For a Si atom, band gap energy is around 1.1 eV which means that an electron in valence band needs at least this much energy to jump to conduction band. Also, at room temperature, typically energy of about 25 meV is 'readily' available. This implies that at room temperature no electron should make the transition from valence to conduction band. Still experimentally it is found that electron concentration of about 1.5*10^10/cc is present in conduction band of Si at room temperature. How is this possible?
Hello Nitesh Choudhary,
It is true that the band gap energy of Si is about 1.1 eV and that thermal energy at room temperature is approximately 25 meV (where 1 eV = 1000 meV). While it seems that there should be no electron transitions from the valence band to the conduction band at room temperature, electrons still do make this transition, albeit with a relatively low probability.
The key to understanding this discrepancy lies in the Boltzmann distribution, which governs the probability of a particle having a certain energy in a system. The Boltzmann distribution states that the probability of a particle having energy E is proportional to exp(-E/kT), where k is the Boltzmann constant (approximately 8.62 x 10^(-5) eV/K), T is the absolute temperature, and E is the energy.
At room temperature (approximately 300 K), there is a distribution of energies for the electrons in the valence band. The majority of electrons will indeed have energies lower than the band gap, but there will be a small fraction of electrons with higher energies due to the probabilistic nature of the Boltzmann distribution.
To calculate the concentration of electrons in the conduction band, we can use the concept of intrinsic carrier concentration (n_i). Intrinsic carrier concentration depends on the material's band gap energy (Eg) and temperature (T), and can be found using the following equation:
n_i = N_c * N_v * exp(-Eg / 2kT)
where N_c and N_v are the effective densities of states in the conduction and valence bands, respectively.
Using this equation, we can compute the intrinsic carrier concentration for Si at room temperature, which gives a value of around 1.5 x 10^10 cm^(-3), as you mentioned. This value represents the concentration of electrons in the conduction band and holes in the valence band for an intrinsic semiconductor.
So, the electron concentration in the conduction band of Si at room temperature can be explained by the Boltzmann distribution and the intrinsic carrier concentration. Despite the relatively low thermal energy available, the probabilistic nature of the distribution allows a small fraction of electrons to have sufficient energy to make the transition from the valence band to the conduction band.
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