1.1. Solar Cell Industry and Efficiency Characteristic
In the global trend, promoting the development of renewable energy utilization is a critical strategy. The renewable energy includes wind energy, solar energy, biomass energy, hydro energy, and geothermal energy. In this paper, we discuss emphasis on the subject of the product quality of the solar photovoltaic manufacturing industry.
In the early application of photovoltaic, Bigger and Kern (1990) discussed the methodology developed with help from Electric Power Research Institute (EPRI) in the electric utility industry. Hasti et al. (1990) reviewed the status of crystalline cell research and presented the recent results through a combination of university. Hamakawa (2003) discussed the technological development of the solar photovoltaic in recent and investigated the some new strategies to develop photovoltaic industry in Japan. With the technological progress, the solar cell productions are various and different from the solar cell industry. Current practices in the solar cell producing include various technological which mainly produced crystal silicon (c-Si) , amorphous Si (a-Si) and CIGS. Many researchers investigated extensively the dynamics of solar cell industry in the literature. Nakata (2011) presented an extensive study to illustrate the technological in business for global solar cell industry.
Szlufcik et al. (1997) discussed silicon solar-cell (mono and multi) modules comprise approximately 85% of all worldwide PV module shipments and presented an extensive study to illustrate which the efficiency-enhancement techniques of commercial cells have investigated extensively. However, the energy conversion efficiency as high as 24% have been achieved on the laboratory.
In recent years, the typical efficiency of industrial crystalline silicon solar cells is in the range of 16–20%. In the photovoltaic industry, the major concern is how to improve the efficiency and decrease the price of the commercial PV modules. Current practices in the high-efficiency features to industrially fabricated solar cells acceptable trend are efficiencies above 18% for multi crystalline and above 20% for mono crystalline silicon solar cells.
Luque and Hegedus (2003) introduced the manufacturing process of solar cell and the relationship characteristic parameters for the I–V curve of the solar cell. Those characteristic parameters are defined in the following: current, Voc is the open-circuit voltage, PMP is the largest rectangle for any point on the I–V curve and Pin is the incident power.
Tasi (2005) discussed the photoelectric for the efficiency of the silicon solar cell.
Spertino and Akilimali (2009) discussed the two factors that influenced the typical large photovoltaic (PV) are the current–voltage (I–V) mismatch and the impact of reverse currents
which is in different operating condition. The I–V curve of the solar cell is computed by the characteristic parameters of the solar cell’s efficiency. The efficiency of the solar cell can contribute the price of PV module down when the manufacturing I–V mismatched. The three important parameters factors to maintain the conversion efficiency and quality are Voc, Isc, and Rsh.
1.2. Process Capability and Tool Replacement Policy
Spertino and Akilimali (2009) discussed the measurements of solar cell and use the diode characteristic to determine I–V curve’s behavior. He also discussed the solar module can be formed as series-parallel network module through the solar cell pole parallel current generator.
The I–V curve’s behavior is following other important parameters including the maximum-power point, Pmax. A simulate natural light is composed by typical I –V curve measurement system. The I–V curve measurement system use the external load or power supply to make voltage and current go through the device then measure them. The measurement system provided many measurements of important parameters including the test bed to mount the device under test, temperature control and sensors, and a data acquisition system to measure the current and voltage.
The efficiency measuring is easily neglected in the process quality. Ruland et al. (2003) presented the quality control of the line resistivity measurements. The I–V curve behavior trend must be controlled to make sure if it maintains the efficiency quality. To control this conversion efficiency, they should control the multiple characteristics parameters like FF, Voc, Isc, Rs, Rsh etc at the same time. However, these three of important parameters as Voc, Isc, and Rsh also affected the I–V curve behavior trend. With the progress of technic of solar cell cell’s producing process, the quality of efficiency measuring is important and variously. Most of current conditions for conversion efficiency quality control are not always fulfilled in many manufacturing situations.
The process capability indices (PCI) can be widely and straightforwardly applied to the product producing performance. Pearn and Wu (2005) discussed to use multi-characteristics process indices to apply to in measuring manufacturing for passive components to optic fiber communications, which are multi-characteristics products with one-side specification. For the product performance, they estimated the bootstrap methods’ confidence bound as follows,
{∏ }.
Furthermore, several authors considered about the decreasing of the tools.
Many researchers discussed to establish the tool replacement policy for executing the tool wear control. Quesenberry (1988) proposed the tool wear should be corrected by a regression model and suggested that the tool wear rate must be estimated accurately. In order to controls multiple characteristics for the quality of product performance, however, the studies must be
consolidated as the tool replacement policy causes has become critical issues. Pearn et al.
(2006) presented the research of process capability indices (PCI) applied to the multiple characteristics processes of the tool wear policy.
However, about the assumption by the researchers to the tool wear of multiple characteristics process capability, the subject of one side of multiple characteristics which combined the tool wear is more critical and important than only discussed about the tool wear.
1.3. Research Objectives
Three realistic examples about the one-side of multiple characteristics process to illustrate the tool wear applications of the propose approaches. The three important parameters as Voc, Isc, and Rsh also affected the I–V curve behavior trend. The real-world case is the investigation of the one side of the multiple characteristics production in the solar process. The method to monitor the products for avoiding producing the unacceptable products is using the control chart to decide if the process should be stopped or should to replace the tools.
We propose the modified which bases on the bootstrap (PB) method in a period dynamic process. Further, the process of capability measurement is the assignable causes.
Considering the influence of systematic assignable cause, we modify the dynamic process of
indices. Since the process mean μ and the standard deviation σ are usually unknown, we apply the percentile bootstrap (PB) method to obtain the confidence bounds to modify
indices. However, the tool must be replaced due to the wear in the producing process. To monitor the tool capable in the producing process, we can monitor the dynamic changes by modifying ̂ indices. Then these results apply the bootstrap (PB) method to find modification of the lower confidence bounds of indices.
2 Multiple Quality Characteristics of Crystalline Silicon Solar Cell
2.1.Isc
Ideal current source (Isc) is one of the characteristics which affected the I–V curve behavior trend. The I–V curve of the solar cell is computed by the characteristic parameters of the solar cell’s efficiency. The efficiency of the solar cell can contribute the price of PV module down when the manufacturing I–V mismatched. In the following sections, we illustrate the relationship between the ideal current source (Isc) and the efficiency of the solar cell.
Luque and Hegedus (2003) is illustrated widely of the characteristics and the efficiency of the silicon solar cell. The efficiency expression of solar cell is based on the ideal current source (Isc) in the two parallel diodes. One of the ideal factors of diode is “1”. It represents the recombination current in the quasi-neutral regions (∝ eqV /kT ) , and the other ideal factor of diode is “2”. It represents the recombination in depletion regions (∝ eqV /2kT ) . Figure 1 presents the simple solar cell model and the two ideal factors of diode “1” and “2”. Then, the general current produced by a solar cell as
( ) ( ).
The short-circuit current and dark saturation are restricted by the solar cell structure, material properties, and the operating conditions. All of the solar cell operated requirements must be investigated from these terms.
Figure 1. Simple solar cell circuit model (Luque and Hegedus (2003)).
Tasi (2005) discussed the efficiency of silicon solar cell. The photocurrents go from n conductor to p conductor when is in the dark. In contrast, the photocurrent go from p conductor to n conductor when there is light. The ideal conductor’s relationship between the circuit (I) and the voltage (V) is as follows
.
Where I is the current, V is the voltage, Is is the saturation current, , Where KB is Boltzman constant, T is the temperature, q0 is the electron unit. When the light shapes the circulated photocurrent from the n conductor to the p conductor, the direction of the electric field will point from the n conductor to the p. The photocurrent which shapes from the
light is negative pole (IL) . The formula which considers about the relationship between the ideal current and negative pole current of voltage and current is as follows
( ) .
The silicon solar cell is a general diode as the IL=0 in the dark. Assuming that the voltage of solar cell becomes zero (V=0) as the short circuit, the short-circuit current should be calculated as Isc=-IL.
2.1.Voc
Figure 2. Current-Voltage (I-V) characteristic curve.
On the other hand, assuming that the silicon solar cell’s current is zero (I=0) as the open circuit, then this voltage should be calculated as
.
The silicon solar cell’s current-voltage (I-V) characteristic curve is plotted in Figure2. The calculation of the solar cell’s output power is voltage multiplies current as follows
( ) .
The output power of solar is the point on IV characteristic curve. Its presenting way is multiplying the maximum of I=IMP and V=VMP as Figure2, but this product is unconcern. The maximum output power Pmax can be decided by dP/dV=0
[ ] .
Thus, the maximum power point Pmax is calculated as Pmax=IpmaxVpmax, as well as the
efficiency of the silicon solar cell is the ratio for the power of incident light (Pin) and shown as
η
.
Another parameter the fill factor, FF, provides a convenient measuring for the silicon solar cell’s efficiency. The fill factor, FF, is a measurement of the two rectangles’ ratio of the I-V characteristic curve, and it is always less than one. The fill factor, FF, is shown or calculated in Figure2 as
In fact, the photovoltaic includes both parasitic series resistance and shunt resistance and the author of Figure1 didn’t present perfectly for the relationship between the current and voltage. Generally, the typically associated resistances as parasitic series resistance and shunt resistances are easily neglected in the real silicon solar cell. Luque and Hegedus (2003) presented extensively to illustrate the author of Figure1 does not reflect the real situation accurately and discussed the formula must to been modified as shown in Figure3 or
( ) ( )
.
Figure 3. The parasitic series resistance and shunt resistance for silicon solar cell (Luque and Hegedus (2003)).
The metal conductor’s structure must accompany with the resistance. The resistance is the parasitic series resistance and the shunt resistance (Rsh) of the photovoltaic, and the shunt resistance (Rsh) defined as the leakage current of silicon solar cell clearly. Similarly, the relationship between the current and the voltage of silicon solar cell must be considered as the resistance by parasitic series resistance and the shunt resistance as
[ ]
.
However, assuming that the voltage is zero (V=0) and will effect the parasitic series resistance (Rs) more than the shunt resistance (Rsh) . Thus, the relationship between the current and voltage have been modified as
.
The shunt resistance (Rsh) won’t effect the short-circuit current, but it will reduce the open-circuit voltage. Furthermore, the plotting slop of Voc and Isc defined Rsh, and it presents as Figure 4.
Figure 4. The shunt resistance (Rsh) and the parasitic series resistance for Isc and Voc.
The shunt resistance is calculated as
.
When the shunt resistance is more, the leakage current of silicon solar cell (Ileak) is less. In the actual model, the shunt resistance (Rsh) is the important parameter.
2.4 Efficiency Characteristics Measurement
In the paper, we discuss the tool replacement policy for the one-side index of the maximum manufacturing specification with multiple characteristics. The ideal current source (Isc) , the open-circuit voltage (Voc) and the shunt resistance (Rsh) are the critical factor that affected the performance of the I-V characteristic curve. These three key parameters’ specifications are shown as Table1.
Table 1. Specifications for the ideal current source (Isc) , the open-circuit voltage (Voc) and the shunt resistance (Rsh).
Parameters Specification
The ideal current source (Isc) ≧8.4 The open-circuit voltage (Voc) ≧0.60
The shunt resistance Rsh ≧60
The measuring method of these three key parameters is to simulate the sunshine and the 1000w/m2 incident light (Pin) . The measuring machine of the silicon solar cell’s efficiency imitates the sunshine shines on the surface of the silicon solar cell and measures it as shows in Figure5. While the surface of the silicon solar cell is shined by the measuring machine, the Photoelectric Effect is occurred then produce the current. I-V characteristic curve and the ideal current source (Isc) , the open-circuit voltage (Voc) and the shunt resistance (Rsh) are measured by the probe of the measuring machine, and they are monitored during the production process.
Figure 5. The measuring machine for the efficiency of the silicon solar cell.
Figure6 illustrates how the probe measures the characteristic of the silicon solar cell.
Moreover, the probe’s wear is one of the important controls of the measuring machine in the tool wear policy.
Figure 6. The probe of the measuring machine.
The process is incapable when the probe’s failure reaches the minimum of the rule.
Therefore, the tool replacement must proceed during the measuring process. The process indices give an accurate measurement to the defective of the tool wear. The process capability indices provide suitable control to the tool wear in the producing process. The ideal current source (Isc) , the open-circuit voltage (Voc) and the shunt resistance (Rsh) are three important parameters that affect the silicon solar cell’s efficiency simultaneously. We discuss to use the one-side process indices of the ideal current source (Isc) , the open-circuit voltage (Voc) and the shunt resistance (Rsh) to control the probe replacement policy in the producing process in the following sections.