermediate Band Solar Cells,” in Photovoltaics, IEEE Journal of , vol.5, no.3, pp.840-845, May 2015
[5] Jan Goldschmidt et al. “Record efficient upconverter solar cell devices”, PV solar energy conference and exhibition, 2014


Shockley Queisser limit

This post offers an intuitive, non-mathematical explanation of the Shockley Queisser (SQ) limit. All research in solar cells today that is focused on energy efficiency , is based on understanding and tackling this limit. Thus a grasp of this limit can help in the analysis, critique and appreciation of research in multi-junction cells, III-V group semiconductors, quantum dot and concentrator solar cells.

The SQ limit is much like the carnot efficiency of heat engines. It puts an upper limit on the maximum achievable efficiency of a solar cell based on fundamental physics, material properties and on the nature of the incident solar radiation. For example, under the assumptions of the limit, commercially popular crystalline solar cells can never exceed an efficiency of 33% in converting sunlight to electricity on earth’s surface. Other considerations further lower this limit, but several techniques can also work around the assumptions and can thus create cells with greater efficiencies. We will go over all these aspects in steps. Some familiarity with the basic working of a solar cell is assumed on the reader’s part.


1. Each incoming photon excites only one electron-hole pair

2. Photovoltaic material consists of a single band gap energy

3. Photons with energy lower than band gap energy are not absorbed. All photons with energy greater than band gap are absorbed (infinite absorption coefficient). Any excess energy is transferred to the the generated electron-hole pair and is subsequently lost by thermal relaxation/thermalisation (collisions with molecules which generate heat)

4. Ideal, infinite mobility of charge carrier. They are able to travel to the probes regardless of where they are generated

5. Loss of electron-hole pairs is through radiative recombination only

6. Illumination of the solar cell is by unconcentrated sunlight under standard test conditions (AM 1.5, 1000 W/m2 and 300K cell temperature)

7. The sun is a black body at 6000K and the solar cell is a black body at 300K

Limiting phenomena:

Spectral mismatch: This aspect can be best illustrated by the diagram below. The sunlight reaching earth has a characteristic spectrum with intensity peaks in the visible and infra-red range. It does not have uniform irradiance across wavelengths and hence, certain wavelengths have poor irradiance even though a solar cell may be capable of absorbing them.


Image courtesy: commons.wikimedia.org

The wavelengths with energy lower than the band-gap energy pass unabsorbed and unutilized. The higher energy wavelengths are completely absorbed but only the ‘band-gap’ amount of energy is used to generate electricity. The excess energy is lost by electron-hole pairs to thermalisation. Thus, in both wavelength ranges we have energy which is lost and not converted to electric current. Additionally, energy lost by thermalisation heats up the solar cell, which in-turn further lowers its efficiency.

This spectral mismatch means that a band-gap of 1.2ev-1.34ev gives the highest efficiency (33.7%) for AM 1.5 solar spectrum. Any deviation from this band-gap gives a lower efficiency. Spectral mismatch accounts for about 48% of the SQ limit.

Radiative recombination: Just as an electron-hole pair can be excited by a photon, they can also recombine to emit a photon. Since this process cannot be stopped, a certain base-line recombination loss is always present in the solar cell. It is quantitatively studied in the detailed balance. It is the simplest form of recombination loss.

Black-body radiation: The solar cell is assumed to be a black-body at 300K, emitting a characteristic radiation that is an internal function of its temperature. It is in thermal equilibrium with its surroundings. This means that the molecules of a solar cell emit the same amount of energy as they thermally absorb. This represent a 7% loss of the incoming radiation which cannot be converted to electricity. This phenomena follows from Prevost’s law and Kirchoff’s theory of black-body radiation.

Voltage losses (Voc): As discussed in the previous section on spectral mismatch, only the photon energy equivalent to the band-gap energy is used to generate current via the collection of the generated electron from the conduction band and the hole from the valence band. However, the maximum voltage a solar cell can generate is rarely ever the band-gap energy voltage, but a lower value due to recombination currents. In this calculation of the SQ limit, only radiative recombination is considered. Nevertheless, this amounts to a loss in the power efficiency of a cell. This open-circuit voltage (Voc) can be up to 40% lower than band-gap voltage (eg: 1V for BG of 1.7V).

Fill factor: Unfortunately, even a cell voltage of Voc is difficult to achievable. A solar cell is rarely operated in an open cirucuit condition. This is usually operated at the point of peak power in the fill factor curve. This gives maximum power, but a voltage that is lower than Voc.

The SQ limit is determined by adding up all these loss mechanisms for a given solar cell.

Other practical losses not accounted for in this limit:

1. If other mechanisms such as shockley-read-hall (SRH) and auger recombination are considered, then efficiencies lower than the SQ limit are predicted. Both of these are non-radiative mechanisms. In indirect band gap materials such as Silicon, auger recombination is more dominant than radiative recombination, thus further reducing the limit to 29.4%. In this regard, the SQ limit is more suited for GaAs single junction cells

2. Optical losses: Reflection, shading, transmission (finite absorption coefficient)

3. Non-ideal fill factor due to series resistance in the bulk of the junction and leakage currents from shunt resistance or local defects.

By looking at the assumptions made in the derivation of this limit, it is apparent that some conditions on a solar cell can be changed in order to exceed the shockley queisser limit. In my next post, I will explain these and hence, touch upon the latest research in PV cells.

Link to the original paper: William Shockley and Hans J. Queisser, “Detailed Balance Limit of Efficiency of p-n Junction Solar Cells”, Journal of Applied Physics, Volume 32 (March 1961), pp. 510-519; doi:10.1063/1.1736034