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Common crystals you may find in everyday life are of sodium chloride (common salt) and silica (the prominent constituent of sand). A basic understanding of crystals is important to the study of VLSI Technology as devices are made in crystals. The crystalline structure and the defects in crystals play important roles in semiconductor processing and also influences the characteristics of the devices made using those processes. On the top right corner you see a scanning electron microgram of salt crystals. Three different kinds of atomic arrangement in solids are shown in the three figures. The crystalline material exhibits perfect periodicity, whereas poly crystalline material exhibits local periodicity. Polycrystalline material in general consist of randomly arranged small crystalline grains. Amorphous material has a random arrangement of atoms in the solid. The same material can exist in all the three phases, namely crystalline, polycrystalline and amorphous depending on the conditions they are formed. 72
The basic building block of a crystal is a unit cell, which when repeated many times over in a systematic fashion constructs the whole crystal lattice. Unit cells are identified in the figure by rectangles. The two vectors a and b are called the basis vectors. To construct the complete crystal, apply integer translations of the unit cell. The magnitude of this statement is illustrated in the photographs of Silicon ingots shown on the top right corner of the slide. These are single crystals of Silicon! The ingots are of varying diameter. The largest diameter ingot has diameter larger than 30cm and has a length of ~ 1m. The unit cell of Silicon has a volume of ~ 1.6e-22 cm 3 73
Of course the unit cells of most of the practical materials should be three dimensional. The two-dimensional view had seen previously was presented mainly for ease of visualization. However graphene and MoS2 monolayers invented recently are 2D crystals. This slide shows three different forms of cubic lattices. 1. simple cubic (sc) 2. body centered cubic (bcc) 3. face centered cubic (fcc) The lattice constant in all these cases is a. Assuming the atoms to be hard spheres, calculate the packing density of body centered and fcc lattices. 74
Silicon, Germanium (two of the most important elemental semiconductors) and Diamond has a lattice structure that is called a zincblende lattice. The ZB lattice is a combination of two interpenetrating fcc lattices. This can be constructed by taking two fcc lattices and placing the second one displaced by a/4, a/4, a/4 of the basis vectors. In the 3D image shown, the red and blue spheres correspond to atoms on the two sublattices. Note that the lattice constant is still a. Each atom is bonded to 4 atoms from the other sublattices. A two dimensional projection of the lattice is also shown. When all the atoms of the lattice are identical, we get a diamond lattice. As mentioned, Si and Ge have diamond lattice structures. When the atoms from the two interpenetrating sub-lattices differ, we have a zinc blend structure. Compound semiconductors like GaAs, InP etc, have zincblende lattices. For example, in GaAs, if the red spheres are Ga, the blue spheres would be As. Note that the hard sphere packing density of the zincblende lattice is low compared to the cubic lattices we discussed on the previous slide. 75
The slide shows transmission electron micrograms of crystalline and poly crystalline forms of Si. Please note the crystal grains in poly-Si. SiO2 shown in the image on the right is amorphous as no regular arrangements of atoms can be seen. 76
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In general the properties of crystalline solids are not isotropic, i.e. they are not the same on different planes and in different directions. For the same reason the performance of devices made on different planes would be different. To give you an example, n-channel MOSFETs made on (100) plane with current flow in <110> direction gives the best performance compared to devices made on other planes and current flow in other directions. P-channel MOSFETs made on (110) plane with current flowing in <110> direction gives the best performance. These are due to direction dependence of hole and electron mobilities. (M. Yang et al., IEEE Electron Device Letters, 2003, pp. 339). Oxidation is faster on the (111) plane than on (100) plane. Orientation dependent etch processes like KOH, NaOH and TMAH (tetra methyl ammonium hydroxide – (CH3)4NOH) etches the {100} and {110} planes faster than {111} planes of Si. This is widely used in micromachining and crystalline Si solar cell processing. There are several other orientation dependent effects that we would discuss during the course. Anisotropy of properties can be qualitatively appreciated by looking at the 2D projections of the unit cell on different planes as shown on the slide. 81
Defects play an important role in deciding various properties of materials. In semiconductor materials, some of the properties of importance are the doping (a defect) 82
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Materials usually used for doping Si are shown in the figure. Depending on the size of the atom, it would generate local stresses in the lattice. This is indicative of how much of dopants can be incorporated in the lattice. The dopant would be usually electrically active when it is occupying a substitutional site, i.e. the dopant atom is occupying a lattice site. For example a phosphorous atom occupying a lattice site would be ionized at room temperature and contribute an electron to the lattice. However the same phosphorous atom in an interstitial site would not contribute any free electrons to the lattice and hence is electrically neutral. Dopants in substitutional sites, depending on whether they are pentavalent of trivalent would contribute one electron or hole to the lattice. The impurities that contribute an electron are called donors and those accept an electron to release a hole are called acceptors. As per the description above, not all dopants incorporated in a semiconductor need be electrically active as some of them can be present in interstitial sites. Arsenic has the smallest misfit factor and hence it can be incorporated in electrically active form to the maximum extent than other dopants. 84
Defect levels introduced by elements from other groups are more complex. They can introduce more than one defect level. Some of the impurities introduce both acceptor and donor types of impurities. Many of the elements shown are transition metals. Chemical bonds involving these materials are formed not only by the electrons from the outermost shell but also from the immediate inner shell. Elements from the same group in the periodic table may not behave similarly. For example, Cu and Au belong to group 1A of the periodic table. But Cu is seen to introduce 3 acceptor levels and Au 2 donor levels and one acceptor level. Some of the impurities like Pt are seen to be active even in interstitial sites. A qualitative understanding of the behavior can be gained by considering Cu. Cu has an electronic configuration of [Ar]3d 10 4s 1 . When Cu is incorporated in a lattice site, it can bond to only one Si atom. In principle Cu can accept 3 more electrons to complete bonds with its neighbors. However a Cu atom which accept one electron would become negatively charged. It becomes more difficult for this ion to accept more atoms. As a consequence the energy level of the acceptor level would be further away from the valence band. Such a model would not strictly explain the case of Au, as it also has a single electron in its outer most shell. 85
Vacancies and interstitials play important role in diffusion of various species in silicon. They also introduce electronic states in the forbidden gap. They are generated by thermal fluctuations in crystals, especially during high temperature processing and a lot of them are done during semiconductor processing. 86
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N V and N C are the effective density of states in the valance and conduction bands respectively. These quantities are also temperature dependent. Refer to page 19 of S. M. Sze, Physics of Semiconductor Devices, Wiley and Sons, 2007. 89
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