A p-type semiconductor has acceptor levels 57 meV above the valence band.Find the maximum wavelength of light which can create a hole.

To determine the maximum wavelength of light that can create a hole in a p-type semiconductor, we first need to understand the relationship between energy and wavelength. The energy required to create a hole corresponds to the energy difference between the valence band and the acceptor level. In this case, the acceptor level is 57 meV above the valence band.

Energy-Wavelength Relationship

The energy of a photon can be calculated using the equation:

E = h * f

Where:

• E is the energy of the photon in joules.
• h is Planck's constant (approximately 6.626 x 10^-34 J·s).
• f is the frequency of the photon in hertz.

We can also relate frequency to wavelength using the equation:

c = f * λ

Where:

• c is the speed of light (approximately 3.00 x 10⁸ m/s).
• λ is the wavelength in meters.

Calculating the Energy in Joules

First, we need to convert the energy from millielectronvolts (meV) to joules. The conversion factor is:

1 eV = 1.602 x 10^-19 J

Thus, to convert 57 meV to joules:

E = 57 meV * (1.602 x 10^-19 J/eV) * (10^-3 eV/meV)

E = 57 x 1.602 x 10^-22 J

E ≈ 9.13 x 10^-15 J

Finding the Frequency

Now that we have the energy in joules, we can find the frequency:

f = E / h

f = (9.13 x 10^-15 J) / (6.626 x 10^-34 J·s)

f ≈ 1.38 x 10¹⁹ Hz

Calculating the Wavelength

Finally, we can find the wavelength using the speed of light equation:

λ = c / f

λ = (3.00 x 10⁸ m/s) / (1.38 x 10¹⁹ Hz)

λ ≈ 2.17 x 10^-11 m

To express this in nanometers (1 nm = 10^-9 m):

λ ≈ 0.0217 nm

Summary

The maximum wavelength of light that can create a hole in the p-type semiconductor, given that the acceptor level is 57 meV above the valence band, is approximately 0.0217 nm. This wavelength falls within the high-energy range of the electromagnetic spectrum, indicating that only very high-energy photons (like X-rays or gamma rays) can excite electrons from the valence band to the acceptor level, thereby creating holes.

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