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 with exercise \(12.21\), which shows the light output of the Sun as a function of wavelength. (d) With respect to silicon, does CdTe absorb a larger or smallerportion of the solar spectrum?

Short answer

The band gap of CdTe is approximately 1.45 eV, and the corresponding wavelength of light is 853 nm. When comparing the absorption of the solar spectrum, CdTe absorbs a larger portion of high-energy photons (shorter wavelengths) compared to Silicon, while Silicon absorbs a larger portion of low-energy photons (longer wavelengths).

Step-by-step solution

(Step 1: Finding the Band Gap of CdTe)

To find the band gap of CdTe, a quick search in reference sources or materials gives us the value. The band gap of CdTe is approximately 1.45 eV (electron volts).

(Step 2: Calculating the Wavelength of Light)

To calculate the wavelength of light that corresponds to the energy of the band gap, we need to use the following formula that relates energy to wavelength: \(E = \dfrac{hc}{\lambda}\) where, E = energy (1.45 eV), h = Planck's constant (4.135667696 × 10^(-15) eV·s), c = the speed of light (approximately 3.00 × 10^8 m/s), and λ = wavelength to be calculated. First, we need to convert the energy from eV to Joules by multiplying it by the charge of an electron (1 eV = 1.602176634 × 10^(-19) J). \(E_J = 1.45 \hspace{2pt}\text{eV} × 1.602176634 × 10^{-19} \hspace{2pt}\text{J/eV} = 2.3225 × 10^{-19} \hspace{2pt}\text{J}\) Now, we can find the corresponding wavelength: \(\lambda = \dfrac{hc}{E_J} = \dfrac{(4.135667696 × 10^{-15} \hspace{2pt}\text{eV}·\text{s})(3 × 10^8 \hspace{2pt}\text{m/s})}{2.3225 × 10^{-19} \hspace{2pt}\text{J}} = 8.53 × 10^{-7} \hspace{2pt}\text{m}\) The corresponding wavelength of light is 853 nm (nanometers).

(Step 3: Sketching the Wavelength on a Light Output Graph)

To sketch the light output of the Sun as a function of wavelength, one can refer to the graph displayed in exercise 12.21. On that graph, locate 853 nm on the x-axis, and draw a vertical line passing through that point. This vertical line represents the wavelength corresponding to the band gap energy of CdTe.

(Step 4: Comparing the Absorption of Solar Spectrum by CdTe and Silicon)

In order to determine whether CdTe absorbs more or less of the solar spectrum compared to Silicon, we can consider the position of the vertical line we sketched in step 3 against the portion of the solar spectrum absorbed by Silicon. The bandgap of Silicon is approximately 1.12 eV which corresponds to a wavelength of 1100 nm. Looking at the graph in exercise 12.21, we can observe that the portion of the solar spectrum absorbed by CdTe is more towards the shorter-wavelength (higher-energy) side than the spectrum absorbed by Silicon. Since shorter-wavelength photons possess higher energy, CdTe absorbs a larger portion of high-energy photons within the solar spectrum compared to Silicon. However, Silicon absorbs a larger portion of low-energy photons (longer wavelengths) than CdTe. Both materials can be advantageous depending on the specific application, and it is important to consider the entirety of the solar spectrum to determine the overall efficiency of solar cells made from these materials.

Key concepts

Solar Cells

Solar cells, also known as photovoltaic cells, are devices that convert sunlight into electricity. They are a critical component in the pursuit of renewable energy and are the building block of solar panels. The principle behind their operation lies in the photovoltaic effect, where the energy from photons (light particles) is absorbed by semiconductor materials, such as cadmium telluride (CdTe), to generate an electric current.

The efficiency of solar cells is dependent on the semiconductor's ability to absorb sunlight and convert it into electricity. This is directly linked to the band gap of the material—the energy difference between the valence band (full of electrons) and the conduction band (where electrons can move freely). Cadmium telluride has a band gap of about 1.45 eV, which is well-suited to absorb light from the sun. In comparison to silicon, a commonly used material in solar cells with a band gap of 1.12 eV, CdTe can absorb higher-energy photons and play a significant role in capturing a wider range of the solar spectrum for energy conversion.

Photon Wavelength Calculation

Understanding the relationship between the energy of photons and their wavelength is fundamental in solar cell technology. The photon's energy, measured in electron volts (eV), and its wavelength are inversely related, as described by the equation \(E = \frac{hc}{\lambda}\), where E is the energy, h is Planck's constant (approximately \(4.135667696 \times 10^{-15} \) eV·s), c is the speed of light (about \(3.00 \times 10^8 \) m/s), and \(\lambda\) is the wavelength.

For cadmium telluride, with a band gap of 1.45 eV, calculating the photon wavelength involves firstly converting eV to Joules, then substituting the known values into the equation to solve for \(\lambda\). This calculation leads us to find that the wavelength of light compatible with CdTe's band gap is approximately 853 nm. This result provides insight into the type of light CdTe-based solar cells can utilize, which is particularly within the near-infrared range of the spectrum.

Absorption of the Solar Spectrum

The solar spectrum encompasses a range of wavelengths, and not all are equally absorbed by solar cell materials. Materials with different band gaps absorb different portions of the spectrum. For instance, CdTe's band gap corresponds to the absorption of light with wavelengths shorter than about 853 nm, which includes visible light and part of the infrared spectrum.

When comparing to silicon, with a band gap that corresponds to longer wavelengths (around 1100 nm), CdTe absorbs a larger portion of the shorter-wavelength, higher-energy photons within the solar spectrum. This affects the overall efficiency and suitability of materials for specific photovoltaic applications. The placement of this absorption range on the solar spectrum graph shows that while CdTe might not capture some of the lower-energy photons that silicon can, it excels at using photons in the high-energy range, potentially leading to higher energy conversion in some circumstances. Solar cell design often balances these factors to optimize performance over the entire solar spectrum.