# Exercise 8.1-5

# IV Characteristics of Real Solar Cells

| We take the diode equation, including generation and recombination in the space charge region part, as given. We will now try to see what we can do with this equation with respect to solar cells. We have
j = | æ ç è | e · L · ni 2 t · NA | + | e · L · ni 2 t · ND | ö ÷ ø | · | æ ç è | exp | eU kT | – 1 | ö ÷ ø | + | æ ç è | e · ni · d(U) t | ö ÷ ø | · | æ ç è | exp | eU 2kT | – 1 | ö ÷ ø | – jPh
| ( | j1 | ) |  |  |  |  |  |  |  | ( | j2 | ) |  |  |  |  |  |  |

|  | We must first look at the important parameters (all others have their usual meaning) and find numerical values:
|  | L = diffusion length = (D t)½ average distance a minority carrier travels between its birth by a generation event (mostly by light in a "working" solar cell) and its death by recombination. A good values for bulk Si that we take for simple calculation is L = 100 µm D is the diffusion coefficient and t the (minority carrier) life time. A good enough value for the life time going with a diffusion length of 100 µm is t = 1 ms ni is the intrinsic carrier concentration. It increases exponentially with temperature T. A good values for Si at room temperature (RT) is ni(RT) = 1010 cm–3. NA and ND are the acceptor and donor concentrations in the p-part (called base; the usually several 100 µm thick part of a bulk Si solar cell) and the n- part (called emitter, the thin "layer" on top) of the solar cell. The base is lightly doped (otherwise the diffusion length suffers) whereas the emitter is heavily doped (good conductivity is important). NA = 1016 cm–3 and ND = 1018 cm–3 are good round numbers for the purpose here. The width of the space charge region we take as d(U) = 1 µm
|  | Now we consider a real good solar cell under "standard" illumination. This gives us the following (simplified) second set of numbers: Area of the Si bulk solar cell = 100 cm2. It's actually more like 200 cm2 in 2008 but let's stay with easy numbers. Photo current density jPh = 30 mA/cm2 for a very good solar cell, less for a not-so-good one. The photo current here is thus jPh = 3 A.
| Question 1:
|  | 1a: Using only the first term in the bracket for j1 as a sufficient approximation, give an equation for the relation of j2/j1 and some numbers for these current densities
|  | 1b: Does the result imply that you can neglect one of the ji terms in the equation above in the forward direction? How about the reverse direction?
| If we now measure the actual UI characteristics of a good real solar cell and fit the curve obtained to our equation from above, we find values for the current densities j1 and j 2 like
|  | j1 = 10–9 A/cm2. j2 = 10–7 A/cm2
| Question 2:
|  | 2a: Do these values and their relation meet your expectations based on your results from question 1?
|  | 2b: If not, what could be reasons for the discrepancy?
| Given the measured ji values from above and the jPh value given, we now can consider the short circuit current ISC and the open circuit voltage UOC
| Question 3:
|  | 3a: What do you get for ISC? Does it depend on ji and j2? If not, what determines its value?
|  | 3b: What can you say about the open circuit voltage UOC?

| Solution

With frame

8.1.1 Basic Solar Cell Topics

Basic IU-Characteristics of Solar Cells

Solution to Exercise 8.1-3: Characteristics of Real Solar Cells

Solution to Exercise 8.1-5 IV Characteristics of Real Solar Cells

© H. Föll (Semiconductor Technology - Script)