# Chapter 7. Solar Cell

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1 Chapter 7 Solar Cell 7.0 Introduction Solar cells are useful for both space and terrestrial application. Solar cells furnish the long duration power supply for satellites. It converts sunlight directly to electricity with good conversion efficiency. It is a form of green energy. 7.1 Solar Radiation The radiative energy output from the sun derives from nuclear fusion reaction. In every second about 6.0x10 11 kg of hydrogen is converted into helium with the net mass loss of about 4x10 3 kg. The mass loss is converted into energy using Einstein s equation E = mc 2 that equates to 4.0x10 21 J. This energy is emitted primarily as electromagnetic radiation in the ultraviolet to infrared region that has wavelength ranges from 0.2µm to 3µm. The total mass of sun is now about 2.0x10 30 kg which can provide constant energy output for over next 10 billion years. Looking at color of the sun, the sun has gone through half of its life time. The intensity of the solar radiation outside the earth atmosphere measured at the average distance of the earth orbit around the sun is 1367W/m 2. This value is also called solar constant. In the terrestrial surface the intensity of the solar energy is attenuated due to scattering of the cloud and atmosphere. The attenuation depends on the length of the light s path through atmosphere or air mass, which is defined as the 1/cosφ, where φ is the angle between vertical line and the sun s position. The air mass can be estimated from the height h of the vertical object and the length s of the shadow of this object. This equation to calculate the air mass is 2 Air mass (AM) = 1+ (s / h) (7.1) Figure 7.1 shows the two solar spectral irradiances (power per unit area per unit wavelength) curves. The one with AM equals to 0 zero is applicable for satellite operating in space and the one with AM equals to 1.5 is specified as reference for terrestrial solar cell application. This is spectrum representing sunlight at the

2 earth s surface when it 48 0 from the vertical line. Showing in the spectral curve is the cutoff wavelengths of silicon and gallium arsenide. Figure 7.1: The spectral irradiance of solar radiation for air mass 0 and 1.5 respectively showing the cutoff wavelengths of silicon and gallium arsenide 7.2 pn Junction Solar Cell A solar cell is a pn junction with no voltage directly applied across the junction. The solar cell converts photon power into electrical power by generation of electron-hole pair EHP and delivers this power to a load. A typical silicon solar cell is shown in Fig Power is generated from solar cell since it operates in forth quadrant of the I-V characteristic curve of the diode. Only photons have the energy hv greater than the energy band-gap E G of the solar cell material, electron-hole pairs are created. Photon energy that has energy less than the energy band-gap of the material will be wasted end with heating the solar cell. In the design of solar cell, the contact area of electrode should be large and at the same time the exposed area for the incident photon should be very much larger than the area of electrode. The silicon pn junction solar cell structure shown in Fig. 7.2 has a p-type substrate and n-type area exposed to sunlight

3 Figure 7.2: Structure of solar cell The conversion efficiency of the solar cell can be derived based on the energy band diagram of the solar cell and the idealized equivalent circuit of a solar cell shown in Fig Figure 7.3: (a) Energy band diagram of a pn junction solar cell and (b) the idealized equivalent of a solar cell

4 The current I op is the photon generated current, I s is the reverse saturation current of the solar cell, and I is the load current. Thus, from Kirchoff s current ev / kt. Thus, law, I op +I = I s ( e 1) I = I / nkt s ( e 1) ev R -I op (7.2) The rate of electron created is AL n g op within electron diffusion length L n and similar the rate of hole created is AL p g op within hole diffusion length L p. g op is the generation rate of electron-hole pair. Similar carriers are generated within depletion width W b is AW b g op. Thus, the resulting optical current due to photon generation is I op = eag op (L p + L n + W b ) (7.4) Since the current is reverse saturation current whereby electron moves to n- region, while hole moves to p-region, therefore, the overall current of the pn junction shall be I ea L p L n p n ( e evr /( nkt) = no + po ) eag op ( L n + L p + W b ) τ p τ n 1 (7.4) It is similar like substitute I op from equation (7.4) into equation (7.2) and replacing the reverse saturation current as a function of diffusion length, diffusion time, and minority concentrations. Equation (7.4) is also equal to where I S [ exp(evr /(nkt) 1] Iop I = I (7.5) L ea τ L + τ p n S = pno n po p n. This shows a lowering of the normal I-V curve, which depends on the amount of optical generated current I op. When there is no bias, the short-circuited current I sc is equal to I op, which is proportional to the EHP-generation rate g op. When open circuit whereby current I = 0, the voltage V R is equal to forward voltage V oc, which is V oc = nkt e L p + L n + Wb ln gop + 1 (7.6) ( Lp / τ p ) p no + ( L n / τ n ) n po

5 Equation (7.6) is also equal to equation (7.7) if we set I = 0 and V R = V oc for equation (7.5). nkt I ln 1 + e I = op oc S V (7.7) The appearance of forward voltage V oc as the result of illumination is called photovoltaic effect. For solar cell, the ideality constant n should be closed to one since there should not have recombination after optical generation of electron-hole pair EHP. From equation (7.7), the open circuit voltage V oc is restricted to kt/e, which is less than 1.0V for silicon of band-gap 1.12eV. Thus, individual solar cell is not capable of delivering sufficient power. Thus, solar cells are commonly connected in the form of large arrays and designed having comb-like structure in order to get sufficient exposure to sunlight and deliver enough power. Figure 7.4 shows the characteristic curve of a solar cell. The power generated is the product of I max and V max. From equation (7.2), which is I = ev R / nkt -I op, the power delivered to the load is PV, which is I s ( e 1) P = IV R = V R I / nkt s ( e 1) ev R -I op V R (7.8) Maximum power is obtained from dp/dv R = 0 or from maximum voltage V m, which is defined as V nkt I = ln e ev / IS + 1 /(nkt) + 1 ev op m V OC - ln 1 + m e kt and maximum current I m which is defined as kt m (7.9) I m = evm IS e kt ev 1 m / kt I op 1 (7.10) evm / kt The maximum power P m is then equal to

6 P m = I m V m I V kt ev ln 1 + e kt kt e m op OC (7.11) 7.3 Conversion Efficiency Figure 7.4: Characteristic curve of a solar cell The conversion efficiency of solar cell can be generally governed by the ideal solar cell design, the sunlight spectrum, and the series resistance and recombination current of the solar cell Ideal Efficiency Many optoelectronic devices have a figure of merit associated with them, which is used to indicate how good the device is. The figure of merit is the fill factor FF of solar cell is defined as FF = P I V I V I V max max max = = 1 - sc oc sc oc kt ev OC ln ev kt kt ev m 1 + (7.12) OC where I sc is the short circuit current, V oc is the open circuit voltage, I max and V max are maximum current and voltage respectively. For most solar cells the fill factor η of 0.6 to 0.8. The power conversion efficiency for a solar cell is given P eff = I FF I mv P P in m op OC = (7.13) in V

7 Solar efficiency η s is defined as η s P = max = P solar FF I P SC solar V OC (7.14) where P solar is the amount of solar power reaching the cell, which is also equal to the integration of all the photons in the solar spectrum shown in Fig Ideally, η s should be equal to one indicating that all incident solar radiations are being converted to electrical power. In reality it is not the case. The known solar efficiency so far is less than 30% utilizing gallium arsenide. It is important to note the photon that has energy hν smaller than the bandgap E G will not produce any electron-hole pair EHP. This energy is dissipated as heat. The photon that has energy greater than the band-gap of semiconductor will produce electron-hole pair EHP, excess energy (hν-e G ) is dissipated as heat. Other factors are reflection and quantum efficiency due to recombination. In general the solar cell efficiency is low and it depends critically how the semiconductor band-gap matches with the solar energy spectra, which is shown by Plank spectral radiation expression 2πhc ρ( λ) = 5 λ [exp(hc / λkt) 1] in Fig In Fig. 7.1, it shows that gallium arsenide has a better efficiency than silicon because its cutoff wavelength is closed to the visible high irradiance region of the spectra. However, the technology to produce GaAs solar cell is far more expensive than silicon solar cell. GaAs solar cell is normally used for space application Spectrum Splitting The simplest way to improve the power conversion efficiency P eff is to split the spectrum. By splitting sunlight into narrow wavelength bands and directing each to a cell that has band-gap optimally chosen to convert just this band-gap as shown in Fig. 7.5(a) that using spectrally sensitive mirror, the solar efficiency in principle above 60.0% can be obtained. Another way to improve the power conversion efficiency P eff is by stacking the solar cells on top of each other with highest band-gap solar cell at the uppermost side. This arrangement would automatically achieve an identical spectrum splitting effect, making the tandem solar cell approach a reasonably practical way of increasing power conversion efficiency.

8 Figure 7.5: Multi-band-gap spectrum concept (a) Spectrum splitting approach and (b) Tandem-cell approach Series Resistance and Recombination Current Many other factors degrade the ideal efficiency of solar cell. One of the issue is the series contact resistance R s from the ohmic loss in the front surface of the cell. The equivalent circuit is shown in Fig From the ideal diode current ev R / nkt -I op, the I-V characteristic is found to be I = equation I = I s ( e 1) e(v I s R IRS kt ( e 1) ) / -I op, which is re-written as I + I ln IS op + 1 = e kt ( V IR ) R S (7.15) Figure 7.6: Model of solar cell with series resistance and I-V characteristic curve of nonideal solar cell

9 The plots in Fig. 7.6 show two values that are with R s = 0Ω and R s = 5Ω. It can shown that with 5Ω series resistance, the power delivered is about 30% of the maximum power with R s = 0Ω. The output current and output power are respectively equal to I e(v IR ) kt R S = IS exp 1 Iop (7.16) kt I + I I ln e IS + IR op = S P (7.17) The series resistance depends on the junction depth, the impurity concentration of the p and n-types and the arrangement of the front-surface ohmic contacts. The resistance of n + p junction is about 0.7Ω and about 0.4Ω for p + n junction. Another factor to be considered is the recombination current in the depletion region of the solar cell. For single level center, the recombination current I rec can be expressed as and I ' evr = IS exp 1 2kT rec (7.18) ' S en iwb = A τpτn I (7.19) ' I S is the saturation current. The energy conversion equation can be put into a non ideal form similar to the ideal case by replacing I s with I ' S and using ideality factor n = 2. For silicon solar cell, the recombination current can reduce the efficiency by 25.0%. 7.4 Silicon and Compound-Semiconductor Solar Cells Silicon is the most important semiconductor for solar cells. It is nontoxic and is second most abundant to oxygen in the earth s crust. Thus, it can be used unlimited. Moreover, the silicon based technology is well established because of its use in microelectronics

10 III-V compound semiconductor and their alloy systems provide wide choices of band-gap with closely matched lattice constants. These compounds are ideal for producing tandem solar cells. For example, AlGa-GaAs, GaInP- GaAs, and GaInAs/InP material system have been developed for solar cells in satellite and space vehicle applications Amorphous Silicon Solar Cell When silicon is deposited by chemical vapor deposition CVD at temperature less than C, an amorphous silicon film is formed regardless of the substrate. Amorphous silicon has large number of energy-state within the band-gap. Owing to short-range crystalline order, the effective mobility is quite small in the order of 10-6 and 10-3 cm 2 /V-s. However, the mobility above E c and below E v is between 1.0 to 10.0cm 2 /V-s. Owing to the difference of mobility, E c and E v are referred to mobility edges and the energy between E c and E v is referred to as mobility gap. The mobility gap can be modified by adding impurities. Typical mobility gap of amorphous silicon is 1.7eV. Amorphous silicon has a very high absorption coefficient, so most sunlight is absorbed with 1.0µm of surface. Consequently, a very thin layer of amorphous silicon is required for making solar cell. Figure 7.7 shows the density of state for amorphous silicon and Fig. 7.8 shows the energy band diagrams of p-i-n amorphous silicon solar cell. Figure 7.7: Density of states of amorphous silicon Amorphous silicon solar cell has the lowest manufacturing cost and it has modest efficiency of 5.0%

11 (a) (b) Figure 7.8: Energy band diagrams (a) at equilibrium and (b) at optical generation mode of p-i-n amorphous silicon solar cell PERL Cell The silicon passivated emitter rear locally-diffused PERL solar cell is shown in Fig The cell has inverted pyramids on the top that are formed by using anisotropic etches to expose the slowing etching (111) crystallographic planes. The pyramids reduce reflection of light incident on the top surface since light incident perpendicularly to the cell will strike on one of the inclined (111) planes indirectly and will be refracted obliquely into the cell. The rear contact is separated from the silicon by an intervening oxide layer. This gives much better rear reflection than an aluminum layer. The PERL cell shows high conversion efficiency of 24.0%. Figure 7.9: Silicon passivated emitter rear locally-diffused PERL solar cell Tandem Solar Cell Figure 7.10 shows the structure of a tandem solar cell. A p-type germanium is used as substrate, which has a lattice constant very close to that of GaAs and

12 Ga 0.51 In 0.49 P.A p-gainp layer is then grown to reduce the minority carrier concentration near the rear contact. The bottom junction is the GaAs (E G = 1.43eV) pn junction and the top junction is the GaInP junction (E G = 1.9eV). A tunneling p + n + GaAs junction is placed between top and bottom junction to connect the cells. The tandem solar cell has efficiency as high as 30.0% has been achieved. 7.5 Optical Concentration Figure 7.10: Monolithic tandem solar cell Sunlight can be focused by using mirror and lenses. Optical concentration offers an attractive and flexible approach to reducing high cell cost by substituting a concentrator are for much of the cell area. It also offers advantages such as a 20.0% increase in efficiency for a concentration of 1,000 suns, an intensity of 963x10 3 W/m 2. Figure 7.11 shows the measured results of a typical silicon solar cell mounted in a concentrated system. Note that the performances improve as the concentration increases one sun toward 1,000 suns. The short-circuit current density increases linearly with concentration. The open-circuit voltage increases at a rate of 0.1V per decade, while the fill factor varies slightly. The efficiency, which is the product of the foregoing three factors divided by the input power, increases at the rate of about 2.0% per decade. With antireflectant coating, the projected efficiency increment of 30.0% at 1,000 suns. Thus, one cell operated under 1,000-sun concentrations can produce the same power output as 1,300 cells under one sun. Potentially optical concentration approach can replace

13 expensive solar cells with less expensive concentrator materials and related tracking and heat removal system for reducing cost of the system. Figure 7.11: Efficiency, open-circuit voltage, short-circuit voltage and fill factor versus solar concentration Exercises 7.1. Calculate the air mass value for a vertical object of height 2.0m and shadow length of 2.5m A Si solar cell has area of 1.0cm 2 at 300K has N A = 5x10 17 cm -3, N D = 1.2x10 16 cm -3, electron diffusion coefficient D n = 20cm 2 s -1, hole D p = 10cm 2 s -1, electron and hole combination time τ n = 2.8x10-7 s, τ p = 1.2x10-7 s and optical generated current I op = 25mA. Calculate the open circuit voltage V oc and optical generation rate g op for the solar cell If the wavelength λ of incident photon for Si solar cell mentioned in question 5 is 0.5µm, calculate the efficiency factor of electron-hole pair EHP creation

14 7.4. If the type of Si solar cell mentioned in question 7.3 is used to power a lighting system in a room that requires 10W at 10V voltage level, how many solar cell of this type is needed? You may assume each solar cell can deliver 90% of its maximum voltage and current, and has a fill factor of 70% respectively A Si solar cell has short-circuit current of 100mA and open-circuit voltage of 0.8V under full illumination. The filled factor is What is the maximum power delivered to a load? 7.6. Given the reverse saturation current and optical generated current of a solar cell are 1.0nA and 100mA respectively, calculate the open-circuit voltage and output power at voltage 0.30V of a solar circuit

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