How solar cells work

Solar cells absorb sunlight to produce the functions of ordinary batteries. But unlike traditional batteries, the output voltage and maximum output power of traditional batteries are fixed, while the output voltage, current, and power of solar cells are related to lighting conditions and load operating points. Because of this, to use solar cells to generate electricity, you must understand the current-voltage relationship and working principle of solar cells.   

Spectral illumination of sunlight:

The energy source of solar cells is sunlight, so the intensity and spectrum of incident sunlight determine the current and voltage output by the solar cell. We know that when an object is placed under the sun, it receives sunlight in two ways, one is direct sunlight, and the other is diffuse sunlight after being scattered by other objects on the surface. Under normal circumstances, direct incident light accounts for about 80% of the light received by a solar cell. Therefore, our following discussion will also focus on direct exposure to sunlight.

The intensity and spectrum of sunlight can be expressed by spectrum irradiance, which is the light power per unit wavelength per unit area (W/㎡um). The intensity of sunlight (W/㎡) is the sum of all wavelengths of spectrum illumination. The spectrum illumination of sunlight is related to the measured position and the angle of the sun relative to the earth's surface. This is because the sunlight will be absorbed and scattered by the atmosphere before reaching the earth's surface. The two factors of position and angle are generally represented by the so-called air mass (AM). For solar illumination, AMO refers to the situation in outer space when the sun is directly shining. Its light intensity is approximately 1353 W/㎡, which is approximately equivalent to the light source produced by blackbody radiation with a temperature of 5800K. AMI refers to the situation on the earth's surface, when the sun is shining directly, the light intensity is about 925 W/m2. AMI.5 refers to the situation on the earth's surface, when the sun is incident at an angle of 45 degrees, the light intensity is about 844 W/m2. AM 1.5 is generally used to represent the average illumination of sunlight on the earth's surface.   Solar cell circuit model:

When there is no light, a solar cell behaves like a p-n junction diode. The current-voltage relationship of an ideal diode can be expressed as

Where I represents the current, V represents the voltage, Is is the saturation current, and VT=KBT/q0, where KB represents the BoItzmann constant, q0 is the unit electric charge, and T is the temperature. At room temperature, VT=0.026v. It should be noted that the direction of the P-n diode current is defined to flow from P-type to n-type in the device, and the positive and negative values ​​​​of the voltage are defined as the P-type terminal potential minus the n-type terminal potential. Therefore, if this definition is followed, when the solar cell is working, its voltage value is positive, its current value is negative, and the I-V curve is in the fourth quadrant. Readers must be reminded here that the so-called ideal diode is based on many physical conditions, and actual diodes will naturally have some nonideal factors that affect the current-voltage relationship of the device, such as generation-recombination current, here We won't discuss it much.   When the solar cell is exposed to light, there will be photocurrent in the p-n diode. Because the built-in electric field direction of the p-n junction is from n-type to p-type, the electron-hole pairs generated by the absorption of photons will run towards the n-type end, while the holes will run towards the p-type end. The photocurrent formed by the two will flow from n-type to p-type. Generally, the forward current direction of a diode is defined as flowing from p-type to n-type. In this way, compared to an ideal diode, the photocurrent generated by a solar cell when illuminated is a negative current. The current-voltage relationship of the solar cell is the ideal diode plus a negative photocurrent IL, whose magnitude is:

In other words, when there is no light, IL=0, the solar cell is just an ordinary diode. When the solar cell is short-circuited, that is, V=0, the short-circuit current is Isc=-IL. That is to say, when the solar cell is short-circuited, the short-circuit current is the photocurrent generated by incident light. If the solar cell is open circuit, that is, if I=0, its open circuit voltage is:

Figure 2. Equivalent circuit of solar cell: (a) without, (b) with series and shunt resistors. It must be emphasized here that open circuit voltage and short circuit current are two important parameters of solar cell characteristics.

The power output of a solar cell is the product of current and voltage:

Obviously, the power output by the solar cell is not a fixed value. It reaches the maximum value at a certain current-voltage operating point, and the maximum output power Pmax can be determined by dp/dv=0. We can deduce that the output voltage at the maximum output power Pmax is:

and the output current is:

The maximum output power of the solar cell is:

The efficiency of a solar cell refers to the ratio of the solar cell converting the power Pin of the incident light into the maximum output electrical power, that is:

 General solar cell efficiency measurements use a light source similar to sunlight with pin=1000W/㎡.

Experimentally, the current-voltage relationship of solar cells does not completely follow the above theoretical description. This is because the photovoltaic device itself has so-called series resistance and shunt resistance. For any semiconductor material, or the contact between a semiconductor and a metal, there will inevitably be a greater or lesser resistance, which will form the series resistance of the photovoltaic device. On the other hand, any current path other than the ideal P-n diode between the positive and negative electrodes of the photovoltaic device will cause the so-called leakage current, such as the generation-recombination current in the device. , surface recombination current, incomplete edge isolation of the device, and metal contact penetration junction.

Usually, we use shunt resistance to define the leakage current of solar cells, that is, Rsh=V/Ileak. The larger the shunt resistance is, the smaller the leakage current is. If we consider the joint resistance Rs and the shunt resistance Rsh, the current-voltage relationship of the solar cell can be written as:

We can also use only one parameter, the so-called fill factor, to summarize both the effects of series resistance and shunt resistance. defined as:

It is obvious that the fill factor is maximum if there is no series resistor and the shunt resistance is infinite (no leakage current). Any increase in series resistance or decrease in shunt resistance will reduce the fill factor. In this way,. The efficiency of solar cells can be expressed by three important parameters: open circuit voltage Voc, short circuit current Isc, and fill factor FF.

Obviously, to improve the efficiency of a solar cell, it is necessary to simultaneously increase its open circuit voltage, short circuit current (that is, photocurrent), and fill factor (that is, reduce series resistance and leakage current).

Open circuit voltage and short circuit current:   Judging from the previous formula, the open circuit voltage of the solar cell is determined by the photocurrent and the saturated cell. From the perspective of semiconductor physics, the open circuit voltage is equal to the Fermi energy difference between electrons and holes in the space charge region. As for the saturation current of an ideal P-n diode, you can use:

to express. where q0 represents the unit charge, ni represents the intrinsic carrier concentration of the semiconductor, ND and NA each represent the concentration of the donor and the acceptor, Dn and Dp each represent the diffusion coefficient of electrons and holes, the above expression is assuming n - The case where both the type region and the p-type region are both wide. Generally, for solar cells using p-type substrates, the n-type area is very shallow, and the above expression needs to be modified.

We mentioned earlier that when a solar cell is illuminated, a photocurrent is generated, and the photocurrent is the closed-circuit current in the current-voltage relationship of the solar cell. Here we will briefly describe the origin of the photocurrent. The generation rate of carriers in unit volume per unit time (unit m -3 s -1 ) is determined by the light absorption coefficient, that is

Among them, α represents the light absorption coefficient, which is the intensity of incident photons (or photon flux density), and R refers to the reflection coefficient, so it represents the intensity of incident photons that are not reflected. The three main mechanisms that generate photocurrent are: the diffusion current of minority carrier electrons in the p-type region, the diffusion current of minority carrier holes in the n-type region, and the drift of electrons and holes in the space charge region. current. Therefore, the photocurrent can be approximately expressed as:

Among them, Ln and Lp each represent the diffusion length of electrons in the p-type region and holes in the n-type region, and is the width of the space charge region. Summarizing these results, we get a simple expression for the open circuit voltage:

where Vrcc represents the recombination rate of electron-hole pairs per unit volume. Of course, this is a natural result, because the open circuit voltage is equal to the Fermi energy difference between electrons and holes in the space charge region, and the Fermi energy difference between electrons and holes is determined by the carrier generation rate and recombination rate.