# What is injection level (semiconductor physics)?

I am currently reading journal articles about semiconductor physics in solar cells. What is injection level?

I'll try to start off with what I understand. Photons hitting the silicon cause its electrons to jump to a higher energy state. Some of these electrons jump high enough that they cross from the valence band into the conduction band, thus contributing to the flow of electric current. Now, how long do these electrons stay in the conduction band and keep flowing? I believe that is what is called carrier lifetime.

I have just read that carrier lifetime depends on injection level. I think that injection level is the rate at which electrons jump into the conduction band. Am I on the right track?

1. What is injection level?
2. What is its unit of measure?
3. What are some common ways of measuring it?
• May I propose the tags semiconductor-physics and photovoltaics? – Kit Jan 15 '11 at 2:48
• sure, good idea. I also added solid-state-physics, but if that tag doesn't really apply to this question, you can remove it. (I'm in particle physics myself so I'm a little fuzzy on exactly what constitutes solid state/condensed matter physics) – David Z Jan 15 '11 at 3:33
• @David: Thanks. solid-state-physics fits quite well. – Kit Jan 15 '11 at 3:53
• @David: it's just as the names suggest, condensed matter physics investigates all forms of condensed matter (but also some related physical systems) while solid state physics studies just the solid phase (crystals for the most part). Of course this is not exactly true, but for the most part: SSP is a subset of the CMP. – Marek Jan 15 '11 at 9:43

1. the injection level is defined as $\delta n/p_0$ where $\delta n$ is the minority carrier (e.g. electrons') density excess at non-equilibrium while $p_0$ is the equilibrium density of the majority carriers (e.g. holes).

2. From the formula which is a ratio of two very similar densities, it's clear that the injection level is dimensionless; "high" and "low" injection level usually means values that are much greater or much smaller than one

3. The methods to determine the level depend on the context and cleverness of the physicist or engineer. In various contexts, it may be determined by the barrier formed at metal-dielectric interface; by the method described by Kobayashi and Kimura; from the absolute value of photoconductivity measured somewhere; from bias illumination; etc. I think it would be bad for me to pretend that I am actually an expert in any of these experimental things.

Cheers LM

• Is it related to the rate at which electrons jump into the conduction band? Was I on the right track in presenting the context? Similarly, based on your Point #1, is injection level defined upon fabrication of the device, or is it situation-specific (e.g. the amount of sunlight hitting the solar cell)? – Kit Jan 18 '11 at 2:51

For 3: it's not that common to measure the injection level itself. For a solar cell you can measure/calculate the electrons created by e.g. illumination and multiply this value with the (minority) carrier lifetime. As a result you get the excess carrier density ($\delta_n$).

The injection level depends, as LM wrote, on the relation between excess carrier density ($\delta_n$) and the majority carrier density p0 (mostly doping N - to keep it simple) $\rightarrow$ The injection level depends on the ratio between $\delta_n$ and $N$.

The injection level is important because it gives you a hint which recombination channel is limiting the performance (aka lifetime) of your solarcell. Under low injection it is limited by defect recombination, under high injection it is limited by Auger (indirect semiconductor as Si) or radiative (direct semiconductor as GaAs) recombination.