Thursday, January 20, 2011

Photovoltaic Capacitance and Time Domain Measurements

I noticed that my PV test blog posts have been getting a lot of hits so I wanted to capture an area of PV test that I have not touched on yet and is out of the normal GPETE realm. That area is photovoltaic capacitance and time domain testing. This type of testing provides deep dive into the physics of PV cell for improving improving the cell's efficiency at the material fabrication level..
We are all familiar with I-V measurements made throughout the PV product design cycle. With I-V measurements we can calculate PV parameters like Isc, Voc, FF, Pmax, etc.Capacitance measurements and time domain measurements are required to completely characterize solar cells. Because traps in the bulk material directly affect carrier recombination at the interface and in the bulk, it is essential to characterize these traps so as to minimize their impact on solar cell performance. Capacitance measurements are the main method to evaluate traps in the bulk. Understanding trap behavior is also important when studying multi-junction PV cells and for controlling the PV cell band gap. To optimize PV cell performance it is also important to know the carrier diffusion length, because it is one of the key parameters impacting PV cell efficiency. Time domain measurement is the principal method used to measure carrier diffusion length. The following figure lists PV parameters that can be obtained from capacitance and time domain measurements.
In the next couple paragraphs I will briefly explain the parameters in capacitance and time domain measurements. I will warn you the math gets a little heavy so if you are just interested in a solution for making these measurements refer to the link at the end of the post.

CV measurements, which are the most common capacitance measurements, can be used to estimate the carrier density (Nc) using the following equation.
Here q is the electron charge, Ks is the semiconductor dielectric constant, ε0 is the permittivity of free space, A is the surface area of a PV cell and Vbi is the built-in potential. A 1/C2 - V plot is called a Mott-Schottky plot, and the Nc distribution over the depletion width (W) is obtained from the slope of Mott-Schottky plot as shown below (click to enlarge).
An AC voltage capacitance measurement (CVac) provides the information about the defect density (Nd). This technique is known as drive-level capacitance profiling (DLCP), and it is used to determine deep defect densities by studying the non-linear response of the capacitor
as a function of the peak-to-peak voltage dV (=Vpp) of the applied oscillating signal. The density that 
can be obtained using DLCP is also called the drive level density (Ndl), and it is defined as shown below. (Note: In the previous equation the subscripted symbols C1, C2, etc. have the units of capacitance per volt, capacitance per volt squared, etc.) 
A capacitance versus frequency (Cf) measurement is helpful to understand the dynamic behavior of PV cells as well. The results of a Cf measurement are often plotted as complex numbers in the impedance plane where this information is known by many names, such as Nyquist plots, Cole-Cole plots, complex impedance plots, etc. 
A variety of time domain measurement methods are being developed to evaluate the recombination parameters of solar cells, such as minority carrier lifetime (τ), surface recombination velocity (S) and minority carrier diffusion length (Ld). One of the most popular techniques is open circuit voltage decay (OCVD) where the excitation is supplied either electrically or optically (see figure below). In the electrical case a constant current equal to Isc is forced into the solar cell and the voltage decay across the solar cell is observed after abruptly terminating the current. In the optical case a light pulse is used to stimulate the solar cell instead of a current. For the short circuit condition the current flow across the solar cell is measured after removing the light stimulus, and this is called the short circuit current decay (SCCD). 

Each of the various measurement parameters just discussed could be measured with a complex setup of multiple GPETE products and some software to post process the results. A much better way to do it is to use  Agilent's B1500A semiconductor device analyzer. The B1500A provides a one box solution with software built-in to make high accuracy and high precision capacitance, time domain, and I-V measurements for PV material testing.

To learn more about the B1500A click here