Materials Science and Engineering/Doctoral review questions/Daily Discussion Topics/01152008

Periodic Table

In Ancient Greece, the influential Greek philosopher Aristotle proposed that there were four main elements: air, fire, earth and water. All of these elements could be reacted to create another one; e.g., earth and fire combined to form lava. However, this theory was dismissed when the real chemical elements started being discovered. Scientists needed an easily accessible, well organized database with which information about the elements could be recorded and accessed. This was to be known as the periodic table.

The original table was created before the discovery of subatomic particles or the formulation of current quantum mechanical theories of atomic structure. If one orders the elements by atomic mass, and then plots certain other properties against atomic mass, one sees an undulation or periodicity to these properties as a function of atomic mass. The first to recognize these regularities was the German chemist Johann Wolfgang Döbereiner who, in 1829, noticed a number of triads of similar elements:

In 1829 Döbereiner proposed the Law of Triads: The middle element in the triad had atomic weight that was the average of the other two members. The densities of some triads followed a similar pattern. Soon other scientists found chemical relationships extended beyond triads. Fluorine was added to Cl/Br/I group; sulfur, oxygen, selenium and tellurium were grouped into a family; nitrogen, phosphorus, arsenic, antimony, and bismuth were classified as another group.

This was followed by the English chemist John Newlands, who noticed in 1865 that when placed in order of increasing atomic weight, elements of similar physical and chemical properties recurred at intervals of eight, which he likened to the octaves of music, though his law of octaves was ridiculed by his contemporaries.[2] However, while successful for some elements, Newlands' law of octaves failed for two reasons:

1. It was not valid for elements that had atomic masses higher than Ca.
2. When further elements were discovered, such as the noble gases (He, Ne, Ar), they could not be accommodated in his table.

In 1869 the Russian chemistry professor Dmitri Ivanovich Mendeleev and four months later the German Julius Lothar Meyer independently developed the first periodic table, arranging the elements by mass. However, Mendeleev plotted a few elements out of strict mass sequence in order to make a better match to the properties of their neighbors in the table, corrected mistakes in the values of several atomic masses, and predicted the existence and properties of a few new elements in the empty cells of his table. Mendeleev was later vindicated by the discovery of the electronic structure of the elements in the late 19th and early 20th century.

Earlier attempts to list the elements to show the relationships between them (for example by Newlands) had usually involved putting them in order of atomic mass. Mendeleev's key insight in devising the periodic table was to lay out the elements to illustrate recurring ("periodic") chemical properties (even if this meant some of them were not in mass order), and to leave gaps for "missing" elements. Mendeleev used his table to predict the properties of these "missing elements", and many of them were indeed discovered and fit the predictions well.

With the development of theories of atomic structure (for instance by Henry Moseley) it became apparent that Mendeleev had listed the elements in order of increasing atomic number (i.e. the net amount of positive charge on the atomic nucleus). This sequence is nearly identical to that resulting from ascending atomic mass.

In order to illustrate recurring properties, Mendeleev began new rows in his table so that elements with similar properties fell into the same vertical columns ("groups").

With the development of modern quantum mechanical theories of electron configuration within atoms, it became apparent that each horizontal row ("period") in the table corresponded to the filling of a quantum shell of electrons. In Mendeleev's original table, each period was the same length. Modern tables have progressively longer periods further down the table, and group the elements into s-, p-, d- and f-blocks to reflect our understanding of their electron configuration.

In the 1940s Glenn T. Seaborg identified the transuranic lanthanides and the actinides, which may be placed within the table, or below (as shown above).

Trends of Electronic Material Properties

Elements in the same period show trends in atomic radius, ionization energy, electron affinity, and electronegativity. Moving left to right across a period, atomic radius usually decreases. This occurs because each successive element has an added proton and electron which causes the electron to be drawn closer to the nucleus. This decrease in atomic radius also causes the ionization energy to increase when moving from left to right across a period. The more tightly bound an element is, the more energy is required to remove an electron. Similarly, electronegativity will increase in the same manner as ionization energy because of the amount of pull that is exerted on the electrons by the nucleus. Electron affinity also shows a slight trend across a period. Metals (left side of a period) generally have a lower electron affinity than nonmetals (right side of a period) with the exception of the noble gases.

Atomic Radus

Atomic radius, and more generally the size of an atom, is not a precisely defined physical quantity, nor is it constant in all circumstances. The value assigned to the radius of a particular atom will always depend on the definition chosen for "atomic radius", and different definitions are more appropriate for different situations.

The term "atomic radius" itself is problematic: it may be restricted to the size of free atoms, or it may be used as a general term for the different measures of the size of atoms, both bound in molecules and free. In the latter case, which is the approach adopted here, it should also include ionic radius, as the distinction between covalent and ionic bonding is itself somewhat arbitrary.

The atomic radius is determined entirely by the electrons: The size of the atomic nucleus is measured in femtometres, 100,000 times smaller than the cloud of electrons. However the electrons do not have definite positions—although they are more likely to be in certain regions than others—and the electron cloud does not have a sharp edge.

Despite (or maybe because of) these difficulties, many different attempts have been made to quantify the size of atoms (and ions), based both on experimental measurements and calculational methods. It is undeniable that atoms do behave as if they were spheres with a radius of 30–300 pm, that atomic size varies in a predictable and explicable manner across the periodic table and that this variation has important consequences for the chemistry of the elements.

Atomic radius tends to decrease on passing along a period of the periodic table from left to right, and to increase on descending a group. This is, in part, because the distribution of electrons is not completely random. The electrons in an atom are arranged in shells which are, on average, further and further from the nucleus, and which can only hold a certain number of electrons. Each new period of the periodic table corresponds to a new shell which starts to be filled up, and so the outermost electrons are further and further from the nucleus as a group is descended.

The second major effect which determines trends in atomic radius is the charge of the nucleus, which increases with the atomic number, Z. The nucleus is positively charged, and tends to attract the negatively-charged electrons. Passing along a period from left to right, the nuclear charge increases while the electrons are still entering the same shell: the effect is that the physical size of the shell (and hence of the atom) decreases in response.

The increasing nuclear charge is partly counterbalanced by the increasing number of electrons in a phenomenon that is known as shielding, which is why the size of atoms usually increases as a group is descended. However, there are two occasions where shielding is less effective: in these cases, the atoms are smaller than would otherwise be expected.

Ionization Energy

The electron affinity, E_ea, of an atom or molecule is the energy required to detach an electron from a singly charged negative ion, i.e., the energy change for the process

X^- → X + e⁻

An equivalent definition is the energy released (E_initial − E_final) when an electron is attached to a neutral atom or molecule. It should be noted that the sign convention for E_ea is the opposite to most thermodynamic quantities: a positive electron affinity indicates that energy is released on going from atom to anion.

All elements whose EA have been measured using modern methods have a positive electron affinity, but older texts mistakenly report that some elements such as alkaline earth metals have negative E_ea, meaning they would repel electrons. This is not recognized by modern chemists. The electron affinity of the noble gases have not been conclusively measured, so they may or may not have slightly negative EAs. Atoms whose anions are relatively more stable than neutral atoms have a greater E_ea. Chlorine most strongly attracts extra electrons; mercury most weakly attracts an extra electron. E_ea of noble gases are close to 0.

Although E_ea vary in a chaotic manner across the table, some patterns emerge. Generally, nonmetals have more positive E_ea than metals.

Material	Symbol	Band gap eV @ 300 K
Silicon	Si	1.11
Germanium	Ge	0.67
Silicon carbide	SiC	2.86
Aluminum phosphide	AlP	2.45
Aluminum arsenide	AlAs	2.16
Aluminium antimonide	AlSb	1.6
Aluminium nitride	AlN	6.3
Diamond	C	5.5
Gallium(III) phosphide	GaP	2.26
Gallium(III) arsenide	GaAs	1.43
Gallium(III) nitride	GaN	3.4
Gallium(II) sulfide	GaS	2.5 (@ 295 K)
Gallium antimonide	GaSb	0.7
Indium(III) phosphide	InP	1.35
Indium(III) arsenide	InAs	0.36
Zinc sulfide	ZnS	3.6
Zinc selenide	ZnSe	2.7
Zinc telluride	ZnTe	2.25
Cadmium sulfide	CdS	2.42
Cadmium selenide	CdSe	1.73
Cadmium telluride	CdTe	1.58
Lead(II) sulfide	PbS	0.37
Lead(II) selenide	PbSe	0.27
Lead(II) telluride	PbTe	0.29

Compound Semiconductor

A compound semiconductor is a semiconductor compound composed of elements from two or more different groups of the periodic table. For e.g. III-V semiconductors are composed of elements from group 13 (B, Al, Ga, In) and from group 15 (N, P, As, Sb, Bi). The range of possible formulae is quite broad because these elements can form binary (two elements, e.g. GaAs), ternary (three elements, e.g. InGaAs) and quaternary (four elements, e.g. InGaAsP). It is worth noting that SiGe is technically an alloy while SiC is a compound since its elements are chemically bound.

Crystal Structure

Wurtzite

Wurtzite unit cell

Wurtzite is a less frequently encountered mineral form of zinc sulfide, named after French chemist Charles-Adolphe Wurtz.

The crystal structure is a member of the hexagonal crystal system and consists of tetrahedrally coordinated zinc and sulfur atoms that are stacked in an ABABAB pattern. The structure is closely related to the structure of lonsdaleite, or hexagonal diamond.

The unit cell parameters of wurtzite are

• a = b = 3.81 Å = 381 pm
• c = 6.23 Å = 623 pm

Several other compounds can take the wurtzite structure, including AgI, ZnO, CdS, CdSe, α-SiC, GaN, AlN, and other semiconductors. In most of these compounds, wurtzite is not the favored form of the bulk crystal, but the structure can be favored in some nanocrystal forms of the material.

Nanostructured Material Phase Diagram

Melting Temperature Related to Bonding of Materials

• There is less bonding at the surface then at the bulk
• Dangling bonds correspond to less bonding energy
  • Drop in melting point
• The effect of the nanosize depends on the surface energy
• The bonding energy is a function of $T_{m}$
  • In bulk, there are more bonds
• The energy of strain is important

SiGe

• Is it possible to make a $SiGe$ wafer?
• Is the melting congruent?

GaAs

Bulk GaAs

• The partial pressure of $As$ is much higher
  • Prevent the evaporation of $As$
• Solidify $GaAs$ congruently
• Use the Bridgmann technique to provide pressure

Thin film GaAs

• Use MOCVD
  • There is a constraint from the substrate
  • There are preferred sites that force stoichiometry
• $\Delta H_{mix}=H_{mix}(m)-H_{AA}-H_{BB}$
  • Epitaxial growth may change the mixing of enthalpy
• The intermetallic region may be increased due to the strain effects
• There is a possible connection between the coherence spinodal and the increase in width of the intermetallic region

High-k Material Deposition

• Hard to make high quality thin films
• Gate oxide consisting of silicon dioxide is created by thermal oxidation
• Remove defect by annealing

Hafnium

• Sputtering would create defects
  • Physical energy from plasma
• ALD is used in deposition
  • Cycle between hafnium and oxygen
• A difficulty in implementing hafnium in a structure is using a metal that is compatible
  • In a MOS structure, the work function influences the structure
    • Low threshold voltage that is still compatible with hafnium
  • The work function contributes to band bending
    • Too much band bending influences threshold voltage
    • The work function of a metal must be in the band of hafnium dioxide

Types of CVD

Low Pressure CVD

• High uniformity
• Conformal films
• Growth rate
• Epitaxial growth
  • Need high temperature
  • Mass transport limited
  • Less conformal

PECVD

Temperature is very high