Session 2 Crystal Structure

2.1 Primitive Cell and Crystal Plane

A crystalis characterized by having a well-structured periodic placement of atoms. The smallest assembly of atoms that can be repeated to form the entire crystal is called a primitive cell，with a dimension of lattice constant a. 1. The smallest assembly of atoms that can be repeated to form the entire crystal is called a primitive cell，with a dimension of lattice constanta. 提示：句中的that引导定语从句，修饰The smallest assembly of atoms；with引导介词短语，修饰primitive cell，起补充说明的作用，注意其翻译成中文时的表达方式。 Fig.2.1 shows some important primitive cells.

Many important semiconductors have diamondor zincblende lattice structureswhich belong to the tetrahedral phases；that is，each atom is surrounded by four equidistant nearest neighbors which lie at the corners of a tetrahedron. The bond between two nearest neighbors is formed by two electrons with opposite spins. The diamond and the zincblende lattices can be considered as two interpenetrating face-centered cubic（fcc）lattices s. For the diamond lattice，such as silicon ［Fig.2.1（d）］，all the atoms are the same；whereas in a zincblende lattice，such as gallium arsenide ［Fig.2.1（e）］，one sublattice is gallium and the other is arsenic. 2. For the diamond lattice，such as silicon ［Fig.2.1（d）］，all the atoms are the same；whereas in a zincblende lattice，such as gallium arsenide ［Fig.2.1（e）］，one sublattice is gallium and the other is arsenic. 提示：句中sublattice有“子晶格”、“次晶格”的意思，对于标准的闪锌矿结构，可以视为由砷子晶格和镓子晶格套构而成。但这句的意思主要是强调组成半导体的两种元素。“whereas”有转折的意思，可译为“然而”。 Gallium arsenide is a Ⅲ-Ⅴ compound，since it is formed from elements of groups Ⅲ and V of the periodic table.

Most Ⅲ-Ⅴ compounds crystallize in the zincblende tructure；however，many semiconductors（including some Ⅲ-Ⅴ compounds）crystallize in the rock-salt or wurtzite structures . Fig.2.1（f）shows the rock-salt lattice，which again can be considered as two interpenetrating face-centered cubic lattices. In this rock-salt structure，each atom has six nearest neighbors. Fig.2.1（g）shows the wurtzite lattice，which can be considered as two interpenetrating hexagonal close-packed lattices（e. g.，the sublattices of cadmium and sulfur）. In this picture，for each sublattice（Cd or S），the two planes of adjacent layers are displaced horizontally such that the distance between these two planes are at a minimum（for a fixed distance between centers of two atoms），hence the name close-packed. The wurtzite structure has a tetrahedral arrangement of four equidistant nearest neighbors，similar to a zincblende structure. Some compounds，such as zinc sulfide and cadmium sulfide，can crystallize in either zincblende or wurtzite structures. 3. Some compounds，such as zinc sulfide and cadmium sulfide，can crystallize in either zincblende or wurtzite structures. 提示：句中either…or…有“或者……或者……”的意思，但这句的意思并不是非此即彼，而是说像硫化锌这样的半导体，既有闪锌矿结构的，也有纤锌矿结构的，存在着多形体。

Fig.2.1 Some important primitive cells（direct lattices）and their representative elements；a is the lattice constant.

Since semiconductor devices are built on or near the semiconductor surface，the orientations and properties of the surface crystal planes are important. A convenient method of defining the various planes in a crystal is to use Miller indices . These indices are determined by first finding the intercepts of the plane with the three basis axes in terms of the lattice constants，and then taking the reciprocals of these numbers and reducing them to the smallest three integers having the same ratio. The result is enclosed in parentheses（hkl）called the Miller indices for a single plane or a set of parallel planes {hkl}. 5. The result is enclosed in parentheses（hkl）called the Miller indices for a single plane or a set of parallel planes {hkl }. 提示：本句语法并不复杂，但在句末有所省略。完整的意思应该是：{hkl } called the Miller indices for a set of parallel planes。 Fig.2.2 shows the Miller indices of important planes in a cubic crystal. For silicon，a single-element semiconductor，the easiest breakage or cleavage planes are the {111} planes. In contrast，gallium arsenide，which has a similar lattice structure but also has a slight ionic component in the bonds，cleaves on {110} planes.

Three primitive basis vectors，a，b and c of a primitive cell，describe a crystalline solid such that the crystal structure remains invariant under translation through any vector that is the sum of integral multiples of these basis vectors. In other words，the direct lattice sites can be defined by the set

R＝ma+nb+pc （2.1）

where m，n and p are integers.

Fig.2.2 Miller indices of some important planes in a cubic crystal.

The primitive cell of a reciprocal latticecan be represented by a Wigner-Seitz cell . The Wigner-Seitz cell is constructed by drawing perpendicular bisector planes in the reciprocal lattice from the chosen center to the nearest equivalent reciprocal lattice sites. 6. The Wigner-Seitz cell is constructed by drawing perpendicular bisector planes in the reciprocal lattice from the chosen center to the nearest equivalent reciprocal lattice sites. 提示：本句描述了维格纳—塞茨原胞的绘制方法，虽然语法并不复杂，但用词晦涩。 This technique can also be applied to a direct lattice. The Wigner-Seitz cell in the reciprocal lattice is called the first Brillouin zone . Fig.2.3（a）shows a typical example for a body-centered cubic（bcc）reciprocal lattice. If one first draws lines from the center point（Г）to the eight corners of the cube，then forms the bisector planes，the result is the truncated octahedron within the cube—a Wigner-Seitz cell. It can be shown that a face-centered cubic（fcc）direct lattice with lattice constant a has a bcc reciprocal lattice with spacing 4π/a. Thus the Wigner-Seitz cell shown in Fig.2.3（a）is the primitive cell of the reciprocal（bcc）lattice for an fcc direct lattice. The Wigner-Seitz cells for bcc and hexagonal direct lattices can be similarly constructed and shown in Fig.2.3（b）and Fig.2.3（c）. The Brillouin zone for the fcc lattice is important because it is relevant to most semiconductor materials of interest here. 7. The Brillouin zone for the fcc lattice is important because it is relevant to most semiconductor materials of interest here. 提示：句中of interest here修饰semiconductor materials，of interest可翻译为“关注的”，here原意为“这里”，根据内容的实际范围，可灵活地翻译为“本章”。

Fig.2.3 Brillouin zones for（a）fcc，diamond，and zincblende lattices，（b）bcc lattice，and（c）wurtzite lattice.