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Problem #1:
Consider the p-i-n structure shown above. Assume that the p and n regions are
uniformly doped and that ND - NA = 0 in the intrinsic region. Please answer the following:
a. Plot the charge, electric field, and potential within the device structure.
b. What is the built-in voltage? Why?
c. Establish relationships for the charge density, electric field, potential, and depletion
widths.
Problem #2:
Consider the p+-n junction pictured above and answer the following:
a. What does the I-V characteristic look like? Can you find an expression for it?
b. How does it change if we make Ο„p > 0 from xb< x <xc?
Problem #3:
The maximum power delivered by a solar cell can be found by maximizing the I-V
product.
π‘žπ‘ž
a. Show that maximizing the power leads to the expression: οΏ½1 + π‘˜π‘˜π‘˜π‘˜ π‘‰π‘‰π‘šπ‘šπ‘šπ‘š οΏ½ 𝑒𝑒 π‘žπ‘žπ‘‰π‘‰π‘šπ‘šπ‘šπ‘š /π‘˜π‘˜π‘˜π‘˜ =
𝐼𝐼
1 + 𝐼𝐼𝑠𝑠𝑠𝑠 where Vmp is the voltage for maximum power, Isc is the magnitude of the shortπ‘‘π‘‘β„Ž
circuit current, and Ith is the thermally induced reverse saturation current.
b. Assume a silicon solar cell with a dark saturation current Ith of 1.5 nA is illuminated
such that the short-circuit current is Isc = 100 mA. Use a graphical solution to obtain the
voltage Vmp at the maximum power delivered.
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