In 3-D nanomaterials, the three spa

In 3-D nanomaterials, the three spatial dimensions are all above the nanoscale. Therefore the two aforementioned effects can be neglected. However, bulk nanocrystalline materials exhibit a high grain boundary area-to-volume ratio, leading to an increase in electron scattering. As a consequence, nanosize grains tend to reduce the electrical conductivity.
In the case of 2-D nanomaterials with thickness at the nanoscale, quantum confinement will occur along the thickness dimension. Simultaneously, carrier motion is uninterrupted along the plane of the sheet. In fact, as the thickness is reduced to the nanoscale, the wave functions of electrons are limited to very specific values along the cross-section (see Figure 7.18). This is because only electron wavelengths that are multiple integers of the thickness will be allowed. All other electron wavelengths will be absent. In other words, there is a reduction in the number of energy states available for electron conduction along the thickness direction. The electrons become trapped in what is called a potential well of width equal to the thickness. In general, the effects of confinement on the energy state for a 2-D nanomaterial with thickness at the nanoscale can be written as
En = 2πmL 222 n2 (7.16)
where h– ≡ h/2π, h is Planck’s constant, m is the mass of the electron, L is the width of the potential well (thickness of 2-D nanomaterial), and n is the principal quantum number. Equation 7.16 assumes an infinite-depth potential well model. As mentioned, the carriers are free to move along the plane of the sheet. Therefore the total energy of a carrier has two components, namely a term related to the confinement dimension (Equation 7.16) and a term associated with the unrestricted motion along the two other in-plane dimensions.
To understand the energy associated with unrestricted motion, let’s assume the z-direction to be the thickness direction and x and y the in-plane directions in which the electrons are delocalized. Under these conditions, the unrestricted motion can be characterized by two wave vectors kx and kx, which are related to the electron’s momentum along the x and y directions, respectively, in the form px = h–kx and py = h–ky. The energy corresponding to these delocalized electrons

Kết quả (Anh) 2:

In 3-D nanomaterials, the three spatial dimensions are all above the nanoscale. Therefore the two aforementioned effects can be neglected. Tuy nhiên, bulk nanocrystalline materials Exhibit a high grain boundary area-to-volume ratio, leading to an electron scattering tăng print. As a consequence, nanosize grains Tend to Reduce the electrical conductivity.
In the case of 2-D nanomaterials with thickness at the nanoscale, quantum confinement along the thickness dimension sẽ occur. Simultaneously, the carrier motion is uninterrupted along the plane of the sheet. In fact, as the thickness is reduced to the nanoscale, the wave functions of electrons are limited to very specific values ​​along the cross-section (see Figure 7:18). This is only electron wavelengths vì có are multiple integers of the thickness Will Be allowed. All other electron wavelengths Will Be absent. In other words, there is a reduction in energy số available for electron conduction states along the thickness direction. The electrons trapped in what is trở gọi a well of width equal potencial to the thickness. In general, the effects of confinement on the energy state for a 2-D nanomaterial with thickness at the nanoscale can be Written as
En = 2πmL n2 222 (7:16)
where h ≡ h / 2π, h is Planck's constant, m is the mass of the electron, L is the width of the potencial well (thickness of 2-D nanomaterial), and n is the principal quantum number. 7:16 Equation assumes infinite-depth security model potencial well. As Mentioned, the carriers are free to move along the plane of the sheet. Therefore the total energy of a carrier has two components, namely a term related to the confinement dimension (Equation 7:16) and a term associated with the unrestricted motion along the two other in-plane dimensions.
To hiểu the energy associated with unrestricted motion, let's the z-direction giả sử to be the thickness direction and x and y, the in-plane directions are chứa delocalized electrons. Under những conditionsEND_SPAN, the unrestricted motion can be Characterized by two wave vectors kx and kx, mà related to the electron's momentum along the x and y directions, respectively, in the form px = py = h-h-kx and ky. The energy electrons delocalized tương ứng to những