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PHYSICS 1070
SEMICONDUCTOR PHYSICS
INTRODUCTION TO TYPICAL SEMICONDUCTING MATERIALS
To identify some typical semiconductors, let’s take a brief look at the Periodic Table. Dmitri Mendeleev published the first periodic table in 1869 by ordering the known elements by atomic weights and chemical properties. He suggested the gaps in the table corresponded to yet undiscovered elements and he was able to predict the properties of these new elements. With an understanding of atomic structure and quantum mechanics we know the ordering is a result of the quantum mechanical behaviour of the atoms in each element. The periodic table arranges the elements in rows in order of increasing atomic number: the rows are called periods. Elements with similar properties form the vertical columns called groups. The properties within each group are similar due to the same number valence electrons. Consider the International Union of Pure and Applied Chemistry Periodic Table of the Elements from Dec. 1, 2018 https://iupac.org/what-we-do/periodic-table-of-elements/.
The groups are numbered 1 to 18, where Group 1 starts with hydrogen H followed by the alkali metals such as Li and Na. These are chemically reactive since they all have one electron in the outer state available to react with other atoms. Group 18 elements starting with He are chemically inert; their outer electrons are bonded tightly to the nucleus so they do not react with other elements nor do the atoms of these elements form molecules. The version of the Periodic Table shown on P. 719 of your textbook shows the groups numbered differently, fr om Group I to VIII. We’ll use this grouping notation in this course. From this Periodic Table you can see Group IV elements include C, Si, Ge, Group III elements include B, Al, Ga, In, while N, P, As, Sb are examples of Group V elements. Zn, Cd and Hg are Group II and O, S, Se and Te are in Group VI. Semiconducting materials are generally classified as elemental or compound. Si, Ge and other Group IV elements in the periodic table are elemental semiconductors. The most common compound semiconductors are formed from Group III and Group V elements eg. AlAs. Semiconductors are also found in compounds formed of IV elements eg. SiC, and II-VI elements eg. CdS. Elemental semiconductors consist of one type of atom eg. Si. Binary semiconductors consist of two types of atoms eg. GaAs while ternary semiconductors contain three elements and quaternary contain four elements.
A BRIEF LOOK AT ATOMIC STRUCTURE
Each atom consists of a nucleus of diameter 10-^15 m consisting of protons and neutrons, 99.9% of the mass of the atom is found in the nucleus where mp= 1.673 x 10-^27 kg and mn = 1.675 x 10-^27 kg. Protons carry the same magnitude of charge as the electrons but are positively charged. The protons and neutrons are held together by a short range nuclear force that overcomes the mutual electromagnetic repulsion of the positive protons. The negatively charged electrons are found outside the nucleus and are bound to the positively charged nucleus by the electromagnetic force. The electron has a mass of only me = 9.109 x 10-^31 kg and carries a charge of e = - 1.60217733 ± 0.00000049 x 10-^19 C. To describe atoms; the number of protons in an atom is called the atomic number Z, N is the neutron number, while A is the nucleon number or mass number…..that is the total number of nucleons (sum of the number of protons and neutrons). A Element Symbol Z Consider boron, the group III element used to produce p-type semiconductors; 11 B 5
This representation tells us boron has A = 11 nucleons, of which Z = 5 are protons, and N = A – Z = 11 – 5 = 6 neutrons. Some elements occur with a different number of neutrons…these are called isotopes. For example, Si has three stable isotopes and approximately 21 unstable isotopes; the mass numbers of the isotopes range from 22 to 45. The stable isotopes have mass numbers of 28, 29 and 30. Most of the natural abundance of Si is stable. The electrons which are least tightly bound to the nucleus can be removed (ionization) leaving behind a charged atom called an ion. Although electrons, or multiples of electrons, are the most likely observed charges, the electron is not the smallest known charge. P rotons and neutrons are composed of quarks with charges +⅓ e, - ⅓ e, +⅔ e and - ⅔ e although isolated quarks have not been observed. Proton uud (+⅔ e) + (+⅔ e) + ( - ⅓ e ) Neutron udd (+⅔ e) + 2( - ⅓ e) Electrons are fermions, with spin +1/2 and - 1/2 which means their behavior is described by the Pauli Exclusion Principle so to understand semiconductors we’ll need to know more about the atom and matter in its solid state, as well as the quantum mechanical properties of the electron and the macroscopic properties of the electromagnetic force.
As we’ll discuss later in more detail, in metals the resistivity, or resistance to the ‘flow’ of charge, is a result of electron - phonon interaction (lattice vibrations) and defects in the crystal. Resistivity and conductivity are characteristics of the material and do not depend on the geometry of the sample. The resistance of a common circuit element, a carbon resistor, includes information about both resistivity and the dimensions of the resistor; R = ρL/A For copper Cu, σ = 5.88 x 10^7 (Ω - m)-^1 and ρ = 1.70 x 10 -^8 (Ω - m). In comparison, glass which is an insulator has a conductivity range of σ ≈ 10 -^10 - 10 -^14 (Ω - m)-^1 and a resis tivity ρ range of 10^10 - 1014 (Ω - m). Carbon has a resistivity of ρ = 3.5 x 10 -^5 (Ω - m) at 20 °C. Resistivity is temperature dependent ρ = ρ 20°C (1 + α ∆T) where α, the temperature coefficient of resistivity, gives the fractional change in ρ per degree C ; α = ( 1 /ρ) dρ /dt Since α changes with temperature this expression can be used only for a small temperature range around 20° C. Metals have a positive α so the resistivity of metals increases as the temperature increases e.g. α Cu = 3.9 x 10-^3 °C-^1.
ρ (Ω - m) at 20°C α/°C Aluminum 2.8 x 10-^8 3.9 x 10-^3 Copper 1.7 x 10-^8 3.9 x 10-^3 Carbon 3.5 x 10-^5 - 5 x 10-^4 Silver 1.6 x 10-^8 3.8 x 10-^3 Nickel 7.8 x 10-^8 6 x 10-^3 CHARACTERISTICS OF SEMICONDUCTORS Semiconductors have interesting and useful electrical properties and we’ll spend many classes in this course describing these characteristics. Once we’ve developed the main concepts of band theory these characteristics will be more easily explained. Semiconductors are characterized by a bandgap of about 1 to 3 eV, conductivity of approximately 1 x 10^2 (Ω - cm)-^1 to 1 x 10-^9 (Ω - cm)-^1 which makes them poor conductors and also poor insulators, negative temperature coefficient of resistivity and, most importantly, conduct ele ctricity by a process called mixed conduction…that is, conduction is due to both - and + charge carriers… negatively charged electrons and positively charge carriers called holes. In addition, the conductivity of semiconductors is strongly affected by chemical impurities. All semiconductors form diamond or zinc blende crystals. The total conductivity of a semiconductor depends on the both charge carriers; electrons and holes. Intrinsic semiconductors have a fairly small bandgap (1.12 eV for Si, 0.67 eV for Ge) so electrons can easily be
(See Table B.4 in Appendix B of your textbook for a list of the properties of silicon, germanium and gallium arsenide and Tables B.5 and B.6 for other semiconductor parameters.)
