# RELATIONSHIP BETWEEN DEVICE VOLTAGE AND CARRIER LIFETIME

The output voltage of a solar cell is principally determined by the excess minority-carrier density at the junction edge of the quasi-neutral base region, defined to be at the plane x = 0 in the following approximate expression:

Dn(0)[NA + Dn(0)] = n2exp^kT=q^ (22)

In open-circuit conditions, this minority-carrier density is the result of a balance between photogeneration and recombination. The conditions are identical to those of the steady-state method to measure the lifetime, described in Section 3. It is therefore possible to obtain Dn from a photoconductance measurement and determine an implicit, or expected voltage. Complete char­acteristic curves can be obtained by plotting the implicit voltage as a function of the illumination, expressed in unit of suns (1 sun = 1 kW/m2).

Direct measurements of the voltage are possible as soon as a junction exists in the wafer. By taking data at a range of illumination intensities, Suns-Voc curves can be constructed and analyzed to obtain diode saturation currents, ideality factors, shunts and ideal efficiencies . Applications of this are shown in Section 5. A generalized expression to obtain the Suns-Voc curves from voltage measurements under quasi-steady-state illumination or during a transient open-circuit decay (OCVD) has also been developed .

Conversely, solving for Dn as a function of voltage and substituting this value in Equation (7) converts any voltage measurement into an effective lifetime value. Note that the equation for the lifetime uses an average carrier density, which in some cases can be substantially lower than the value of Dn(0) obtained from the voltage through Equation (22) . Temperature control, knowledge of the intrinsic carrier density ni, and the dopant density are necessary to obtain the lifetime from a voltage measurement, and vice versa. In contrast, photoconductance lifetime measurements require knowledge of carrier mobilities and are relatively insensitive to temperature.

Photoluminescence can provide a contactless probe of the electrochemical potential, or implicit voltage, within a sample, since the PL signal is propor­tional to the left-hand side of Equation (22). This method, sometimes called Suns-PL , is analogous to the Suns-Voc methodology described earlier, without requiring junction formation or probing.

Updated: August 18, 2015 — 4:04 am