A Study of the Quantitative Relationship of ChargeDensity Changes and the Design Area of a Fabricated Solar Cell
 Author: Jeon KyeongNam, Kim SeonHun, Kim HoyJin, Kim InSung, Kim SangHyun
 Organization: Jeon KyeongNam; Kim SeonHun; Kim HoyJin; Kim InSung; Kim SangHyun
 Publish: Transactions on Electrical and Electronic Materials Volume 12, Issue5, p204~208, 25 Oct 2011

ABSTRACT
In this paper, the design area of a fabricated solar cell has been analyzed with respect to its charge density. The mathematical calculation used for chargedensity derivation was obtained from the 2001 version of a MATHCAD program. The parameter range for the calculations was ±1 × 10^{17} cm^{3}, which is in the normal parameter range for ntype doping impurities (7.0 × 10^{17} cm^{3}) and also for
p type impurities (4.0 × 10^{17} cm^{3}). Therefore, it can be said that the fabricated solarcell design area has a direct effect on chargedensity changes.

KEYWORD
Gallium arsenide , Silicon , Impurity , Doping , Fabricated design area , Charge density

1. INTRODUCTION
The determination of the fabricated design area in research and development of solar cells for highefficiency power conversion is very important. There is a direct relationship between the design area and charge density in the
pn junction depletion region. However, the scientific literature contains no direct studies of the effects on charge density of the design area of solar cells. The research described in this paper indicates how changes in the solarcell design area can be used to affect charge density in fabrication design for both silicon and gallium arsenide (GaAs) solar cells. In addition, the thickness and the area of semiconductor thin film in solarcell fabrication was found to be related to the carrier lifetime. Therefore, the carrier lifetime of solarcell semiconductor thin film is related to highefficiency power conversion.Basically, the objective of increasing electron density in most solarcell fabrication designs leads to a thicker design for negative types than for positive types.Therefore, this design technology involves a set of technologies to increase powerconversion efficiency by increasing electron density. A typical device structure which is routinely used for highefficiency device fabrication consists of a
pn silicon front contact and a GaAs material back contact, as shown in Fig. 1.The following sequence of processing steps is generally used for device fabrication. This paper investigates the changes in charge density with various solarcell fabrication design areas (width [cm] × length [cm]) for standard, type 1, type 2, type 3, type 4, and type 5 designs. In addition, the effects of chargedensity changes and current output were investigated as direct effects. The charge density is the total amount of charge in a fixed length or area divided by the material volume [1].
2. THEORETICAL BACKGROUND
The electrical properties of semiconductors related to doping and to states which exist deep in the band gap can be conveniently measured using the depletion capacitance of a diode.
The present treatment of
p+n junctions will be limited, and it should be noted that the result for the depletion capacitance of Schottky diodes is identical. Bothpn junctions and Schottky diodes can serve this purpose. However, minority carrier effects can be studied only withpn junctions because Schottky diodes are majority carrier devices. The term “abrupt junctions” refers to junctions which contain ideally abrupt doping profiles as shown in Fig.2 (a), and the term “onesided” means that the concentration of dopant is much higher on one side. Any variation lateral to the junction is ignored, and the overall junction must be neutral, which implies that N_{A}X_{p} = N_{D}X_{n}. The solutions for the electric field and electrostatic potential are shown in Figs. 2(b) and (c). These can be straightforwardly obtained by integrating Poisson’s equation, which for the n side is given by (meterkilogramsecond [MKS] units),where ε is the dielectric constant and
q is the charge of an electron. The result for the electric field is:and that for the electrostatic potential is:
where V
_{x} is the integration constant corresponding to the total electrostatic potential across the diode. For a onesided abrupt junction, V (x = 0) ？ 0 , which implies that:where V_{bi} is the “builtin” potential and V is the applied bias. For onesided and abrupt junctions, the depletion depth is given by:
The solution for the electrostatic potential is often drawn superimposed on the band structure as shown in Fig.2 (d) as a “bandbending diagram.” Here, the Fermi level does not vary across the junction if no bias is applied because the Fermi level is the chemical potential of the carriers, which must be constant in equilibrium. The crossing point between the Fermi level and the donor level determines the depletion depth. If a slight bias, ΔV, is applied, then according to Eq. 6,
ΔV = qN_{D}WΔW/ε. Because the amount of donor charge which is uncovered at the edge of the depletion region is given byΔQ = N_{D}AΔW , where A is the square of the diode, the differential capacitance is given by:This is a basic result which is easy to remember because it is identical to that for a parallelplate capacitor. If there is a quiescent applied bias, V, which increases the depletion depth (i.e., the reverse bias), then the capacitance is decreased, and this affords a convenient way to ascertain the polarity of a diode. It follows from Eqs. (4) and (6) that:
This key result implies that by plotting
A^{2}/C^{2} as a function of reverse bias, the space charge density can be obtained from the slope. A similar procedure can be shown to be valid even if the space charge density is not uniform. it is still true that:which is often stated as:
where
N(x) is the net space charge density in the depletion region. These relations are the basis for a popular doping profiler known as the “Miller profiler” which enables placement of a diode at the end of a coaxial cable of essentially arbitrary length. The charge distribution in the treatment was assumed to change abruptly fromN_{D} to zero atx_{n} . Actually, the electrons spill over into the depletion region according to:where
l_{D} is the Debye length, given by:K is Boltzmann’s constant, and T is the temperature.
3. CALCULATION PARAMETERS FOR THE DERIVATION OF THE INTERNAL ELECTRIC FILED
The impurity doping concentrations for a
pn junction process for solar cells are shown in Table .1 These are standard values of impurity doping parameters for epitaxial growth using a metal organic chemicalvapor developer process.The doping impurity concentrations in solarcell fabrication are determined by the different electrical properties in the two kinds of surface material. For
n type, the concentration is determined by Si_{2}H_{6} in the IV compound, and forp type, by DEZn in the II compound.Table 2 shows an experimental design for solarcell chargedensity calculations.
The design multiplier for different solarcell areas of standard, type 1, type 2, type 3, type 4, and type 5 designs are shown in Table .3The solarcell area is calculated as width (cm) × length (cm). The solarcell area is directly related to the short circuit current (A). However, the relation between powerconversion efficiency (η) and area is not a direct relationship.
4. CONCLUSIONS
In this section, the results obtained on the basis of the chargedensity fabrication experimental design will be discussed. The discovery of the
pn junction is usually attributed to American physicist Russell Ohl of Bell Laboratories [3]. Variations in thepn junction depletionregion parameters of a solar cell with impurity doping concentration are shown in Fig. .2 Parameter values are shown for both positivetype and negativetype transitions. Both types of transition parameter depend on the impurity doping concentration. However, fabricated solarcell area is unrelated to charge density over most of the depletion region.
The depletion parameter for the normal range of standard impurity doping concentrations was calculated as 8.0 × 10^{6} μm. In addition, the
pn junction electricfield parameters of the solar cell were determined in relation to the ionization carrier, whichincludes both positive and negative ions. The minimum dopant impurity concentrations were 6.0 × 10^{17} cm^{3} and 3.0 × 10^{17} cm^{3} for Si_{2}H_{6} and DEZn respectively. The maximum impurity doping concentrations were 8.0 × 10^{17} cm^{3} and 5.0 × 10^{17} cm^{3} for Si_{2}H_{6} and DEZn respectively. Figure 5 shows the variation of the
pn junction electric field with impurity doping concentration. In this plot, the depletion region is concentrated around the transition region and depends on impurity doping concentrations of both negative and positive types. The transition region is determined by the ionization carrier and by changes in the Fermi level due to variations in impurity doping concentrations.
The electric field created by the space charge region opposes the diffusion process for both electrons and holes. Figures 610 show changes in charge density which reflect the results obtained for the fabricated solar cells.
The fabricated solarcell experimental design was implemented for standard, type 1, type 2, type 3, type 4, and type 5 solar cells. The charge density was found to be very high for the solar cell of 4.5 cm^{2} area. In addition, the charge density was found to increase with increasing solarcell area. The carrier density was determined with silicon and GaAs material.
So far, this discussion has considered the basic pn junction structure. The average length that an electron travels through the ptype material before recombining is called the diffusion length and is typically on the order of microns [4]. The builtin potential barrier maintains an equilibrium between the majority carrier electrons in the
n region and the minority carrier electrons in thep region, and also between the majority carrier holes in thep region and the minority carrier holes in then region [5]. Most semiconductor devices contain at least one junction between a ptype and ann type semiconductor.In conclusion, this research has examined variations in the charge density according to a solarcell fabrication experimental
design. The current was found to vary as a function of the charge density and the solarcell area. The Fermi level was also affected by the impurity doping concentration; in the depletion region, the relationship was direct. The ionization carrier is a space of continuous motion in the osmosis interface between the two kinds of semiconductors. A mathematical foundation was also presented in this paper for the analysis of chargedensity variations as a function of solarcell area.

[Fig. 1.] Typical pn junction of solarcell device structure.

[Fig. 2.] (a) space charge (b) electric field (c) electrostatic potential (d) electron energy for an abrupt p+n junction diode.

[Table 1.] Concentration range of doping impurities for calculations.

[Table 2.] Experimental design for solarcell chargedensity analysis in the depletion region.

[Table 3.] Multipliers for various solarcell areas according to the experimental design.

[Fig. 3.] Transitionregion as a function of impurity doping concentrations.

[Fig. 4.] Depletionregion as a function of Negative type and Positive type in amount.

[Fig. 5.] Variation in electric field with impurity doping concentration in the pn junction of a solar cell.

[Fig. 6.] Variations in electrical charge (C) with impurity doping concentration and solarcell area for the type 1 data shown in Table 2.

[Fig. 7.] Variations in electrical charge (C) with impurity doping concentration and solarcell area for the type 2 data shown in Table 2.

[Fig. 8.] Variations in electrical charge (C) with impurity doping concentration and solarcell area for the type 3 data shown in Table 2.

[Fig. 9.] Variations in electrical charge (C) with impurity doping concentration and solarcell area for the type 4 data shown in Table 2.

[Fig. 10.] Variations in electrical charge (C) with impurity doping concentration and solarcell area for the type 5 data shown in Table 2.