**3.3 Optical properties**

*Solar Cells - Theory, Materials and Recent Advances*

molecular configurations of P-CPDTBT3 and SM-CPDTDPP.

The simultaneous interactions of donor and acceptor groups are the responsible of the electron delocalization and thus producing the electronic charge distribution within the HOMOs and LUMOs. As it can be seen from **Figure 4**, there is considerable discrepancy of molecular orbital distributions resulting from the particular

The spatial distribution of the HOMO orbital of P-CPDTBT3 is dominantly localized over the main conjugated backbone. While, that of SM-CPDTDPP is mainly located on the central part of the conjugated framework. The LUMOof P-CPDTBT3 is dispersed over the central CPDT unit indicating a high steric hindrance rising from the strong electron withdrawing group effect of dicyanomethylene group [50]. In the case of SM-CPDTDPP, the LUMO is centered over the DPP substituted group and the thiophene π-spacer units. These distributions may increase the π → π\* electronic transitions and reinforce the ICT ability. Besides, these materials dispose narrow band gap energies (1.62 eV) for P-CPDTBT3 and 1.42 eV for SM-CPDTDPP) that lead to improve the electron transition and light harvesting. The 2D molecular electrostatic maps of studied materials have been simulated to better understand the intra-molecular interactions (See **Figure 5**). As revealed from **Figure 5**, the central part is the most conjecturable zone into the conjugated framework of the studied molecules that is in good agreement with the

Ionization potential (IP) and Electron Affinity (EA) were calculated from the neutral, cation and anion optimized structures. IP and EA describe the barrier injection energies of electron and hole, respectively. The application of the considered materials in OCSs requires relevant IP and EA in order to promote the electron injection and hole transport. Thus, it is revealed from the FMOs analysis the significant effect of building blocks on the electronic properties that are related

**70**

**Figure 5.**

*2D molecular electrostatic maps of studied materials.*

FMOs analysis.

to the charge delocalization.

The optical absorption spectrum in the solar spectral zone also its intensity are the main factors that influence the value of short-circuit current density (JSC) of OSCs [51]. Fundamentally, the JSC is a function of the external quantum efficiency (EQE) with the photon number *S*(λ ) coveringall the frequencies providedfrom the solar spectrum, as above [52]:

$$J\_{\rm SC} = q \left[ EQE.S(\lambda)d\lambda \right] \tag{1}$$

Where, EQE presents the product of light harvesting efficiency (ηλ), exciton diffusion efficiency (ηED), charge separation efficiency (ηCS), and charge collection efficiency (ηCC). As revealed from the following expression, the donor material absorption capability remains a crucial parameter for increasing the organic solar cell efficiency. The light harvesting efficiency (ηλ) is related to the oscillator strength (f) of the maximum optical absorption wavelength as expressed above [53]:

$$
\boldsymbol{\eta}\_{\boldsymbol{\lambda}} = \mathbf{1} - \mathbf{1} \mathbf{0}^{-\boldsymbol{\beta}} \tag{2}
$$

In order to explore the photo-physical properties of the considered compounds, the optical absorption spectra were simulated using TD-DFT approach as costeffective method [54, 55].

**Figure 6.** *Optical absorption spectra of P-CPDTBT3 and SM-CPDTDPP simulated at TD-DFT//B3LYP/6-311 g(d,p) level of theory.*


**Table 2.**

*Calculated electronic transition energy Eex (eV), maximum absorption wavelengths,* λ*max (nm), oscillator strength (f) and major configuration at TD-DT//B3LYP/6-311 g(d,p) level.*

TD-DFT simulations were performed at the optimized ground state (S0) geometries in gaseous phase (See **Figure 6**) and the related optical parameters are listed in **Table 2**.

As we can see from **Figure 6**, these materials exhibit, as expected, abroad absorption bands in the wavelength range from 550 nm to 900 nm which covers a relevant part of the solar spectrum, where the maximum optical absorption within the solar spectrum is at about 700 nm [56]. The broad absorption in the visible and near infrared region, displayed by the considered materials, leads to reinforce BHJ-OCSs performances. The maximum absorption peaks were found at 693 nm and 737 nm for P-CPDTBT3 and SM-CPDTDPP, respectively.

In fact, these maximum wavelengths are generated mainly from HOMOs to LUMOs electronic transitions of ground to first excited state (S0 → S1) of electrons associated with high oscillator strength (f) values. Where, the pronounced absorption peaks are generated by π → π\* electronic transitions from the electron donating CPDT moieties to theelectron acceptor BT or DPP moieties [57]. The simulated absorption spectrum of P-CPDTBT3 is in convenient agreement with the experimental results reported in ref. [58], that confirms the accuracy of TD-DFT approach in reproducing the experimental data.

SM-CPDTDPP absorption spectrum was found red shifted by 44 nm compared to that of P-CPDTBT3. The slight red shift detected can be explained by the present of the thiophene π-spacer that may enhance the electron delocalization within the main conjugated framework.

The large absorption band ranging from 900 nm to 1500 nm is attributed to the ICT generated from the sulfur rich electron to the electron withdrawing dicyanomethylene group within the CPDT units [59]. A promising organic donor material should exhibit a large light harvesting efficiency (ηλ) in order to reach high photocurrent signal [60, 61]. From **Table 2**, we reveal that these materials exhibit high ηλ values close to one leading to an important light harvesting.

Overall, the molecules under investigation have shown interesting absorption properties by covering the amount of the visible and the near infrared regions which leads to potential photo-physical properties and JSC improvement.

#### **3.4 Charge transfer properties**

Efficient BHJ-OSCs dispose high charge carrier's mobility. The free chargers generated from the exciton dissociation/separation will be diffused/transported within the compound. Thus, efficient donor material should exhibit high hole transport ability to improve the photo-generation of charge carriers, and then the JSC.

The charge hopping process is selected to arrange the hole mobility into the compound at room temperature. This process is commonly described as the

**73**

*Designing Well-Organized Donor-Bridge-Acceptor Conjugated Systems Based…*

λ

λ

self-exchange and charge transport between two adjacent molecules. The hole transport rate (khole) is approximated based on Marcus theory, as above [62]:

**P-CPDTBT3** 0.255 0.205 1.66 <sup>14</sup> 10<sup>+</sup> × **SM-CPDTDPP** 0.224 0.315 4.99 <sup>14</sup> 10<sup>+</sup> ×

<sup>2</sup> 2 <sup>2</sup>

λ

Where, h is Planck's constant, *kB* is Boltzmann's constant and *T* is the

From Eq. (3), hole transfer integral (thole) and reorganization energy for hole

abilities. The hole transfer integral is influenced by the intra-molecular staking of

Where, EHOMO and EHOMO-1 define the energies of HOMO and HOMO-1 at neutral state, respectively. This expression defines the electron coupling strength of

determined fromenergy system's variation between neutral and charge states. The

explained by the electronegative discrepancy within the over conjugated framework. As well, thole value found for P-CPDTBT3 is lower than that found for SM-CPDTDPP, which shows the higher energy levels overlap within the polymer than the small molecule. Mostly, the investigated materials possess interesting hole mobility capability that will improve the electrical properties of BHJ-OSC devices.

Transition density matrix (TDM) analysis provides an insight into the interactions of donor and acceptor fragments at the first excited state (S1), the electron excitation process and the electron–hole coherence. TDM is a helpful tool to estimate the exciton escape possibility from the Coulomb attraction [64, 65]. The efficient separation of created exciton improves the charge transfer ability within

TDM plots simulated upon S0 → S1 excitation configuration are shown in **Figure 7**. It is observed from the **Figure 7** that the electron–hole coherences are primarily concentrated upon the diagonal box (D-D, A-A) and the off-diagonal (D-A) for photo-excitation. The wide distribution in the diagonal box (D-D, A-A)

validates the high π → π\* transitions within donor and acceptor regions.

two adjacent segments of the molecule. The hole reorganization energy (

λ

*hole*

*of the considered molecules. All these parameters are given in eV.*

conjugated molecules, as expressed bellow [63]:

**3.5 Transition density matrix (TDM) analysis**

temperature (298 K).

**Compound**

**Table 3.**

λ

charge transport properties (

transport (

in **Table 3**. The λ

the BHJ-OSC.

*<sup>t</sup> <sup>k</sup>*

π

1

 π<sup>−</sup> <sup>=</sup>

*hole B B*

*hole* ) arecrucial parameters to precisely evaluate the charge transport

( HOMO HOMO 1 ) <sup>1</sup> E E

*hole* value of SM-CPDTDPP is lower than that of P-CPDTBT3 that could be

*kT kT*

 λ

hole *), hole integral transfer (thole) and hole transport rate (khole)* 

hole **thole khole**

<sup>2</sup> *hole <sup>t</sup>* = − <sup>−</sup> (4)

*hole* , thole and khole) of the studied materials are listed

(3)

λ*hole* ) is

exp h 4 *hole hole*

*DOI: http://dx.doi.org/10.5772/intechopen.94874*

*Reorganization energies for hole transport (*

*Designing Well-Organized Donor-Bridge-Acceptor Conjugated Systems Based… DOI: http://dx.doi.org/10.5772/intechopen.94874*


**Table 3.**

*Solar Cells - Theory, Materials and Recent Advances*

in **Table 2**.

**Table 2.**

TD-DFT simulations were performed at the optimized ground state (S0) geometries in gaseous phase (See **Figure 6**) and the related optical parameters are listed

**P-CPDTBT3** 1.7887 693 1.0184 H → L + 3 (50%) 0.9041 1.2065 1027 0.5411 H → L (82%) **SM-CPDTDPP** 1.6803 737 1.1021 H → L + 2 (60%) 0.9209 1.1318 1095 0.3962 H → L (88%)

ηλ

As we can see from **Figure 6**, these materials exhibit, as expected, abroad absorption bands in the wavelength range from 550 nm to 900 nm which covers a relevant part of the solar spectrum, where the maximum optical absorption within the solar spectrum is at about 700 nm [56]. The broad absorption in the visible and near infrared region, displayed by the considered materials, leads to reinforce BHJ-OCSs performances. The maximum absorption peaks were found at 693 nm and

*Calculated electronic transition energy Eex (eV), maximum absorption wavelengths,* λ*max (nm), oscillator* 

**Compound Eex** λ**max f Major configuration**

In fact, these maximum wavelengths are generated mainly from HOMOs to LUMOs electronic transitions of ground to first excited state (S0 → S1) of electrons associated with high oscillator strength (f) values. Where, the pronounced absorption peaks are generated by π → π\* electronic transitions from the electron donating CPDT moieties to theelectron acceptor BT or DPP moieties [57]. The simulated absorption spectrum of P-CPDTBT3 is in convenient agreement with the experimental results reported in ref. [58], that confirms the accuracy of TD-DFT approach

SM-CPDTDPP absorption spectrum was found red shifted by 44 nm compared to that of P-CPDTBT3. The slight red shift detected can be explained by the present of the thiophene π-spacer that may enhance the electron delocalization within the

The large absorption band ranging from 900 nm to 1500 nm is attributed to the ICT generated from the sulfur rich electron to the electron withdrawing dicyanomethylene group within the CPDT units [59]. A promising organic donor material should exhibit a large light harvesting efficiency (ηλ) in order to reach high photocurrent signal [60, 61]. From **Table 2**, we reveal that these materials exhibit high ηλ

Overall, the molecules under investigation have shown interesting absorption properties by covering the amount of the visible and the near infrared regions which leads to potential photo-physical properties and JSC improvement.

Efficient BHJ-OSCs dispose high charge carrier's mobility. The free chargers generated from the exciton dissociation/separation will be diffused/transported within the compound. Thus, efficient donor material should exhibit high hole transport ability to improve the photo-generation of charge carriers, and then

The charge hopping process is selected to arrange the hole mobility into the compound at room temperature. This process is commonly described as the

737 nm for P-CPDTBT3 and SM-CPDTDPP, respectively.

*strength (f) and major configuration at TD-DT//B3LYP/6-311 g(d,p) level.*

values close to one leading to an important light harvesting.

in reproducing the experimental data.

main conjugated framework.

**3.4 Charge transfer properties**

**72**

the JSC.

*Reorganization energies for hole transport (* λhole *), hole integral transfer (thole) and hole transport rate (khole) of the considered molecules. All these parameters are given in eV.*

self-exchange and charge transport between two adjacent molecules. The hole transport rate (khole) is approximated based on Marcus theory, as above [62]:

$$\mathcal{k}\_{\text{hole}} = \frac{2\pi t\_{\text{hole}}^2}{\text{h}} \left(\frac{\pi}{\mathcal{A}\_{\text{hole}} k\_B T}\right)^{\frac{1}{2}} \exp\left(\frac{-\mathcal{A}\_{\text{hole}}}{4k\_B T}\right) \tag{3}$$

Where, h is Planck's constant, *kB* is Boltzmann's constant and *T* is the temperature (298 K).

From Eq. (3), hole transfer integral (thole) and reorganization energy for hole transport ( λ*hole* ) arecrucial parameters to precisely evaluate the charge transport abilities. The hole transfer integral is influenced by the intra-molecular staking of conjugated molecules, as expressed bellow [63]:

$$\mathbf{t}\_{\text{hole}} = \frac{\mathbf{1}}{\mathbf{2}} (\mathbf{E}\_{\text{HOMO}} - \mathbf{E}\_{\text{HOMO}-1}) \tag{4}$$

Where, EHOMO and EHOMO-1 define the energies of HOMO and HOMO-1 at neutral state, respectively. This expression defines the electron coupling strength of two adjacent segments of the molecule. The hole reorganization energy ( λ*hole* ) is determined fromenergy system's variation between neutral and charge states. The charge transport properties ( λ*hole* , thole and khole) of the studied materials are listed in **Table 3**.

The λ*hole* value of SM-CPDTDPP is lower than that of P-CPDTBT3 that could be explained by the electronegative discrepancy within the over conjugated framework. As well, thole value found for P-CPDTBT3 is lower than that found for SM-CPDTDPP, which shows the higher energy levels overlap within the polymer than the small molecule. Mostly, the investigated materials possess interesting hole mobility capability that will improve the electrical properties of BHJ-OSC devices.

#### **3.5 Transition density matrix (TDM) analysis**

Transition density matrix (TDM) analysis provides an insight into the interactions of donor and acceptor fragments at the first excited state (S1), the electron excitation process and the electron–hole coherence. TDM is a helpful tool to estimate the exciton escape possibility from the Coulomb attraction [64, 65]. The efficient separation of created exciton improves the charge transfer ability within the BHJ-OSC.

TDM plots simulated upon S0 → S1 excitation configuration are shown in **Figure 7**. It is observed from the **Figure 7** that the electron–hole coherences are primarily concentrated upon the diagonal box (D-D, A-A) and the off-diagonal (D-A) for photo-excitation. The wide distribution in the diagonal box (D-D, A-A) validates the high π → π\* transitions within donor and acceptor regions.

**Figure 7.** *TDM plots at the first excited state (S1) of the investigated materials.*

The weaker coupling of electron and holes makes easier the dissociation of exciton. The contour plots of TDM show also the exciton dissociation in the studied molecules may be easy regarding the weak electron–hole correlation that involves the charge transfer from main CPDT units to the dicyanomethylene bridge group [66]. The coefficients correlation of D-A within P-CPDTBT3 are slightly higher than those of SM-CPDTNDPP. Hence, the exciton dissociation is expected to be comparatively easier in the case of SM-CPDTNDPP than that in the case of P-CPDTBT3. The TDM analysis demonstrates the efficiency of charge separation within these molecules which leads to a considerable improvement of the Jsc.
