Revisiting the Theory of Photocurrent in Solar Cells

TL;DR

The paper addresses how the built-in potential $V_{bi}$ quantitatively influences photocurrent in p-n junction solar cells, a factor often neglected in classical theory. It develops an improved analytical form for the photocurrent by applying corrected boundary conditions that account for photoexcited majority carriers, revealing a second, backward photocurrent term dependent on $V_{bi}$ and the applied voltage $V$. The total photocurrent thus comprises a forward component and a backward component, and there exists a fixed crossing point with $V^* = V_{bi} - (k_B T/q) \ln \alpha$ and $I^* = I_s(\exp(q V^*/(k_B T)) - 1)$ where the two contributions cancel. Experimental lock-in photovoltage measurements on a commercial crystalline silicon cell verify the predicted intersection point, showing $V^*$ is independent of illumination intensity and shifts with temperature in a way consistent with $V_{bi}$. These results clarify the intrinsic role of $V_{bi}$ in photovoltaic operation and suggest new avenues for performance optimization, especially for devices operating under infrared illumination or with narrow bandgaps.

Abstract

The built-in potential of p-n junctions plays a pivotal role in charge separation, a fundamental process underlying the photovoltaic effect.However, conventional classical theories of photovoltaic behavior in p-n junctions often neglect its quantitative influence. In this work, we revisit the classical framework and derive an improved analytical expression for photocurrent by incorporating more accurate boundary conditions. Our analysis reveals that the photocurrent comprises two distinct components: the conventional forward photocurrent and a previously unrecognized backward photocurrent, which depends on the built-in potential and the applied voltage. The theoretical analysis predicts that, under specific forward-bias conditions, these two components may partially or completely cancel each other. This prediction was experimentally verified by optical lock-in measurements performed on a commercial silicon solar cell. These findings provide new insights into the fundamental mechanisms governing photovoltaic devices and suggest potential pathways for performance optimization.

Figures (4)

• Figure 1: The I-V characteristics of a p-n junction under dark and illuminated conditions, based on the conventional model [Equation (\ref{['I_ph']})] and our model [Equation (\ref{['I_ph2']})], are presented. The intersection point at ($V^*$, $I^*$) in the first quadrant [I] is indicated.
• Figure 2: (a) Photoexcitation in a p-n junction solar cell under illumination. (b) Band diagram of a p-n junction under illumination under illumination ($G > 0$). $E_C$ and $E_V$ denote the conduction and valence band-edge energies, respectively. $V_{bi}$ is the built-in potential, and $V$ is the voltage between the cathode and anode, and it varies depending on the current. (c) - (e) Schematic illustration of the carrier concentration distribution of electrons in the conduction band under dark conditions (broken lines, $n_p$ and $n_n$) under illumination condition (solid lines, $n'_p$ and $n'_n$). Carrier concentrations are shown for three conditions: $V = 0$ (short-circuit condition), $V_{OC}$ (open-circuit condition), and $V = V^*$ (intersection point), respectively. The carrier concentrations far from the depletion layer are given by: $n_{p0}' = n_{p0} + \Delta n_p$, $n_{n0}' = n_{n0} + \Delta n_n$, and the excess carrier concentrations are given by: $\Delta n_p = G \tau_n$, $\Delta n_n = G \tau_p$.
• Figure 3: Experimental setup for lock-in photovoltage measurement of a single p-n junction solar cell. An optical chopper rotates above the solar cell device, periodically shading light from the solar simulator at a frequency of $f_1$. A constant DC current, $I_{dc}$, is applied to the solar cell using a DC current source (Keithley 6220). The output voltage between the electrodes of the solar cell exhibits a periodic signal with a fundamental frequency of $f_1$. The voltage difference $\Delta V$ represents the difference between the voltages under dark and illuminated conditions. The fundamental component of $v(t)$ is measured using a lock-in amplifier synchronized to $f_1$.
• Figure 4: (a) Fundamental component $V_1$ of output signal $v(t)$ as a function of applied DC current measured using the lock-in technique at various temperatures. The frequency of the optical chopper is $f_1 = 135.5\ \mathrm{Hz}$. (b) Temperature dependence of the voltages at the intersection points for different chopper frequencies. (c) Voltages at the intersection points under different illuminance conditions, measured with $f_1 = 85.6\ \mathrm{Hz}$. $d$ is the distance between the light source and the solar cell, as depicted in Figure \ref{['fig3']}.