EE 346: Semiconductor Devices 02/08/2017 Tewodros A. Zewde 1
DOPANT ATOMS AND ENERGY LEVELS Without help the total number of carriers (electrons and holes) is limited to 2ni. For most materials, this is not that much, and leads to very high resistance and few useful applications. The intrinsic semiconductor may be an interesting material, but the real power of semiconductors is realized by adding small, controlled amounts of specific dopant, or impurity, atoms. This process is known as doping the crystal. Adding controlled amounts of dopant atoms, either donors or acceptors, creates a material called an extrinsic semiconductor. An extrinsic semiconductor will have either excess electrons (n-type) or excess holes (ptype).
Donor impurity atom: Consider adding a group IV element as a substitutional impurity to silicon. Example: P, As, Sb in Si The fifth valence electron is denoted as a donor electron, and a donor impurity atom donates an electron to the conduction band.
The electron in the conduction band can now move through the crystal generating a current, while the positively charged ion is fixed in the crystal.
Concept of a Donor adding extra electrons: Band diagram equivalent view The energy level, E D, is the energy state of the donor electron. The donor impurity atoms add electrons to the conduction band without creating holes in the valence band. The resulting material is referred to as an n-type semiconductor (n for the negatively charged electron).
Acceptor impurity atom: consider adding a group III element as a substitutional impurity to silicon. One covalent bonding position appears to be empty. Example: B, Al, In in Si One less bond means the acceptor is electrically satisfied One less bond means the neighboring silicon is left with an empty state.
The "empty" position associated with the boron atom becomes occupied, and other valence electron positions become vacated. These other vacated electron positions can be thought of as holes in the semiconductor material. +
The hole can move through the crystal generating a current, while the negatively charged boron atom is fixed in the crystal. +
The hole can move through the crystal generating a current, while the negatively charged boron atom is fixed in the crystal. +
Concept of an Acceptor adding extra hole : Band diagram equivalent view The electron occupying the "empty" position does not have sufficient energy to be in the conduction band, so its energy is far smaller than the conductionband energy. The energy level, E A, is the energy state of the acceptor electron. The group III atom accepts an electron from the valence band and so is referred to as an acceptor impurity atom. This type of material is referred to as a p-type semiconductor (p for the positively charged hole).
Equilibrium Distribution of Electrons and Holes in extrinsic semiconductor Adding donor or acceptor impurity atoms to a semiconductor will change the distribution of electrons and holes in the material. The Fermi energy level in a semiconductor changes as the electron and hole concentrations change and, again, the Fermi energy changes as donor or acceptor impurities are added. If the Fermi energy changes from near the midgap value, the density of electrons in the conduction band and the density of holes in the valence band will change.
In an n-type semiconductor where n o > p o, electrons are referred to as the majority carrier and holes as the minority carrier. In a p-type semiconductor where p o > n o, holes are the majority carrier and electrons are the minority carrier. The thermal-equilibrium electron concentration in the extrinsic semiconductor can be written as which leads to If E F > E Fi, n-type Similarly, we have If E F < E Fi, p-type
The n o p o Product becomes which may be written as This product is always a constant for a given semiconductor material at a given temperature.
Statistics of donors and acceptors The probability statistics of donors and acceptors describe probability that a particular energy state, i. e., the donor and acceptor energy states, will be occupied by an electron. The probability function of electrons occupying the donor state is given as follows: where n d is the density of electrons occupying the donor level and E d is the energy of the donor level.
The above equation can also be written in the form where N d + is the concentration of ionized donors. Similarly, where N a is the concentration of acceptor atoms, E a is the acceptor energy level, p a is the concentration of holes in the acceptor states, and N a - is the concentration of ionized acceptors.
The ratio of electron the donor state to the total number of electrons in the conduction band plus donor state becomes where the factor (E c - E d ) is just the ionization energy of the donor electrons. At room temperature, the donor states are essentially completely ionized and, almost all donor impurity atoms have donated an electron to the conduction band.
Similarly, the ratio of holes in the acceptor state to the total number of holes in the valence band plus acceptor state becomes
The charge neutrality condition for a compensated semiconductor is expressed by equating the density of charges to the density of positive charges, and hence we have where n o and p o are the thermal-equilibrium concentrations of electrons and holes in the conduction band and valence band, respectively. The electron and hole concentration can be determined in terms of donor and acceptor atoms, or impurities, as follows: *A compensated semiconductor is one that contains both donor and acceptor impurity atoms in the same region.
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POSITION OF FERMI ENERGY LEVEL (A) w.r.t. donor/acceptor impurities For n-type semiconductor in which N d >> n i, As the donor concentration increases, the Fermi level moves closer to the conduction band. For a p-type semiconductor, As the acceptor concentration increases, the Fermi level moves closer to the valence band.
Nd (crri- 3 ) 10 12 10 13 10 14 10 1 5 10 16 10 17 10 18 E, """'T"---"T", --- "T", ---"T", ----, ---, --, ntype -------------------------------- p type Ev 1012 1013 I t I I I I 1016 I 017 1018
(B) w.r.t. temperature The intrinsic carrier concentration n i is a strong function of temperature, so that E f is a function of temperature also. As the temperature increases, n i increases, and E F moves closer to the intrinsic Fermi level. As the temperature increases, additional electron-hole pairs are thermally generated so that the n i term the previous equations may begin to dominate. The semiconductor will eventually lose its extrinsic characteristics.
At high temperature, the semiconductor material begins to lose its extrinsic characteristics and begins to behave more like an intrinsic semiconductor. At the low temperature where freeze-out occurs, the Fermi level goes above E d for the n-type material and below E a for the p-type material. At absolute zero degrees, all energy states below EF are full and all energy states above E F are empty.