PHYSICS OF
`
`DEVICES
`
`Jcan—Pierre Colinge
`
`Cynthia A. Colinge
`
`SEMICONDUCTOR
`
`
`
`KLUWER ACADEMIC PUBLISHERS
`
`SEL 2009
`Bluehouse v. SEL
`|PR2018—01405
`
`1
`
`SEL 2009
`Bluehouse v. SEL
`IPR2018-01405
`
`

`

`PHYSICS OF SEMICONDUCTOR
`DEVICES
`
`by
`
`J.P. Colinge
`Department of Electrical and Computer Engineering
`University of California, Davis
`
`C. A. Colinge
`Department of Electrical and Electronic Engineering
`California State University
`
`KLUWER ACADEMIC PUBLISHERS
`Boston I Dordrecht I London
`
`2
`
`

`

`Chapter I
`
`1. Energy Band Theory
`
`=
`N
`2n/(a+b)
`
`= N(a+b) = l:_
`2n
`2n
`
`15
`
`(1.1.32)
`
`:e (period = a+ b ), the
`7n
`·+b. The E(k) curve can
`f 2 n
`h. h
`· ·
`·
`iod1c1ty o a+b , w 1c
`one-dimensional crystal
`
`1ited to k-values ranging
`
`·rmation. This particular
`
`ouin zone. The second
`n
`2n
`rom a+b
`to a+b' the
`2n
`3n
`a+b to a+b' etc.
`
`tions (Expression 1.1.12)
`'or k:
`
`!:l,±2,±3,. . .)
`
`(1.1.30)
`
`:rystal (or the number of
`he length of the crystal is
`first Brillouin zone, the k(cid:173)
`~i ven by the following
`
`-is excluded because it is a
`I
`
`orresponding values for n
`:s of k to consider are:
`
`'), -N/2)
`
`(1.1.31)
`
`;t Brillouin zone, which
`ice cells. For every wave
`ch energy band. By virtue
`band can thus contain a
`
`rillouin zone is equal to
`sity of k-values in the first
`
`values
`e zone
`
`In the case of a three-dimensional crystal, energy band calculations are, of
`course, much more complicated, but the essential results obtained from
`the one-dimensional calculation still hold. In particular, there exist
`permitted energy bands separated by forbidden energy gaps. The 3-D
`volume of the first Brillouin zone is 8n3N/V, where Vis the volume of the
`crystal, the number of wave vectors is equal to the number of elementary
`crystal lattice cells, N. The density of wave vectors is given by:
`
`n(. ) -
`k
`-
`
`k
`.
`enszty of
`d
`
`number o[k-vectors NV
`V
`- - - - -
`volume of the zone - 8n3N- 8n3
`
`-
`-
`
`(1.1.33)
`
`1.1.4. Valence band and conduction band
`
`Chemical reactions originate from the exchange of electrons from the
`outer electronic shell of atoms. Electrons from the most inner shells do
`not participate in chemical reactions because of the high electrostatic
`attraction to the nucleus. Likewise, the bonds between atoms in a crystal,
`as well as electric transport phenomena, are due to electrons from the
`outermost shell. In terms of energy bands, the electrons responsible for
`forming bonds between atoms are found in the last occupied band, where
`electrons have the highest energy levels for the ground-state atoms.
`However, there is an infinite number of energy bands. The first (lowest)
`bands contain core electrons such as the 1 s electrons which are tightly
`bound to the atoms. The highest bands contain no electrons. The last
`ground-state band which contains electrons is called the valence band,
`because it contains the electrons that form the -often covalent- bonds
`between atoms.
`
`The permitted energy band directly above the valence band is called the
`conduction band. In a semiconductor this band is empty of electrons at
`low temperature (T=OK). At higher temperatures, some electrons have
`enough thermal energy to quit their function of forming a bond between
`atoms and circulate in the crystal. These electrons "jump" from the
`valep.ce band into the conduction band, where they are free to move. The
`energy difference between the bottom of the conduction band and the top
`of the valence band is called "forbidden gap" or "bandgap" and is noted
`Eg.
`
`In a more general sense, the following situations can occur depending on
`the location of the atom in the periodic table (Figure 1.11):
`
`A: The last (valence) energy band is only partially filled with electrons,
`even at T=OK.
`
`3
`
`

`

`16
`
`Chapter 1
`
`B: The last (valence) energy band is completely filled with electrons at
`T=OK, but the next (empty) energy band overlaps with it (i.e.: an
`empty energy band shares a range of common energy values; Eg < 0).
`
`C: The last (valence) energy band is completely filled with electrons and
`no empty band overlaps with it (Eg > 0).
`
`In cases A and B, electrons with the highest energies can easily acquire an
`infinitesimal amount of energy and jump to a slightly higher permitted
`energy level, and move through the crystal. In other words, electrons can
`leave the atom and move in the crystal without receiving any energy. A
`material with such a property is a metal. In case C, a significant amount
`of energy (equal to E g or higher) has to be transferred to an electron in
`order for it to "jump" from the valence band into a permitted energy
`level of the conduction band. This means that an electron must receive a
`significant amount of energy before leaving an atom and moving "freely"
`in the crystal. A material with such properties is either an insulator or a
`semiconductor.
`
`E
`
`A
`
`B
`
`c
`
`Figure 1.11: Valence band (bottom) and conduction band in a metal
`(A and B) and in a semiconductor or an insulator (C).[6]
`
`The distinction between an insulator and a semiconductor is purely
`quantitative and is based on the value of the energy gap. In a
`semiconductor Eg is typically smaller than 2 eV and room-temperature
`thermal energy or excitation from visible-light photons can give
`electrons enough energy for "jumping" from the valence into the
`conduction band. The energy gap of the most common semiconductors
`are: 1.12 eV (silicon), 0.67 eV (germanium), and 1.42 eV (gallium
`arsenide). Insulators have significantly wider energy bandgaps: 9.0 eV
`(Si02), 5.47 eV (diamond), and 5.0 eV (Si3N4). In these materials room(cid:173)
`temperature thermal energy is not large enough to place electrons in the
`conduction band.
`
`4
`
`