**4. Dependence of PL temperature behavior on energy and kinetic factors**

As was mentioned in previous sections, the dependence of the PL intensity on temperature *I*T(*T*) can be described by a decreasing or increasing function or a curve with an extremum. According to Eq. (1), the form of *I*T(*T*) function depends on the relations between the kinetic and activation parameters of luminescent centers. Thus, if the certain conditions determining the form of function will be known, one can associate the shape of *I*T(*T*) curve with the energy and vibrational characteristics of the emission center. In the framework of two-step PL mechanism, the shape of the curves *I*T(*T*) is determined by the multipliers ηISC(*T*) and ηR(*T*). **Figure 5** shows the calculated functions ηISC(*T*) and ηR(*T*) and their multiplication. The curve (3) reproduces qualitatively the temperature dependence *I*T(*T*) normalized to the number of photons incident on the surface of the sample. The next step is to discuss the influence of parameters from Eq. (1) on the form of the *I*T(*T*) dependence.

#### **4.1 Triplet luminescence quenching**

Other triplet PL relaxation schemes can be considered in the same way. The energy transfer of free matrix excitons (FE) to quantum dots is confirmed experimentally [4, 5, 13]. In other words, the absorption of high-energy light quanta with the formation of free excitons (**Figure 4**, transition 6) can excite luminescence of QDs. The direct transition of the excitation to the triplet state T1 (transition 7) illustrates the simplest scheme of this process. The indicated option is similar to the direct excitation of QDs described by a two-stage process [10, 13]. The expression for the intensity of triplet luminescence (Eq. (2)) can be written assuming that transition 7 occurs without a barrier, and the formation of a self-trapped exciton (transition 8) is a competing process and also leads to luminescence (transition 9).

*kT*

tion energy *E*<sup>11</sup> and frequency factor *p*<sup>011</sup> as a sequence of thermal transitions HES ! ... ! T1. A generalized transition 12 with the corresponding effective parameters *E*<sup>12</sup> and *p*<sup>012</sup> will be considered a sequence of competing processes. The energy transfer rate *P*<sup>10</sup> to highly excited states will be assumed to be independent of temperature, and the thermal activation barrier of such a transfer is equal to zero. Then the triplet-singlet PL will be described by the following three-stage model:

1 þ δ*P*oc exp

The latter is taking into account the quantum efficiencies (ηT, ηoc, ηR) for energy transfer, triplet state occupation, and radiative triplet-singlet transitions, respectively. Eq. (3) is the variant of Eq. (2), where by taking into account an additional step there are six parameters, corresponding to transition 10 (δ*P*<sup>T</sup> и Δ*E*ST), transition 11 (δ*P*oc и Δ*E*oc), and transition 4 (δ*P*<sup>R</sup> и *E*Q). The energy transfer from the matrix to the quantum dot is denoted identically in Eqs. (2) and (3) and is described by the parameters δ*P*<sup>T</sup> and Δ*E*ST. However, it should be clarified that in Eq. (2) quantum energy transfer efficiency η<sup>T</sup> characterizes transition 7, while in Eq. (3)—transition 10.

�<sup>1</sup>

Δ*E*oc *kT*

<sup>1</sup> <sup>þ</sup> <sup>δ</sup>*P*<sup>R</sup> exp � *<sup>E</sup>*<sup>Q</sup>

*kT*

(3)

where η<sup>R</sup> and η<sup>T</sup> are quantum efficiencies characterizing radiative triplet-singlet transitions and energy transfer from FE to QDs, respectively. Eq. (2) has four fitting parameters: δ*P*<sup>R</sup> and *E*<sup>Q</sup> (transition 4) and δ*P*<sup>T</sup> and Δ*E*ST (transition 7), similar to Eq. (1). At the same time, the parameters (δ*P*<sup>R</sup> and *E*Q) of nonradiative decay of excitons are independent of the excitation method, as can be seen from Eqs. (1) and (2). An analysis of the data for direct excitation of PL (**Figure 4**, transitions 4 and 5) allows one to determine these two parameters from independent measurements and then use them in the analysis of indirect excitation processes. Using this approach, one can significantly improve the procedure for approximating the experimental temperature dependences of PL and reduce the number of variable parameters. At the same time, the large difference between the energy levels of excitons in QDs and free excitons in a dielectric matrix should be taken into account. In this regard, Eq. (2) is approximate and describes only a simplified scheme of luminescence. In fact, transition 7 cannot be considered elementary, and energy from the FE is transferred to the high-energy states (HES) of the QDs (see **Figure 4**, transition 10). Further, successive thermal transitions from HES lead to the filling of the lower triplet state T1. The indicated energy transfer sequence cannot be considered barrierfree, and triplet-singlet luminescence should be described by a multistage model. Let us consider the generalized transition 11 with effective parameters: activa-

<sup>1</sup> <sup>þ</sup> <sup>δ</sup>*P*<sup>R</sup> exp � *<sup>E</sup>*<sup>Q</sup>

�<sup>1</sup>

*kT*

, (2)

*IT*

*IT*″ <sup>¼</sup> *<sup>I</sup>*0ηTηocη<sup>R</sup>

**28**

<sup>¼</sup> *<sup>I</sup>*<sup>0</sup> <sup>1</sup> <sup>þ</sup> <sup>δ</sup>*P*<sup>T</sup> exp � *<sup>E</sup>*ST

*kT*

<sup>0</sup> <sup>¼</sup> *<sup>I</sup>*0ηTη<sup>R</sup> <sup>¼</sup> *<sup>I</sup>*<sup>0</sup> <sup>1</sup> <sup>þ</sup> <sup>δ</sup>*P*<sup>T</sup> exp � *<sup>E</sup>*ST

*Quantum Dots - Fundamental and Applications*

In case both temperature-dependent factors of Eq. (1) decrease with an increasing of temperature, the *I*T(*T*) function is characterized by a negative slope, wherein the quantum efficiency ηR(*T*) is decreasing (see **Figure 5**, curve 1) within the range from 1 to 1/(1 + δ*P*R). It has a minimum which depends on the ratio *p*05/*P*4. If δ *P*<sup>R</sup> ! 0, then η<sup>T</sup> will weakly depend on the temperature, keeping a value that is very close to 1 over the entire temperature range. However, the situation δ*P*<sup>R</sup> > 1 is most often realized, since the radiative triplet-singlet transitions are spin forbidden [30], and their rate *P*<sup>4</sup> is less than the frequency factor *p*<sup>05</sup> for the nonradiative relaxation.

The ratio between activation barriers *E*<sup>2</sup> and *E*<sup>3</sup> determines the form of ηISC(*T*) function, which decreases ranging from 1 to 1/(1+ δ*P*ISC) if Δ*E*ISC < 0. In this case,

#### **Figure 5.**

*Calculated temperature dependences of the quantum efficiency factors for different processes: (1) triplet-singlet radiative transitions; (2) intersystem crossing; (3) two-step process ηISC(T)*�*ηR(T).*

the form of ηISC(*T*) function is similar to that for ηR(*T*), as was shown in **Figure 5**, curve 1. Thus, the PL quenching curve will have an asymptote corresponding to a certain value *I*<sup>∞</sup> (**Figure 6**, curve 1). If Δ*E*ISC = 0, the first exponent in Eq. (1) is equal to 1, which causes a temperature independence of ηISC quantum efficiency. For this case, the *I*T(*T*) dependence can be described by the Mott function [31] (**Figure 6**, curve 2), and quenching of triplet PL occurs due to the nonradiative transition 5 (**Figure 4**).

The *I*<sup>∞</sup> value is determined by the parameters of the competing processes. The *I*<sup>∞</sup> value increases if δ*P*ISC and δ *P*<sup>R</sup> kinetic factors decrease. It should be noted that the *I*<sup>∞</sup> parameter is some hypothetical constant, because the quenching at high temperatures isn't considered in the model of direct excitation. In fact, the *I*T(*T*) dependences will tend to zero in the range of high temperatures. However, in some cases the experimental *I*T(*T*) curves can have a saturation region at room temperature [10, 12, 13]. The PL intensity in the saturation region can be contingently accepted as *I*<sup>∞</sup> value. This helps to simplify the mathematical processing.

#### **4.2 Triplet luminescence growth**

For the case of triplet PL growth, the ηISC(*T*) function has an increasing character because the ηR(*T*) function definitely decreases. As Eq. (1) shows, the quantum efficiency of the intersystem crossing (ηISC) increases with increasing of temperature if Δ*E*ISC > 0 (see **Figure 5**, curve 2), wherein the intensity of triplet PL increases up to the *I*<sup>∞</sup> value (**Figure 6**, curve 4) or the *I*T(*T*) curve has a maximum (see **Figure 6**, curve 5). If the maximum is absent, the occupation of the triplet state predominates over the process of the luminescence quenching. It is possible, when d*I*T/d*T* > 0 condition is realized, which can be transformed as:

$$\eta\_{\rm ISC}(T)\ $P\_{\rm ISC}(\Delta E\_{\rm ISC})\exp\left(\frac{\Delta E\_{\rm ISC}}{kT}\right) > \eta\_{\rm R}(T)\$ P\_{\rm R}E\_{\rm Q}\exp\left(-\frac{E\_{\rm Q}}{kT}\right) \tag{4}$$

After some mathematical transformations. we can write:

$$n > l\infty + m,\tag{5}$$

where

*x* ¼ exp

where

points:

**31**

Δ*E*ISC

*kT* ; *<sup>n</sup>* <sup>¼</sup> *<sup>E</sup>*<sup>Q</sup>

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

Δ*E*ISC

Since n > 1, finally one can obtain the following:

*<sup>С</sup>* <sup>¼</sup> <sup>1</sup> δ*P*ISC

þ 1; *l* ¼ δ*P*<sup>R</sup> �

*Temperature Effects in the Photoluminescence of Semiconductor Quantum Dots*

þ 1 1

The inequality (Eq. (7)) shows that in general the temperature dependence *I*T(*T*) is determined by both the peculiarities of the QD energy structure and their vibrational properties. From Eq. (8) one can see that the coefficient *C* is responsible for the relations between the kinetic factors (δ*P*ISC, δ *P*R) for the radiative transitions and intersystem crossing. In the case of slow kinetics of PL (δ*P*ISC >> 1 andδ

Δ*E*ISC = *C*�*E*Q, the *I*T(*T*) dependence will be presented as the function with satura-

The maximum for *I*T(*T*) curve occurs under the condition that the derivative of (1) is equal to zero. Thus, the energy factor of the singlet-triplet intersystem crossing Δ*E*ISC and the activation barrier of quenching (*E*Q) have the following relationship:

Previously we noted that *C* coefficient is introduced for accounting the influence of the rate of the vibrational processes on the form of PL temperature dependence for the QDs. However, the triplet luminescence is characterized by a relatively slow kinetics, when the *C* parameter is close to 1. Thus, we can state the following key

1.Rapidly decreasing *I*T(T) curves mean that the thermal activation barrier is higher than the activation energy for the intersystem crossing (Δ*E*ISC < 0).

(Δ*E*ISC = 0), the PL quenching can be described by the Mott type function (see **Figure 6**, curve 2). The nonradiative triplet-singlet channel is responsible for

3. If the intersystem crossing barrier is high (Δ*E*ISC > *C*�*E*Q), the intensity of the triplet luminescence increases. In this case the efficiency of intersystem

temperature *T*<sup>S</sup> when Δ*E*ISC = *C*�*E*Q. This saturation point corresponds to the balance between the quenching process and the occupation of T1 triplet states.

2. In the case of temperature-independent occupation of the triplet states

4.The luminescence intensity increases until some point of saturation at

this process (see **Figure 4**, transition 5).

crossing reaches its saturation at high temperatures.

*P*<sup>R</sup> >> 1) the C ! 1, one can neglect the vibrational properties of the QDs. If instead of inequality (Eq. (7)) we will deal with the strict equality

tion point at temperature *T*<sup>S</sup> >> Δ*E*ISC/*k* (see **Figure 6**, curve 4).

**4.3 Extremal temperature dependence of triplet luminescence**

δ*P*<sup>R</sup> þ 1 �<sup>1</sup>

*E*<sup>Q</sup> � Δ*E*ISC Δ*E*ISC

; *<sup>m</sup>* <sup>¼</sup> <sup>δ</sup>*P*<sup>R</sup> δ*P*ISC

Δ*E*ISC >*C* � *E*<sup>Q</sup> , (7)

0< Δ*E*ISC <*C* � *E*<sup>Q</sup> (9)

� *<sup>E</sup>*<sup>Q</sup> Δ*E*ISC

(6)

(8)

#### **Figure 6.**

*PL temperature dependences for different ratios of energy factor Δ*E*ISC of intersystem crossing and PL quenching thermo-activation barrier* E*Q: (1) Δ*E*ISC < 0; (2) Δ*E*ISC = 0; (3) Δ*E*ISC >* C�E*Q; (4) Δ*E*ISC =* C�E*Q; (5) 0 < Δ*E*ISC <* C�E*Q.*

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

where

the form of ηISC(*T*) function is similar to that for ηR(*T*), as was shown in **Figure 5**, curve 1. Thus, the PL quenching curve will have an asymptote corresponding to a certain value *I*<sup>∞</sup> (**Figure 6**, curve 1). If Δ*E*ISC = 0, the first exponent in Eq. (1) is equal to 1, which causes a temperature independence of ηISC quantum efficiency. For this case, the *I*T(*T*) dependence can be described by the Mott function [31] (**Figure 6**, curve 2), and quenching of triplet PL occurs due to the nonradiative

The *I*<sup>∞</sup> value is determined by the parameters of the competing processes. The *I*<sup>∞</sup> value increases if δ*P*ISC and δ *P*<sup>R</sup> kinetic factors decrease. It should be noted that the *I*<sup>∞</sup> parameter is some hypothetical constant, because the quenching at high temperatures isn't considered in the model of direct excitation. In fact, the *I*T(*T*) dependences will tend to zero in the range of high temperatures. However, in some cases the experimental *I*T(*T*) curves can have a saturation region at room temperature [10, 12, 13]. The PL intensity in the saturation region can be contingently accepted as *I*<sup>∞</sup> value. This helps to simplify the mathematical processing.

For the case of triplet PL growth, the ηISC(*T*) function has an increasing character because the ηR(*T*) function definitely decreases. As Eq. (1) shows, the quantum efficiency of the intersystem crossing (ηISC) increases with increasing of temperature if Δ*E*ISC > 0 (see **Figure 5**, curve 2), wherein the intensity of triplet PL

increases up to the *I*<sup>∞</sup> value (**Figure 6**, curve 4) or the *I*T(*T*) curve has a maximum (see **Figure 6**, curve 5). If the maximum is absent, the occupation of the triplet state predominates over the process of the luminescence quenching. It is possible, when

> Δ*E*ISC *kT*

*PL temperature dependences for different ratios of energy factor Δ*E*ISC of intersystem crossing and PL quenching thermo-activation barrier* E*Q: (1) Δ*E*ISC < 0; (2) Δ*E*ISC = 0; (3) Δ*E*ISC >* C�E*Q; (4) Δ*E*ISC =* C�E*Q;*

<sup>&</sup>gt; *<sup>η</sup>*Rð Þ *<sup>T</sup>* <sup>δ</sup>*P*R*E*<sup>Q</sup> exp � *<sup>E</sup>*<sup>Q</sup>

*n*> *lx* þ *m*, (5)

*kT* 

(4)

d*I*T/d*T* > 0 condition is realized, which can be transformed as:

After some mathematical transformations. we can write:

*η*ISCð Þ *T* δ*P*ISCð Þ Δ*E*ISC exp

**Figure 6.**

**30**

*(5) 0 < Δ*E*ISC <* C�E*Q.*

transition 5 (**Figure 4**).

*Quantum Dots - Fundamental and Applications*

**4.2 Triplet luminescence growth**

$$\infty = \exp\left(\frac{\Delta E\_{\rm ISC}}{kT}\right); n = \frac{E\_{\rm Q}}{\Delta E\_{\rm ISC}} + 1; l = \delta P\_{\rm R} \cdot \frac{E\_{\rm Q} - \Delta E\_{\rm ISC}}{\Delta E\_{\rm ISC}}; m = \frac{\delta P\_{\rm R}}{\delta P\_{\rm ISC}} \cdot \frac{E\_{\rm Q}}{\Delta E\_{\rm ISC}} \tag{6}$$

Since n > 1, finally one can obtain the following:

$$
\Delta E\_{\rm ISC} > \mathbf{C} \cdot E\_{\rm Q}, \tag{7}
$$

where

$$C = \left(\frac{1}{\delta P\_{\rm ISC}} + 1\right) \left(\frac{1}{\delta P\_{\rm R}} + 1\right)^{-1} \tag{8}$$

The inequality (Eq. (7)) shows that in general the temperature dependence *I*T(*T*) is determined by both the peculiarities of the QD energy structure and their vibrational properties. From Eq. (8) one can see that the coefficient *C* is responsible for the relations between the kinetic factors (δ*P*ISC, δ *P*R) for the radiative transitions and intersystem crossing. In the case of slow kinetics of PL (δ*P*ISC >> 1 andδ *P*<sup>R</sup> >> 1) the C ! 1, one can neglect the vibrational properties of the QDs.

If instead of inequality (Eq. (7)) we will deal with the strict equality Δ*E*ISC = *C*�*E*Q, the *I*T(*T*) dependence will be presented as the function with saturation point at temperature *T*<sup>S</sup> >> Δ*E*ISC/*k* (see **Figure 6**, curve 4).

#### **4.3 Extremal temperature dependence of triplet luminescence**

The maximum for *I*T(*T*) curve occurs under the condition that the derivative of (1) is equal to zero. Thus, the energy factor of the singlet-triplet intersystem crossing Δ*E*ISC and the activation barrier of quenching (*E*Q) have the following relationship:

$$0 < \Delta E\_{\rm ISC} < C \cdot E\_{\rm Q} \tag{9}$$

Previously we noted that *C* coefficient is introduced for accounting the influence of the rate of the vibrational processes on the form of PL temperature dependence for the QDs. However, the triplet luminescence is characterized by a relatively slow kinetics, when the *C* parameter is close to 1. Thus, we can state the following key points:


Analysis of Eqs. (2) and (3) can be performed in a similar way. These analytical equations describe the temperature behavior of the QD triplet luminescence at excitation within the spectral range of the exciton absorption in a wide bandgap matrix. As shown by Eq. (2), the simplified two-step model of this process corresponds to the decreasing function of the first type (see **Figure 6**, curve 1). All of the five above mentioned types of *I*T(*T*) can be described by Eq. (3) for different *E*<sup>Q</sup> , *E*ST, and Δ *E*oc values. The main condition for increasing of this function is Δ*E*oc > 0.

Summarizing, the δ *P*<sup>T</sup> and Δ*E*ST parameters characterizing the occupation of radiative states are the key parameters for the approximation of the PL temperature dependence for QDs. The values of these parameters differ for the direct and indirect excitation mechanisms. Herewith, for all three models, transition 4 is the same, so one can fix the parameters δ*P*<sup>R</sup> and *E*<sup>Q</sup> in the approximation operation.

### **5. Theory and experiment comparison**

#### **5.1 A case of direct excitation**

In order to check the adequacy of the model for direct excitation (Eq. (1)), we have performed the analysis of the experimental PL temperature dependences for silicon QDs with the well-known luminescence properties [4, 5, 12, 13, 31]. There are selective PL bands at 1.7–1.8 eV with a full-width maximum at half-height (FWHM) of 0.18–0.15 eV at direct excitation.

**Figure 7** (curves 1 and 2) shows the experimental temperature dependences *IT*(T), constructed from the integrated intensities of the Si QD luminescence bands excited by the radiation 3.6 eV of nitrogen laser in the temperature range 9–300 K. To clarify the effect of the energy parameters *E*ISC and *E*<sup>Q</sup> on the shape and the luminescence intensity, we built simulated curves *I*T(*T*), which are presented in **Figure 7b**.

PL temperature dependence (curves 6 and 7 in **Figure 7**) are of a great interest. Thus, both high intensity and stability of PL for a wide temperature range can be achieved if the activation energy *E*<sup>Q</sup> of the PL quenching increases. The main attention was paid to the relationship between the activation energies of the nonradiative processes on the basis of the analysis of Eq. (1) and the parameters, which impact on the form of experimental PL quenching curves. However, it must not be neglected that the kinetic parameters of the emission centers also influence

*PL intensity at directly excited Si QDs versus temperature in silica films implanted by Si and C ions (a): (1) – SiO2/Si (emission 1.7 eV); (2) – SiO2/Si/C (emission 1.8 eV); (b) – simulated curves IT(T),*

*Temperature Effects in the Photoluminescence of Semiconductor Quantum Dots*

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

The PL intensity additionally increases, if the pre-exponential factors δ*P*ISC and δ*P*<sup>R</sup> decreases, as shown by Eq. (1). If the corresponding parameters will be tenfold

different (*p*<sup>02</sup> > 10 *p*<sup>03</sup> and *P*<sup>4</sup> > 10 *p*05), this effect will be more noticeable. However, such relationships are unlikely in the case of slow kinetics of the triplet luminescence. At the same time, the PL intensity can decrease due to the influence of reducing factors, such as the ratio of the kinetic parameters. So, a wider series of real experimental dependencies should be considered and analyzed. It allows to

the shape of the temperature behavior and intensity of PL.

**Figure 7.**

**33**

*obtained by using the Eq. (1).*

In **Table 1** the calculated parameters of considered PL temperature dependences (curves 3–7) are listed. **Table 1** and **Figure 7** show that increase of Δ*E*ISC causes the reducing of PL intensity due to the reducing of the efficiency of intersystem crossing. On the contrary, increase of the activation barrier *E*<sup>Q</sup> for the competing process leads to an increase in the PL intensity due to the decrease of the quenching effectiveness. For all cases, the increasing of the activation energies leads to an increasing of the Tm temperature, which corresponds to the maximum of *I*T(*T*) curve.

As was discussed in the section "Extremal temperature dependence for the triplet luminescence," all calculated curves except curve 5 belong to the fifth type of form. Curves 4 and 7 have the maxima outside the temperature range, which is shown in **Figure 7**. Curve 5 corresponds to the form of the third type. From **Table 1**, it is seen that this curve satisfies the condition (Eq. (7)).

The third-type curves demonstrate the lowest PL intensity. In the framework of developing the effective nanophosphors, the materials with the fifth-type form of

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

**Figure 7.**

5. If 0 < Δ*E*ISC < *CE*Q, the curve *I*T(*T*) has an extremum. In the range of *I*T(*T*), increasing the occupation process of triplet states dominates. The decreasing of

6.The shape of the *I*T(*T*) dependence isn't affected by the vibrational properties of the luminescent QDs (*C* ≈ 1), if the PL kinetic is relatively slow (kinetic

Analysis of Eqs. (2) and (3) can be performed in a similar way. These analytical equations describe the temperature behavior of the QD triplet luminescence at excitation within the spectral range of the exciton absorption in a wide bandgap matrix. As shown by Eq. (2), the simplified two-step model of this process corresponds to the decreasing function of the first type (see **Figure 6**, curve 1). All of the five above mentioned types of *I*T(*T*) can be described by Eq. (3) for different *E*<sup>Q</sup> , *E*ST, and Δ *E*oc values. The main condition for increasing of this function is

Summarizing, the δ *P*<sup>T</sup> and Δ*E*ST parameters characterizing the occupation of radiative states are the key parameters for the approximation of the PL temperature dependence for QDs. The values of these parameters differ for the direct and indirect excitation mechanisms. Herewith, for all three models, transition 4 is the same, so one can fix the parameters δ*P*<sup>R</sup> and *E*<sup>Q</sup> in the approximation operation.

In order to check the adequacy of the model for direct excitation (Eq. (1)), we have performed the analysis of the experimental PL temperature dependences for silicon QDs with the well-known luminescence properties [4, 5, 12, 13, 31]. There are selective PL bands at 1.7–1.8 eV with a full-width maximum at half-height

**Figure 7** (curves 1 and 2) shows the experimental temperature dependences *IT*(T), constructed from the integrated intensities of the Si QD luminescence bands excited by the radiation 3.6 eV of nitrogen laser in the temperature range 9–300 K. To clarify the effect of the energy parameters *E*ISC and *E*<sup>Q</sup> on the shape and the luminescence intensity, we built simulated curves *I*T(*T*), which are presented in

In **Table 1** the calculated parameters of considered PL temperature dependences (curves 3–7) are listed. **Table 1** and **Figure 7** show that increase of Δ*E*ISC causes the reducing of PL intensity due to the reducing of the efficiency of intersystem crossing. On the contrary, increase of the activation barrier *E*<sup>Q</sup> for the competing process leads to an increase in the PL intensity due to the decrease of the quenching effectiveness. For all cases, the increasing of the activation energies leads to an increasing of the Tm

As was discussed in the section "Extremal temperature dependence for the triplet luminescence," all calculated curves except curve 5 belong to the fifth type of form. Curves 4 and 7 have the maxima outside the temperature range, which is shown in **Figure 7**. Curve 5 corresponds to the form of the third type. From **Table 1**,

The third-type curves demonstrate the lowest PL intensity. In the framework of developing the effective nanophosphors, the materials with the fifth-type form of

temperature, which corresponds to the maximum of *I*T(*T*) curve.

it is seen that this curve satisfies the condition (Eq. (7)).

PL intensity is due to the prevalence of the luminescence quenching.

factors δ*P*ISC and δ*P*<sup>R</sup> significantly greater than 1).

*Quantum Dots - Fundamental and Applications*

**5. Theory and experiment comparison**

(FWHM) of 0.18–0.15 eV at direct excitation.

**5.1 A case of direct excitation**

Δ*E*oc > 0.

**Figure 7b**.

**32**

*PL intensity at directly excited Si QDs versus temperature in silica films implanted by Si and C ions (a): (1) – SiO2/Si (emission 1.7 eV); (2) – SiO2/Si/C (emission 1.8 eV); (b) – simulated curves IT(T), obtained by using the Eq. (1).*

PL temperature dependence (curves 6 and 7 in **Figure 7**) are of a great interest. Thus, both high intensity and stability of PL for a wide temperature range can be achieved if the activation energy *E*<sup>Q</sup> of the PL quenching increases. The main attention was paid to the relationship between the activation energies of the nonradiative processes on the basis of the analysis of Eq. (1) and the parameters, which impact on the form of experimental PL quenching curves. However, it must not be neglected that the kinetic parameters of the emission centers also influence the shape of the temperature behavior and intensity of PL.

The PL intensity additionally increases, if the pre-exponential factors δ*P*ISC and δ*P*<sup>R</sup> decreases, as shown by Eq. (1). If the corresponding parameters will be tenfold different (*p*<sup>02</sup> > 10 *p*<sup>03</sup> and *P*<sup>4</sup> > 10 *p*05), this effect will be more noticeable. However, such relationships are unlikely in the case of slow kinetics of the triplet luminescence. At the same time, the PL intensity can decrease due to the influence of reducing factors, such as the ratio of the kinetic parameters. So, a wider series of real experimental dependencies should be considered and analyzed. It allows to


**Table 1.**

*Energy and kinetic parameters of the nonradiative processes for the curves IT(T) in Figure 7. Comment: For strings 1 and 3–7, the correction is C = 1.13 (δPISC = 1.80, δPR = 2.65); for string 2 C = 1 (δPISC = 1.10, δPR = 1.09); the intensity scale parameter is I0 = 317 a.u.*

determine which model parameters are more prone to changes in the characteristics of QDs and how they respond to these changes.

To solve this task, we considered the experimental results on PL of Si QDs in SiO2 films obtained by Wang et al. [12]. In this work, authors obtained the Si QDs with different sizes by using the various doses of silicon ions. The emission bands are red-shifted from 1.65 to 1.43 eV with an increasing of ion dose. In addition, the broadening of emission bands from 0.2 to 0.4 eV was observed. However, the emission bands experienced a slight red shift (<0.1 eV) and a change in width (<0.05 eV) with an increasing of temperature.

The temperature dependences of the luminescence and their approximation by using Eq. (1) are shown in **Figure 8**. It is seen that the form of quenching curves depends on the ion fluence. On the one hand, еру curves 1 and 2 show a monotonic increase at low fluence. On the other hand, curves 3 and 4 have maxima around 158 and 163 K, respectively, at high fluence. Herewith, all temperature dependences correspond to the fifth type, as was shown by results of fitting (**Figure 8** and **Table 2**; see also "Extremal temperature dependence for the triplet luminescence" section). Maxima of curves 1 and 2 are observed outside the given temperature range. The larger Δ *E*ISC energy factor of the intersystem crossing compared to this parameter for curves 3 and 4 explains their high-temperature position. The position of the temperature maximum is also affected by the activation barrier *E*<sup>Q</sup> for the triplet-singlet PL quenching. The maximum is shifted to the high-temperature region if the barrier increases (**Table 2**). This effect is especially pronounced for the amorphous clusters.

In addition, a change in the ion fluence also impacts the kinetic factors of the exciton relaxation, which is reflected in the PL intensity. In particular, there is a significant reduction in the conversion kinetic factor δ*P*ISC (**Table 2**, pp. 3 and 4) in the initial stages of exposure, which leads to a strong increase in the PL intensity (see **Figure 8**, curves 1 and 2). At higher ion fluences, there is increasing of the radiation kinetic factor δ*P*<sup>R</sup> (**Table 2**, pp. 5 and 6), which results in the decreasing of the PL intensity (see **Figure 8**, curves 3 and 4), wherein the relaxation processes, which compete with the triplet PL, are characterized by a faster kinetics (δ*P*ISC > 1 and δ*P*<sup>R</sup> > 1). From **Table 2** one can see that the corresponding kinetic factors are varied in the values that range between 1.5 and 7.

**5.2 A case of indirect excitation**

**Figure 8.**

**Table 2.**

**35**

integrated PL intensity (circles).

for QDs should be performed with Eq. (2) or Eq. (3).

The low density of the QD electronic states and the high density of matrix states

*PL intensity at directly excited Si QDs versus temperature in SiO2/Si films implanted with different ion fluences. The circles denote an experiment [12], while the curves represent the calculated data using Eq. (1). Amorphous Si-clusters, curves (1, 2); crystalline Si-clusters, curves (3, 4). The excitation by argon laser (2.4 eV).*

*Temperature Effects in the Photoluminescence of Semiconductor Quantum Dots*

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

**QD-kind hνPL, eV δ***PISC* **δ***PR* **C Δ***EISC***, eV** *EQ***, eV** *CEQ***, eV** *Tm***, K** Amorphous 1.8 1.10 1.09 1.00 0.0007 0.0090 0.0090 33

Crystalline 1.5 1.50 2.80 1.23 0.0040 0.0540 0.0664 158

*The approximation results of temperature dependencies for the directly excited PL in Si QDs at implanted SiO2 films.*

1.7 1.80 2.65 1.13 0.0017 0.0258 0.0292 75 1.65 7.10 2.91 0.85 0.0100 0.0640 0.0544 271 1.6 2.12 2.06 0.99 0.0110 0.1290 0.1277 438

1.43 2.40 7.20 1.24 0.0050 0.0710 0.0880 163

To check the models describing the indirect QD PL excitation, we have used the experimental data of QD luminescence under the synchrotron excitation (11.6 eV).

cause a low probability for direct excitation of QDs PL by high-energy photons (10–12 eV). By this reason, the analytical processing of PL temperature dependence

The luminescence of Si QDs in amorphous SiO2 films is observed at 1.8 eV (FWHM = 0.15 eV) [4, 5]. **Figure 9** shows the temperature dependences of the

For all curves the correction parameter *C* is close to 1 (**Figures 7** and **8**). It means the energy parameters have a great impact on the form of PL quenching curve. This conclusion is made on the basis of our theoretical (*C* = 1–1.13) evaluations and experimental results (*C* = 0.85–1.24) obtained in the work [12].

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

#### **Figure 8.**

determine which model parameters are more prone to changes in the characteristics

*Energy and kinetic parameters of the nonradiative processes for the curves IT(T) in Figure 7. Comment: For strings 1 and 3–7, the correction is C = 1.13 (δPISC = 1.80, δPR = 2.65); for string 2 C = 1 (δPISC = 1.10, δPR =*

**Curves Δ***EISC***, eV** *EQ***, eV** *C EQ***, eV** *Tm***, K** 0.0020 0.0260 0.0294 33 0.0007 0.0090 0.0090 75 0.0100 0.0260 0.0294 166 0.0200 461 5 0.0300 — 0.0020 0.0400 0.0452 104 0.2000 0.2260 378

To solve this task, we considered the experimental results on PL of Si QDs in SiO2 films obtained by Wang et al. [12]. In this work, authors obtained the Si QDs with different sizes by using the various doses of silicon ions. The emission bands are red-shifted from 1.65 to 1.43 eV with an increasing of ion dose. In addition, the broadening of emission bands from 0.2 to 0.4 eV was observed. However, the emission bands experienced a slight red shift (<0.1 eV) and a change in width

The temperature dependences of the luminescence and their approximation by using Eq. (1) are shown in **Figure 8**. It is seen that the form of quenching curves depends on the ion fluence. On the one hand, еру curves 1 and 2 show a monotonic increase at low fluence. On the other hand, curves 3 and 4 have maxima around 158 and 163 K, respectively, at high fluence. Herewith, all temperature dependences correspond to the fifth type, as was shown by results of fitting (**Figure 8** and **Table 2**; see also "Extremal temperature dependence for the triplet luminescence" section). Maxima of curves 1 and 2 are observed outside the given temperature range. The larger Δ *E*ISC energy factor of the intersystem crossing compared to this parameter for curves 3 and 4 explains their high-temperature position. The position of the temperature maximum is also affected by the activation barrier *E*<sup>Q</sup> for the triplet-singlet PL quenching. The maximum is shifted to the high-temperature region if the barrier increases (**Table 2**). This effect is especially pronounced for the

In addition, a change in the ion fluence also impacts the kinetic factors of the exciton relaxation, which is reflected in the PL intensity. In particular, there is a significant reduction in the conversion kinetic factor δ*P*ISC (**Table 2**, pp. 3 and 4) in the initial stages of exposure, which leads to a strong increase in the PL intensity (see **Figure 8**, curves 1 and 2). At higher ion fluences, there is increasing of the radiation kinetic factor δ*P*<sup>R</sup> (**Table 2**, pp. 5 and 6), which results in the decreasing of the PL intensity (see **Figure 8**, curves 3 and 4), wherein the relaxation processes, which compete with the triplet PL, are characterized by a faster kinetics (δ*P*ISC > 1 and δ*P*<sup>R</sup> > 1). From **Table 2** one can see that the corresponding kinetic factors are

For all curves the correction parameter *C* is close to 1 (**Figures 7** and **8**). It means the energy parameters have a great impact on the form of PL quenching curve. This conclusion is made on the basis of our theoretical (*C* = 1–1.13) evaluations and

of QDs and how they respond to these changes.

*1.09); the intensity scale parameter is I0 = 317 a.u.*

*Quantum Dots - Fundamental and Applications*

(<0.05 eV) with an increasing of temperature.

varied in the values that range between 1.5 and 7.

experimental results (*C* = 0.85–1.24) obtained in the work [12].

amorphous clusters.

**34**

**Table 1.**

*PL intensity at directly excited Si QDs versus temperature in SiO2/Si films implanted with different ion fluences. The circles denote an experiment [12], while the curves represent the calculated data using Eq. (1). Amorphous Si-clusters, curves (1, 2); crystalline Si-clusters, curves (3, 4). The excitation by argon laser (2.4 eV).*


**Table 2.**

*The approximation results of temperature dependencies for the directly excited PL in Si QDs at implanted SiO2 films.*

#### **5.2 A case of indirect excitation**

The low density of the QD electronic states and the high density of matrix states cause a low probability for direct excitation of QDs PL by high-energy photons (10–12 eV). By this reason, the analytical processing of PL temperature dependence for QDs should be performed with Eq. (2) or Eq. (3).

To check the models describing the indirect QD PL excitation, we have used the experimental data of QD luminescence under the synchrotron excitation (11.6 eV). The luminescence of Si QDs in amorphous SiO2 films is observed at 1.8 eV (FWHM = 0.15 eV) [4, 5]. **Figure 9** shows the temperature dependences of the integrated PL intensity (circles).

The results of using Eqs. (2) and (3) for approximation are listed in **Table 3**. The OriginPro software was used for analytical processing of the obtained data and for determining the errors associated with the parameters of model. The analytical dependences of the three-stage (*I*T"(*T*)) and two-stage (*I*T'(*T*)) processes are shown in **Figure 9** as solid and dashed lines, respectively. The fitting error (0.3–0.8%) does not exceed the measurement error (2%) for both cases. It means the two models are in good agreement with the experimental data for investigated temperature range. So, preferred models should be selected, taking into account experimental conditions and physical considerations regarding the energy structure of the SiO2 matrix and nanoparticles.

On the basis of experimental results, the PL quenching for Si QDs starts from the liquid-helium temperature, as shown in **Figure 9**. A characteristic plateau at 100–160 K temperatures is in a good agreement with the chosen models for the indirect excitation and confirms the non-elementary mechanism of the process. The form of experimental PL quenching curve indicates the barrier-free (*E*<sup>7</sup> = 0) character for the transfer of the excitation energy from SiO2 matrix states to Si QDs in accordance with the two-stage scheme (Eq. (2)). The decreasing dependences *I*T"(*T*) show not only the barrier-free excitation transfer (*E*<sup>10</sup> = 0) but also the negative energy factor of population of T1 states (Δ*E*oc < 0) in accordance with the three-stage scheme (Eq. (3)).

high activation barrier (*E*ST = 101–110 meV) for self-trapping of the free excitons in the matrix (**Table 3**), the effective transfer of excitation FE ! QDs is possible only at low temperatures. The efficiency of generation of the self-trapped excitons increases with an increasing of the temperature. As a consequence, the intensity of QD PL strongly decreases due to the additional quenching, appreciable at *T* > 150 K

*Results of approximation for the PL temperature dependences under direct and indirect excitations of Si QDs in*

**Characteristics Two-stage model Three-stage model** Self-trapping barrier of FE *EST*, eV 0.104 0.110 Energy factor of T1 occupation Δ*EOC*, eV — –0.002 Barrier of PL quenching *EQ*, eV 0.006 0.009 Transfer factor of kinetic energy δ*PT\** 125.51 153.07 Kinetic factor of T1 occupation δ*POC* — 0.36 Kinetic factor for PL radiative δ*PR* 1.36 1.09 *\*For the two-step process, δ*P*<sup>T</sup> corresponds to transition 7 (Figure 4) and for the three-step process—transition 10.*

*Temperature Effects in the Photoluminescence of Semiconductor Quantum Dots*

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

The obtained results show that the multistage relaxation of excited states at indirect excitation causes the complex character of the PL temperature dependence for QDs. So, one can ignore the participation of the highly excited states of the confined exciton and consider the two relaxation stages for the analysis of the

In addition, the excitation method of QD luminescence also affects significantly the form of PL quenching curve. Depending on the type of excitation (direct or indirect), the form of the PL quenching curve changes dramatically. On the basis of comparison of the experimental curves (**Figures 7** and **9**), we can assume that indirect energy transfer occurs directly on the triplet state of QD by passing through the singlet state. In another case, the stage of intersystem crossing should be included in the transition scheme. Then there is also the increasing region in the PL

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

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

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

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>

, 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

inversely proportional to the square of its radius (Δ*h*<sup>ν</sup> � *<sup>R</sup>*�<sup>2</sup>

subjected to the effect of strong quantum confinement.

In the present study, we examined the temperature dependences of the Si QD PL

) [1–3, 32, 33]. On the

mechanism of indirect excitation of Si QDs in the SiO2 matrix [6].

temperature dependence at indirect excitation.

**and dimensional factors**

with the previous literature [12].

and 1017 cm�<sup>2</sup>

**37**

(**Figure 9**).

**Table 3.**

*SiO2 films.*

Transitions 10 and 11 (**Figure 4**) in the total scheme of the population process of levels T1 can be ignored for the case of the thin-film SiO2 matrix implanted with silicon and carbon ions, as was proven by the acceptable accuracy of the two-stage model. On the contrary, the energy factor of population of states T1 (Δ*E*oc) has a low absolute value, as was shown in **Table 3**. As noted above, this condition excludes the contribution of highly excited states to the kinetics of thermal relaxation of confined excitons. So, for the describing of PL temperature behavior for Si QDs in SiO2 host at indirect excitation, the two-stage model is quite an acceptable mathematical tool.

The value of the kinetic factor (δ*P*T) (**Table 3**) shows that the energy transfer to the QD occurs relatively slowly. The frequency factor (*p*08) of the exciton selftrapping is 125–150 times larger than the rate of this process. Due to the relatively

#### **Figure 9.**

*PL intensity at indirectly excited amorphous Si QDs versus temperature in SiO2/Si/C films. The triangles— Experimental data (emission at 1.8 eV, excitation at 11.6 eV) [4, 5]. A dashed line denotes Eq. (2) for the two-step process. The solid line represents Eq. (3) for the three-step process.*

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


#### **Table 3.**

The results of using Eqs. (2) and (3) for approximation are listed in **Table 3**. The OriginPro software was used for analytical processing of the obtained data and for determining the errors associated with the parameters of model. The analytical dependences of the three-stage (*I*T"(*T*)) and two-stage (*I*T'(*T*)) processes are shown in **Figure 9** as solid and dashed lines, respectively. The fitting error

(0.3–0.8%) does not exceed the measurement error (2%) for both cases. It means the two models are in good agreement with the experimental data for investigated temperature range. So, preferred models should be selected, taking into account experimental conditions and physical considerations regarding the energy structure

On the basis of experimental results, the PL quenching for Si QDs starts from the

Transitions 10 and 11 (**Figure 4**) in the total scheme of the population process of levels T1 can be ignored for the case of the thin-film SiO2 matrix implanted with silicon and carbon ions, as was proven by the acceptable accuracy of the two-stage model. On the contrary, the energy factor of population of states T1 (Δ*E*oc) has a low absolute value, as was shown in **Table 3**. As noted above, this condition excludes the contribution of highly excited states to the kinetics of thermal relaxation of confined excitons. So, for the describing of PL temperature behavior for Si QDs in SiO2 host at indirect excitation, the two-stage model is quite an acceptable

The value of the kinetic factor (δ*P*T) (**Table 3**) shows that the energy transfer to

the QD occurs relatively slowly. The frequency factor (*p*08) of the exciton selftrapping is 125–150 times larger than the rate of this process. Due to the relatively

*PL intensity at indirectly excited amorphous Si QDs versus temperature in SiO2/Si/C films. The triangles— Experimental data (emission at 1.8 eV, excitation at 11.6 eV) [4, 5]. A dashed line denotes Eq. (2) for the*

*two-step process. The solid line represents Eq. (3) for the three-step process.*

liquid-helium temperature, as shown in **Figure 9**. A characteristic plateau at 100–160 K temperatures is in a good agreement with the chosen models for the indirect excitation and confirms the non-elementary mechanism of the process. The form of experimental PL quenching curve indicates the barrier-free (*E*<sup>7</sup> = 0) character for the transfer of the excitation energy from SiO2 matrix states to Si QDs in accordance with the two-stage scheme (Eq. (2)). The decreasing dependences *I*T"(*T*) show not only the barrier-free excitation transfer (*E*<sup>10</sup> = 0) but also the negative energy factor of population of T1 states (Δ*E*oc < 0) in accordance with the

of the SiO2 matrix and nanoparticles.

*Quantum Dots - Fundamental and Applications*

three-stage scheme (Eq. (3)).

mathematical tool.

**Figure 9.**

**36**

*Results of approximation for the PL temperature dependences under direct and indirect excitations of Si QDs in SiO2 films.*

high activation barrier (*E*ST = 101–110 meV) for self-trapping of the free excitons in the matrix (**Table 3**), the effective transfer of excitation FE ! QDs is possible only at low temperatures. The efficiency of generation of the self-trapped excitons increases with an increasing of the temperature. As a consequence, the intensity of QD PL strongly decreases due to the additional quenching, appreciable at *T* > 150 K (**Figure 9**).

The obtained results show that the multistage relaxation of excited states at indirect excitation causes the complex character of the PL temperature dependence for QDs. So, one can ignore the participation of the highly excited states of the confined exciton and consider the two relaxation stages for the analysis of the mechanism of indirect excitation of Si QDs in the SiO2 matrix [6].

In addition, the excitation method of QD luminescence also affects significantly the form of PL quenching curve. Depending on the type of excitation (direct or indirect), the form of the PL quenching curve changes dramatically. On the basis of comparison of the experimental curves (**Figures 7** and **9**), we can assume that indirect energy transfer occurs directly on the triplet state of QD by passing through the singlet state. In another case, the stage of intersystem crossing should be included in the transition scheme. Then there is also the increasing region in the PL temperature dependence at indirect excitation.
