Question

Cadmium telluride is an important material for solar cells. (a) What is the band gap of CdTe? (b) What wavelength of light would a photon of this energy correspond to? (c) Draw a vertical line at this wavelength in the figure shown in Exercise \(12.75,\) which shows the light output of the sun as a function of wavelength. (d) With respect to silicon, does CdTe absorb a larger or smaller portion of the solar spectrum?

Short answer

The band gap of Cadmium telluride (CdTe) is approximately 1.44 eV. The corresponding wavelength of light for this energy is about \(8.62 \times 10^{-7} m\) or 862 nm. Comparing CdTe to Silicon, which has an absorption wavelength of 1100 nm, CdTe absorbs a larger portion of the solar spectrum.

Step-by-step solution

Finding the band gap of CdTe

Look up the literature to find the band gap value of Cadmium telluride (CdTe). The band gap value for CdTe is approximately 1.44 eV (electron volts).

Calculating the wavelength of light corresponding to the band gap

To calculate the wavelength, we need to recall the energy-wavelength relation which is given by: \(E = \frac{h \cdot c}{\lambda}\) Where E is the energy (in electron volts), h is the Planck's constant (\(6.63 \times 10^{-34} Js\)), c is the speed of light (\(3 \times 10^8 m/s\)), and λ is the wavelength we need to determine. First, we need to convert the energy from electron volts to joules using the relation that 1 eV = \(1.6 \times 10^{-19} J\). The energy of the CdTe band gap in joules is: \(E_{Joules} = 1.44\,\text{eV} \times 1.6 \times 10^{-19}\,\text{J/eV} = 2.304 \times 10^{-19}\,\text{J}\) Now, we can calculate the wavelength using the energy-wavelength relation: \(\lambda = \frac{h \cdot c}{E_{Joules}} = \frac{6.63 \times 10^{-34} Js \cdot 3 \times 10^8 m/s}{2.304 \times 10^{-19} J} \approx 8.62 \times 10^{-7} m\) The wavelength corresponding to the bandgap of CdTe is approximately \(8.62 \times 10^{-7} m\) or 862 nm.

Drawing a vertical line on the given figure at the calculated wavelength

Unfortunately, we're unable to draw on this platform, but you can follow these steps to complete the task: Take the figure from Exercise 12.75 that shows the light output of the sun as a function of wavelength. Locate the value 862 nm on the horizontal wavelength axis. Draw a vertical line from the 862 nm point on the horizontal axis till the curve of solar radiation. This line represents the approximate absorption edge of CdTe material.

Comparing CdTe and Silicon in terms of solar spectrum absorption

In order to compare the solar spectrum absorption of CdTe and Silicon, you need to look up the absorption wavelengths of these two materials. The bandgap for Silicon is approximately 1.12 eV, which corresponds to a wavelength of about 1.10 micrometers (1100 nm). The shorter the wavelength, the higher the energy. Since the absorption wavelength for CdTe is shorter than that of Silicon (862 nm vs. 1100 nm), it can be concluded that CdTe absorbs a larger portion of the solar spectrum compared to Silicon.

Key concepts

Band Gap Energy

Band gap energy is a fundamental property of semiconductors, such as cadmium telluride (CdTe), which is commonly used in solar cell technology. It denotes the minimum amount of energy needed for an electron to break free from its bound state within an atom and become a charge carrier that can conduct electricity. The band gap of CdTe, as mentioned in the provided solution, is approximately 1.44 electron volts (eV).

This characteristic is crucial as it determines at what wavelength the semiconductor will begin to absorb light and convert it into electrical energy. In simple terms, photons with energy equal to or greater than the band gap energy can excite electrons and generate an electric current, while photons with less energy will pass through without contributing to the electricity generation.

The band gap of CdTe allows it to absorb energy from the solar spectrum efficiently, leading to its popularity in the making of photovoltaic cells. A thorough understanding of band gap energy is essential due to its significant impact on the design and efficiency of solar panels.

Solar Spectrum Absorption

Solar spectrum absorption refers to the ability of a material to absorb different wavelengths of light from the sun's spectrum. Each material interacts with the solar spectrum based on its inherent properties, such as its band gap energy. As the provided solution indicates, cadmium telluride (CdTe) solar cells have an edge due to their favorable absorption characteristics within the solar spectrum.

CdTe cells are designed to take advantage of the portion of the solar spectrum that contains a high number of photons with energies around and above their band gap. This region is particularly plentiful in visible and near-infrared light. With a band gap of 1.44 eV, corresponding to a wavelength of around 862 nm, CdTe can absorb a larger portion of the solar spectrum compared to silicon, which has a band gap of 1.12 eV and absorbs at a longer wavelength of about 1100 nm.

This becomes more significant when considering that a good portion of the sun's radiation is emitted in the range where CdTe has a strong absorption. The exercise comparing CdTe to silicon highlights the importance of the match between the solar spectrum and the semiconductor absorption properties in determining the efficiency of solar cells.

Energy-Wavelength Relation

The energy-wavelength relation is a fundamental concept in the study of light and semiconductors. It reflects the inverse relationship between the energy of a photon and its wavelength, described by the equation

\(E = \frac{h \cdot c}{\lambda}\)

where E represents the photon's energy, h is Planck's constant, c is the speed of light, and λ is the wavelength. This equation is key in determining the appropriate wavelength of light that a photon must have to match the band gap energy of a semiconductor like CdTe.

In practical terms, this means that to find the specific type of light that a CdTe solar cell can convert most effectively into electricity, we must use the known band gap energy and apply the energy-wavelength relation. Given the band gap energy of 1.44 eV for CdTe, and after the necessary unit conversions and calculations, the wavelength equates to approximately 862 nanometers, which is within the near-infrared range. The energy-wavelength relationship is essential for understanding how solar cells can be engineered to maximize absorption and efficiency based on the characteristics of the sunlight they receive.