*1.3.2 Effect of tensile strain on Ge band structure*

Efficient direct gap light emission in Ge requires a large amount of electrons in the direct valley. The ratio of the number of the direct valley electrons to the indirect L valleys electrons is determined by the energy difference between the direct band gap and the indirect band gap at quasi-equilibrium. Band structure is associated with crystal lattice, which can be changed by the existence of strain. This effect can be calculated using a strain-modified k·p formalism, which is known to provide an accurate description of the valence and conduction bands all over the Brillouin zone [14]. Such a calculation shows that strain changes the energy levels of the

**75**

**Figure 5.**

*strain [14].*

*New Material for Si-Based Light Source Application for CMOS Technology*

direct Γ valley, the indirect L valleys the light-hole band, and the heavy-hole band relative to vacuum level. Moreover, the light-hole and the heavy-hole band become nondegenerate and separate at Γ point. **Figure 5** illustrates the variation of direct and the indirect band gaps of Ge under strain [14]. We can see both the direct band gap and the indirect band gap shrink with tensile strain and the direct band gap shrinks faster than the indirect band gap. The direct band gap becomes equal to the indirect band gap at ε// ≈ 1.8–1.9% where Ge becomes a direct band gap material. The carrier distribution and the light emission properties of 1.8% tensile-strained Ge under injection are schematically shown in **Figure 6**. Since the Ge becomes a direct gap material, a considerable amount of the excess electrons occupying the direct Γ valley capable of radiative recombination leading to efficient direct gap light emission. The overall emission efficiency of the strained Ge is comparable to

Biaxial tensile strain is thus an effective way to transform Ge to a direct band gap

Firstly, highly strained, high-quality single crystalline Ge film is difficult to form because the large lattice change causes thermodynamic instability resulting in dislocations, surface roughness, and other lattice defects. Tensile strain can be induced either by lattice mismatch or by thermal mismatch. The former approach requires a substrate material with larger lattice constant than that of Ge. The latter approach

*Energy dependence at low temperature (4 K) of the Γ, Δ2, L, and lh extrema as a function of the in-plane biaxial strain; (b) variations of the direct and indirect band gap energies as a function of the in-plane biaxial* 

*DOI: http://dx.doi.org/10.5772/intechopen.84994*

that of direct band gap semiconductors.

material, nevertheless two issues exist:

**Figure 4.** *Distributions of electrons and the holes in Ge at equilibrium and under injection [3].*

#### *New Material for Si-Based Light Source Application for CMOS Technology DOI: http://dx.doi.org/10.5772/intechopen.84994*

*Silicon Materials*

Eg = 0.664 eV. Because the direct energy gap EΓ2 is much larger than EΓ1 and Eg, almost no electrons can occupy such high energy levels. Therefore, we refer direct band gap only to EΓ1 throughout this thesis. The part of the conduction band near Γ point is called direct valley and the part near L point is called indirect valley. Since the energy is 4-fold degenerate with regard to the changes of the secondary total

**Figure 4** shows the electron and the hole distributions of Ge at equilibrium at equilibrium and under injection conditions. At equilibrium, most of the thermally activated electrons occupy the lowest energy states in the indirect L valleys while it is worth noting that in a direct band gap material such as GaAs or InGaAs most of

Under injection conditions, there are a non-negligible amount of electrons in the Γ valley owing to the small energy difference (140 meV) between the direct band gap and the indirect band gap of Ge, as shown in **Figure 4(b)**. The excess electrons in the Γ valley lead to recombination with the holes in the valence band, which is a highly efficient light emission process because that the direct band-to-band radiative recombination is generally faster than the nonradiative recombinations, such as Auger and defect-assisted processes. But the overall light emission efficiency is very low because most of the injected electrons, staying in the L valleys, recombine nonradiatively due to a slower indirect phonon-assisted radiative recombination than the non-radiative recombinations. On the contrary, the light emission in a direct band gap material such as InGaAs is very efficient because almost all injected electrons are in the Γ valley thus recombine radiatively. To improve the light emission efficiency in Ge, more injected electrons are required to be pumped into Γ valley at the same carrier injection level. Thus, the band structure of Ge can be

Efficient direct gap light emission in Ge requires a large amount of electrons in the direct valley. The ratio of the number of the direct valley electrons to the indirect L valleys electrons is determined by the energy difference between the direct band gap and the indirect band gap at quasi-equilibrium. Band structure is associated with crystal lattice, which can be changed by the existence of strain. This effect can be calculated using a strain-modified k·p formalism, which is known to provide an accurate description of the valence and conduction bands all over the Brillouin zone [14]. Such a calculation shows that strain changes the energy levels of the

angular-momentum quantum number, four L valleys are considered.

the electrons stay in the direct Γ valley.

engineered to accomplish this goal.

*1.3.2 Effect of tensile strain on Ge band structure*

*Distributions of electrons and the holes in Ge at equilibrium and under injection [3].*

**74**

**Figure 4.**

direct Γ valley, the indirect L valleys the light-hole band, and the heavy-hole band relative to vacuum level. Moreover, the light-hole and the heavy-hole band become nondegenerate and separate at Γ point. **Figure 5** illustrates the variation of direct and the indirect band gaps of Ge under strain [14]. We can see both the direct band gap and the indirect band gap shrink with tensile strain and the direct band gap shrinks faster than the indirect band gap. The direct band gap becomes equal to the indirect band gap at ε// ≈ 1.8–1.9% where Ge becomes a direct band gap material. The carrier distribution and the light emission properties of 1.8% tensile-strained Ge under injection are schematically shown in **Figure 6**. Since the Ge becomes a direct gap material, a considerable amount of the excess electrons occupying the direct Γ valley capable of radiative recombination leading to efficient direct gap light emission. The overall emission efficiency of the strained Ge is comparable to that of direct band gap semiconductors.

Biaxial tensile strain is thus an effective way to transform Ge to a direct band gap material, nevertheless two issues exist:

Firstly, highly strained, high-quality single crystalline Ge film is difficult to form because the large lattice change causes thermodynamic instability resulting in dislocations, surface roughness, and other lattice defects. Tensile strain can be induced either by lattice mismatch or by thermal mismatch. The former approach requires a substrate material with larger lattice constant than that of Ge. The latter approach

#### **Figure 5.**

*Energy dependence at low temperature (4 K) of the Γ, Δ2, L, and lh extrema as a function of the in-plane biaxial strain; (b) variations of the direct and indirect band gap energies as a function of the in-plane biaxial strain [14].*

**Figure 6.** *Electron and hole distributions and light emission at 1.8% tensile-strained Ge.*

requires different thermal expansion coefficient between Ge and the substrate material, which is adopted in this research. Up to 0.25–0.30% tensile strain has been achieved in Ge epitaxially grown on Si substrate, which will be discussed later. The second issue is the excessive change of the band gap in highly tensile-strained in Ge. Both the direct band gap and the indirect band gap become 0.53 eV at 1.8% tensile strain, as shown in **Figure 6**. This optical band gap is corresponding to an emission wavelength of about 2300 nm, which is far away from the 1550 nm telecommunication wavelength band, which is also the primary choice for Si photonics. These two issues suggest that very high tensile strains are not favorable in both material growth and photonics applications. Thus, the increase of the number of the injected excess electrons in the Γ valley owing to strain effect is limited. This problem can be solved by n-type doping in Ge.
