**5. GaAs Fermi level and lattice constant**

**Figure 7** shows that the drawing of the energy band of the semiconductor, which demonstrates the bandgap along with valence and conduction electrons. An electron leaves a hole in the valence band on moving to the conduction band from

*Elastic, Optical,Transport, and Structural Properties of GaAs DOI: http://dx.doi.org/10.5772/intechopen.94566*

**Figure 7.**

*Room-temperature band gap energy, Eg, as a function of lattice constant for several semiconductors. Lines connecting binary compounds such as GaAs and AlAs represent alloy composition with either a direct band gap (thick solid line) or indirect band gap (thin red line). The III–V and II–VI semiconductor compounds in the figure have the zinc blende crystal structure. Si and Ge have the diamond crystal structure [40].*

the valence band. For the other electrons in the valence band energy levels, this hole is an empty state and behaves in a manner similar to a +*ve* charged particle in the valence band. The number of electrons in the conduction band per unit volume, written as cm<sup>3</sup> , is counted to quantify the electron concentration, and is represented by 'n' [41, 42].

The density of holes in the valence band equals the density of electrons in the conduction band.

$$\mathbf{n} = \mathbf{1}$$

$$N\_C = \exp\left[\frac{E\_F - E\_C}{K\_B T}\right] = N\_v \exp\left[\frac{E\_v - E\_F}{K\_b T}\right] \tag{5}$$

In the above formula,

*EF* - Fermi energy.

*NV* - effective density of states in the valence band.


T - temperature in K.

*NC* - effective density of states in the conduction band. Reordering the above equation, we have

$$\exp\left(\frac{2E\_F - E\_C - E\_V}{K\_B T}\right) = \frac{N\_V}{N\_C} \tag{6}$$

Taking log we have

$$\left(\frac{2E\_F - E\_C - E\_V}{K\_B T}\right) = In \frac{N\_V}{N\_C} \tag{7}$$

Solving for *EF*

$$E\_F = \frac{E\_C + E\_V}{2} + \frac{K\_B T}{2} \ln\left(\frac{N\_V}{N\_C}\right) \tag{8}$$

It is in the middle of the bandgap that we have the Fermi energy (*EC* + *EV*)/2. Therefore, as shown in 7, the energy bandgap latticed matched for several semiconductors that is related to GaAs and band alignments for sever III-V semiconductor with GaAs (**Figure 8**).

#### **Figure 8.**

*Band alignments for sever III-V semiconductor with GaAs. (a) Lattice constants and band gaps of different semiconductor materials. The lattice constants of Ge and GaAs are close to a variety of semiconductors with different band gaps, thereby commonly used as substrates for tandem cells. (b) Schematics of a triple-junction tandem cell with optimized compositions of InGaAs and InGaP, which correspond to the blue dots in (a). A buffer layer has to be applied to accommodate the lattice mismatch between the Ge substrate and In 0.17 Ga 0.83 As; (c) Proposed latticematched GeSn/InGaAs/InGaP tandem cell [42].*

## **6. GaAs transport properties**

An ionic bond exists between the electrons in the valence band of GaAs atoms. Therefore, in solids, they are not free to transport. However, they can move through a solid if the electron gets excited to the conduction band. Hence, an electron leaves a hole in the valence band on moving to the conduction band from the valence band. An electron jump from one bond to another enables the hole to move in the valence band. Further, these holes and electrons can move upon affected by an electric field [43–45].

The equation that helps derive the acceleration of the electrons (ae) is-

*Elastic, Optical,Transport, and Structural Properties of GaAs DOI: http://dx.doi.org/10.5772/intechopen.94566*

$$a\_{\epsilon} = \frac{eE\_{\text{x}}}{m\_{\epsilon}} \tag{9}$$

Where *me*is the electron's rest mass and *EX* is the electric field. Under an electric field, the interaction of electrons with the solid atoms should also be considered.

In the case of an electron in a solid, under an external field, the interaction with the solid atoms should also be taken into account. Let this interaction of electrons with the atoms of the solid be summed up as P *fint* [46, 47].

$$a\_{\varepsilon} = \frac{eE\_{\text{x}} + \sum f\_{\text{int}}}{m\_{\varepsilon}} \tag{10}$$

The conduction electrons are initially in the lowest energy valley, Γ minimum. Here, they are distinguished by a low effective mass and have high mobility. On applying the electric field, these electrons are rapidly accelerated by the field to high velocities: they gain kinetic energy. The electrons' ability gains enough energy to transfer from this valley to the next higher valley, the L minimum. These upper valleys are distinguished by a larger effective mass, and consequently both lower electron mobility and a greater density of available electron positions. The great density of states encourages transfer to these valleys of electrons with suitable energy. There is a fall in the average velocity of all the electrons as the energetic electrons transfer to the upper levels. There is much work available which is focused on the calculation of hot electron transport properties in GaAs. Gallium arsenide exhibits the `transferred electron' which is commonly known as the TE effect. This transfer of electrons from one region to another energy band structure is an electric-induced field transfer. It has high electron mobility, with a negative resistance being observed and has a small dielectric constant. This is primarily because of extensive utilization of GaAs in ultrahigh frequency, high-temperature resistance and low power circuits and devices [48–53].

$$\text{Average velocity } \nu = \frac{n\_{\Gamma}\nu\_{\Gamma} + n\_{r}\nu\_{r}}{n\_{\Gamma} + n\_{l}} \tag{11}$$
