[Paper Review] Measurements and analysis of current-voltage characteristic of a pn diode for an undergraduate physics laboratory

Enrico Cataldo, A. Di Lieto+2 more|arXiv (Cornell University)|Aug 18, 2016

Photovoltaic System Optimization Techniques20 references3 citations

TL;DR

This paper presents an undergraduate-level laboratory experiment using a LabVIEW-controlled system to measure and analyze the I–V characteristics of a 1N4148 silicon pn diode across varying temperatures. It demonstrates that a four-parameter modified Shockley model (including series and parallel resistances) provides superior agreement with experimental data compared to the ideal Shockley equation, and successfully extracts the silicon band gap as 1.161 ± 0.002 eV, validating the model’s physical consistency.

ABSTRACT

We show that in a simple experiment at undergraduate level, suitable to be performed in classes of science and engineering students, it is possible to test accurately, on a popular 1N4148 p-n diode, the range of the junction currents where the Shockley equation model can be considered satisfactory. The experiment benefits from a system of temperature control and data collection driven in a LabVIEW environment. With these tools a large quantity of data can be recorded in the temporal frame of a lab session. Significant deviations of the experimental I-V with respect to the ideal behaviour curve predicted by the Shockley equation are observed, both at low and high current. A better agreement over the entire range is obtained introducing, as is customary, a four parameters model, including a parallel and a series resistance. A new iterative fitting procedure is presented which treats the I-V data of different regimes on the same level, and allows a simultaneous determination of the four parameters for each temperature selected. Moreover, the knowledge of the temperature dependence of saturation current is used to estimate the energy gap of silicon. The connection of a macroscopic measure with a microscopic quantity is another valuable feature of this experiment, from an educational point of view.

Motivation & Objective

• To provide an accessible, hands-on laboratory experience for undergraduate physics and engineering students to study the non-ideal current-voltage (I–V) behavior of a pn diode.
• To test the validity of the ideal Shockley diode equation across a wide range of currents and temperatures.
• To demonstrate the limitations of the ideal model and the necessity of including series and parallel resistances for accurate fitting.
• To enable students to extract the silicon band gap from temperature-dependent I–V data, linking macroscopic measurements to microscopic material properties.
• To highlight common pitfalls in fitting procedures and promote critical thinking about model selection and parameter estimation.

Proposed method

• A LabVIEW-based data acquisition system controls temperature and records I–V data across multiple temperatures and current regimes.
• The experiment uses a 1N4148 silicon diode with active temperature stabilization to ensure reproducible measurements.
• An iterative fitting procedure is developed to simultaneously determine four parameters: saturation current $I_S$, ideality factor $n$, series resistance $R_s$, and parallel resistance $R_p$.
• The modified Shockley equation $I = I_S \left[ \exp\left( \frac{V - I R_s}{n V_T} \right) - 1 \right] - \frac{V}{R_p}$ is used to model the I–V curve.
• Temperature-dependent I–V curves are analyzed to extract $T(V)$ data at fixed current, enabling linear fitting to estimate the band gap.
• The band gap is calculated via $E_G = -b/a$ from the linear fit of $T = -aV + b$, with uncertainties propagated through the fitting process.

Experimental results

Research questions

• RQ1 To what extent does the ideal Shockley equation accurately describe the I–V characteristics of a real 1N4148 diode across varying currents and temperatures?
• RQ2 How do deviations from the ideal model—particularly at low and high currents—manifest, and what physical mechanisms (e.g., series and parallel resistances) explain them?
• RQ3 Can a four-parameter model including $R_s$ and $R_p$ provide a consistent and accurate fit across the entire I–V range, and how do the parameters vary with temperature?
• RQ4 What value of the silicon band gap $E_G$ can be extracted from temperature-dependent I–V measurements, and how does it compare to accepted values?
• RQ5 How do different fitting procedures affect the extracted parameters, and what insights do discrepancies offer for student learning about model limitations?

Key findings

• The ideal Shockley equation shows significant deviations from experimental data at both low and high currents, particularly due to series and parallel resistance effects.
• The four-parameter modified Shockley model provides a significantly better fit across the entire current range compared to the ideal model.
• The saturation current $I_S$ exhibits an exponential dependence on inverse temperature, consistent with the theoretical form $I_S = I_0 \exp(-E_G / kT)$.
• The extracted band gap value is $E_G = 1.161 \pm 0.002$ eV, in excellent agreement with accepted values and consistent across different current levels.
• The iterative fitting procedure successfully determines all four model parameters simultaneously, reducing bias and improving consistency across regimes.
• The study reveals that fitting method choice significantly affects parameter estimates, highlighting the importance of methodological awareness in experimental physics.