**2. GaAs and semiconductors direct bandgap concept**

The band structure is the major part of the semiconductors. Briefly explaining it, at absolute zero, a bandgap or an energy gap separates the conduction band (lowest empty band) with the valence band (highest filled band). Therefore, at T = 0, electricity is not conducted by the material. The electrons are enabled to be excited into the conduction band through several processes, such as optical absorption or thermal excitation, at finite temperatures and electrical conduction is allowed as there are empty states in the valence band. Energy, in the forms of heat or photons, is released when the electrons return to the valence band [12, 13].

As mentioned in **Figure 1**, two types of bandgaps are there based on different conditions. The first one is if, over the top of the valence bond, the bottom of the conduction band does not rest. As a result of this, it is called an indirect gap. Also, photon is necessary in order to provide the momentum required to reach the state in the conduction band, and the electronic transition to happen. However, in case of GaAs and other direct band type semiconductor, the bottom of the conduction band site and the top of the valence band are on top of each other, Therefore even without a change in the wave vector, the electron is able to get excited from the

**Figure 1.** *Schematic of the valence band, direct bandgap, and indirect bandgap conduction bands [13].*

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

valence band. A photon on absorbing required energy is sufficient enough for this. Moreover, through the emission of a photon, transition to the valence band from the conduction band can easily be done by the electron. While no interaction of photon is required, emission of light energy of the desired wavelength of 850 nm bandgap occurs and it allows the direct band recombination of holes and electrons. In the absence of defects, the energy released by the dominant mechanism of the indirect bandgap is by photons via electromagnetic radiation. However, photons release energy in the form of heat in the case of indirect bandgap semiconductors [14–16].

Being a good optoelectronic material, direct bandgap in GaAs is considered a useful material in the field of optoelectronics and other electronic fields and is used comprehensively in semiconductor lasers as well as light-emitting diodes. Its use has also been encouraged in the making of high-efficiency solar cells, Gunn diodes, Infrared LEDs, solid-state detectors and radar systems. We have a classification of 1–3 categories depending upon the magnitude of bandgap energy of the materials, namely, narrow, mid and wide-bandgap. Of all the properties of a semiconductor, the presence of energy gap leads all others [16, 17].

Not only band-gap engineering permits the making of band diagrams that have continuous as well as arbitrary band-gap variations, but it is also considered among the strongest tools for the new semiconductor devices and materials. For a specific application, the transport properties of holes, as well as electrons, may be continuous and independent. This approach leads us to a new generation of devices having unique capabilities ranging from resonant tunneling transistors to solid-state photomultipliers. More than for any semiconductor, many band structures for GaAs are precisely known. **Figures 2** and **3** make it clear, showing 1.519 eV as the fundamental energy gap for Gallium Arsenide. Also, the high-temperature performance of GaAs is largely attributed to its wide bandgap [20–22].

Other than this, photoconductivity, a feature semiconductor exhibit under suitable trial conditions is another benefit associated with the bandgap [23]. This occurs when an increase in electrical conductivity happens when an incident light falls on a semiconductor. The suitability of the semiconductor material in optoelectronic devices is also decided by its photoconductive response. Such materials which respond well to the photoconductivity, find themselves useful in the making of infrared sold state detectors. Also, in GaAs, the transport properties of hot electrons

**Figure 2.** *Structure of GaAs energy band gap [18].*

**Figure 3.**

*(a) Calculated band structure of GaAs using the tight binding method. (b) Sketch of GaAs band structure near the Γ-symmetry point showing conduction band, heavy hole band (hh), light hole band (lh), and split-off band (so) in the X [100] and L [19].*

are largely affected due to the bandgap. Alloying is another controllable bandgap which useful property of the GaAs [22, 24–26].

The usefulness of GaAs and its alloys in optoelectronics such as sold state lasers and LEDs lies in the bandgap of GaAs which, in the infra-red range results in the emission of photon. The ability of GaAs to retain their semiconductor properties at high temperatures, giving stability to the GaAs comes from the wider bandgap of GaAs [19]. **Figure 3** shows that Calculated band structure of GaAs using the tight binding method with different semiconductor materials.

## **3. GaAs and semiconductor carrier density**

That GaAs is an extremely poor conductor is corroborated by the fact that GaAs has low flow intrinsic carrier density when present in an undoped or pure form. Hence it is mostly considered as semi-insulating. Adding the dopants of either the p- or the n- that is the positive and the negative types respectively, alters this property. Many active devices have been able to be made on a single substrate due to this semi-insulating property, where each device's electrical isolation is provided by the GaAs. For contraction of the electronic circuitry, this characteristic has been found be quite important [27, 28].

With regards to the transport properties, two important questions that come up where the incorporation of dopants has been done – a) mobility, b) effective carrier concentration [29, 30].

$$m\_i = \sqrt{N\_C N\_V} \exp\left(-\frac{E\_\text{g}}{K\_B T}\right) \tag{1}$$

*Nc*and *NV*, the effective density of states at the band edges, are dependent on temperature and the effective mass of the electron and holes respectively.

$$N\_C = 2\left(\frac{2\pi m^\* \, \_eK\_B T}{h^2}\right)^{\frac{3}{2}}\tag{2}$$

$$N\_v = 2\left(\frac{2\pi m^\* \, \_hK\_B T}{h^2}\right)^{\frac{3}{2}}\tag{3}$$

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

**Figure 4.** *Bandgap energy inverse T for Ge, Si, GaAs in the range 200–1000 K. T [31].*

The conductivity is given by

$$
\sigma\_i = n\_i e (\mu\_e + \mu\_h) \tag{4}
$$

Eq. (1) and **Figure 4** can be used to understand the effect of temperature on the concentration of the carrier. It shows the entry of temperature in both exponential as well as pre-exponential terms. There are two effects of increased temperature [31, 32]:


## **4. GaAs crystal structure**

In solid-state physics, the central theoretical problem happens to be the determination of the energy bands. In other words, in case of solids, the central theoretical problem is the calculation of energy levels of electrons. In order to calculate physical properties such as mechanical properties, magnetic order, optical dielectric or the vibrational spectra, in principle knowledge of the electrons and the energies associated with them is required. In contrast, calculation of lattice constants and other bulk ground state properties such as atomic positions and bulk modulus is considered to be important in physics associated with condensed matter. Such bulk calculations not only help understand as well as characterize the mechanical properties of the matter, but they also help predict their properties in extreme conditions [33–35].

Having a basis and a cubic lattice that is two face centered, the structure of crystal of GaAs is a zincblende structure or cubic sphalerite. In the classic basis, at the origin of the lattice, there is one GaAs molecule. From (0,0,0), the vector of one atom to another at (1/4,1/4,1/4) of the molecule constitutes the basis. Two FCC lattices, one of as while the other being of Ga can also form a crystal as shown in

**Figure 5**. While arsenic atoms are represented in orange color, the Gallium ones are shown in purple color. As shown, there are 4 arsenic atoms against 14 gallium atoms. This makes a tetrahedral bond, similar to the one in a diamond lattice, but replaced with Ga and as where each Ga is connected to four other atoms. It shows ionic bonding with the presence of two types of atoms [37–39] (**Figure 6**).

**Figure 5.** *P-V plot of GaAs up to 25 GPA [36].*

**Figure 6.** *The crystal structure of GaAs cubic unit cell of GaAs [38].*
