Social Studies High School

Fermi level in intrinsic semiconductors Using the values of the density of states effective masses m*e and m*h in Table 5.1, find the position of the Fermi energy in intrinsic Si, Ge, and GaAs with respect to the middle of the bandgap (Eg∕2).

Answers

Answer 1

In intrinsic semiconductors, the Fermi level lies at the middle of the bandgap (Eg/2) at absolute zero temperature. However, at finite temperatures, the position of the Fermi level shifts slightly due to the presence of thermally excited carriers.

Fermi level in intrinsic semiconductors

To determine the position of the Fermi level in intrinsic Si, Ge, and GaAs at room temperature, we need to use the following equation:

[tex]n_i = N_c exp[-(Eg/2 - E_F)/(k_B T)] (1)[/tex]

where

n_i is the intrinsic carrier concentration, [tex]N_c[/tex] is the effective density of states in the conduction band, Eg is the bandgap energy,[tex]E_F[/tex] is the Fermi level energy, [tex]k_B[/tex] is the Boltzmann constant, and T is the temperature.

Taking the logarithm of both sides of equation (1), we get:

[tex]ln(n_i) = ln(N_c) - (Eg/2 - E_F)/(k_B T) (2)[/tex]

Rearranging equation (2), we get:

[tex]E_F = Eg/2 - k_B T ln(n_i/N_c) (3)[/tex]

Using the values of [tex]N_c[/tex], me, and mh from Table 5.1, we can calculate the intrinsic carrier concentration for Si, Ge, and GaAs at room temperature (T = 300 K) using the following equation:

[tex]n_i = 2 [(2\pi$ m_e$ k_BT/h^2)^3/2] exp[-E_g/(2k_BT)] (4)[/tex]

where h is the Planck constant.

Substituting the values of N_c, me, and mh from Table 5.1 and T = 300 K into equation (4), we get:

[tex]For Si: n_i = 1.01 \times 10^10 cm^-3\\For Ge: n_i = 2.37 \times 10^13 cm^-3\\For GaAs: n_i = 1.79 \times 10^6 cm^-3[/tex]

Substituting these values into equation (3), we can calculate the position of the Fermi level in each material with respect to the middle of the bandgap (Eg/2) as follows:

[tex]For Si: E_F = 0 eV\\For Ge: E_F = -0.12 eV\\For GaAs: E_F = 0.17 eV[/tex]

Therefore, at room temperature, the Fermi level in intrinsic Si lies exactly at the middle of the bandgap, while in Ge and GaAs, it lies slightly below and above the middle of the bandgap, respectively.

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The process by which living things give rise to offspring is called reproduction. Reproduction is a fundamental characteristic of living organisms, and it is essential for the survival and continuation of a species.

Reproduction can be divided into two broad categories: sexual and asexual reproduction. Sexual reproduction involves the fusion of gametes (reproductive cells) from two individuals, resulting in offspring that inherit genetic traits from both parents. In contrast, asexual reproduction involves the production of offspring without the involvement of gametes. Asexual reproduction can occur through various mechanisms such as budding, fragmentation, and regeneration.In both sexual and asexual reproduction, the offspring inherit genetic material from the parent(s). This genetic material is encoded in the DNA, which contains the instructions for the development and functioning of the organism. The passing on of genetic material from one generation to the next allows for the evolution of species over time. Reproduction is a complex and diverse process, varying among different groups of organisms. However, the ultimate goal of reproduction is to ensure the survival of the species by producing offspring that can grow, develop, and reproduce themselves.

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