By H.-S. Philip Wong, Deji Akinwande
Explaining the homes and function of sensible nanotube units and comparable functions, this is often the 1st introductory textbook at the topic. all of the primary innovations are brought, in order that readers with out a sophisticated medical history can persist with the entire significant rules and effects. extra issues lined contain nanotube transistors and interconnects, and the fundamental physics of graphene. challenge units on the finish of each bankruptcy let readers to check their wisdom of the fabric coated and achieve a better knowing of the analytical ability units constructed within the textual content. this is often an awesome textbook for senior undergraduate and graduate scholars taking classes in semiconductor gadget physics and nanoelectronics. it's also an ideal self-study advisor for pro machine engineers and researchers.
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Extra info for Carbon Nanotube and Graphene Device Physics
To see this visually, consider cos ka = 0, which corresponds to the horizontal bands demarcated by γ a = π . For example, the energies of the nth band satisfy the restriction lieing within γ a = [(n − 1)π , nπ]. Once the energies are known, the wavevector is computed from Eq. 25). 30 Chapter 2 Electrons in solids: a basic introduction E Band 3 Bandgap Band 2 Bandgap Band 1 –3π –2π –π π 0 2π 3π ka Fig. 6 The dispersion of an electron in the Kronig–Penney model showing allowed bands separated by bandgaps.
25). The gray lines between ±1 dashed lines are the allowed solutions. Only the positive γ a is shown here; the negative γ a is the mirror image. clearly reveals a set of allowed energy bands separated by bandgaps. For comparison, the dispersion of a free electron in space has also been included in the ﬁgure. 6, beyond the discussion of allowed bands separated by bandgaps. → Brillouin Zone: Eq. 25) does not have a unique solution. For every allowed energy that yields an LHS value within ±1 there will be correspondingly an inﬁnite set of wavevectors k.
These precise totals are determined from symmetry properties of Bravais lattice points. For instance, the square lattice is invariant under rotation of 90◦ about a ﬁxed lattice point in 2D space. The hexagonal lattice, on the other hand, is invariant under rotation of 60◦ . By carefully taking into account the rotation symmetry, and symmetry present in lattice spacing, the Bravais lattices can be fully enumerated. The mastery of all the details of crystallographic symmetry13 is (fortunately) not necessary for an advanced working knowledge of crystalline solids.