The dark current density for a silicon solar cell at 40 degr

The dark current density for a silicon solar cell at 40 degree C is 2.0 times 10^-8 A/m^2 and the short circuit current density is 250 A/m^2 when exposed to solar radiation of 1000 W/m^2. Find: Open circuit voltage Voltage at maximum power Current density at maximum power The maximum power The maximum efficiency The cell area needed for an output of 30 Watts

Solution

1) To find open circuit voltage, we use the solar cell equation with the condition that net current in the system is zero-

V_OC=(nkT/q)*ln(IL/I0+1)

where IL= light generated current

I0=dark current

n=ideality factor=1

T=313K

Thus V_OC=0.627V

2) The maximum power voltage for a solar cell can be determined by differentiating the power from a solar cell with respect to voltage and finding where this is equal to zero. (d(IV)/dV=0)

Thus giving V_MP=V_OC- nkT/q*ln(V_MP/(nKT/q)+1).

Now using wolframalpha to solve the above equation. you get V_MP=0.545V

3) Now I=I0*[exp(qV/nKT-1)]-IL

Thus plugging in the values you get I_MP=238A/m2

4)Maximum power =I_MP*V_MP=238*0.545=129.71W/m^2