**6. Dependence of the PL kinetic and energy parameters on structural and dimensional factors**

In the present study, we examined the temperature dependences of the Si QD PL experimentally and observed that the energy radiative transitions are different (**Figures 7** and **8**). It's known that the spectral shift of emission band for QDs is inversely proportional to the square of its radius (Δ*h*<sup>ν</sup> � *<sup>R</sup>*�<sup>2</sup> ) [1–3, 32, 33]. On the basis of this relationship, we estimate the size of Si QDs, as listed in **Table 2**. The diameter of luminescent QDs is about 3.6–5.4 nm. This assessment is consistent with the previous literature [12].

The high-resolution transmission electron microscopy (HRTEM) shows that when the samples are implanted by Si ions with the fluences between 1.5 � <sup>10</sup><sup>17</sup> cm�<sup>2</sup> and 1017 cm�<sup>2</sup> , the average size of nanocrystal is between 3.8 � 1.2 nm and 3.5 � 1.5 nm, respectively (**Figure 10**). Based on the fact that the radius of exciton in the bulk silicon [3] is about 4.2–4.9 nm, we assume that all the samples are subjected to the effect of strong quantum confinement.

3.The activation barrier *EQ* for the nonradiative relaxation increases (**Figure 12**,

4.The kinetic factors of the intersystem crossing (δ*PISC*) and radiation (δ*PR*) take a maximum value at 1.65 eV for the case of amorphous Si nanoparticles. The intersystem crossing (δ*PISC*) and radiation (δ*PR*) increase for the case of

When the structure of Si QDs is transformed from amorphous to crystalline, a dramatic reduction in the thermal activation characteristics occurs. From **Figure 12** we can see that after crystallization the transition energy parameters (Δ*E*ISC and *E*Q) are significantly reduced. Experimentally, this effect can be observed as the

The right interpretation of the abovementioned key points is impossible without knowledge of system of configuration curves for the emission center. The following reasons can result in the changes of the kinetic parameters and the activation

1.The terms (configuration curves) of exciton are shifted either on the energy

shift of the maximum for the *I*T(*T*) curve from 438 to 158 K (**Figure 8**).

*Temperature Effects in the Photoluminescence of Semiconductor Quantum Dots*

curve 2).

**Figure 11.**

**39**

*(c) 5 <sup>10</sup><sup>16</sup> cm<sup>2</sup>*

crystalline Si nanoparticles.

*DOI: http://dx.doi.org/10.5772/intechopen.91888*

barriers for nonradiative transitions:

scale or on the coordinate configuration scale.

*Selected area diffraction (SAD) pattern images; (a) fluence 1.5 <sup>10</sup><sup>17</sup> cm<sup>2</sup>*

*, (d) 2 1016 cm<sup>2</sup> [12].*

*, (b) 1017 cm<sup>2</sup>*

*,*

#### **Figure 10.**

*HRTEM images of lattice fringe of SiO2 films (250 nm), implanted by Si-ions; (a) fluence 1.5 1017 cm<sup>2</sup> , (b) 1017 cm<sup>2</sup> [12].*

However, according to the diffraction data, the nanoparticles differ in size and internal structure. **Figure 11(a)** and **(b)** clearly confirms the presence of Si crystals in samples implanted by ions with fluences A and B; however, SAD does not show any sign of diffraction rings originating from anything but amorphous SiO2 in **Figure 11(c)** and **(d)**. Studies have shown that the PL bands with maxima at 1.8–1.6 eV are found for the amorphous Si nanoparticles, while the emission bands at 1.5–1.43 eV are related with the crystalline Si nanoparticles [4, 5, 10, 12]. Consequently, the change in the size, morphology, and structural ordering of QDs strongly affects the dependence of PL temperature curves on the ion fluence. In addition, the disorder degree in atomic structure and position of emission bands heavily depend on the size of QDs.

The form of the PL quenching curves is determined by the activation barriers and frequency factors, which are strongly affected by the all abovementioned factors (**Figures 7** and **8**).

The analysis of physical properties of the PL of Si QDs was performed on the basis of the data listed in **Table 2**. So, when the size of QDs increases:


*Temperature Effects in the Photoluminescence of Semiconductor Quantum Dots DOI: http://dx.doi.org/10.5772/intechopen.91888*


When the structure of Si QDs is transformed from amorphous to crystalline, a dramatic reduction in the thermal activation characteristics occurs. From **Figure 12** we can see that after crystallization the transition energy parameters (Δ*E*ISC and *E*Q) are significantly reduced. Experimentally, this effect can be observed as the shift of the maximum for the *I*T(*T*) curve from 438 to 158 K (**Figure 8**).

The right interpretation of the abovementioned key points is impossible without knowledge of system of configuration curves for the emission center. The following reasons can result in the changes of the kinetic parameters and the activation barriers for nonradiative transitions:

1.The terms (configuration curves) of exciton are shifted either on the energy scale or on the coordinate configuration scale.

#### **Figure 11.**

*Selected area diffraction (SAD) pattern images; (a) fluence 1.5 <sup>10</sup><sup>17</sup> cm<sup>2</sup> , (b) 1017 cm<sup>2</sup> , (c) 5 <sup>10</sup><sup>16</sup> cm<sup>2</sup> , (d) 2 1016 cm<sup>2</sup> [12].*

However, according to the diffraction data, the nanoparticles differ in size and internal structure. **Figure 11(a)** and **(b)** clearly confirms the presence of Si crystals in samples implanted by ions with fluences A and B; however, SAD does not show any sign of diffraction rings originating from anything but amorphous SiO2 in **Figure 11(c)** and **(d)**. Studies have shown that the PL bands with maxima at 1.8–1.6 eV are found for the amorphous Si nanoparticles, while the emission bands at 1.5–1.43 eV are related with the crystalline Si nanoparticles [4, 5, 10, 12]. Consequently, the change in the size, morphology, and structural ordering of QDs strongly affects the dependence of PL temperature curves on the ion fluence. In addition, the disorder degree in atomic structure and position of emission bands

*,*

*HRTEM images of lattice fringe of SiO2 films (250 nm), implanted by Si-ions; (a) fluence 1.5 1017 cm<sup>2</sup>*

The form of the PL quenching curves is determined by the activation barriers and frequency factors, which are strongly affected by the all abovementioned

The analysis of physical properties of the PL of Si QDs was performed on the

2.The value of parameter Δ*E*ISC corresponding to the intersystem crossing of

1.The extremum of the PL quenching curve shifts to the range of higher

basis of the data listed in **Table 2**. So, when the size of QDs increases:

excitons increases (**Figure 12**, curve 1).

heavily depend on the size of QDs.

*Quantum Dots - Fundamental and Applications*

factors (**Figures 7** and **8**).

**Figure 10.**

*(b) 1017 cm<sup>2</sup> [12].*

temperatures.

**38**

#### **Figure 12.**

*The relationship between the energies of radiative PL transitions and the activation parameters of nonradiative transitions in silicon QDs in crystalline and amorphous state, which shows their dependence on structural and dimensional factors. The energy factor of the intercombining conversion is designated as* E*ISC, and the thermally activated barrier of PL quenching is* E*Q. the filled circles show the results of the data presented in [4, 5, 10, 13] and the open circles [12, 13].*


A system of hypothetical configuration curves with the terms of singlet ground state S0 and terms of singlet and triplet excited states (S1 and T1, respectively) is shown in **Figure 13**. For clarity, the distribution of terms caused by the continual disorder isn't shown. It is assumed that the parameters Δ*E*ISC and *E*<sup>Q</sup> take some effective values, which correspond to the maxima of distribution functions.

The main observation of the reduction in size of nanoparticles is the increase of the optical transitions energy, owing to the shift of the terms relative to each other [1–3]. We assume that S0, S1, and T1 have a parabolic form; we can see that the shift of S1 to the position of S1' will lead to a decrease in the energy factor Δ *E*ISC of the intersystem crossing (see **Figure 13a**).

This is well consistent with the curve 1 of **Figure 12**. However, a similar shift of the position for T1 toward T1' (**Figure 13b**) implies that increasing the energy of the radiative transition (*h*ν) will increase the activation barrier (*E*Q'). At the same time, according to the experimental results (see **Figure 12**, curve 2), this barrier has to be decreased. **Figure 12** shows that this contradiction can be solved if the displacement of T1 is accompanied by its extension (T1"). This effect corresponds to the decrease of the frequency factor *p*<sup>05</sup> and kinetic factor δ*P*<sup>R</sup> where the approximation results confirm the increasing of the energy of radiative transition (**Table 2**).

is a sharp decrease in activation barriers at transition from amorphous to crystalline QDs. From this point of view, the structural disorder is becoming a negligible factor. On the other hand, the dependence of shift and broadening of the configuration curves on the QD size also are observed for the case of crystalline QDs. **Table 2** shows that the energy and the kinetic parameters of nonradiative transi-

*Schematic illustration of the change in the energy factor Δ*EISC *of intercombination conversion (a) and the activation barrier* E*<sup>Q</sup> of the PL quenching (b) with a decrease in the size of quantum dots. The figure shows the initial terms of the ground and excited triplet and singlet states (S0,T1, S1), the displaced terms of the excited triplet and singlet states (T1', S1'), and the shifted and broadened term of the excited triplet state (T1").*

*Temperature Effects in the Photoluminescence of Semiconductor Quantum Dots*

*DOI: http://dx.doi.org/10.5772/intechopen.91888*

The effect on structural and dimensional factors on the activation parameters of the radiative and nonradiative relaxations can be estimated from the three-level system of QD luminescence (**Figure 13**). However, for this task it is necessary to conduct special experiments and theoretical modeling (ab initio calculations). This

The developed ideas are a powerful tool for the control of the optical properties of QDs depending on the size, composition, and structure factors. We believe, the proposed approach is universal and can be applied to semiconductor QDs (such as Si, Ge, C) in dielectric hosts. The estimation of the applicability of this model to QDs of another type (e.g., with complex composition or special structural features

tions depend on the size of QDs.

**Figure 13.**

**41**

issue is outside the scope of this work.

[34]) can be performed using a special experimental check.

The abovementioned four key points were found experimentally [4, 5, 12, 13]. There is a red shift of emission bands from 1.8 to 1.4 eV with an increasing of QD size. In addition, the PL band broadening is observed (0.15–0.4 eV), which can be caused by the broadening of the configuration curve for the T1 excited triplet state (**Figure 13b**).

In the case of amorphous nanoparticles (**Figure 12**), the increase of the effective parameters Δ*E*ISC and *E*<sup>Q</sup> in a larger QD size can be due to the variations in the corresponding distribution functions of energy levels. Since the size effect in the amorphous nanoparticles manifests itself more strongly in comparison with the crystalline nanoparticles, we can assume the quite importance of the continual disordering in the formation of QD optical properties. It should be noted that there

*Temperature Effects in the Photoluminescence of Semiconductor Quantum Dots DOI: http://dx.doi.org/10.5772/intechopen.91888*

#### **Figure 13.**

2.The broadening or narrowing of configuration curves is observed.

configuration curves on the energy and configuration scales.

confirm the increasing of the energy of radiative transition (**Table 2**).

intersystem crossing (see **Figure 13a**).

(**Figure 13b**).

**40**

**Figure 12.**

*and the open circles [12, 13].*

*Quantum Dots - Fundamental and Applications*

3.The changes in the degree of continual disorder result in the distribution of

*The relationship between the energies of radiative PL transitions and the activation parameters of nonradiative transitions in silicon QDs in crystalline and amorphous state, which shows their dependence on structural and dimensional factors. The energy factor of the intercombining conversion is designated as* E*ISC, and the thermally activated barrier of PL quenching is* E*Q. the filled circles show the results of the data presented in [4, 5, 10, 13]*

A system of hypothetical configuration curves with the terms of singlet ground state S0 and terms of singlet and triplet excited states (S1 and T1, respectively) is shown in **Figure 13**. For clarity, the distribution of terms caused by the continual disorder isn't shown. It is assumed that the parameters Δ*E*ISC and *E*<sup>Q</sup> take some effective values, which correspond to the maxima of distribution functions.

The main observation of the reduction in size of nanoparticles is the increase of the optical transitions energy, owing to the shift of the terms relative to each other [1–3]. We assume that S0, S1, and T1 have a parabolic form; we can see that the shift of S1 to the position of S1' will lead to a decrease in the energy factor Δ *E*ISC of the

This is well consistent with the curve 1 of **Figure 12**. However, a similar shift of the position for T1 toward T1' (**Figure 13b**) implies that increasing the energy of the radiative transition (*h*ν) will increase the activation barrier (*E*Q'). At the same time, according to the experimental results (see **Figure 12**, curve 2), this barrier has to be decreased. **Figure 12** shows that this contradiction can be solved if the displacement of T1 is accompanied by its extension (T1"). This effect corresponds to the decrease of the frequency factor *p*<sup>05</sup> and kinetic factor δ*P*<sup>R</sup> where the approximation results

The abovementioned four key points were found experimentally [4, 5, 12, 13]. There is a red shift of emission bands from 1.8 to 1.4 eV with an increasing of QD size. In addition, the PL band broadening is observed (0.15–0.4 eV), which can be caused by the broadening of the configuration curve for the T1 excited triplet state

In the case of amorphous nanoparticles (**Figure 12**), the increase of the effective

parameters Δ*E*ISC and *E*<sup>Q</sup> in a larger QD size can be due to the variations in the corresponding distribution functions of energy levels. Since the size effect in the amorphous nanoparticles manifests itself more strongly in comparison with the crystalline nanoparticles, we can assume the quite importance of the continual disordering in the formation of QD optical properties. It should be noted that there *Schematic illustration of the change in the energy factor Δ*EISC *of intercombination conversion (a) and the activation barrier* E*<sup>Q</sup> of the PL quenching (b) with a decrease in the size of quantum dots. The figure shows the initial terms of the ground and excited triplet and singlet states (S0,T1, S1), the displaced terms of the excited triplet and singlet states (T1', S1'), and the shifted and broadened term of the excited triplet state (T1").*

is a sharp decrease in activation barriers at transition from amorphous to crystalline QDs. From this point of view, the structural disorder is becoming a negligible factor. On the other hand, the dependence of shift and broadening of the configuration curves on the QD size also are observed for the case of crystalline QDs. **Table 2** shows that the energy and the kinetic parameters of nonradiative transitions depend on the size of QDs.

The effect on structural and dimensional factors on the activation parameters of the radiative and nonradiative relaxations can be estimated from the three-level system of QD luminescence (**Figure 13**). However, for this task it is necessary to conduct special experiments and theoretical modeling (ab initio calculations). This issue is outside the scope of this work.

The developed ideas are a powerful tool for the control of the optical properties of QDs depending on the size, composition, and structure factors. We believe, the proposed approach is universal and can be applied to semiconductor QDs (such as Si, Ge, C) in dielectric hosts. The estimation of the applicability of this model to QDs of another type (e.g., with complex composition or special structural features [34]) can be performed using a special experimental check.
