The dependence of the N composition on the growth temperature as shown in Figure 5 can be explained qualitatively as follows. A rapid decrease in the N composition with increasing the growth temperature in the low growth temperature region is due to both the increases in the growth rate and desorption rate of N species at the growing surface. Here, we assume that the amount of N species supplied to the growing surface is independent of growth temperatures. Then, the higher growth rate caused the decrement of the N source supply per unit layer growth, since the N source flow rate was constant in every growth conditions. In the middle growth temperature region, the decrement of the growth rate as increasing the growth temperature would enhance the N source supply per unit layer growth. However, the N composition did not increase. It indicates that the desorption rate of N species prevailed in the middle growth temperature region to reduce the N composition as the growth temperature increased. In the high growth temperature region, the N composition again markedly de‐ creases with increasing the growth temperature. The fact that the growth rate remains almost

**C]**

**0.1**

**2.3. Crystal quality of GaAsN grown by CBE**

a large amount of impurities, such as hydrogen and carbon.

**Figure 5.** The dependence of growth temperature on the N composition in GaAsN thin films.

**1.0**

**N composition [%]**

286 Solar Cells - Research and Application Perspectives

**5.0**

### **3.1. Hall hole mobility**

The hole mobility in p-GaAsN films grown by CBE, MBE, and MOCVD is shown in Figure 7 as a function of N composition [16, 21]. Those grown by the CBE in our group were obtained by Van der Pauw method. The dashed line represents the mobility obtained theoretically by considering the alloy and phonon scatterings. The hole mobility monotonically decreases as increasing the N composition and they are smaller than the theoretical values. The deviation of the mobility from the ideal value is at the same level despite the different impurity concen‐ trations [16, 21]. This indicates that some N-related defects are generated due to the N incorporation, which determine the hole mobility at the room temperature. To evaluate the number of N-related defects, the temperature dependence (77-400K) of the hole mobility was 1 **3. Hole mobilities**

20 follows:

21

guide for the eye.

2 **3.1. Hall hole mobility**

obtained as shown in Figure 8. The result suggests that there are several different scattering mechanisms. To determine the amount of the N-related scattering centers, we analyzed this temperature dependence. Here, ionized impurity scattering, alloy scattering, phonon scatter‐ ing, and N-related carrier scattering were considered [22, 23]. The inverse of the mobility limited by the N-related carrier scattering 1/μN, which is proportional to the density of Nrelated scattering centers, was determined by excluding the contributions of the mobility limited by ionized impurity (μII), alloy scattering (μAL), and phonon scattering (μPN) from the measured mobility (μexp), as follows: 7 monotonically decreases as increasing the N composition and they are smaller than the 8 theoretical values. The deviation of the mobility from the ideal value is at the same level 9 despite the different impurity concentrations[17], [16].This indicates that some N-related 10 defects are generated due to the N incorporation, which determine the hole mobility at the 11 room temperature. To evaluate the number of N-related defects, the temperature 12 dependence (77-400K) of the hole mobility was obtained as shown in Figure 8. The result 13 suggests that there are several different scattering mechanisms. To determine the amount of

8 Book Title

3 The holemobility in p-GaAsN films grown by CBE, MBE, and MOCVD is shown in Figure7 4 as a function of N composition[17], [16]. Those grown by the CBE in our group were

6 obtainedtheoretically by considering the alloy and phonon scatterings. The hole mobility

$$\frac{1}{\mu\_{\rm N}} = \frac{1}{\mu\_{\rm exp}} - \frac{1}{\mu\_{\rm II}} - \frac{1}{\mu\_{\rm AL}} - \frac{1}{\mu\_{\rm PN}}.\tag{1}$$

Here, 1/μPN is the sum of the contributions from the acoustical phonon (μAC), polar optical phonon (μPO), and non-polar optical phonon scattering (μNPO) as 17 scattering 1/μN, which is proportional to the density of N-related scattering centers, was 18 determined by excluding the contributions of the mobility limited by ionized impurity (μII),

19 alloy scattering (μAL), and phonon scattering (μPN) from the measured mobility (μexp), as

$$\frac{1}{\mu\_{\rm PN}} = \frac{1}{\mu\_{\rm AC}} + \frac{1}{\mu\_{\rm PO}} + \frac{1}{\mu\_{\rm NPO}}.\tag{2}$$

**Fig. 7.**Hole mobility at room temperature in p-GaAsN films grown by CBE, MBE, and MOCVD as a function of N composition. The mobility is the value at room temperature. The **Figure 7.** Hole mobility at room temperature in p-GaAsN films grown by CBE, MBE, and MOCVD as a function of N composition. The mobility is the value at room temperature. The dashed line represents the estimated mobility limited by the alloy and phonon scatterings. In the case of CBE, the growth rate (GR) is shown in the unit of μm/h. The dotted lines are a guide for the eye.

dashed line represents the estimated mobility limited by the alloy and phonon scatterings. In the case of CBE, the growth rate (GR) is shown in the unit of μm/h. The dotted lines are a

9

**Fig. 8.** Temperature dependence of the hole mobility of p-GaAsN films with N composition of approximately 0.34% (μexp.) and its components denoted in eq. (1). The contribution from **Figure 8.** Temperature dependence of the hole mobility of p-GaAsN films with N composition of approximately 0.34% (μexp.) and its components denoted in eq. (1). The contribution from N-related scattering centers (μN) is ob‐ tained by using eq. (1). The mobility with N composition of approximately 0.79% (μ\*exp.) and contribution from the Nrelated scattering centers (μ\*N) are also shown.

N-related scattering centers (μN) is obtained by using eq. (1). The mobility with N

. 1 1 1 1 1

*AL*

**N composition [%]**

*PN*

*II*

**0.0 0.5 1.0 0 Figure 9.** 1/μN at each N composition in p-GaAsN films.

*N*

**Fig. 9.**1/μNat each N composition in p-GaAsN films.

exp

1 (1)

obtained as shown in Figure 8. The result suggests that there are several different scattering mechanisms. To determine the amount of the N-related scattering centers, we analyzed this temperature dependence. Here, ionized impurity scattering, alloy scattering, phonon scatter‐ ing, and N-related carrier scattering were considered [22, 23]. The inverse of the mobility limited by the N-related carrier scattering 1/μN, which is proportional to the density of Nrelated scattering centers, was determined by excluding the contributions of the mobility limited by ionized impurity (μII), alloy scattering (μAL), and phonon scattering (μPN) from the

3 The holemobility in p-GaAsN films grown by CBE, MBE, and MOCVD is shown in Figure7 4 as a function of N composition[17], [16]. Those grown by the CBE in our group were 5 obtained by Van der Pauw method. The dashed line represents the mobility 6 obtainedtheoretically by considering the alloy and phonon scatterings. The hole mobility 7 monotonically decreases as increasing the N composition and they are smaller than the 8 theoretical values. The deviation of the mobility from the ideal value is at the same level 9 despite the different impurity concentrations[17], [16].This indicates that some N-related 10 defects are generated due to the N incorporation, which determine the hole mobility at the 11 room temperature. To evaluate the number of N-related defects, the temperature 12 dependence (77-400K) of the hole mobility was obtained as shown in Figure 8. The result 13 suggests that there are several different scattering mechanisms. To determine the amount of 14 the N-related scattering centers, we analyzed this temperature dependence. Here, ionized 15 impurity scattering, alloy scattering, phonon scattering, and N-related carrier scattering 16 were considered[22], [23].The inverse of the mobility limited by the N-related carrier 17 scattering 1/μN, which is proportional to the density of N-related scattering centers, was 18 determined by excluding the contributions of the mobility limited by ionized impurity (μII), 19 alloy scattering (μAL), and phonon scattering (μPN) from the measured mobility (μexp), as

8 Book Title

exp

phonon (μPO), and non-polar optical phonon scattering (μNPO) as

**50**

**100**

**150**

**Mobility [cm2**

lines are a guide for the eye.

**V-1**

**-1**

**s**

**]**

**200**

**250**

1 111 1 . *N II AL PN*

111 1 . *PN AC PO NPO*

Here, 1/μPN is the sum of the contributions from the acoustical phonon (μAC), polar optical

**0.4 0.6 0.8 1.0 1.2**

0.46

Lower GR

0.52

**N compositon [%]**

1.60

**Fig. 7.**Hole mobility at room temperature in p-GaAsN films grown by CBE, MBE, and MOCVD as a function of N composition. The mobility is the value at room temperature. The dashed line represents the estimated mobility limited by the alloy and phonon scatterings. In the case of CBE, the growth rate (GR) is shown in the unit of μm/h. The dotted lines are a

**Figure 7.** Hole mobility at room temperature in p-GaAsN films grown by CBE, MBE, and MOCVD as a function of N composition. The mobility is the value at room temperature. The dashed line represents the estimated mobility limited by the alloy and phonon scatterings. In the case of CBE, the growth rate (GR) is shown in the unit of μm/h. The dotted

1.06

1.41

Alloy & Phonon Scatterings

= -- - (1)

288 Solar Cells - Research and Application Perspectives Running Title

=++ (2)

 CBE MBE [1,2] MOCVD [1]

0.23

measured mobility (μexp), as follows:

1 **3. Hole mobilities**

20 follows:

21

guide for the eye.

2 **3.1. Hall hole mobility**

The expressions of each component of the mobility are described, for example, in ref. [16].

The relationship between 1/μN and N composition is shown in Figure 9. The inverse of the mobility limited by the N-related carrier scattering center (1/μN) was determined, which is proportional to the amount of N-related scattering centers. Independent of growth technique, the number of N related scattering centers (1/μ∝ ) increases as N composition increases.

### **3.2. Improvement of mobility by controlling the growth rate**

The above result suggested that the number of N-related defects may be determined by the N concentration of the GaAsN independent of the growth technique. However, here we show the increase of the mobility by controlling the growth rate in CBE. The hole mobility at room temperature and the N composition in p-GaAsN films as a function of growth rate are shown in Figure 10. The higher mobilities are obtained by decreasing the growth rate. Generally, the hole mobility is decreased by the increase in the N composition owing to the alloy scattering. To discuss the reason for the increase in the hole mobility, the relationship between the 1/μN and N composition are shown in Figure 11. When the growth rate is higher than 1.41 μm/h, there is no improvement of the mobility. By decreasing the growth rate lower than 1.04 μm/h, the 1/μN (the number of the N-related defects) remains almost constant despite the increase in the N composition. (μN [N])-1 as a function of the growth rate is shown in Figure 12. This is a relative amount of the N-related scattering centers to the total amount of N atoms. (μN [N])-1 is decreased by decreasing the growth rate monotonically. Then, the controlling growth rate in CBE is effective to suppress the formation of N-related scattering centers and to improve the mobility, especially for a higher N composition.

**Figure 10.** Hole mobility at room temperature and N composition in p-GaAsN films as a function of growth rate.

The expressions of each component of the mobility are described, for example, in ref. [16].

**3.2. Improvement of mobility by controlling the growth rate**

290 Solar Cells - Research and Application Perspectives

the mobility, especially for a higher N composition.

**250**

**100**

**150**

**Hole mobility [cm**

**2**

**V -1**

**s-1**

**]**

**200**

The relationship between 1/μN and N composition is shown in Figure 9. The inverse of the mobility limited by the N-related carrier scattering center (1/μN) was determined, which is proportional to the amount of N-related scattering centers. Independent of growth technique, the number of N related scattering centers (1/μ∝ ) increases as N composition increases.

The above result suggested that the number of N-related defects may be determined by the N concentration of the GaAsN independent of the growth technique. However, here we show the increase of the mobility by controlling the growth rate in CBE. The hole mobility at room temperature and the N composition in p-GaAsN films as a function of growth rate are shown in Figure 10. The higher mobilities are obtained by decreasing the growth rate. Generally, the hole mobility is decreased by the increase in the N composition owing to the alloy scattering. To discuss the reason for the increase in the hole mobility, the relationship between the 1/μN and N composition are shown in Figure 11. When the growth rate is higher than 1.41 μm/h, there is no improvement of the mobility. By decreasing the growth rate lower than 1.04 μm/h, the 1/μN (the number of the N-related defects) remains almost constant despite the increase in the N composition. (μN [N])-1 as a function of the growth rate is shown in Figure 12. This is a relative amount of the N-related scattering centers to the total amount of N atoms. (μN [N])-1 is decreased by decreasing the growth rate monotonically. Then, the controlling growth rate in CBE is effective to suppress the formation of N-related scattering centers and to improve

**0.0 0.5 1.0 1.5**

**Figure 10.** Hole mobility at room temperature and N composition in p-GaAsN films as a function of growth rate.

**Growth Rate [m/h]**

**0.0**

**0.5**

**N composition [%]**

**1.0**

**1.5**

 Mobility N composition

**Figure 11.** μN-1 at room temperature as a function of N composition in p-GaAsN films. μN -1 is proportional to the amount of N-ralated scattering centers. In the case of CBE, the growth rate (GR) is shown in the unit of μm/h. The dotted lines are a guide for the eye.

**Figure 12.** (μN [N])-1 as a function of growth rate of p-GaAsN films. (μN [N])-1 is the relative amount of the N-related scattering centers to the total amount of N atoms. The dotted line is a guide for the eye.

We inferred two reasons for the reduction of the amount of N-related scattering centers by decreasing the growth rate: i) The amount of N adsorbed species which are desorbed from a terrace increases by decreasing the growth rate. We expect that the N adsorbed species adsorbed from a terrace is a cause of N-related scattering centers. The desorption from a terrace is expected to be more frequent than that from a step, since the number of connected bonds of N adsorbed species to the growing surface is smaller at terrace than at step; ii) The decrease in the growth rate increases the diffusion length of N adsorbed species on the growing surface. A large diffusion length is expected to increase the probability of a N adsorbed species to come over a step. Therefore, the probability of a N adsorbed species adsorbed at a step increases. Then, i) and ii) are expected to be advantageous for the improvement of the carrier mobility and lifetime.

## **4. Mobility contributed from N-related scattering center**

### **4.1. Minority-carrier lifetime**

#### *4.1.1. Improvement of minority carrier lifetime by controlling growth rate*

As the control of the growth rate improved the mobility, here we show that the decreasing the TEGa flow rate improves the minority carrier lifetime.. The minority-carrier lifetime at room temperature was obtained by time-resolved photoluminescence (TR-PL). A titanium sapphire pulse laser was used for the carrier excitation. The excitation power, wavelength, pulse width, and recurrence frequency were 900 mW, 800 nm, ∼100 fs, and 80 MHz, respectively. To evaluate the minority carrier lifetime of p-GaAsN, the structure of GaAs buffer layer (500 nm)/ p-GaAsN layer (140∼950 nm)/GaAs cap layer (30 nm) was adopted. The cap layer reduced the surface recombination. The PL lifetime (τPL) was obtained by PL decay curves. τPL consists of minority-carrier lifetimes in the bulk of the p-GaAsN layer (τB) and at GaAs/GaAsN interfaces (τS). The contribution of τS to τPL changes as a function of the p-GaAsN layer thickness (d)16) as follows:

$$\frac{1}{\tau\_{PL}} = \frac{1}{\tau\_B} + \frac{1}{\tau\_S} = \frac{1}{\tau\_B} + \frac{2S}{d}.\tag{3}$$

Here, S is the GaAs/GaAsN interface recombination velocity. PL lifetime as a function of GaAsN layer thickness was obtained and τB was determined by eq. (3). The amount of nonradiative recombination centers were estimated qualitatively based on eq. (4),

$$N\_{NR} \propto \frac{1}{\tau\_{NR}} = \frac{1}{\tau\_B} - \frac{1}{\tau\_R} \, \tag{4}$$

We inferred two reasons for the reduction of the amount of N-related scattering centers by decreasing the growth rate: i) The amount of N adsorbed species which are desorbed from a terrace increases by decreasing the growth rate. We expect that the N adsorbed species adsorbed from a terrace is a cause of N-related scattering centers. The desorption from a terrace is expected to be more frequent than that from a step, since the number of connected bonds of N adsorbed species to the growing surface is smaller at terrace than at step; ii) The decrease in the growth rate increases the diffusion length of N adsorbed species on the growing surface. A large diffusion length is expected to increase the probability of a N adsorbed species to come over a step. Therefore, the probability of a N adsorbed species adsorbed at a step increases. Then, i) and ii) are expected to be advantageous for the improvement of the carrier mobility

As the control of the growth rate improved the mobility, here we show that the decreasing the TEGa flow rate improves the minority carrier lifetime.. The minority-carrier lifetime at room temperature was obtained by time-resolved photoluminescence (TR-PL). A titanium sapphire pulse laser was used for the carrier excitation. The excitation power, wavelength, pulse width, and recurrence frequency were 900 mW, 800 nm, ∼100 fs, and 80 MHz, respectively. To evaluate the minority carrier lifetime of p-GaAsN, the structure of GaAs buffer layer (500 nm)/ p-GaAsN layer (140∼950 nm)/GaAs cap layer (30 nm) was adopted. The cap layer reduced the surface recombination. The PL lifetime (τPL) was obtained by PL decay curves. τPL consists of minority-carrier lifetimes in the bulk of the p-GaAsN layer (τB) and at GaAs/GaAsN interfaces (τS). The contribution of τS to τPL changes as a function of the p-GaAsN layer thickness (d)16)

> 1 1 1 12 . *PL B S B*

ttt

nonradiative recombination centers were estimated qualitatively based on eq. (4),

t

1 11 , *NR NR B R*

 tt *S*

=+= + (3)

µ =- (4)

*d*

Here, S is the GaAs/GaAsN interface recombination velocity. PL lifetime as a function of GaAsN layer thickness was obtained and τB was determined by eq. (3). The amount of

**4. Mobility contributed from N-related scattering center**

*4.1.1. Improvement of minority carrier lifetime by controlling growth rate*

t

*N*

and lifetime.

as follows:

**4.1. Minority-carrier lifetime**

292 Solar Cells - Research and Application Perspectives

**Table 2.** Summary of growth rate (GR), N composition ([N]), minority-carrier lifetime in the bulk of p-GaAsN (τB), and radiative, nonradiative recombination lifetime (τR, τNR). τB was estimated by the PL lifetime dependence on the thickness of the p-GaAsN layer. τR was determined by using the hole concentration (p). τNR is obtained by using eq. (3).

**Figure 13.** Fitting results of PL lifetime (τPL) dependence on GaAsN layer thickness (d). The inserted figure shows a typi‐ cal PL decay curve at room temperature, which is for the sample with GaAsN layer thickness of approximately 500 nm grown at a growth rate of 0.4 μm/h.

where NNR is the density of the nonradiative recombination centers, and τNR and τR are the nonradiative and radiative recombination lifetimes, respectively. τR was determined by the hole concentration (p) theoretically.

The decay of PL intensity was shown in Figure 13. The following equation

$$I\_{PL}(t) = I\_0 \exp\left(-\frac{t}{\tau}\right). \tag{5}$$

explains well about the PL decay curve. Here, IPL(t) is the PL intensity at the time t, and I0 is the PL intensity at t = 0, just after the carriers are excited. The lifetime τ obtained by eq. (5) is the PL lifetime (τPL) in eq. (3). To estimate the minority-carrier lifetime in the bulk of the pGaAsN layer (τB), τPL dependence on GaAsN layer thickness (d) was obtained (Figure 13). When the growth rate was 2 μm/h, τB was 3.2 x 10-1 ns ([N] = 0.6%). By decreasing the growth rate to 0.4 μm/h, τB was increased to 9.0 x 10-1 ns ([N] = 0.8%) despite the increase in the N composition. Therefore, decreasing the growth rate in CBE is effective to improve τB. Further, the improvement is more effective when the N composition is higher.

The density of the nonradiative recombination centers determines the nonradiative recombi‐ nation lifetime (τNR). To discuss the amount of nonradiative recombination centers, τNR is estimated by eq. (4). The recombination lifetime (τR) depends on the hole concentration (p), as follows:

$$
\tau\_R = \frac{1}{Bp}.\tag{6}
$$

Here, B is the radiative recombination probability,

$$\begin{aligned} B &= 0.58 \times 10^{-12} \sqrt{\varepsilon} \left( \frac{1}{m\_p^\* + m\_n^\*} \right)^{1.5} \\ \times \left( 1 + \frac{1}{m\_p^\*} + \frac{1}{m\_n^\*} \right) \left( \frac{300}{T} \right)^{1.5} E\_g^{-2} \end{aligned} \tag{7}$$

where ε is the dielectric constant, mp\* and mn\* are the hole and electron effective masses, respectively, in units of the free electron mass, T is the temperature, and Eg is the band gap. For the p-GaAsN layers discussed here, B calculated by eq. (7) was 1.2 x 10-10 cm3/s. When the growth rate was 2 μm/h, the carrier concentration was 1 x 1017 cm-3. By decreasing the growth rate to 0.4 μm/h, it was decreased to 5 x 1016 cm-3. From eqs. (4) and (6), τNR and τR were obtained to be τNR = 3.2 x 10-1 ns and τR = 8.0 x 101 ns for the growth rate of 2 μm/h, and τNR = 9.0 x 10-1 ns and τR = 1.7 x 102 ns for the growth rate of 0.4 μm/h. These results are summarized in Table 2. Since τNR is much smaller than τR, τB is mainly determined by τNR. Therefore, the improvement of τB is mainly due to the increase in τNR. These results suggest that decreasing the growth rate in CBE is effective to suppress the formation of nonradiative recombination centers and to improve the carrier lifetime. Then, CBE is highly expected to realize the minority-carrier lifetime of more than 1 ns and the diffusion length of more than 1 μm with the target value of the N composition (3%).

#### **4.2. Improvement of minority carrier lifetime by controlling substrate orientation**

The effect of the surface orientation on the minority carrier lifetime is studied. GaAsN films were grown on GaAs(311)A, (311)B, and (100) substrates. The (311) surface consists of (111) and (100) components. The surface configurations of the (311)A and (311)B surfaces are shown in Figure 14. On the (311)A surface, a Ga atom connects to three As atoms, while an As atom connects to two Ga atoms. The same bond configuration holds for the (311)B surface by exchanging Ga and As atoms.

GaAsN layer (τB), τPL dependence on GaAsN layer thickness (d) was obtained (Figure 13). When the growth rate was 2 μm/h, τB was 3.2 x 10-1 ns ([N] = 0.6%). By decreasing the growth rate to 0.4 μm/h, τB was increased to 9.0 x 10-1 ns ([N] = 0.8%) despite the increase in the N composition. Therefore, decreasing the growth rate in CBE is effective to improve τB. Further,

The density of the nonradiative recombination centers determines the nonradiative recombi‐ nation lifetime (τNR). To discuss the amount of nonradiative recombination centers, τNR is estimated by eq. (4). The recombination lifetime (τR) depends on the hole concentration (p), as

> 1 . *R Bp* t

> > 12

1 0.58 10

= ´ ç ÷

e- æ ö

1 1 300 1 ,

**4.2. Improvement of minority carrier lifetime by controlling substrate orientation**

The effect of the surface orientation on the minority carrier lifetime is studied. GaAsN films were grown on GaAs(311)A, (311)B, and (100) substrates. The (311) surface consists of (111) and (100) components. The surface configurations of the (311)A and (311)B surfaces are shown in Figure 14. On the (311)A surface, a Ga atom connects to three As atoms, while an As atom

where ε is the dielectric constant, mp\* and mn\* are the hole and electron effective masses, respectively, in units of the free electron mass, T is the temperature, and Eg is the band gap. For the p-GaAsN layers discussed here, B calculated by eq. (7) was 1.2 x 10-10 cm3/s. When the growth rate was 2 μm/h, the carrier concentration was 1 x 1017 cm-3. By decreasing the growth rate to 0.4 μm/h, it was decreased to 5 x 1016 cm-3. From eqs. (4) and (6), τNR and τR were obtained to be τNR = 3.2 x 10-1 ns and τR = 8.0 x 101 ns for the growth rate of 2 μm/h, and τNR = 9.0 x 10-1 ns and τR = 1.7 x 102 ns for the growth rate of 0.4 μm/h. These results are summarized in Table 2. Since τNR is much smaller than τR, τB is mainly determined by τNR. Therefore, the improvement of τB is mainly due to the increase in τNR. These results suggest that decreasing the growth rate in CBE is effective to suppress the formation of nonradiative recombination centers and to improve the carrier lifetime. Then, CBE is highly expected to realize the minority-carrier lifetime of more than 1 ns and the diffusion length of more than 1

\* \*

æ öæ ö ´+ + ç ÷ç ÷ ç ÷è ø è ø

*p n*

*m m T*

= (6)

(7)

1.5

\* \*

*p n*

*g*

*E*

1.5 2

*m m*

ç ÷ + è ø

the improvement is more effective when the N composition is higher.

Here, B is the radiative recombination probability,

294 Solar Cells - Research and Application Perspectives

*B*

μm with the target value of the N composition (3%).

follows:

**Figure 14.** The surface structures of GaAs(311)A (left figure) and (311)B (right figure) substrates.

**Figure 15.** Typical PL decay curves at 4.5K of GaAsN with different growth orientations. The growth temperature was 440 ℃.

The results of the TR-PL measurements at 4.5K of GaAsN films with each growth orientation are shown in Figure 15. The PL lifetime is estimated by approximating the decay curve of the PL intensity as a straight line. The film with (311)B orientation has a longer PL lifetime, which indicates the longer minority carrier lifetime. The PL spectra at 4.5K of as-grown films with various substrate orientations are shown in Figure 16(a). The growth temperature was 440 ℃. There are two GaAsN-related peaks denoted as BE (near-band edge) and DL (deep levels) and one GaAs-related peaks in the spectra. The GaAsN-related peaks are in the range of 1.25 – 1.40 eV and 1.1 – 1.2 eV which are caused by BE and DL emissions, respectively. To understand the orientation-dependent photoluminescence of GaAsN films, the ratio of the integrated inten‐ sities of DL to BE (PDL/PBE) were calculated. The PDL/PBE ratio of the film grown on (311)A had the lowest value at any growth temperatures as shown in Figure 16 (b). The film grown on (311)A has almost the same N composition as that of (100). Therefore, N composition is not related to the difference in the integrated intensity ratios. This result indicates that the highindex substrate surfaces contribute to reduce defects and composition fluctuations in the epilayers [24]. On the other hand, in contrast to the continuous increase in total emission intensities of (3 1 1)B sample, a decreasing tendency with a rise in growth temperature was recorded for (3 1 1)A.

**Figure 16.** (a) PL spectra at 4.5K of as-grown films with different substrate orientations. The growth temperature was 440 ℃. (b) Growth-temperature dependences of N composition in GaAsN layers on (3 1 1)A/B and (1 0 0) substrates.

### **5. Lattice defects in GaAsN grown by CBE**

GaInAsN suffers from three main N-related problems: (i) the shortening lifetime of minority carriers, (ii) the lowering of their mobility, and (iii) the increase of carrier concentration with increasing N concentration in the alloy [25-27]. Indeed, the incorporation of a small atomic fraction of N in the lattice of GaAs gives rise to the formation of high density acceptor states, recombination centers, and scattering levels [28]. It is; therefore, clear that the degradation of electrical properties of GaAsN may be attributed only to the formation of lattice defects. These defects were expected to be formed during growth owing to the smaller atomic size of N than of As, as well as, to the large gap miscibility between GaAs and GaN. For that, extensive works on the distribution of lattice defects in the forbidden gap of Ga(In)AsN and their effects on their electrical properties were published during the last decade. Indeed, the summary of experimental results reported by Geisz and Friedman provides a basic knowledge of these defects [4]. Furthermore, undoped Ga(In)AsN alloys grown by chemical compound sources present a high density of residual impurities [29]. This property is a hindrance to a flexible design of Ga(In)AsN based solar cell and reduces the lifetime of minority carriers. Despite the very interesting results about the distribution of lattice defects in GaAsN, the main causes of short diffusion length of minority carriers and high background doping are still elusive. In this section of the chapter, we summarize the distribution of energy states in the forbidden gap of GaAsN grown by CBE, which was obtained using deep level transient spectroscopy and some related methods. Furthermore, we report the relationship of some defects and the poor electrical properties of the alloy, as well as, our recent results to decrease their impacts. All GaAsN samples were grown by CBE on GaAs (100) 2° off toward (110) substrate, under a growth temperature and a pressure of 420-460 °C and 2 x 10-2 Pa, respectively. TEGa, TDMAAs, and MMHy were used as Ga, As, and N chemical compound sources, respectively. SiH4 was used as n-type doping source, whereas undoped films are p-type. The detail of growth conditions using CBE can be found elsewhere [30-33]. The N concentration in each sample were evaluated from the Bragg angles of the GaAs and GaAsN reflection obtained by high resolution X-ray diffraction (HRXRD) method. The Schottky and ohmic contacts were evapo‐ rated through metal masks at a vacuum pressure of 10-4 Pa. The free donor and acceptor concentrations were calculated by the fitting of the Mott-Schottky plot using the capacitancevoltage method. DLTS spectra were collected using a BIO-RAD digital DLTS system (DL8000). The activation energies Ea [Ev + ET (eV)] for hole traps and Ea [EC - ET (eV)] for electron trap were determined from the slope of the Arrhenius plot of the DLTS signals, whereas the capture cross sections n/p (cm2) were evaluated from the intercept values [34]. Illustrated in Figure 17 (a) is the distribution of energy states in the forbidden gap of GaAsN0.005 grown by CBE. The main electron and hole traps in GaAsN were recorded by DLTS method and shown in Figure 17 (b) and (c). For electrons traps, two peaks (E1) and (E2) were observed in as grown film around 150 and 300 K, respectively. After rapid thermal annealing, E2 disappears completely and a new electron trap (E3) appears at 200 K. Compared with the electron traps in N-free GaAs, only E1 appears after the introduction of a small amount of N. Therefore, we have strongly suggested that E2 and E3 could be considered as native defects in GaAs. Based on the classification of electron traps in GaAs by Maunitton et al., E2 and E3 were considered to be EL2 (+/0) and EL5, respectively [35]. On the other hand, three hole traps, labeled H0, H2, and H5 were commonly observed in the DLTS spectrum of Figure 17 (c). Compared with the hole traps in N-free GaAs, we could only attribute H5 to the double donor state of EL2 with the charge state (+/++) [36], however, H2 and H0 appear to be newly observed. The hole trap H0 was confirmed to be a radiative recombination center using single and double carrier pulse DLTS method [30]. Since, our interest is only on the N-related defects which could be correlated with the poor electrical properties and the high carrier density in the alloy, we will focus only on the electron trap E1 and the hole trap H2, which were confirmed to be the main cause of the shortening of minority carrier lifetime and the high background doping in GaAsN films,

one GaAs-related peaks in the spectra. The GaAsN-related peaks are in the range of 1.25 – 1.40 eV and 1.1 – 1.2 eV which are caused by BE and DL emissions, respectively. To understand the orientation-dependent photoluminescence of GaAsN films, the ratio of the integrated inten‐ sities of DL to BE (PDL/PBE) were calculated. The PDL/PBE ratio of the film grown on (311)A had the lowest value at any growth temperatures as shown in Figure 16 (b). The film grown on (311)A has almost the same N composition as that of (100). Therefore, N composition is not related to the difference in the integrated intensity ratios. This result indicates that the highindex substrate surfaces contribute to reduce defects and composition fluctuations in the epilayers [24]. On the other hand, in contrast to the continuous increase in total emission intensities of (3 1 1)B sample, a decreasing tendency with a rise in growth temperature was

(a) (b)

**Figure 16.** (a) PL spectra at 4.5K of as-grown films with different substrate orientations. The growth temperature was 440 ℃. (b) Growth-temperature dependences of N composition in GaAsN layers on (3 1 1)A/B and (1 0 0) substrates.

GaInAsN suffers from three main N-related problems: (i) the shortening lifetime of minority carriers, (ii) the lowering of their mobility, and (iii) the increase of carrier concentration with increasing N concentration in the alloy [25-27]. Indeed, the incorporation of a small atomic fraction of N in the lattice of GaAs gives rise to the formation of high density acceptor states, recombination centers, and scattering levels [28]. It is; therefore, clear that the degradation of electrical properties of GaAsN may be attributed only to the formation of lattice defects. These defects were expected to be formed during growth owing to the smaller atomic size of N than of As, as well as, to the large gap miscibility between GaAs and GaN. For that, extensive works

**0.6 0.8 1.0 1.2 1.4 1.6**

**Energy (eV)**

**5. Lattice defects in GaAsN grown by CBE**

**80**

**120**

**PL lifetime [ps]**

**BE**

**DL GaAs**

**160**

**200**

**0.1 1 10 100**

**Intensity ratio of DL/BE**

**(100)**

**420 o C 440 o C 460 o C**

**(311)A**

**(311)B**

recorded for (3 1 1)A.

**PL intensity (arb.unit)**

**(311)A**

**(311)B**

**(100)**

**4.5K**

296 Solar Cells - Research and Application Perspectives

Running Title

respectively. The properties of these two defects are summarized respectively in the two next sub-sections.

19

**Fig. 17.**(left)Distribution of lattice defects in GaAsN grown by CBE for a N concentration of 0.5%, DLTS spectra for (a) as grown and annealed GaAs, (b) as grown GaAsN, (c) annealed **Figure 17.** (left) Distribution of lattice defects in GaAsN grown by CBE for a N concentration of 0.5%, DLTS spectra for (a) as grown and annealed GaAs, (b) as grown GaAsN, (c) annealed GaAsN, (d) Arrhenius plot for electron traps, (e) DLTS spectrum for hole traps in GaAsN, and (f) Arrhenius plot for hole traps.

GaAsN, (d) Arrhenius plot for electron traps, (e) DLTS spectrum for hole traps in GaAsN,

#### **5.1. N-related non radiative recombination center**

and (f) Arrhenius plot for hole traps.

1

The electron trap E1 was confirmed to be related to the N atom, since its density increas‐ es with increasing the N concentration in GaAsN films [31]. Furthermore, it was not observed in N-free GaAs [31]. The activation energy of E1 was found to vary between 0.3 and 0.4 eV below the conduction band minimum (CBM) [31-33]. This variation in energy level was explained by the effect of the electrical field on the thermal emission of carriers from E1, since the carrier concentration in GaAsN was not identical in all studied sam‐ ples [4]. In addition, E1 was not only observed in CBE grown GaAsN but also in the DLTS spectra of MOCVD and MBE grown GaAsN and InGaAsN [37, 38]. Moreover, E1 approx‐ imately exhibited similar density and tendency with varying the N concentration, despite the quite difference in residual carrier densities between the three growth methods [31, 38, 39]. This result implies that the possible structure of E1 is independent of impurities. The thermal capture cross section of E1 is too large compared with that of native defects in GaAs. For that, it was found that the DLTS peak height of E1 saturates promptly with increasing the time of injection of electrons through the filling pulse parameter [33]. In view of the effective role of E1 in the degradation of electrical properties of GaAsN, we were able to provide evidence that E1 trap plays a major role in the degradation of minority carrier lifetime and acts as a recombination center [33]. For this, we carried out an experiment based on minority carrier capture at majority carrier trap by double carrier pulse DLTS method [30]. In this experiment, E1 was filled with majority carriers during the first pulse, so that E1 centers are occupied with electrons. Then, a forward bias minority carrier injection of short duration was applied in order to introduce capture of minority carriers. When the junction returned of quiescent reverse bias, E1 centers that remained occupied with majority carriers were emptied by thermal emission. The amplitude of this thermal emission provides a measure of the number of carriers that were trapped by E1 and not filled with minority carriers at the end of the injection pulse. A decrease of E1 peak height was observed and confirmed with varying the rate of injection through the duration and the voltage of the second pulse [33]. This result, indeed, indicates that E1 is a recombina‐ tion center [33]. After this step, it was essential to identify the nature of this recombina‐ tion mechanism. For that, the temperature dependence of the capture cross section of E1 (σE1( was investigated. As known in DLTS measurements, varying the emission rate window shifts the peak of the defect and the capture cross section may change. From the Arrhe‐ nius plots of each emission rate, we established the relationship between σE1 and the reciprocal temperature [33]. Absolutely, the recombination process through E1 was confirmed to be nonradiative, since σE1 presents a thermal activation energy of 0.13 eV [33]. Furthermore, σE1 was evaluated at room temperature to around 10-13 cm2 [33]. This result proves that E1 is an active recombination center. In addition, this recombination activity may rises with increasing N in the film, since the activation energy of E1, comes closer to the midgap, following the decrease of the conduction band minimum. The recombination mechanism through E1 was quantified by evaluating the lifetime of electrons from the conduction band the energy level of the electron trap in the forbidden gap of the alloy. Using the SRH model for generationrecombination, the lifetime of electrons from the CBM to E1 was calculated to 0.2 ns [33-39]. This value was experimentally verified by timeresolved photoluminescence measurements. We, therefore, suggest that E1 is the main cause of short minority carrier lifetime in GaAsN alloys.

respectively. The properties of these two defects are summarized respectively in the two next

**(a)**

19

**(b)**

**(c)**

sub-sections.

1

Running Title

1.29

298 Solar Cells - Research and Application Perspectives

*Average Thermal Activation Energy***Ea**

0.15

0.48

0.59

0.84

**H5**  *EL2 (+/++)*

**E2** *EL2 (+/0)*

0.99 **E1((N‐As)As)**

*Main cause of short minority carriers' lifetime: NR recombination* t

*CBM: GaAsN0.00 5, Eg =1.29 eV,*

**E3** EL5 *type defect*

0.05 **H1**

and (f) Arrhenius plot for hole traps.

**5.1. N-related non radiative recombination center**

*Radiative recombination. center*

*VBM*

DLTS spectrum for hole traps in GaAsN, and (f) Arrhenius plot for hole traps.

**Fig. 17.**(left)Distribution of lattice defects in GaAsN grown by CBE for a N concentration of 0.5%, DLTS spectra for (a) as grown and annealed GaAs, (b) as grown GaAsN, (c) annealed GaAsN, (d) Arrhenius plot for electron traps, (e) DLTS spectrum for hole traps in GaAsN,

**Figure 17.** (left) Distribution of lattice defects in GaAsN grown by CBE for a N concentration of 0.5%, DLTS spectra for (a) as grown and annealed GaAs, (b) as grown GaAsN, (c) annealed GaAsN, (d) Arrhenius plot for electron traps, (e)

The electron trap E1 was confirmed to be related to the N atom, since its density increas‐ es with increasing the N concentration in GaAsN films [31]. Furthermore, it was not

*Principal cause of high background doping*

**H2 (N‐H‐VGa)**

 **(eV)**

**Figure 18.** The split intestinal (N-As)As (left) and N-H-VGa (right) as a possible origins of E1 and H2, respectively.

To understand the formation process of E1 and limit its effect, it was necessary to investigate its origin. First, it was mentioned above that E1 is independent of impurities, such as H, O, and C. Furthermore, E1 was observed in undoped p-type (minority carrier trap), n-type, and Si-doped GaAsN films, which exclude the doping atom from its origin. Therefore, E1 was tentatively suggested to be sensitive only to the host atoms (N, As, and Ga). In addition, using the isothermal capacitance transient method, the density profiling of E1 was found to be quasiuniform distributed GaAsN [31]. This result indicates that the formation of E1 starts and goes on with the growth process. An obvious reason of this behavior is the compensation for the tensile strain, which could be caused by the small atomic size of N compared with that of As. Theoretically, the split interstitials (N-As)As and (N-N)As were expected to form two electron traps at 0.4 and 0.6 eV below the CBM of GaAsN, respectively [40]. These two defects were qualified to be energetically favorable on the growth surface [40]. As the N-dependence of the density of E1 did not show a straight line and since the total N concentration in the film could not be obtained using HRXRD measurements, we have proceed to investigate the relationship between the density of E1 and the flux of the As source. Indeed, we found that the density of E1 shows a peaking behavior with increasing TDMAAs [41]. This result implies that the formation of E1 is sensitive to both N and As atoms. However, this relationship could not be quantified since the atomic fractions between As and N in GaAsN films are quite different [41]. As shown in Figure 18, the split interstitial (N-As)As is, therefore, expected to be the possible origin for E1. However, more experiments are required to clarify the formation process of this recombination center and to limit its density.

### **5.2. N-related acceptor like state in GaAsN**

The high background doping in undoped GaAsN films is a serious problem for solar cell design and fabrication. A small atomic fraction of N changes the conductivity in the film from n-type in GaAs to p-type. Obviously, the formation of N-related acceptors with high density is the main reason of donor compensation. Indeed, two acceptor levels, A1 and A2, were confirmed using Hall Effect measurements [42]. Their thermal activation energies were evaluated to EA1 = 130 ± 20 meV and EA2 = 55 ± 10 meV, respectively. On another hand, the ionized acceptor density NA, obtained using capacitance voltage (C-V) method, showed a linear dependence with N concen‐ tration in undoped films grown under a Ga flow rate of TEGa = 0.1 sccm [32]. This indicates that NA depends strongly on a N-related acceptor [32]. However, this linear dependence tends to saturate when TEGa is reduced, even the N concentration is enhanced [32]. The reason of this saturation was clarified using SIMS measurements, where the concentration of H impurity decreasesslightlywithdecreasingTEGa[32].Hence,thisresultimpliesthatNA dependsstrongly to N and H atomic concentrations in the film. To identify this N-H related acceptor level, we carried out C-V measurements in the temperature range 20 - 330 K in order to get the tempera‐ ture dependence of NA. A sigmoid increase of NA was observed between 70 and 100 K [32]. Its amplitude showed a strong dependence with N concentration [32]. It approximately reflects the relationshipbetweenNA andNconcentrationatroomtemperature[39].Thisresultindicatesthat the sigmoid increase of NA between 70 and 100 K is owing to the thermal ionization of a Nrelated acceptor-like state, which thermal ionization energy can be estimated to be between 0.1 and 0.2 eV. Furthermore, as given in Figure 17 (c), the hole trap H2 was observed in the temper‐ ature range of sigmoid increase of NA. The activation of H2 is within the expected range of the Nrelatedacceptor stateanditis inconformitywiththeoretical calculation[32,44].Furthermorethe density of H2 was found to be in linear dependence with N concentration in the samples grown under TEGa = 0.1 sccm. Hence, H2 is suggested to be the main acceptor state which governs the tendency of NA and it is the cause of the increase of junction capacitance in the temperature range 70 to 100 K. The origin of H2 was investigated using the results of carrier concentration and the density of residual impurities in undoped GaAsN grown by CBE under various Ga flow rates, obtained using Hall Effect, FT-IR, and SIMS [32, 42]. From SIMS measurements, which were carried out on GaAsN grown under different TEGa flow rates, it was found that NA depends on the atomic concentrations of N and H [32, 42]. In addition, using FTIR measurements, a linear relationship was established between the concentration of N-H complexes and N concentra‐ tion [29]. Therefore, H2 was strongly suggested to be an acceptor state and its origin is related to the N-H bond. However, the slope of the linear relationship between NA and the concentration of N-H complexes showed an increase with increasing the growth temperature (TG ∈ [400, 430] C)[29].This indeedindicates thattheN-Hcomplexescouldbeaccompaniedwithanotherdefect, which binding energy was evaluated to 2.5 eV [29]. On another hand, using theoretical calcula‐ tion, the formation energy of (N-H-VGa) -2 was found to be lower than (N-VGa) -3, (H-VGa) -2, and isolated VGa-3 [43]. These results may expect VGa as a possible origin of the unknown intrinsic defect. These predictions were experimentally supported using positron annihilation spectro‐ scopyresults [44].Therefore,H2mayhaveN-H-VGa asapossiblestructureas showninFigure18.

## **6. Conclusion**

**Figure 18.** The split intestinal (N-As)As (left) and N-H-VGa (right) as a possible origins of E1 and H2, respectively.

recombination center and to limit its density.

300 Solar Cells - Research and Application Perspectives

**5.2. N-related acceptor like state in GaAsN**

To understand the formation process of E1 and limit its effect, it was necessary to investigate its origin. First, it was mentioned above that E1 is independent of impurities, such as H, O, and C. Furthermore, E1 was observed in undoped p-type (minority carrier trap), n-type, and Si-doped GaAsN films, which exclude the doping atom from its origin. Therefore, E1 was tentatively suggested to be sensitive only to the host atoms (N, As, and Ga). In addition, using the isothermal capacitance transient method, the density profiling of E1 was found to be quasiuniform distributed GaAsN [31]. This result indicates that the formation of E1 starts and goes on with the growth process. An obvious reason of this behavior is the compensation for the tensile strain, which could be caused by the small atomic size of N compared with that of As. Theoretically, the split interstitials (N-As)As and (N-N)As were expected to form two electron traps at 0.4 and 0.6 eV below the CBM of GaAsN, respectively [40]. These two defects were qualified to be energetically favorable on the growth surface [40]. As the N-dependence of the density of E1 did not show a straight line and since the total N concentration in the film could not be obtained using HRXRD measurements, we have proceed to investigate the relationship between the density of E1 and the flux of the As source. Indeed, we found that the density of E1 shows a peaking behavior with increasing TDMAAs [41]. This result implies that the formation of E1 is sensitive to both N and As atoms. However, this relationship could not be quantified since the atomic fractions between As and N in GaAsN films are quite different [41]. As shown in Figure 18, the split interstitial (N-As)As is, therefore, expected to be the possible origin for E1. However, more experiments are required to clarify the formation process of this

The high background doping in undoped GaAsN films is a serious problem for solar cell design and fabrication. A small atomic fraction of N changes the conductivity in the film from n-type in GaAs to p-type. Obviously, the formation of N-related acceptors with high density is the main reason of donor compensation. Indeed, two acceptor levels, A1 and A2, were confirmed using Hall Effect measurements [42]. Their thermal activation energies were evaluated to EA1 = 130 ± 20 meV and EA2 = 55 ± 10 meV, respectively. On another hand, the ionized acceptor density NA,

InGaAsN is a candidate material to realize the ultrahigh efficiency multi-junction solar cell. The efficiency of the 4-junction solar cell, InGaP/InGaAs/InGaAsN/Ge, is expected to be 41% under 1-sun (AM0) and 52% under 500-sun (AM1.5). In order to achieve the expected super high efficiency, the electrical property of the InGaAsN should be improved. In this paper, we have shown the following results:

## **Author details**

Kazuma Ikeda, Han Xiuxun, Bouzazi Boussairi and Yoshio Ohshita

Toyota Technological Institute, Japan

## **References**

**1.** The CBE method was developed for the growth of GaAsN films. The growth temperature region was divided into three parts. In the middle growth temperature region (390 – 445 °C), the higher N composition without broadening of the XRD rocking curve width was obtained. In this temperature region, a typical characteristics in the growth process is that the amount of the N incorporation into crystal at the surface is not only dominated by the

**2.** Decreasing the growth rate was effective to improve the hole mobility and minoritycarrier lifetime in p-GaAsN films grown by the chemical beam epitaxy (CBE). The mobility

temperature dependence of the mobility, μN, which was inversely proportional to the amount of N-related scattering centers, was estimated. By decreasing the growth rate, μN

was reduced especially when the N composition was higher. The result indicates the improved mobility by decreasing the N-related scattering centers. The minority-carrier lifetime in the bulk of p-GaAsN films, τB, estimated by PL decay curves was improved from 3.2×10-1 ([N] = 0.6%) to 9.0×10-1 ns ([N] = 0.8%) despite the higher N composition. The bulk minority-carrier lifetime τB was mainly determined by the nonradiative recombina‐ tion lifetime (τNR). This means that the nonradiative recombination centers were reduced

V-1s-1 for the N composition of 0.6%. Based on the

growth rate but also the desorption rate of N species at the surface.

by decreasing the growth rate, which resulted in the improvement of τB.

to be the potential substrate to achieve efficient N incorporation.

Kazuma Ikeda, Han Xiuxun, Bouzazi Boussairi and Yoshio Ohshita

**3.** The electron lifetime of p-GaAsN was also improved by controlling the GaAs substrate orientations. The investigation of the effects from GaAs substrate surface orientation and polarity indicates that N incorporation can be enhanced on the (3 1 1)B plane but reduced on (3 1 1)A compared with (1 0 0), where the three dangling bond sites on the (3 1 1) growing surface are considered to play the dominant role. The examination of intensity ratio between emissions from band edge and deep levels evidenced the improved luminescence efficiency of GaAsN layers on (3 1 1) substrates with both polarity. In response to variations in the growth temperature and the postgrowth annealing, optical behavior shows strong dependence on the epitaxial orientation, as illustrated by the relative intensity and low-energy tail of the band-edge emission. (3 1 1)B is distinguished

**4.** The electron trap E1 located at 0.99 eV above VBM is a dominant non radiative recombi‐ nation center. The formation of E1 is sensitive to both the amounts of N and As atoms. A possible structure of this defect is (N-As)As. The hole trap H2 located at 0.15 eV above VBM is suggested to be the main acceptor state. The origin of H2 is related to the N-H bond. A

was increased from 120 to 150 cm2

302 Solar Cells - Research and Application Perspectives

possible structure is N-H-VGa.

Toyota Technological Institute, Japan

**Author details**

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## **Solar Cell Efficiency vs. Module Power Output: Simulation of a Solar Cell in a CPV Module**

Egbert Rodríguez Messmer

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/52707

## **1. Introduction**

[40] Zhang SB, Wei SH. Nitrogen Solubility and Induced Defect Complexes in Epitaxial

[41] Bouzazi B, Lee JH, Suzuki H, Kojima N, Ohshita Y, Yamaguchi M. Origin Investiga‐ tion of a Nitrogen-Related Recombination Center in GaAsN Grown by Chemical

[42] Saito K, Nishimura K, Suzuki H, Kojima N, Ohshita Y, Yamaguchi M. Hydrogen re‐ duction in GaAsN thin films by flow rate modulated chemical beam epitaxy. Thin

[43] Janotti A, Wei SH, Zhang SB, S. Kurtz, Van de Walle CG. Interactions between nitro‐ gen, hydrogen, and gallium vacancies in GaAs1-xNx alloys. Physical Review B 2003;67

[44] Toivonen J, Hakkarainen T, Sopanen M, Lipsanen H, Oila J, Saarinen K. Observation of defect complexes containing Ga vacancies in GaAsN. Applied Physics Letters

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306 Solar Cells - Research and Application Perspectives

161201. DOI: 10.1103/PhysRevB.67.161201.

2003;82 40-42. DOI: 10.1063/1.1533843.

In the past few years Concentrating Photovoltaics (CPV) has moved from R&D and pilot projects (typically installations below 500 kilowatts) to multi-megawatt power plants. The starting point of the commercial deployment of this technology was in 2006 when the Insti‐ tute for Concentration Photovoltaic Systems (ISFOC) purchased several CPV power plants of different technologies and provider that were installed in Puertollano (Spain). Each sup‐ plier provided a power plant that had a size between 200kW and 500kW. These power plants are operating since 2008 and the results are very promising [1]. After these first instal‐ lations several MW-size power plants have been installed ([2], [3] and [4]), and the first mul‐ ti-megawatt CPV power plants are under construction, like a 150MW power plant that Soitec is developing for the San Diego Gas & Electric in California [5], demonstrating here with that CPV technology can be a cost efficient alternative to conventional silicon-based flat-plate photovoltaic (PV) plants in areas of high direct solar irradiation.

A CPV module consists typically of a high-efficient solar cell and a concentrator that concen‐ trates light and that can be made out of a mirror, a parabolic dish or lenses. These modules are then mounted on a 2-axis tracking system to make sure that the module is always per‐ pendicular to the sun, so that the light spot reaches the active area of the solar cell. A CPV system is therefore more complex than a conventional PV system, and, in order to be com‐ mercially competitive with standard systems, it is important to control its cost figure. When making a cost analysis of a CPV system, from manufacturing of solar cells to a finished in‐ stallation [6], the cost figure is given in terms of a monetary unit per Watt (€/W or \$/W). This cost figure should be kept as low as possible, and can be done either for a complete installa‐ tion including all the costs relative to the deployment of the system or it can be done partly, considering only the module or the module and tracking system.There are two possibilities

© 2013 Rodríguez Messmer; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2013 Rodríguez Messmer; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

to reduce the value of this cost figure, which are either reducing the cost of the system, which is typically done reducing the cost of the raw materials or optimizing production processes, or by increasing the output power of the CPV module, which can be achieved by reducing possible sources of losses inside a module (these can be optical, electrical o ther‐ mal).The advantage of increasing the output power of a module is that this has an important impact to other related costs, since also the manufacturing and installation costs are reduced due to the need of fewer modules or even trackers for a CPV power plant of a given size.

The output power of a CPV module can be optimized by reducing the internal losses that appear in the module design. Therefore a good match of the materials from which a module is made should be aimed. The need of a good match is especially true for the interaction be‐ tween the solar cell and the optical system, where the solar cell can be adapted in size, light spectrum, concentration ratio and interface to the optical system. In practice it is very diffi‐ cult to achieve good matching of different materials, since the different parts of a CPV mod‐ ule are made by different manufacturers. These might have different interests as compared to a system developer, so that a compromise is needed. In order to keep the manufacturing cost of the CPV module low, all elements of the module should be standardized, but, on the other hand, CPV module manufacturer want to have components that are customized to their own module design to maximise their output power. Some CPV module manufacturer use parabolic dishes to concentrate light, while others use lenses, and also the concentration ratio at which the modules work differ from manufacturer to manufacturer. This means that from a technological point of view, a CPV module manufacturer desires to have components that are customized to its own system.

To go more into detail in this issue of matching of materials inside a CPV module, and to analyse its effect on module performance, the interface between solar cell and optical system of the module is analysed in this chapter. A solar cell can be designed to have either a maxi‐ mum efficiency when it is measured as a stand-alone device (having air as the surrounding medium) or to have maximum efficiency when it is surrounded in any other optical medi‐ um that is used inside the CPV module (e.g. glass or an optical encapsulant). This fact has an important impact technically and commercially. The solar cell efficiency is usually defined when it is measured in air, and should for commercial purpose be designed to have maxi‐ mum efficiency under these conditions. On the other hand, if the solar cell is going to be op‐ erated embedded in an encapsulant and a lens, the CPV manufacturer should choose a solar cell that is designed for this operating condition, even though the solar cell will have less efficiency when measured at air. In summary, it is important to consider a CPV module as one system during its development, and not composed of independent components that have to be developed independently.

In order to explain better how the embedding medium affects the solar cell performance and to quantify this effect, a series of simulations has been done with a simulation program that has been developed by Isofotón in collaboration with the University of Granada (Spain). This program is called ISOSIM and is able to simulate the performance of a multijunction solar cell, including its anti-reflection coating (ARC) and taking into consideration the con‐ centration and the medium in which the solar cell is used (e.g. air or an optical gel to couple the light from the lens to the solar cell). It is also possible to add optical layers on top of the solar cell structure and simulating thereby a CPV module.

For the sake of simplicity, in this chapter it has been considered a double junction solar cell that is operating at a temperature of 320K (50ºC). The obtained results give a qualitative in‐ dication on the effect of different parameters, but quantitatively the effects that are descri‐ bed in this chapter will exceeded at real operating conditions. On one hand the solar cells that are used are triple-junction cells and also the operating temperature is usually higher. It is estimated that when adapting the solar cell to an optical system instead of using a stand‐ ard solar cell, an increase of output power of up to 10% can be achieved.

## **2. Outline of experimental work**

to reduce the value of this cost figure, which are either reducing the cost of the system, which is typically done reducing the cost of the raw materials or optimizing production processes, or by increasing the output power of the CPV module, which can be achieved by reducing possible sources of losses inside a module (these can be optical, electrical o ther‐ mal).The advantage of increasing the output power of a module is that this has an important impact to other related costs, since also the manufacturing and installation costs are reduced due to the need of fewer modules or even trackers for a CPV power plant of a given size.

The output power of a CPV module can be optimized by reducing the internal losses that appear in the module design. Therefore a good match of the materials from which a module is made should be aimed. The need of a good match is especially true for the interaction be‐ tween the solar cell and the optical system, where the solar cell can be adapted in size, light spectrum, concentration ratio and interface to the optical system. In practice it is very diffi‐ cult to achieve good matching of different materials, since the different parts of a CPV mod‐ ule are made by different manufacturers. These might have different interests as compared to a system developer, so that a compromise is needed. In order to keep the manufacturing cost of the CPV module low, all elements of the module should be standardized, but, on the other hand, CPV module manufacturer want to have components that are customized to their own module design to maximise their output power. Some CPV module manufacturer use parabolic dishes to concentrate light, while others use lenses, and also the concentration ratio at which the modules work differ from manufacturer to manufacturer. This means that from a technological point of view, a CPV module manufacturer desires to have components

To go more into detail in this issue of matching of materials inside a CPV module, and to analyse its effect on module performance, the interface between solar cell and optical system of the module is analysed in this chapter. A solar cell can be designed to have either a maxi‐ mum efficiency when it is measured as a stand-alone device (having air as the surrounding medium) or to have maximum efficiency when it is surrounded in any other optical medi‐ um that is used inside the CPV module (e.g. glass or an optical encapsulant). This fact has an important impact technically and commercially. The solar cell efficiency is usually defined when it is measured in air, and should for commercial purpose be designed to have maxi‐ mum efficiency under these conditions. On the other hand, if the solar cell is going to be op‐ erated embedded in an encapsulant and a lens, the CPV manufacturer should choose a solar cell that is designed for this operating condition, even though the solar cell will have less efficiency when measured at air. In summary, it is important to consider a CPV module as one system during its development, and not composed of independent components that

In order to explain better how the embedding medium affects the solar cell performance and to quantify this effect, a series of simulations has been done with a simulation program that has been developed by Isofotón in collaboration with the University of Granada (Spain). This program is called ISOSIM and is able to simulate the performance of a multijunction solar cell, including its anti-reflection coating (ARC) and taking into consideration the con‐ centration and the medium in which the solar cell is used (e.g. air or an optical gel to couple

that are customized to its own system.

308 Solar Cells - Research and Application Perspectives

have to be developed independently.

In this Chapter, first, the capabilities and performance of the simulation program are ex‐ plained, followed by several studies that show which factors affect the performance of a so‐ lar cell outside and inside of a CPV module.

The first study shows that the performance of a solar cell does not depend only on the mate‐ rial and thickness of the AR- coating layer(s), but also on the refractive index of the sur‐ rounding medium in which this solar cell is measured or operated. A solar cell does not have the same efficiency when it is operated in air (refractive index of 1) or when it is oper‐ ated in a medium of refractive index of e.g. 1.5, (if the solar cell is covered by glass).

Afterwards the performance of the solar cell in air and when it is assembled in a CPV mod‐ ule will be compared. It has been analyzed the current matching of the double-junction solar cell, varying the thickness of the base of the top cell, and it has been identified the limiting subcell (either top-cell or bottom-cell), which is attributed to be due to different spectral losses (absorption or reflection) in the materials and interfaces of the elements of the system.

In the last part a practical example is given, in which the power output of a CPV module is quantified when it is assembled either with a double-junction solar cell that has been opti‐ mized having air as the interface or a solar cell that is optimized to the CPV module. It shows that even if the variation in efficiency of the solar cell is little, the difference in output power can be significant. This chapter summarizes previous work that has been done with the ISOSIM package ([7], [8] and [9]).

## **3. ISOSIM software and experimental parameters**

There are currently several approaches and solutions proposed from module manufacturer and system integrator that develop CPV modules. On the market are currently several tech‐ niques to concentrate the light, since many companies have developed their own propriet‐ ary technological solution. The type of concentrator can be either based on mirrors, dishes, or lenses, and using only primary optics or also secondary and even tertiary optics. In order to maximize the output power of a module, solar cells have to be optimized for each optical system. The problem that arises is that a solar cell that has been optimized for a given opti‐ cal system does not necessarily have an optimum performance also in another optical sys‐ tem. It is also difficult for a solar cell manufacturer to predict how a solar cell will perform inside a given module type. To take into consideration various types of concentrator tech‐ nology, and to be able to analyze also a stand-alone solar cell, the simulation software is or‐ ganized in layers, in which each layer represents a material with its own material properties and function. In this manner it is possible to simulate any type of CPV module and at any operating condition (temperature, concentration ratio).

The software used for the simulations has been specifically designed for the analysis of mul‐ tijunction solar cells in order to get a tool to aid the design of solar cells and concentrator PV systems. This software, that is called *ISOSIM*, is capable of modelling the performance from stand-alone single junction solar cells up to the performance of multijunction solar cells in‐ side a CPV module under real operating conditions. The simulation program solves the Poisson and continuity equations by using a procedure optimized for multilayer structures. It includes the radiative interband, Shockley-Read-Hall and Auger recombination mecha‐ nisms, and computes the generation function of electron-hole pairs from the optical parame‐ ters of the cell materials. The dependence of these optical parameters on the photon energy has been included, taking into account the doping level and its effect on bandgap narrow‐ ing. The software uses the Rakic model for the calculation of the complex dielectric function, absorption coefficient, extinction and refraction index calculation, with the Gaussian broad‐ ening proposed by Kim. Additionally, several effects are included in the software, such as indirect transition contributions, the shift in the optical band gap due to doping, and freecarrier absorption, among others. The material parameters of several anti-reflection coatings were obtained either empirically by ellipsometry measurements or extracting them from the SOPRA database of refractive indexes [10].

The program also takes into consideration the optical medium that surrounds the solar cell, which can be either air which represents the case of a stand-alone solar cell that is measured, or any other medium, representing the case of a solar cell that is mounted in a CPV module (e.g. epoxies, solar glasses, optical gel). Apart of that, also the illumination spectra (space, terrestrial or any customized spectra), the concentration of the light source and the tempera‐ ture of the solar cell can be modified for simulations. It is therefore possible to simulate the whole system, considering solar cell, lenses, optical gels that are used to couple optical com‐ ponents, possible air gaps between lenses inside the module, concentration ratio and operat‐ ing temperature. It is therefore possible to estimate the total loss of a system if e.g. a wrong choice of materials or of its process parameters has been chosen for the manufacturing of a CPV module.

For the simulations in this chapter, I-V curves and spectral response of a stand-alone solar cell are obtained by simulating a typical solar cell structure. If not otherwise specified, the structure used for the studies in this chapter (Figure 1.) see is a dual-junction GaInP/GaAs solar cell with the two photovoltaic junctions connected by a GaAs tunnel junction, and the antireflection coating consisting of a double layer of TiO2 and Al2O3 [11]. Light concentration and operating temperature were fixed at 1000 suns and 320 K, respectively. It has been used the AM1.5D spectrum and has also been assumed a shadowing loss of the solar cell of 2% due to the area below the grid. Some of the parameters of the materials that are used for simulations show high dispersion. For instance, the band-gap of GaInP depends on the or‐ dering level, and could vary from 1.66 eV for a fully ordered lattice to 2.01 eV for a totally disordered one. For the simulations presented in this article, we assumed that the band-gap of GaInP is 1.9 eV at 300K. In a previous paper in which we presented this software, it has been shown that the results of the simulations obtained by the ISOSIM software match rea‐ sonably well with experimentally observed results [7].

to maximize the output power of a module, solar cells have to be optimized for each optical system. The problem that arises is that a solar cell that has been optimized for a given opti‐ cal system does not necessarily have an optimum performance also in another optical sys‐ tem. It is also difficult for a solar cell manufacturer to predict how a solar cell will perform inside a given module type. To take into consideration various types of concentrator tech‐ nology, and to be able to analyze also a stand-alone solar cell, the simulation software is or‐ ganized in layers, in which each layer represents a material with its own material properties and function. In this manner it is possible to simulate any type of CPV module and at any

The software used for the simulations has been specifically designed for the analysis of mul‐ tijunction solar cells in order to get a tool to aid the design of solar cells and concentrator PV systems. This software, that is called *ISOSIM*, is capable of modelling the performance from stand-alone single junction solar cells up to the performance of multijunction solar cells in‐ side a CPV module under real operating conditions. The simulation program solves the Poisson and continuity equations by using a procedure optimized for multilayer structures. It includes the radiative interband, Shockley-Read-Hall and Auger recombination mecha‐ nisms, and computes the generation function of electron-hole pairs from the optical parame‐ ters of the cell materials. The dependence of these optical parameters on the photon energy has been included, taking into account the doping level and its effect on bandgap narrow‐ ing. The software uses the Rakic model for the calculation of the complex dielectric function, absorption coefficient, extinction and refraction index calculation, with the Gaussian broad‐ ening proposed by Kim. Additionally, several effects are included in the software, such as indirect transition contributions, the shift in the optical band gap due to doping, and freecarrier absorption, among others. The material parameters of several anti-reflection coatings were obtained either empirically by ellipsometry measurements or extracting them from the

The program also takes into consideration the optical medium that surrounds the solar cell, which can be either air which represents the case of a stand-alone solar cell that is measured, or any other medium, representing the case of a solar cell that is mounted in a CPV module (e.g. epoxies, solar glasses, optical gel). Apart of that, also the illumination spectra (space, terrestrial or any customized spectra), the concentration of the light source and the tempera‐ ture of the solar cell can be modified for simulations. It is therefore possible to simulate the whole system, considering solar cell, lenses, optical gels that are used to couple optical com‐ ponents, possible air gaps between lenses inside the module, concentration ratio and operat‐ ing temperature. It is therefore possible to estimate the total loss of a system if e.g. a wrong choice of materials or of its process parameters has been chosen for the manufacturing of a

For the simulations in this chapter, I-V curves and spectral response of a stand-alone solar cell are obtained by simulating a typical solar cell structure. If not otherwise specified, the structure used for the studies in this chapter (Figure 1.) see is a dual-junction GaInP/GaAs solar cell with the two photovoltaic junctions connected by a GaAs tunnel junction, and the antireflection coating consisting of a double layer of TiO2 and Al2O3 [11]. Light concentration

operating condition (temperature, concentration ratio).

310 Solar Cells - Research and Application Perspectives

SOPRA database of refractive indexes [10].

CPV module.

**Figure 1.** Structure of the double junction solar cell used for the analysis in this chapter. The layers in light blue are the ones corresponding to the top-cell, the grey ones to the tunnel junction and the green ones to the bottom cell [12].

**Figure 2.** Schematic representation of the layer sequence that light has to pass through until it reaches the solar cell. It represents a CPV module that is made out of a primary and secondary lens.

The structure of the ISOSIM simulation program makes it possible to add several layers and their parameters (thickness, doping level and gradient, doping type, composition, recombi‐ nation velocity, recombination time constant, refractive index). It is also needed to specify the function of each layer, like e.g. *optical layer* for the window layer of the solar cell or the layers that represent the optical system (e.g. lenses, encapsulating material, air gaps between materials, cover glass). For running a simulation, the parameters that are specified are con‐ centration ratio (in suns), solar cell operating temperature, shadowing loss, series resistance of the contact layer and refractive index of the medium that surrounds the solar (e.g. n=1 if the simulation should be done considering that the solar cell is measured in air). This high degree in flexibility makes it possible to simulate almost any type of multijuncion solar cells and any type of CPV module.

For the simulations presented in this chapter, three different type of simulations were made, a solar cell that is in air (refractive index is 1), a solar cell that is surrounded by a medium with refractive index equal to 1.5 (e.g. glass) and a solar cell that is mounted in a CPV mod‐ ule that is made of a cover glass, primary and secondary lenses, encapsulating materials, and an air gap between primary and secondary lens. A schematic description is shown in Figure 2.

In order to show the usefulness of the simulation software for the prediction of the behavior of solar cells under real operating conditions (i.e. under light concentration and at tempera‐ tures higher than room temperature), several figures are shown (Figure 3. to Figure 7.). These simulations can be of interest to extrapolate the measured parameter at room temper‐ ature to real operating conditions. The two parameters that affect mostly the solar cell per‐ formance when it is mounted in a CPV module are the operating temperature and the optical coupling of the sunlight to the solar cell. Even if the short-circuit current Isc increases slightly with increasing temperature (Figure 3.), the predominant effect is the decreases of the open-circuit voltage Voc (Figure 4.) and the fill-factor FF (Figure 5.), reducing the solar cell efficiency (Figure 6.) and thereby also the output power of a module. Figure 7 shows the efficiency of the solar cell when the concentration is increased. The temperature is set to 320K. It shows the typical shape of this type of curves, although the maximum in efficiency is in our simulation at a concentration of around 2000 suns, which is higher than typical val‐ ues observed experimentally [13]. More details about the performance of the ISOSIM soft‐ ware, as well as the discussion of the figures shown here can be found elsewhere [7].

**Figure 2.** Schematic representation of the layer sequence that light has to pass through until it reaches the solar cell. It

The structure of the ISOSIM simulation program makes it possible to add several layers and their parameters (thickness, doping level and gradient, doping type, composition, recombi‐ nation velocity, recombination time constant, refractive index). It is also needed to specify the function of each layer, like e.g. *optical layer* for the window layer of the solar cell or the layers that represent the optical system (e.g. lenses, encapsulating material, air gaps between materials, cover glass). For running a simulation, the parameters that are specified are con‐ centration ratio (in suns), solar cell operating temperature, shadowing loss, series resistance of the contact layer and refractive index of the medium that surrounds the solar (e.g. n=1 if the simulation should be done considering that the solar cell is measured in air). This high degree in flexibility makes it possible to simulate almost any type of multijuncion solar cells

For the simulations presented in this chapter, three different type of simulations were made, a solar cell that is in air (refractive index is 1), a solar cell that is surrounded by a medium with refractive index equal to 1.5 (e.g. glass) and a solar cell that is mounted in a CPV mod‐ ule that is made of a cover glass, primary and secondary lenses, encapsulating materials, and an air gap between primary and secondary lens. A schematic description is shown in

In order to show the usefulness of the simulation software for the prediction of the behavior of solar cells under real operating conditions (i.e. under light concentration and at tempera‐ tures higher than room temperature), several figures are shown (Figure 3. to Figure 7.). These simulations can be of interest to extrapolate the measured parameter at room temper‐ ature to real operating conditions. The two parameters that affect mostly the solar cell per‐ formance when it is mounted in a CPV module are the operating temperature and the optical coupling of the sunlight to the solar cell. Even if the short-circuit current Isc increases slightly with increasing temperature (Figure 3.), the predominant effect is the decreases of

represents a CPV module that is made out of a primary and secondary lens.

and any type of CPV module.

312 Solar Cells - Research and Application Perspectives

Figure 2.

**Figure 3.** Simulation of the short-circuit current density (Isc) of a double-junction solar cell as a function of temperature at a concentration of 1000 suns.

**Figure 4.** Simulation of the open-circuit Voltage (Voc) of a double-junction solar cell as a function of temperature at a concentration of 1000 suns.

**Figure 5.** Simulation of the fill factor (FF) of a double-junction solar cell as a function of temperature at a concentra‐ tion of 1000 suns.

Solar Cell Efficiency vs. Module Power Output: Simulation of a Solar Cell in a CPV Module http://dx.doi.org/10.5772/52707 315

**Figure 6.** Simulation of the efficiency of a double-junction solar cell as a function of temperature at a concentration of 1000 suns.

**Figure 4.** Simulation of the open-circuit Voltage (Voc) of a double-junction solar cell as a function of temperature at a

**Figure 5.** Simulation of the fill factor (FF) of a double-junction solar cell as a function of temperature at a concentra‐

concentration of 1000 suns.

314 Solar Cells - Research and Application Perspectives

tion of 1000 suns.

**Figure 7.** Simulation of the solar cell efficiency of a double-junction solar cell as a function of light concentration at a temperature of 320 K.

## **4. Effect of the surrounding medium on solar cell efficiency**

There are currently several techniques used to concentrate light inside a CPV module. They can be made of primary and secondary lenses, as in the case of the examples given in this chapter, of only a primary lens or a (parabolic) mirror. To avoid losses due to changes in the refraction in‐ dex, encapsulating materials might be used when using a secondary lens. The refraction index of this type of gels can be chosen to achieve the highest efficiency in the module. In all cases sun‐ light has to be properly guided and matched from air through several materials of different re‐ fractive index to the solar cell until if finally reaches each single junction of a multijunction solar cell, where the light is recombined. This leads to the question on how much is the output power of the CPV module affected due to the optical system. To analyze this issue, several simulations are made on a double-junction solar cell as the one described earlier.

The obtained results can be extrapolated to a triple-junction solar cell, at least qualitatively, since the third junction (typically made out of a germanium p-n junction) generates much more current than either the 1st or 2nd junction, and it does therefore not limit the multijunc‐ tion solar cell. Figure 8 shows the simulated I-V curves of a triple-junction solar cell and all of its subcells, the bottom cell (typically a Ge cell, red curve), the middle cell (typically an InGaAs cell, green curve), the top cell (typical an InGaP cell, blue curve) and the resulting I-V curve of the triple junction solar cell (grey curve). This figure shows a triple-junction cell in which the top cell is the limiting subcell and also that the Ge junction generates much more current than any of the other two.

**Figure 8.** I-V curves of a triple-junction solar cell. There are given the three I-V curves of the subcells (top-cell, middlecell and bottom cell) and the resulting I-V curve of the resulting 3J cell.

The efficiency of a double-junction solar cell with two different ARC layers, either a double layer of TiO2/Al2O3 or a single layer of Si3N4 is analysed. The refractive index of the sur‐ rounding medium has been increased from 1 (air) to 1.5 (e.g. glass). The result of the simu‐ lated efficiency is shown in Figure 9 for a given thickness of the ARC layer. If the solar cell would be operated in air (n=1) the best choice would be to use a TiO2/Al2O3 double layer and the solar cell would have an efficiency of 31.14%. But, if the solar cell would be operated in a medium with a refractive index higher than 1, e.g. 1.5, a Si3N4 single layer would be a better choice, yielding an efficiency of 31.87%. It can also be observed that if the solar cell has been optimized for being measured in air (ARC double layer of TiO2/Al2O3), the efficiency of the system is reduced by around 1% when it is being operated in a medium with a refractive index of 1.5. On the other hand, a solar cell that has an ARC layer that is optimized to a me‐ dium with n=1.5, has a lower efficiency when measured at air. In the case that the solar cell is operated in a medium of n=1.5 and a wrong antireflection coating has been chosen (in this example TiO2/Al2O3 instead of Si3N4), the solar cell would have an efficiency of 30.16% in‐ stead of 31.87%, having a loss in efficiency of 1.71%. It should be remembered that these val‐ ues depend very much on the material and thickness of the ARC layer, and each system configuration has to be analysed separately.

**4. Effect of the surrounding medium on solar cell efficiency**

are made on a double-junction solar cell as the one described earlier.

more current than any of the other two.

316 Solar Cells - Research and Application Perspectives

There are currently several techniques used to concentrate light inside a CPV module. They can be made of primary and secondary lenses, as in the case of the examples given in this chapter, of only a primary lens or a (parabolic) mirror. To avoid losses due to changes in the refraction in‐ dex, encapsulating materials might be used when using a secondary lens. The refraction index of this type of gels can be chosen to achieve the highest efficiency in the module. In all cases sun‐ light has to be properly guided and matched from air through several materials of different re‐ fractive index to the solar cell until if finally reaches each single junction of a multijunction solar cell, where the light is recombined. This leads to the question on how much is the output power of the CPV module affected due to the optical system. To analyze this issue, several simulations

The obtained results can be extrapolated to a triple-junction solar cell, at least qualitatively, since the third junction (typically made out of a germanium p-n junction) generates much more current than either the 1st or 2nd junction, and it does therefore not limit the multijunc‐ tion solar cell. Figure 8 shows the simulated I-V curves of a triple-junction solar cell and all of its subcells, the bottom cell (typically a Ge cell, red curve), the middle cell (typically an InGaAs cell, green curve), the top cell (typical an InGaP cell, blue curve) and the resulting I-V curve of the triple junction solar cell (grey curve). This figure shows a triple-junction cell in which the top cell is the limiting subcell and also that the Ge junction generates much

**Figure 8.** I-V curves of a triple-junction solar cell. There are given the three I-V curves of the subcells (top-cell, middle-

cell and bottom cell) and the resulting I-V curve of the resulting 3J cell.

**Figure 9.** Solar cell efficiency as a function of the refractive index of the surrounding medium, for two alternatives of anti-reflection coatings.

This is a simplified example of how important the condition in which the solar cell operates is. If the solar cell would be encapsulated in a medium with a refractive index of 1.5, the sit‐ uation would be as described above. In reality CPV modules are in general much more com‐ plex, and even more layers might interfere with the sun rays on its way to the solar cell. This means, on one hand, that if the solar cell is optimized to be operating in air, the expected decrease in efficiency when operating in the CPV module might be even higher than in the previous simulations. On the other hand, if the complexity of the module increases, it is also much more difficult to optimize a solar cell to be operating in that specific CPV module. In any case, according to these simulations, it is strongly recommended not to develop sepa‐ rately the solar cell and the optics of the CPV module, rather than optimizing the system as one unit.

## **5. Effect of AR coating material on solar cell efficiency**

Anti-reflection coatings are needed to match the refractive index of the solar cell window layer to the surrounding medium, increasing thereby the amount of light that penetrates in‐ to the photovoltaic structure [11]. These must be carefully designed to have the highest transmission and the broadest bandwidth. The tuning of these could yield by multijunction solar cells to different limiting cell configurations, since different spectral parts of the sun‐ light are absorbed or reflected differently during operation. For this reason, our software is capable to handle spectral responses of complete systems and with different irradiation spectra.

In this section the design of the AR coating is analysed. With a correct design of the AR coat‐ ing, the solar cell can be adapted to the surrounding medium, reducing losses due to un‐ wanted reflections. It is possible to increase the final efficiency of the cell, increasing it up to around 30% of its initial value in a cell/air interface. As this medium is fully dependent on the system design (epoxy, air, lens, potting, etc.), the AR coating should be designed taking into consideration the design of the CPV module. We performed some simulations with sev‐ eral materials that are typically used as AR coating in optoelectronic devices. These are alu‐ minum oxide (Al2O3), titanium dioxide (TiO2), silicon nitride (Si3N4), and magnesium difluoride (MgF2). The result for a double-junction solar cell is shown in Figure 10.

This figure shows that there is a strong dependence of the efficiency of a solar cell on the material of the antireflection coating and on its thickness. The efficiency can therefore be maximised e.g. when it is measured in air. Whenever we change the medium from air to a different higher refractive index medium (glass, epoxy, lens, potting, etc.), results vary. Fig‐ ure 11 shows simulations for the same solar cell as in Figure 10 but considering that the solar cell is mounted in a CPV module. This means that the optical system has a big influence in modifying the spectral performance of the CPV system.

Comparing Figure 10 and Figure 11 we see that the behaviour of the efficiency against AR coating thickness differ if the solar cell is either measured on air or mounted inside a CPV module. It is observed e.g. that an efficiency of 29% of a standalone solar cell with an ap‐ proximately 80 nm thick MgF2 AR coating layer, has only 24% efficiency when this solar cell is mounted in the CPV module.

Solar Cell Efficiency vs. Module Power Output: Simulation of a Solar Cell in a CPV Module http://dx.doi.org/10.5772/52707 319

**Figure 10.** Stand-alone solar cell efficiency vs. AR coating thickness for several materials.

plex, and even more layers might interfere with the sun rays on its way to the solar cell. This means, on one hand, that if the solar cell is optimized to be operating in air, the expected decrease in efficiency when operating in the CPV module might be even higher than in the previous simulations. On the other hand, if the complexity of the module increases, it is also much more difficult to optimize a solar cell to be operating in that specific CPV module. In any case, according to these simulations, it is strongly recommended not to develop sepa‐ rately the solar cell and the optics of the CPV module, rather than optimizing the system as

Anti-reflection coatings are needed to match the refractive index of the solar cell window layer to the surrounding medium, increasing thereby the amount of light that penetrates in‐ to the photovoltaic structure [11]. These must be carefully designed to have the highest transmission and the broadest bandwidth. The tuning of these could yield by multijunction solar cells to different limiting cell configurations, since different spectral parts of the sun‐ light are absorbed or reflected differently during operation. For this reason, our software is capable to handle spectral responses of complete systems and with different irradiation

In this section the design of the AR coating is analysed. With a correct design of the AR coat‐ ing, the solar cell can be adapted to the surrounding medium, reducing losses due to un‐ wanted reflections. It is possible to increase the final efficiency of the cell, increasing it up to around 30% of its initial value in a cell/air interface. As this medium is fully dependent on the system design (epoxy, air, lens, potting, etc.), the AR coating should be designed taking into consideration the design of the CPV module. We performed some simulations with sev‐ eral materials that are typically used as AR coating in optoelectronic devices. These are alu‐ minum oxide (Al2O3), titanium dioxide (TiO2), silicon nitride (Si3N4), and magnesium

This figure shows that there is a strong dependence of the efficiency of a solar cell on the material of the antireflection coating and on its thickness. The efficiency can therefore be maximised e.g. when it is measured in air. Whenever we change the medium from air to a different higher refractive index medium (glass, epoxy, lens, potting, etc.), results vary. Fig‐ ure 11 shows simulations for the same solar cell as in Figure 10 but considering that the solar cell is mounted in a CPV module. This means that the optical system has a big influence in

Comparing Figure 10 and Figure 11 we see that the behaviour of the efficiency against AR coating thickness differ if the solar cell is either measured on air or mounted inside a CPV module. It is observed e.g. that an efficiency of 29% of a standalone solar cell with an ap‐ proximately 80 nm thick MgF2 AR coating layer, has only 24% efficiency when this solar cell

difluoride (MgF2). The result for a double-junction solar cell is shown in Figure 10.

modifying the spectral performance of the CPV system.

is mounted in the CPV module.

**5. Effect of AR coating material on solar cell efficiency**

one unit.

318 Solar Cells - Research and Application Perspectives

spectra.

**Figure 11.** CPV system efficiency vs. AR coating thickness for several materials, using the same cell structure as for the plots in Figure 10.

## **6. Current matching: Stand-alone solar cell vs. performance in CPV module**

In this section the spectral loss of the optical system is analysed. Several simulations were made starting from a double-junction solar cell in which the thickness of the base of the top cell is increased from 500 nm to 950 nm for the case of a stand-alone solar cell, and from 500nm to 1150nm for a solar cell that is assembled in a module. The obtained results are again specific to each configuration of solar cell and type and materials of a CPV module. Nevertheless, the general tendency of the results that is observed (i.e. the switching from a top-cell limiting configuration to a bottom-cell limiting configuration with increasing topcell base thickness) is generally valid.

Figure 12 shows the behavior of the efficiency when increasing the thickness of the base of the top-cell of a double-junction solar cell. It can be seen that when increasing the thickness from 500nm until approximately 700nm, also the efficiency increases. This shows (and is confirmed by the plots of the I-V curves not shown here) that the top-cell of the double-junc‐ tion solar cell is limiting. Increasing the thickness of the base further, from approximately 800nm to 950nm the efficiency decreases, and the bottom-cell is the limiting one. The reason for the drop in efficiency is on one hand that the series resistance of the top-cell increases, and that there is more light absorbed in the top-cell and therefore less light available for cur‐ rent generation in the bottom-cell.

**Figure 12.** Simulation of the efficiency of a stand-alone double-junction solar cell as a function of top cell base thick‐ ness.

**6. Current matching: Stand-alone solar cell vs. performance in CPV**

In this section the spectral loss of the optical system is analysed. Several simulations were made starting from a double-junction solar cell in which the thickness of the base of the top cell is increased from 500 nm to 950 nm for the case of a stand-alone solar cell, and from 500nm to 1150nm for a solar cell that is assembled in a module. The obtained results are again specific to each configuration of solar cell and type and materials of a CPV module. Nevertheless, the general tendency of the results that is observed (i.e. the switching from a top-cell limiting configuration to a bottom-cell limiting configuration with increasing top-

Figure 12 shows the behavior of the efficiency when increasing the thickness of the base of the top-cell of a double-junction solar cell. It can be seen that when increasing the thickness from 500nm until approximately 700nm, also the efficiency increases. This shows (and is confirmed by the plots of the I-V curves not shown here) that the top-cell of the double-junc‐ tion solar cell is limiting. Increasing the thickness of the base further, from approximately 800nm to 950nm the efficiency decreases, and the bottom-cell is the limiting one. The reason for the drop in efficiency is on one hand that the series resistance of the top-cell increases, and that there is more light absorbed in the top-cell and therefore less light available for cur‐

**Figure 12.** Simulation of the efficiency of a stand-alone double-junction solar cell as a function of top cell base thick‐

**module**

ness.

cell base thickness) is generally valid.

320 Solar Cells - Research and Application Perspectives

rent generation in the bottom-cell.

**Figure 13.** Simulation of the efficiency of a double-junction solar cell that is mounted inside a CPV module as a func‐ tion of top cell base thickness.

The same series of simulations have been done for a solar cell mounted in a double lens CPV system like the one shown in Figure 2 and the result is plotted in Figure 13. Even though the general tendency of switching from a top-cell limiting configuration to a bottom-cell limiting configuration is true in both examples, the thickness at which this switching occurs is differ‐ ent, and occurs at higher thickness when the solar cell is mounted inside a module. This fig‐ ure shows that when embedding the cell in the CPV system the current matching for the individual solar cell in a dual junction solar cell moves towards around a 1000 nm-thick topcell base. This can be explained by the fact that part of the sun light gets either absorbed by the materials of the system or get reflected on the interfaces of them, so that less light is available for generating current in the solar cell. It also follows that the efficiency of the solar cell and system is lower than that of only the solar cell.

Continuing with the analysis of the system as a whole, it can be seen that the efficiency of this system is in all the range lower than that of a stand-alone solar cell. As an example two solar cells with different width of the top-cell base will be compared, one of 750 nm and the other one of 950 nm. If the final design of a solar cell is with a 750 nm thick top cell base, its efficiency is 31.21%, and if the final design is with a 950 nm thick top cell base, its efficiency will be 30.82%. If these two solar cells are mounted in the system, the first solar cell will have an efficiency of 27.09%, and the latter one an efficiency of 27.55%. This means that the solar cell with a top-cell base thickness of 750 nm performs better when it is operated in air (i.e. 0.39% higher), whereas the solar cell with a top cell base thickness of 950 nm performs better when it is mounted in the module. According to these simulations, if the thickness of the base of the top-cell is increased from 650 nm to 950 nm in a solar cell that is going to be operated in the optical system described earlier, the overall system efficiency would be in‐ creased by 0.46%. The very important conclusion of this analysis is, once more, that the pri‐ ority should be to optimize the module efficiency and not only the solar cell efficiency.

The previous simulations can be complemented with simulations of the spectral response of a solar cell. In Figure 14 is plotted the spectral response of the solar cell for a stand-alone solar cell of a 650 nm and a 950 nm thick top-cell base. This figure is similar to the ones measured on real devices, like e.g. in [14]. Figure 15 shows the same plot for a solar cell that is mounted in a CPV system. When increasing the width of the top-cell base, the generated current in the top cell increases (blue curve). This behaviour is also true when the solar cell is inserted in a module, even though it is less enhanced.

**Figure 14.** Simulation of the spectral response of a double-junction solar cell for two different TC base thicknesses (650 nm and 950 nm).

the base of the top-cell is increased from 650 nm to 950 nm in a solar cell that is going to be operated in the optical system described earlier, the overall system efficiency would be in‐ creased by 0.46%. The very important conclusion of this analysis is, once more, that the pri‐ ority should be to optimize the module efficiency and not only the solar cell efficiency.

The previous simulations can be complemented with simulations of the spectral response of a solar cell. In Figure 14 is plotted the spectral response of the solar cell for a stand-alone solar cell of a 650 nm and a 950 nm thick top-cell base. This figure is similar to the ones measured on real devices, like e.g. in [14]. Figure 15 shows the same plot for a solar cell that is mounted in a CPV system. When increasing the width of the top-cell base, the generated current in the top cell increases (blue curve). This behaviour is also true when the solar cell

**Figure 14.** Simulation of the spectral response of a double-junction solar cell for two different TC base thicknesses

(650 nm and 950 nm).

is inserted in a module, even though it is less enhanced.

322 Solar Cells - Research and Application Perspectives

**Figure 15.** Simulation of the spectral response of a double-junction solar cell mounted inside a CPV module. The simu‐ lations are made for two different top cell base thicknesses (650 nm and 950 nm).

## **7. Power loss in a CPV module due to a non-matched solar cell**

It has been shown in this chapter with the help of a simulation program that the performance of a solar cell depends on the medium in which it operates. A solar cell that is measured in air as a standalone device does not perform in the same way as in a system that is composed of solar cell and optical concentrator system. The system efficiency is typically lower than the efficien‐ cy of a standalone solar cell, due to losses that are attributed to (spectral) absorption of the ma‐ terials and reflections on the interfaces of different type of materials. These losses between a stand-alone solar cell and the efficiency of the system can be minimized, if the right materials are chosen and the solar cell and the optical system are adapted to each other.

In order to get a feeling on how big the impact of the efficiency loss is on the module power out‐ put, simple calculations are given. It has been shown in previous sections that due to a wrong choice of anti-reflection coating the loss in efficiency of the CPV system can be 1,71%, and that if the thickness of the base of the top cell is not adapted to the system, it is possible to lose another 0,46% in efficiency. This means that by adapting the ARC and the thickness of the base of the so‐ lar cell, it is possible to gain (or not to lose) more than 2% in system efficiency, according to the simulations of the system and parameters described earlier. The simulations were made for a double-junction solar cell, and it can be expected that the loss of 2% that is observed for a nonoptimized solar cell will be even higher for a system with a triple-junction solar cell.

As an example, it is assumed that the optimized system efficiency of a CPV module is 30%, whereas the efficiency of the not optimized CPV module is 28%. Assuming that a given CPV module has 10 solar cells of 1 cm2 of active area each and works at a concentration of 500 suns, then the output power would be 127,5 W for 30% system efficiency and 119 W for 28% system efficiency, assuming an irradiation of 850 W/m2 . With this simple example it is in‐ tended to visualize that a seemingly small difference of 2% in system efficiency has an effect of approx. 6,7% on module level and therefore also on the installation cost of a CPV power plant. The effect that a 2% efficiency difference makes on module level depends on its de‐ sign (number of solar cells, concentration ratio, etc.), and should be therefore only consid‐ ered qualitatively.

## **8. Conclusion**

In this chapter simulations of double-junction solar cells were discussed. The ISOSIM simu‐ lation software is a powerful tool to obtain characteristic curves of solar cells. With this soft‐ ware package it is also possible to understand and predict experimental behaviour of solar cells under real operating conditions. The results obtained in this chapter can be extrapolat‐ ed to triple-junction solar cells, since typically the third junction is made out of Germanium and is far from limiting the multijunciton solar cell. It has been analysed the efficiency of a solar cell and a system composed of solar cell and additional layers that should represent the optical system of a CPV module. It has been analysed the effect of the anti-reflection coating material and its thickness on the efficiency of the solar cell, and has also been shown that when increasing the width of the base to the top cell, the double-junction solar cell switches from being top cell limiting to bottom cell limiting. These two parameters, the type and thickness of the ARC layer and the thickness of the top-cell base thickness play an im‐ portant role on the efficiency of the solar cell. When the solar cell is assembled in a CPV module the optimum values of ARC coating material and its thickness and the optimum thickness of the base layer of the top cell changes. This means that in order to obtain maxi‐ mum module power output, a solar cell and optical system should match each other well, in a way that the design of the solar cell should take into account the optical system of the CPV module or the other way around, the design of the optical system should be adapted to a given solar cell. It is also shown that a small variation in efficiency of a solar cell has a big impact on CPV module power output and therefore also on the installation cost of a CPV power plant.

## **Author details**

Egbert Rodríguez Messmer

Isofotón S.A, Spain

## **References**

As an example, it is assumed that the optimized system efficiency of a CPV module is 30%, whereas the efficiency of the not optimized CPV module is 28%. Assuming that a given CPV

suns, then the output power would be 127,5 W for 30% system efficiency and 119 W for 28%

tended to visualize that a seemingly small difference of 2% in system efficiency has an effect of approx. 6,7% on module level and therefore also on the installation cost of a CPV power plant. The effect that a 2% efficiency difference makes on module level depends on its de‐ sign (number of solar cells, concentration ratio, etc.), and should be therefore only consid‐

In this chapter simulations of double-junction solar cells were discussed. The ISOSIM simu‐ lation software is a powerful tool to obtain characteristic curves of solar cells. With this soft‐ ware package it is also possible to understand and predict experimental behaviour of solar cells under real operating conditions. The results obtained in this chapter can be extrapolat‐ ed to triple-junction solar cells, since typically the third junction is made out of Germanium and is far from limiting the multijunciton solar cell. It has been analysed the efficiency of a solar cell and a system composed of solar cell and additional layers that should represent the optical system of a CPV module. It has been analysed the effect of the anti-reflection coating material and its thickness on the efficiency of the solar cell, and has also been shown that when increasing the width of the base to the top cell, the double-junction solar cell switches from being top cell limiting to bottom cell limiting. These two parameters, the type and thickness of the ARC layer and the thickness of the top-cell base thickness play an im‐ portant role on the efficiency of the solar cell. When the solar cell is assembled in a CPV module the optimum values of ARC coating material and its thickness and the optimum thickness of the base layer of the top cell changes. This means that in order to obtain maxi‐ mum module power output, a solar cell and optical system should match each other well, in a way that the design of the solar cell should take into account the optical system of the CPV module or the other way around, the design of the optical system should be adapted to a given solar cell. It is also shown that a small variation in efficiency of a solar cell has a big impact on CPV module power output and therefore also on the installation cost of a CPV

of active area each and works at a concentration of 500

. With this simple example it is in‐

module has 10 solar cells of 1 cm2

324 Solar Cells - Research and Application Perspectives

ered qualitatively.

**8. Conclusion**

power plant.

**Author details**

Isofotón S.A, Spain

Egbert Rodríguez Messmer

system efficiency, assuming an irradiation of 850 W/m2

**Chapter 12**

## **Electric Energy Management and Engineering in Solar Cell System**

Purnomo Sidi Priambodo, Didik Sukoco, Wahyudi Purnomo, Harry Sudibyo and Djoko Hartanto

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/52572

## **1. Introduction**

[12] Olson, J. (2003). Growth and characterization of high efficiency III-V multijunction solar cells for terrestial and space applications, Proceedings of the 10th European

[13] R.R. King, D.C. Law, K.M. Edmondson, C.M. Fetzer, G.S. KinseyH. Yoon, D.D. Krut, J.H. Ermer, R.A. Sherif, and N.H. Karam; Advances in high-efficiency III-V multi‐ junction solar cells, In: Advances in OptoElectronics, Volume 2007, 29523, doi:

[14] I. García, I. Rey-Stolle, B. Galiana, and C. Algora; A 32.6% efficient lattice-matched dual-junction solar cell working at 1000 suns, Applied Physics Letters 94, 053509

Workshop on MOVPE, Lecce (Italy) 2003

10.1155/2007/29523(2007).

326 Solar Cells - Research and Application Perspectives

(2009).

Solar cell system has many competitive advantages in comparisson to other renewable ener‐ gy resources. For instance, wind-turbin is very dependable to geographical location and has very high noise pollution if applied in residential area. Other example is micro-hydro, which depends on altitude and available in very limited locations. Furthermore, nuclear energy should be forgotten since its high radioactive risk. On the other side, solar cell system has characteristics of zero pollution, no radioactive risk, compact, portable and can be installed in any residential areas and has relatively high energy availability in any location on the earth surface in a year round. In general, solar cell array, which cover a residential roof house can supply the basic electrical energy needs of the residences who live in the house, almost a year round. These competitive advantages of solar cell system over other renewa‐ ble energy resources, make solar cell system the most favorite renewable energy resource.

There are 2 main topics and will be discussed in accordance to energy management of re‐ newable energy resources, based on solar cell system. **The first topic** is how to keep the sys‐ tem sustainable to supply the applied electrical load. As we have already known that solar energy is not available continuosly in a day and year round. For instance, at noon, the avail‐ ability of solar energy is abundant, however, at night there is not available at all. In the rain or winter season, the availability of solar energy is less than in the dry or summer season. On the other hand, the needs of electrical energy may be in opposite situation of the availa‐ bility of solar energy. In order to keep the solar cell system able to serve the total electrical load, it is necessary to design the system, which has sufficient number of solar cells and bat‐

© 2013 Priambodo et al.; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2013 Priambodo et al.; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

teries to get and store the electrical energy from solar energy at the most available energy time (noon), and delivering to the consumers at the non-available solar energy time (night). In this first topic, in order to keep sustainable, it is conducted by designing the sufficient number of solar cells and batteries to supply the predicted electrical load.

In the first topic, the sustainability perspective in an energy network is emphasized in the form of designing the sufficient number of solar cells and batteries to supply the predicted electrical load. **The second topic** is sustainability to deliver energy perspective. It is focused on how conducting collaboration between several autonomy units of renewable energy sys‐ tem to build a renewable energy resource grid. Even, if possible, to do integration between autonomy units of solar system and the conventional electrical state own company. Here, we emphasize that the key problem of electric energy management of renewable energy re‐ souces such as solar cell system is sustainability.

## **2. Electric energy management in an autonomy unit of solar cell system: A perspective**

There are at least 2 strategic ways to implement renewable energy resources especially solar cell systems to fulfill the national electrical energy needs. The first strategy is to encourage the people to fulfill their own basic residential electric energy need by building private solar cell system. The second strategy is to let the Government as the regulator to drive a consorti‐ um of companies to build large plants of solar cell system to fulfill the regional or national electric energy need. Of course, the consortium will require a large amount of financial in‐ vestment at the starting point, however along with the time, the long term electric cost will be getting lower and more cost effective, since solar cell system requires very minimum maintenance cost and free of solar energy.

A solar cell system as an autonomy energy resource unit must have an energy manage‐ ment control unit, which embeded in the system. In general, there are at least 5 parts should exist in a electrical renewable energy resource system, as shown on Fig 1 below, i.e.: (1) solar cell array; (2) management energy control system; (3) energy storage (s); (4) DC to AC and AC to DC converters and (5) delivery bus. Thus 5 parts should be de‐ signed such that the system becomes more efficient to manage the gathered electrical en‐ ergy and to reach higher sustainability with low investment cost. We need 100% sustainability to fulfill the electrical energy need.

In order to reach 100% sustainability, first of all, the designer has to know how much en‐ ergy need in average in every single day (prediction). Then, the designer must consider the region, where the solar cell system is located and it relates to the earth latitude. Fur‐ ther, it counts to the statistical condition of how long the total time the sun shines on thus region in a year round. Another important info is the statistical info of the longest dura‐ tion of NO sunshine days, which relates to the seasons and weather. Thus are the most critical information to determine the requirement of the total number of solar cells and batteries in the system.

**Figure 1.** Big picture of Solar Cell Based Renewable Energy Unit System.

teries to get and store the electrical energy from solar energy at the most available energy time (noon), and delivering to the consumers at the non-available solar energy time (night). In this first topic, in order to keep sustainable, it is conducted by designing the sufficient

In the first topic, the sustainability perspective in an energy network is emphasized in the form of designing the sufficient number of solar cells and batteries to supply the predicted electrical load. **The second topic** is sustainability to deliver energy perspective. It is focused on how conducting collaboration between several autonomy units of renewable energy sys‐ tem to build a renewable energy resource grid. Even, if possible, to do integration between autonomy units of solar system and the conventional electrical state own company. Here, we emphasize that the key problem of electric energy management of renewable energy re‐

**2. Electric energy management in an autonomy unit of solar cell system:**

There are at least 2 strategic ways to implement renewable energy resources especially solar cell systems to fulfill the national electrical energy needs. The first strategy is to encourage the people to fulfill their own basic residential electric energy need by building private solar cell system. The second strategy is to let the Government as the regulator to drive a consorti‐ um of companies to build large plants of solar cell system to fulfill the regional or national electric energy need. Of course, the consortium will require a large amount of financial in‐ vestment at the starting point, however along with the time, the long term electric cost will be getting lower and more cost effective, since solar cell system requires very minimum

A solar cell system as an autonomy energy resource unit must have an energy manage‐ ment control unit, which embeded in the system. In general, there are at least 5 parts should exist in a electrical renewable energy resource system, as shown on Fig 1 below, i.e.: (1) solar cell array; (2) management energy control system; (3) energy storage (s); (4) DC to AC and AC to DC converters and (5) delivery bus. Thus 5 parts should be de‐ signed such that the system becomes more efficient to manage the gathered electrical en‐ ergy and to reach higher sustainability with low investment cost. We need 100%

In order to reach 100% sustainability, first of all, the designer has to know how much en‐ ergy need in average in every single day (prediction). Then, the designer must consider the region, where the solar cell system is located and it relates to the earth latitude. Fur‐ ther, it counts to the statistical condition of how long the total time the sun shines on thus region in a year round. Another important info is the statistical info of the longest dura‐ tion of NO sunshine days, which relates to the seasons and weather. Thus are the most critical information to determine the requirement of the total number of solar cells and

number of solar cells and batteries to supply the predicted electrical load.

souces such as solar cell system is sustainability.

328 Solar Cells - Research and Application Perspectives

maintenance cost and free of solar energy.

sustainability to fulfill the electrical energy need.

batteries in the system.

**A perspective**

Solar cell produces DC electrical energy, which fits to be storage in batteries. In designing solar cell system, as explained above, it must be determined the assumption of average need of energy per day, for example A Watt-hour/day. Further, the estimate of statistical condition of how long the total time of NO sunshine days on thus region in a year round must be determined, for example N days. The amount of solar cells and batteries needed by the system is written in the following equation:

$$\begin{pmatrix} 1+c \\ \end{pmatrix} \cdot N \cdot A \quad \text{Watt hour} \tag{1}$$

where *c* is a leak energy coefficient of the battery. In general, it has been known that the bat‐ tery is not perfect to store DC electrical energy, it is always a part of stored energy in battery leaks. This is a inefficiency factor of battery and presented as "*c"* coefficient.

Solar cell system performance fully depends on the performance of thus 5 parts in building the system; which has been listed above (Fig 1). The following is explanation of every part.

## **3. Solar cell and eficiency**

The main characteristic of solar cell is I-V curve. It has several derivative parameters such as*Isc* (short circuit current), *Voc* (open circuit voltage) and the maximum possible delivered energy *Pmp* =*Vmp* ⋅ *Imp*, as shown on the following Fig 2.

**Figure 2.** The Graph of the I-V characteristics of an ideal diode solar cell when non-illuminated (dark) and illuminated [1].

The main parameter that determines the solar cell efficiency is the maximum square area (power) as form of multiplication I-V (*Pmp* =*Vmp* ⋅ *Imp*), which is a maximum square formed inside I-V curve as shown on Fig 2 above. The next derivative parameter is fill factor *FF* that represents the ratio PMP to the product *VOC* and *ISC*. This parameter gives an insight abou‐ thow "square" is the output characteristic.

$$FF = \frac{P\_{MP}}{V\_{OC} \cdot I\_{SC}} = \frac{V\_{MP} \cdot I\_{MP}}{V\_{OC} \cdot I\_{SC}} \tag{2}$$

In the case of solar cell with sufficient efficiency, in general, it has FF between 0.7 and 0.85. The energy–conversion efficiency, η can be written as [2]

$$\ln \eta = \frac{V\_{MP} \cdot I\_{MP}}{P\_{in}} = \frac{V\_{OC} \cdot I\_{SC} \cdot FF}{P\_{in}} \tag{3}$$