Solar cell test method, solar cell test device and computer-readable medium

Abstract

The invention relates to a solar cell test method, a solar cell test device and a computer readable medium for implementing the solar cell test method. In the solar cell test method, two current-voltage curves are ascertained at a contacted solar cell. Then, from each of the two curves, an emitter voltage curve is derived is each case, from which a charge change curve is ascertained by means of point-wise difference calculation. Then, a diffusion capacity curve is ascertained by means of point-wise quotient calculation between the charge change curve and a numeric temporal derivation of the emitter voltage curve. Then, a diffusion capacity function, which depends on a doping concentration as a free parameter, is adjusted to the ascertained diffusion capacity curve such that as a result of the adjustment, a doping concentration value for the doping concentration of the contacted solar cell is determined.

Description

[0001] Solar cell test method, solar cell test device and computer-readable medium

[0002] Description:

[0003] The invention relates to a solar cell testing method, a solar cell testing device and a computer-readable medium for implementing the solar cell testing method.

[0004] The doping concentration, or the conductivity required to determine it, of a solar cell is an important building block for the theoretical analysis of its performance and for identifying potential causes of process problems. This conductivity is measured in solar cell production at the beginning of the production chain during incoming goods inspection. However, conductivity changes primarily due to thermal processes during production, so it would be advantageous to measure it only at the end of production or even later. However, due to emitter diffusion and contacting via printed metal, the measurement method used during incoming goods inspection is no longer usable.

[0005] US 10,027,278 B2 (Sinton) describes a method for determining substrate doping concentration using a light pulse. A constant voltage is applied to the solar cell contacts while the cell is exposed to the light pulse. The applied contact voltage is then increased, and the change in charge density resulting from the voltage increase is determined. The substrate doping concentration is then calculated from the change in charge density. This method uses two voltage points on the IV characteristic curve, which are influenced by noise and measurement inaccuracies. The doping determined in this way is accordingly inaccurate.

[0006] In "Determination Of Base Doping Concentration Of Silicon Solar Cells From Light IV-curves", AIP Conference Proceedings 2487, 030008 (2022), K. Ramspeck et al. describe an alternative method in which the charge stored in the cell is calculated from a hysteresis-affected IV curve and an IV curve without hysteresis by first subtracting the two curves and then piecewise integrating the charge curve. From the stored charge of the solar cell calculated in this way, the minority charge carrier density An can be calculated. The thickness of the solar cell is required for this calculation. Due to Ndop = ni A2 / An * exp ( q Vj / k T )- An, the doping concentration can then be plotted against the voltage Vj. However, the resulting curve does not show a constant doping concentration, but rather a voltage-dependent curve. The authors therefore propose calculating the doping concentration by averaging over a so-called evaluation range. It is not clear how this evaluation range is defined, and therefore the doping concentration depends on the choice of evaluation range. In addition, measurement errors, e.g., due to noise, affect all subsequently calculated charges due to the integration of the difference curve for the stored charge.

[0007] The object of the invention is to provide a method and a device with which the doping concentration of a solar cell can be determined quickly and reliably.

[0008] The object is achieved according to the invention by a solar cell testing method having the features of claim 1, by a solar cell testing device having the features of claim 8, and by a computer-readable medium having the features of claim 9. Advantageous developments of the invention are listed in the subclaims.

[0009] According to one aspect of the invention, a solar cell test method for determining the doping concentration of a contacted solar cell is proposed. The basic idea here, similar to that described in the prior art, is to use stationary and / or hysteresis-affected characteristic curves to calculate the doping concentration. However, unlike the prior art, according to the invention, a diffusion capacity curve for the solar cell is first calculated from measured current-voltage curves. A diffusion capacity function, which depends on the doping concentration as a free parameter, is then fitted to this diffusion capacity curve determined from measurements. The result is a single doping concentration value and not a doping concentration curve that depends on the respective measurement voltage. This eliminates the step of averaging over an evaluation range, the selection of which is subject to a certain degree of arbitrariness.In addition, this procedure is less sensitive to measurement errors because curve fitting is performed over the entire measuring range.

[0010] The method requires two current-voltage curves, preferably with the same short-circuit current. These are selected from the following five current-voltage curves: a primary and a secondary hysteretic forward current-voltage curve, a primary and a secondary hysteretic reverse current-voltage curve, and a steady-state current-voltage curve. In other words, it is sufficient to use one steady-state current-voltage curve and one hysteretic (forward or reverse) current-voltage curve, or to use two hysteretic current-voltage curves instead of a steady-state current-voltage curve. The hysteresis current-voltage curve can be one forward and one reverse current-voltage curve, or two forward current-voltage curves or two reverse current-voltage curves.The stationary current-voltage curve can be calculated from two non-stationary current-voltage curves, i.e. two hysteresis-affected current-voltage curves, in order to then use one of the two hysteresis-affected current-voltage curves and the calculated stationary current-voltage curve for the procedure.

[0011] If two hysteretic current-voltage curves are determined in the same direction—i.e., two hysteretic reverse current-voltage curves or two hysteretic forward current-voltage curves—then the two curves should be scanned at different speeds. This means that the electrical voltage or current is varied at a different speed when determining one curve than when determining the other. To distinguish between the two hysteretic current-voltage curves determined in this way, one is referred to as the primary hysteretic current-voltage curve and the other as the secondary hysteretic current-voltage curve.

[0012] However, it should be noted that even when using a hysteresis-affected forward current-voltage curve and a hysteresis-affected reverse current-voltage curve, these two curves can be traversed at different speeds. However, the distinction is already established by the forward and reverse traversal, so the terms "primary" and "secondary" are not meaningful.

[0013] Preferably, the two current-voltage curves are determined from the following four current-voltage curves: a primary hysteretic forward current-voltage curve, a secondary hysteretic forward current-voltage curve, a primary hysteretic reverse current-voltage curve and a secondary hysteretic reverse current-voltage curve.

[0014] To determine the forward current-voltage curve, a varying electrical voltage is applied to the contacted solar cell and an associated current dependent on the applied voltage is measured. As with all measurements of current-voltage pairs of a characteristic curve, a varying electrical current can alternatively be applied and an associated voltage dependent on the applied current can be measured. In any case, to determine the forward current-voltage curve, the applied voltage or the applied current is varied such that the applied or measured voltage passes through voltage values ​​from a lower voltage to a higher voltage in one forward sweep, with the electrical voltage or the electrical current being varied so quickly that the voltage values ​​and the associated current values ​​are arranged on the hysteresis-affected forward current-voltage curve.The procedure for determining the reverse current-voltage curve is the same as for the forward current-voltage curve, with the difference that in a reverse sweep the voltage passes through voltage values ​​from a higher voltage to a lower voltage.

[0015] Highly efficient silicon solar cells are known for their high "capacitance." This means they react more slowly to changes in voltage. When measuring the current-voltage characteristic (current-voltage curve, or IU curve for short) of a solar cell, capacitive errors occur due to this effect if the voltage value specified by the measuring device changes too quickly during the characteristic measurement, and the solar cell cannot adjust sufficiently quickly to a change in the applied voltage or current. This effect is often observed in power measurements of crystalline silicon solar cells or solar modules and is known as the hysteresis effect. The effect is observed with increasing measurement speed and increasing solar cell efficiency, especially at high efficiencies, in crystalline silicon solar cells, but can also be significant in other solar cells.The faster the measurement is made and the better the solar cell, the stronger the effect.

[0016] To measure the current-voltage curve, the solar cell is contacted, and a measuring voltage is applied to the contacts, which passes through a voltage measurement range. The applied voltage is selected so that the solar cell, under illumination, passes through operating points between open-circuit voltage (Voc) and short-circuit current (Isc), including the maximum power point (MPP). The current-voltage curve can also be measured in the same voltage range without illumination.

[0017] The current-voltage curve is the steady-state current-voltage curve (also called the steady-state IV curve). This curve is obtained when sufficient time is allowed for each set voltage value of the solar cell to decay within a settling phase and for an equilibrium state to be established. The waiting time required for each point on the steady-state current-voltage curve to reach this equilibrium state depends on properties of the solar cell, such as its material composition, structure, doping and doping distribution, and the like.

[0018] If the current-voltage curve is passed through too quickly, i.e., during a rapid measurement run in which the applied voltage or current varies too rapidly for the equilibrium state to be established, the measured current-voltage curve deviates from the steady-state current-voltage characteristic, particularly in the MPP region. Hysteresis also develops, as the deviation depends not only on the measurement speed but also on the measurement direction. If the voltage is passed through from a lower voltage value to a higher voltage value, this corresponds to the steady-state current-voltage curve passing from a short-circuit state (Isc) to an open-circuit state (Voc) when the solar cell is illuminated.In this hysteresis-affected situation, a curve is obtained which is referred to here as the forward current-voltage curve, or forward curve for short, and which runs below the steady-state current-voltage curve in the current-voltage diagram. If, on the other hand, the voltage is passed through from a higher voltage value to a lower voltage value, this corresponds to the current-voltage curve running from the open-circuit state to the short-circuit state when the solar cell is illuminated. In the hysteresis-affected situation, a curve is obtained which is referred to below as the reverse current-voltage curve, or backward curve for short, and which runs above the steady-state current-voltage curve in the current-voltage diagram. If a complete sweep occurs, in which the voltage across the solar cell is passed through from zero to a maximum value and back to zero, then hysteresis results.The steady-state current-voltage curve can be determined by scanning the current-voltage curve at a correspondingly slow rate. The hysteresis effect can be avoided by scanning the current-voltage curve slowly. However, with particularly high-quality solar cells, several seconds would be required for one scan to avoid hysteresis. However, with modern production facilities, the time available for solar cell testing on a production line is only about 40 ms. An attempt to explain the behavior of a solar cell with a hysteresis-prone current-voltage curve using a model based on capacitive effects was made in the publication "Assessing Transient Measurement Errors for High-Efficiency Silicon Solar Cells and Modules," by R.A. Sinton, IEEE Journal of Photovoltaics (November 2017).It also proposes an alternative to a direct measurement of the stationary current-voltage curve and explains how the stationary current-voltage curve, or at least an approximation thereof, can be calculated from the two previously determined hysteresis-affected current-voltage curves, namely the forward curve and the backward curve.

[0019] As explained in the introduction, at least two current-voltage curves are determined from five possible current-voltage curves, wherein the two determined current-voltage curves preferably have the same short-circuit current value Isc. An emitter voltage curve is determined from the voltage values ​​and the corresponding current values ​​of the two determined current-voltage curves. In other words, a first emitter voltage curve is determined from the first of the two determined current-voltage curves and a second emitter voltage curve is determined from the second determined current-voltage curve. This is done for the first emitter voltage curve by calculating a voltage at the emitter, i.e. an emitter voltage value, Vj, for each point on the first current-voltage curve from the voltage value V and the corresponding current value I at that point. In other words, the voltage values ​​for the two determined current-voltage curves are converted to the emitter voltage values.This means that for all pairs of current values ​​and corresponding voltage values ​​from which the two current-voltage curves are formed, the current values ​​remain the same or essentially the same, while the voltage values ​​are converted to emitter voltage values ​​(Vj - junction voltage).

[0020] The conversion can be performed, for example, using the formula Vj = V + Rs * I. In this configuration, the series resistance Rs of the solar cell must have been previously measured or determined by another method. Alternatively, one can consider, for example, that Rs depends on the voltage, so the conversion formula is Vj = V + Rs(V) * I.

[0021] A charge change curve is then determined from the two emitter voltage curves by calculating a point-by-point difference between a current value from the first emitter voltage curve and a current value from the second emitter voltage curve at points of equal emitter voltage. In other words, for each emitter voltage value, a corresponding first current value on the first emitter voltage curve and a corresponding second current value on the second emitter voltage curve are selected, and a difference is calculated between the two current values. The difference value thus determined is then a value on the charge change curve (dQ / dt) dependent on the emitter voltage.

[0022] In addition, a time derivative (dVj / dt) of the emitter voltage curve is generated numerically, particularly of the first or second emitter voltage curve. By forming a point-by-point quotient, a diffusion capacity curve (dQ / dVj = dQ / dt dVj / dt) is determined or calculated from the charge change curve and the time derivative. Alternatively, the diffusion capacity curve (dQ / dVj) can be calculated theoretically. This curve is referred to below as the diffusion capacity function. The diffusion capacity function has the desired doping concentration (NA) of the solar cell as a free parameter. Among other things, the wafer thickness w and the temperature T can appear as constants in the diffusion capacity function, which must be determined beforehand by measurement.

[0023] In one embodiment, the diffusion capacity function has the following form: dQ / dVj = e • w • m 2 / (Vth • exp(Vj / V t h) • (NA 2 + 4 n,-2 exp(Vj / V t h)))

[0024] In this formula, e denotes the elementary charge, n the intrinsic charge carrier concentration of the solar cell material, in particular silicon, Vth=kßT / e the thermal stress, kß the Boltzmann constant, and NA the doping concentration, from which the base conductivity can be directly determined. In other embodiments of the method, the diffusion capacity function can have a different form. For example, it is possible that the intrinsic charge carrier concentration n depends on the temperature and / or the doping, depending on the physical model used, and is accordingly taken into account in the diffusion capacity function.

[0025] In a next step, the diffusion capacity function is fitted to the determined diffusion capacity curve in such a way that, as a result of the fitting, a doping concentration value for the doping concentration (NA) of the contacted solar cell is determined.

[0026] According to a preferred embodiment, determining the steady-state current-voltage curve comprises determining the hysteresis-affected forward current-voltage curve, determining the hysteresis-affected reverse current-voltage curve, and calculating the steady-state current-voltage curve from the forward current-voltage curve and the reverse current-voltage curve.

[0027] Preferably, one of the two current-voltage curves or both current-voltage curves are determined during exposure of the solar cell. In particular, it can be provided that both determined current-voltage curves are measured at the same exposure. Alternatively, both current-voltage curves can be measured without exposure.

[0028] The diffusion capacitance function is fitted to the determined diffusion capacitance curve within a specified range, i.e., a specified voltage or current range. For example, this can be a voltage range that includes an emitter voltage value at which the solar cell is at its maximum power point (MPP) on its steady-state current-voltage characteristic. Alternatively, the specified range can include the range between the open-circuit voltage and the short-circuit current.

[0029] In addition to the doping concentration, the diffusion capacity function can also depend on one or more other parameters, which are then considered as additional free parameters during the fitting. This is a multidimensional fitting in which the diffusion capacity function depends, for example, on a wafer thickness or cell thickness of the solar cell and / or a temperature as additional free parameters. The multidimensional fitting is then performed in such a way that a cell thickness, a temperature, and / or one or more other parameters are determined as a result of the fitting.

[0030] In a further aspect of the invention, a solar cell testing device is provided. The solar cell testing device is preferably part of a solar cell production system and is arranged, for example, at the end of the system for so-called end-of-line testing. The embodiments and advantages listed above and below in connection with the solar cell testing method also apply accordingly to the solar cell testing device. This also applies to the computer-readable medium, which forms a further aspect of the invention. The invention is explained below using exemplary embodiments with reference to the figures. Herein:

[0031] Fig. 1 shows a current-voltage diagram of different current-voltage curves determined according to the invention; and Fig. 2 shows a flowchart of the method steps of a solar cell testing device according to a preferred embodiment.

[0032] Fig. 1 shows a current-voltage diagram in which the voltage is plotted linearly along the x-axis in volts (V) and the current is plotted linearly along the y-axis in amperes (A). The diagram shows three curves 1, 2, 3, which are measured characteristic curves of a solar cell. They were measured in three different runs. During all runs, the solar cell was illuminated with a light source. The IU characteristic curve 1 was measured by applying a voltage to the solar cell from a voltage value of -0.1 V up to a maximum value of approximately 0.7 V. The resulting current value was measured for each voltage value. The pairs of voltage value and corresponding current value determined in this way were then plotted in the diagram to obtain the IU characteristic curve 1. Each individual point in the IU characteristic curve represents one of these pairs and thus an operating point of the solar cell.The IU characteristic curve 1 is obtained in this way if the sweep is so slow that a steady-state current value is established at each voltage value. The IU characteristic curve 1 is therefore a steady-state current-voltage curve. The line that appears to connect the points of the IU characteristic curve 1 is a curve fit to the points.

[0033] The IU characteristic curve 1 crosses the x-axis at an open circuit voltage of approximately Voc = 0.7 V and the y-axis at a short-circuit current of approximately Isc = 1.67 A. It can be roughly divided into three different regions 11, 12, 13. In the first characteristic curve region 11, the characteristic curve runs approximately parallel to the x-axis, while in the third characteristic curve region 13 it drops steeply. The transition between these two regions 11, 13 lies in a middle, second characteristic curve region 12. This middle characteristic curve region 12 has the operating point of maximum power (MPP), in which the product of the current value and the voltage value reaches a maximum value. While the characteristic curves / curves 1, 2, 3 in this diagram were determined using an illuminated solar cell, the method works accordingly for unilluminated solar cells.

[0034] If the voltage values ​​are cycled through so quickly that a hysteresis effect develops, different curve progressions result during a forward sweep compared to a reverse sweep. The curves determined in this way are also shown in Figure 1. They are a hysteresis-affected forward current-voltage curve, or forward curve 2 for short, and a hysteresis-affected reverse current-voltage curve, or reverse curve 3 for short. While forward curve 2 runs below the IU characteristic curve 1, reverse curve 3 runs above the IU characteristic curve 1.

[0035] Fig. 2 shows a flowchart of a solar cell testing method according to a preferred embodiment. The ultimate goal of the method shown in Fig. 2 is to determine the doping concentration of a solar cell. This is equivalent to determining the base conductivity (p bulk) of the solar cell. The test procedure utilizes the hysteresis of the solar cell, which is caused by the diffusion capacity dependent on the doping concentration. The test requires the current-voltage characteristic (IU characteristic) or current-voltage curve in the steady state, i.e., the stationary current-voltage curve or IU characteristic 1 and at least one hysteresis-affected curve 2, 3. Alternatively, another combination of two of the three curves / characteristics shown in Fig. 1 can be used.

[0036] The hysteresis-prone curves 2 and 3 can be created by quickly scanning from low to high voltages (forward curve 2) or from high to low voltages (backward curve 3). Backward curve 3 is preferred.

[0037] The determination of the two curves is shown in Fig. 1 as the first step 101 of the method. Both selected curves are compared based on their voltage at the emitter Vj (junction voltage) and not on the external measured voltage. For this purpose, the measured voltage V at each point of the respective curve must be compared with current I with a previously measured series resistance R s to the voltage at the emitter Vj according to Vj = V + R s * I [1] must be converted (step 102).

[0038] Furthermore, the time derivative of the emitter voltage the thickness of the wafer w, as well as the temperature T at which the measurement was made. From the two currents of the IU characteristic curve 1 and the hysteresis curve 2, 3, the temporal change of the charge ^ of the solar cell is then calculated at each point of the same emitter voltage using i.e. a charge change curve, is calculated (step 103). The diffusion capacity is then calculated from [2] and [3] as

[0039] The diffusion capacity curve is thus determined by forming a point-by-point quotient between the charge change curve and a numerical time derivative of the emitter voltage curve (step 104).

[0040] The theoretical course of the diffusion capacity is described in [1] and is Here, e is the elementary charge, the intrinsic

[0041] Charge carrier concentration of silicon, V th = the thermal stress, k B the Boltzmann constant and N A the doping concentration, from which the base conductivity can be directly determined.

[0042] The theoretical curve of the diffusion capacity can now be adapted to the measured curve (step 105), with N Aas a free parameter. As a result of the adjustment, a doping concentration value for the doping concentration of the contacted solar cell is output (step 106).

Claims

Patent claims: 1 . Solar cell test method for determining a doping concentration of a contacted solar cell, comprising the following method steps: - Determining two current-voltage curves from the following five Current-voltage curves: A primary hysteresis-related forward current-voltage curve, a secondary hysteresis-related forward current-voltage curve, a primary hysteresis-related reverse current-voltage curve, a secondary hysteresis-related reverse current-voltage curve, and a stationary current-voltage curve, wherein, to determine the forward current-voltage curve, a varying electrical voltage is applied to the contacted solar cell and an associated current dependent on the applied voltage is measured, or by applying a varying electrical current and measuring an associated voltage dependent on the applied current, wherein the applied voltage or the applied current is varied such that the applied or measured voltage in a forward sweep passes through voltage values ​​from a lower voltage towards a higher voltage, wherein the electrical voltage or the electrical current is varied so quickly,that the voltage values ​​and the associated current values ​​are arranged on the hysteresis-affected forward current-voltage curve, and to determine the reverse current-voltage curve, a varying electrical voltage is applied to the contacted solar cell and an associated current dependent on the applied voltage is measured, or by applying a varying electrical current and measuring an associated voltage dependent on the applied current, wherein the applied voltage or the applied current is varied such that the applied or measured voltage passes through voltage values ​​from a higher voltage towards a lower voltage in a backward pass, wherein the electrical voltage or the electrical current is varied so rapidly that the voltage values ​​and the associated current values ​​are arranged on the hysteresis-affected reverse current-voltage curve, wherein to determine the respective primary curve the electrical voltage or the electrical current is varied at a different variation speed than when determining the respective secondary curve; - determining a first emitter voltage curve from the voltage values ​​and current values ​​of the first of the two determined current-voltage curves and determining a second emitter voltage curve from the voltage values ​​and current values ​​of the second of the two determined current-voltage curves; - Determining a charge change curve by forming a point-by-point difference between the current values ​​of the first of the two determined emitter voltage curves and the current values ​​of the second of the two emitter voltage curves, the difference being formed at points of equal emitter voltages; - Determining a diffusion capacity curve by means of point-by-point quotient formation between the charge change curve and a numerical time derivative of the first or second emitter voltage curve; - Fitting a diffusion capacity function dependent on a doping concentration as a free parameter to the determined diffusion capacity curve in such a way that a doping concentration value for the doping concentration of the contacted solar cell is determined as a result of the fitting.

2. Solar cell test method according to claim 1, characterized in that determining the steady-state current-voltage curve comprises determining two current-voltage curves from the following four current-voltage curves: a primary hysteresis-affected forward current-voltage curve, a secondary hysteresis-affected forward current-voltage curve, a primary hysteresis reverse current-voltage curve, a secondary hysteresis reverse current-voltage curve, and calculating the steady-state current-voltage curve from the two current-voltage curves.

3. Solar cell testing method according to claim 1 or 2, characterized in that one or both of the two current-voltage curves is / are determined during exposure of the solar cell.

4. Solar cell test method according to claim 3, characterized in that the two determined current-voltage curves are measured under the same exposure.

5. Solar cell test method according to one of the preceding claims, characterized in that the adaptation of the diffusion capacity function to the diffusion capacity curve takes place over a voltage range which includes an emitter voltage value at which the solar cell is at its point of maximum power on its stationary current-voltage characteristic curve.

6. Solar cell testing method according to one of the preceding claims, characterized in that the step of adjusting comprises a multi-dimensional adjusting, in which the diffusion capacity function depends on a cell thickness of the solar cell and / or on a temperature as further free parameters and in which the adjusting is carried out in such a way that a cell thickness and / or a temperature is determined as a result of the adjusting.

7. A solar cell testing device for determining a doping concentration of a solar cell, comprising a contacting device with contacts for contacting the solar cell, a current source or voltage source electrically connected to the contacts, and a control device configured to carry out the following method steps on the solar cell: - Determining two current-voltage curves from the following five current-voltage curves: a primary hysteresis-related forward current-voltage curve, a secondary hysteresis-related forward current-voltage curve, a primary hysteresis-related reverse current-voltage curve, a secondary hysteresis-related reverse current-voltage curve, and a stationary current-voltage curve, wherein, to determine the forward current-voltage curve, a varying electrical voltage is applied to the contacted solar cell and an associated current dependent on the applied voltage is measured, or by applying a varying electrical current and measuring an associated voltage dependent on the applied current, wherein the applied voltage or the applied current is varied such that the applied or measured voltage passes through voltage values ​​from a lower voltage to a higher voltage in a forward sweep,wherein the electrical voltage or the electrical current is varied so rapidly that the voltage values ​​and the associated current values ​​are arranged on the hysteresis-affected forward current-voltage curve, and to determine the reverse current-voltage curve, a varying electrical voltage is applied to the contacted solar cell and an associated current dependent on the applied voltage is measured, or by applying a varying electrical current and measuring an associated voltage dependent on the applied current, wherein the applied voltage or the applied current is varied such that the applied or measured voltage passes through voltage values ​​from a higher voltage towards a lower voltage in a backward pass, wherein the electrical voltage or the electrical current is varied so rapidly,that the voltage values ​​and the corresponding current values ​​are arranged on the hysteresis-affected reverse current-voltage curve, whereby, to determine the respective primary curve, the electrical voltage or the electrical current is varied at a different rate than when determining the respective secondary curve; - determining a first emitter voltage curve from the voltage values ​​and current values ​​of the first of the two determined current-voltage curves and determining a second emitter voltage curve from the voltage values ​​and current values ​​of the second of the two determined current-voltage curves; - Determining a charge change curve by forming a point-by-point difference between the current values ​​of the first of the two determined emitter voltage curves and the current values ​​of the second of the two emitter voltage curves, the difference being formed at points of equal emitter voltages; - Determining a diffusion capacity curve by means of point-by-point quotient formation between the charge change curve and a numerical time derivative of the first or second emitter voltage curve; - Fitting a diffusion capacity function dependent on a doping concentration as a free parameter to the determined diffusion capacity curve in such a way that a doping concentration value for the doping concentration of the contacted solar cell is determined as a result of the fitting.

8. A computer-readable medium having computer-executable instructions which, when executed, implement a method according to any one of claims 1 to 6.

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