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Question #43472

Difficulty: 8/10 | 🟢 Free

The Question

A specialized $p^+-n$ junction solar cell operates under a reverse bias voltage $V_R = 1.20 \pm 0.06 \text{ V}$ . The built-in potential of the junction is $V_0 = 0.80 \text{ V}$ (assume exact). The depletion region width $W$ is determined by the donor doping concentration $N_D$ in the lighter doped $n$ -region, given by $W = \sqrt{\frac{2\epsilon (V_0 + V_R)}{e N_D}}$ , where $\epsilon$ and $e$ are exact constants. The photoelectric conversion efficiency $\eta$ of the cell scales with the depletion width as $\eta = \alpha W^{4/3}$ , where $\alpha$ is a constant. If the manufacturing tolerance (maximum percentage error) in the donor doping concentration $N_D$ is $6\%$ , what is the maximum percentage error in the efficiency $\eta$ ?

Options

A.
$6\%$
B.
$4.5\%$
C.
$9\%$
D.
$2\%$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Variable_Constraint

Develop pure symbolic logic skills by mastering algebraic constraints without relying on numerical data.

Concepts Behind This Question

Solar Cell Efficiency|Depletion Region Dynamics|Relative Error Propagation in Powers

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to correctly propagate experimental uncertainties through nested physical dependencies.

A common trap is calculating the percentage error of the reverse bias voltage $V_R$ ( $5\%$ ) instead of the total junction potential $V$ ( $3\%$ ).

Furthermore, students often misapply the power rule in error propagation by either directly adding the given percentage errors ( $3\% + 6\% = 9\%$ ), forgetting the exponent multiplier entirely, or incorrectly subtracting the errors ( $\frac{2}{3}(6\%) - \frac{2}{3}(3\%) = 2\%$ ) because $N_D$ is in the denominator, forgetting that maximum error requires the sum of absolute values.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Semiconductor Electronics: Materials, Devices, and Simple Circuits - Class 12
Concept	Solar Cell Efficiency
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free