The principle of limiting efficiency of solar cell

One, the detailed balance principle is put forward.

Detailed balance principle considers solar energy battery limit theory of efficiency is the most important and the most commonly used methods.

Detailed balance Roosbroeck and Shockley this concept is 1954 in the journal of applied physics (Journal of Applied Physics) send an article.

1961 William Shockley, HansJ Queisser sent in applied physics Detailed balance limit of efficiency of pnjunction solar cells articles, in this article puts forward the detailed balance limit (detailed balance limit of efficiency) the concept of efficiency, on the basis of some assumptions to deduce a formula used to calculate the efficiency limit, it is concluded that single junction solar cell efficiency limit of 31%.

Of the several assumptions as follows:

1, the sun and the battery was assumed as the temperature of 6000 k and 300 k respectively in bold.

2, the electrons and holes in the compound only a radiative recombination (radiativere combination), this is required by the detailedbalance principle.

3, Radiativere combination just a fraction of the total compound specific, the rest are radiation (nonradiative).

Temperature (Tsource) and 300 k to 6000 k (Tsink) between the two heat reservoir energy conversion efficiency is restricted by the carnot cycle is 95%.

This value does not take into account the battery photon emission loss, the model assumes that the loss of energy back to the sun, to keep the sun's own temperature. Correction model considering the photon losses, and assumes that the process is reversible and meet the conditions of carnot cycle, the resulting conversion efficiency is 93.3%.

Second, all the factors of optimization, the solar cell can eventually reached the limit of the efficiency

If all the factors are optimized, including electrical, optical, material, then the efficiency of the solar cell can eventually reached the limit of what? It is one of the most concern of the people, and all kinds of optimization in the desired direction. The importance of detailed balance principle is that it is the theoretical minimum limits, now found below carlo efficiency, lower than lang fort (Landsberg) limit, it is objectively can reach the highest efficiency.

This theory has such several assumptions:

1, only energy is greater than the bandwidth of photon can be absorbed, not small.

2, a photon can only produce a pair.

3, absorption of the photon energy is used to stimulate the pair and stored as potential energy of electron hole pair.

4, only the radiative recombination.

5, semiconductor materials completely accords with the behavior of blackbody.

Careless about it: if the sun is 6000 k blackbody hypothesis (usually), he will be in accordance with "Planck blackbody radiation distribution" way of the energy flow in different radiation out of different wavelength of the photon energy, starting from 0 wavelength, to the bandwidth for the lower limit of the semiconductor. Exposure to the solar cells, such as we assume that the temperature of 300 k battery (room temperature), as part of the energy loss is inevitable, there is a battery as objects of a certain temperature is bound to be radiation energy. What is the way of radiation? First of all must obey under 300 k "Planck blackbody radiation distribution; Can second because energy is a "bad" (I call it the potential energy) of the distribution of the electron hole to form, so the wavelength corresponding to the lower limit of the energy is tearing up all the bandwidth of the value of "potential energy".

The sun's photon energy distribution to get the total cell absorbs energy as a variable integral energy; When the battery short circuit current density = (from the radiation photons - the battery itself off electrons) X (electronic power);Voltage = "difference" pair; Output power = X current voltage; Theoretical limit = energy output/input energy.

Is a complex but digging the essence of math is not so trouble. Means you have limited from the sun, and you in addition to absorbing the radiation does other you also have to go out part (if it is hard to understand but physical that is the case), the last available limit you is the efficiency limit. Some interesting data about the impression in brain: when 1 sun (battery) without concentrator, if you can do N layer (N infinite) as the bandwidth covered the entire wavelength range, then you will get up to no more than 68.2% efficiency; In 45800 sun concentrator silicon solar battery is not higher than 40.8% at most;1 sun up to no more than 30.0% of silicon cells.

This is the theory of limit, is higher than this, according to the understanding of people now, it is not possible.

This basic equation we can use a program to calculate, the general first step is according to the blackbody radiation formula to calculate the short circuit current and reverse saturation current, then the current voltage will be used to say, the output power Po which became the only including voltage function, derivative to get the best voltage, then find out the best efficiency. Use this theory when calculate current one of the assumptions, is "a photon can create a pair", so when you know how many photons are used effectively, how many charge generation, basic electricity is then multiplied by the current.

Detailed balance limit efficiency is not high, because its assumptions are very strict. Such as "a photon can only hit a pair" (actually, by the method of impact ionization can already do more than one photon hit pair);Again, energy is less than the forbidden band width of the photon energy is not absorbed (the actual situation and the experiment has showed that is not completely absorbed, a lot of is a kind of call "exciton absorption, also the existence of energy transmission).

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