*2.1.3 Self-assembled QD as DFL*

Since it is the Peach-Koehler force in strained layer to bend the TDs to encourage annihilation, self-organized QDs possess an even stronger Peach-Koehler forces, which means QDs are expected to bent TDs more efficiently [48]. Meanwhile, the strain field surrounding QD is 3 dimensions which is superior than 2 dimensions in SLSs.

**Figure 16.** *Summary of the efficiency of dislocation filter for Sample 1, 2 and 3 respectively (Reproduced from Ref. [28]).*

*GaAs Compounds Heteroepitaxy on Silicon for Opto and Nano Electronic Applications DOI: http://dx.doi.org/10.5772/intechopen.94609*

## **Theoretical models.**

Where n(experiment) denotes the number of dislocations just above the DFL, and n(predict) denotes the dislocations predicted by the equation n(x) = D0hm, where m = �0.5. The efficiencies of different types of DFL are shown in **Figure 16**. From the figure, it can be known that almost half of TDs propagate through the first set of DFL regardless of indium composition of InxGa1-xAs layer. However, the sample with In0.18Ga0.82As/GaAs SLSs shows a superior ability in filtering

efficiency compared to others, which achieves over 80%. The demonstrated highest efficiency presents a good balance between TD generation and strain induced to

Apart from the InGaAs/GaAs SLSs, InAlAs/GaAs SLSs is also another great option severing as DFL [45–47]. Due to the larger shear modulus of InAlAs, it is expected that the critical misfit for generating new TDs is much larger than that of InGaAs. We compared In0.15Ga0.85As/GaAs DFL and In0.15Al0.85As/GaAs DFL by growing InAs/GaAs QD samples on Si (100) substrates [41]. The In0.15Ga0.85As/ GaAs DFL composed three repeats of 5 period of 10-nm In0.15Al0.85As and 10-nm GaAs SLS separated by 400 nm GaAs spacer layer, while the In0.15Al0.85As/GaAs DFL had almost same structure except replacing the In0.15Ga0.85As to In0.15Al0.85As. EPD were counted for both samples. After three sets of SLSs, the defects density of

with InGaAs/GaAs DFL was round 5 � <sup>10</sup><sup>6</sup> cm�<sup>2</sup> [41]. In addition, the sample with InAlAs/GaAs DFL had a higher PL peak intensity as well as thermal activation

Since it is the Peach-Koehler force in strained layer to bend the TDs to encourage annihilation, self-organized QDs possess an even stronger Peach-Koehler forces, which means QDs are expected to bent TDs more efficiently [48]. Meanwhile, the strain field surrounding QD is 3 dimensions which is superior than 2 dimensions

*Summary of the efficiency of dislocation filter for Sample 1, 2 and 3 respectively (Reproduced from Ref. [28]).*

, while the other one

the sample with InAlAs/GaAs DFL was around 2 � <sup>10</sup><sup>6</sup> cm�<sup>2</sup>

energy compared to the sample with InGaAs/GaAs [41].

*2.1.3 Self-assembled QD as DFL*

in SLSs.

**Figure 16.**

**142**

annihilate TDs.

*Post-Transition Metals*

Several parameters need to be considered when using self-organized QDs as DFLs including QD composition, size, areal density, and the number of dots. The theoretical simulation of the effectiveness of dislocation bending is developed by J. Yang et al. [48], which assuming QD islands are coherently strained with pyramidal in shape. The energy ΔErel releases when the MD formed to bend the TDs can be calculated through

$$\frac{\Delta E\_{rel}}{L} = \frac{2G\_{det}(1+\nu)}{(1-\nu)} f\_{\sharp\sharp} b\_{\sharp\sharp} h\_{\sharp}$$

While the dislocation self-energy ΔEdis can be described as

$$\frac{\Delta E\_{di}}{L} = \frac{1}{2\pi} \frac{G\_{buff}G\_{dot}}{G\_{buff} + G\_{dot}} b^2 \left(\frac{\mathbf{1} - \nu \cos^2 \beta}{\mathbf{1} - \nu}\right) \left[\ln\left(\frac{\mathbf{2}r}{b}\right) + \mathbf{1}\right]$$

The bending will occur when the ΔErel ≥ ΔEdis. Here, L is the length of the MD, Gdot (Gbuff) is the shear module of dot (buffer layer), ν is the Poisson ration,b is the Burger's vector, beff is the project of Burger's vector on the buffer layer, feff is the effective lattice mismatch between the QD and the underlying buffer layer, h is the height of QD, β is the angle between the Burger's vector and the dislocation line, r denotes an outer cutoff radius of the dislocation strain field.

According to the simulations, the bending area ratio, which denotes the bending area divided by the area of QD bases, is shown in **Table 3**. InAs QDs are proved to be the most suitable self-organized QD serving as dislocation filters with the largest bending area and largest critical layer numbers for QD multilayers [48].

#### **Experiment Techniques**

Considering the theory and results above, InAs QDs DFL has the highest efficiency compared with other QD DFLs for GaAs monolithically grown on Si. In order to investigate the TD behavior in QD DFL region, a buffer structure shown in **Figure 17** is grown with N-type doped InAs QD dislocation filter on Si (001) substrate with 4° misorientation towards [111]. A thin (<2 μm) GaAs layer is first grown by MOVPE with free of antiphase domain. The TDD at its surface is estimated to be (2–5) � <sup>10</sup><sup>7</sup> cm�<sup>2</sup> . The dislocation filter consists of 10 layers of InAs QD separated by 50 nm GaAs layers. On the top of QD dislocation filter, a 800 nm GaAs is grown.

#### **Effectiveness of DFL composed of QDs**

Cross-sectional TEM measurements were applied to investigate the propagation of dislocations in the QD DFLs. Images were obtained with various g, including [2,2,0], [1,1,1], and [0,0,4] as shown in **Figure 18a, b** and **c**, respectively. Two different types of TDs can be observed: pure edge dislocation labeled as C and 60° mixed TDs labeled as A and B. It is obvious from the cross-sectional TEM images


**Table 3.**

*Bending area ratios for different QDs (Reproduced from Ref. [48]).*

technique has promoted the implement of III-V materials directly grown on Si such

As germanium material has lattice parameter and thermal expansion coefficient

heteroepitaxy on silicon developments to reduce the structural defects in the GaAs layer [31, 41, 51–53]. This way, we avoid additional threading dislocation nucleation. Currently, the TDD in a 1.5 μm thick Ge-buffer on Si(100) is in the 10<sup>7</sup> cm<sup>2</sup> range by using [54, 55] a thermal cycle annealing (TCA). The **Figure 19a**, extract from the works of Bogumilowicz et al. [56], shows the TDD evolution in function of the Ge buffer and GaAs total thickness, with a GaAs layer fixed at 270 nm thick. The

described in the previous section. The TDD was estimated by using three methods: (i) from the XRD rocking curve width, the value is extracted with the Ayer's model [57] (ii) by counting the dark spots on the cathodoluminescence (CL) image of the GaAs surface, (iii) by counting the pits on the AFM image of the GaAs surface. Whatever the method, the authors show that the TDD tends to reach a plateau at a

method is the wafer bowing due to the difference between the thermal expansion coefficients (around 120% for Ge and Si). The **Figure 19b** is a plot of the 300 mm wafer bow versus the film thickness. For the thickest Ge buffer layer (1.38 μm) the bow is measured at 240 μm. Such a value is still a hurdle for the wafer handling

Selective growth method is often used in heteroepitaxy of semiconductors where cavities are used to block geometrically the propagation of structural defects that generate at the interface of lattice mismatch semiconductors. Different techniques could be implemented such as Epitaxial Lateral Overgrowth (ELOG) and Aspect

ART allows to block inside the cavities some of the threading dislocations and planar defects propagating perpendicularly to the trench direction. Still, a few structural defects propagate through the film. **Figure 20a** summarizes the principle

*(a) Plot of the TDD in the GaAs overlayers as a function of the total Ge + GaAs thickness. The light gray area corresponds to the expected TDD values in Ge or GaAs single layers as a function of thickness. Estimated error bars are shown for the TDD extracted from AFM and CL. The TDD error bar for the XRD data is* 107*cm*<sup>2</sup>*.*

Ratio Trapping (ART). We will describe more in details the last one.

. Nevertheless, the downside of the Ge virtual substrate

close to those of the GaAs, a common strategy is to benefit from all the Ge

*GaAs Compounds Heteroepitaxy on Silicon for Opto and Nano Electronic Applications*

GaAs layer is smooth (<1 nm RMS) and free of APBs thanks to the process

as growth of III-V lasers on Si substrates [27, 50].

*DOI: http://dx.doi.org/10.5772/intechopen.94609*

value around 3 <sup>10</sup><sup>7</sup> cm<sup>2</sup>

**Figure 19.**

**145**

**2.2 GaAs growth on Germanium strain relaxed buffer**

and processing with the 200/300 mm foundry tools.

**2.3 TDD reduction by selective area growth**

*(b) Plot of the substrate bow versus the total Ge + GaAs thickness.*

**Figure 17.**

*GaAs grown on Si with 10 InAs QD layer as dislocation filter. (reproduced from Ref. [48]).*

**Figure 18.**

*Cross-section TEM images of dislocation propagation in the ten-layers InAs QD with various diffraction conditions: (a) g = [2,*2*,0], (b) g = [1,*1*,1], (c) g = [0,0,4]. (Reproduced from Ref. [48]).*

that the QD DFL can bend 60° mixed TDs effectively. In addition, pure edge TDs, which cannot be blocked by the 2-D SLS [49], can be terminated within the QD DFL. Although the detail of this termination is not fully understood, it is believed that the formation of a dislocation loop or the annihilation with a dislocation with reverse Burger's vector result in the termination [48]. Recently, with the help InAs QD DFL, J. Wang et al. demonstrated a low dislocation density of 2 <sup>10</sup><sup>6</sup> cm<sup>2</sup> [50], with a high efficiency of 96% calculated.
