Flaw

In solid state physics and materials science, an impurity is a missing atom ( vacancies ) or a substitution atom ( zero-dimensional lattice defect ) in a (highly pure) crystal , i.e. it is a disruption of the regular crystal lattice structure .

The disturbance can result in additional electronic energy levels locally. In the case of semiconductors, these can be in the forbidden band and thus have a decisive influence on the electronic and optical properties. For example, the targeted introduction of foreign atoms ( doping ) can increase the electrical conductivity by several orders of magnitude, cf. Defect line . However, as a potential trap and recombination center , an impurity can also reduce electrical conductivity.

Donors and Acceptors

As already mentioned, the presence of imperfections (of a different valence ) increases the conduction properties of electrical current at lower temperatures. The reason for this lies in the generation of intermediate levels in the band gap of the semiconductor. A distinction is made between two types of impurities: donors and acceptors.

Donor atoms (phosphorus) in the silicon crystal lattice and their effect in the band diagram

Acceptor atoms (boron) in the silicon crystal lattice and their effect in the band diagram

In relation to electrons, impurities with a valence band electron more than the semiconductor element are referred to as (electron) donors ( Latin donare = to give). If such foreign atoms are substituted in the semiconductor, that is, exchanged with the semiconductor atoms, each of these foreign atoms (in the case of phosphorus and silicon) brings with it an electron that is not required for the bond and can be easily detached. An impurity level forms near the lower energy edge of the conduction band (donor level). Correspondingly doped areas of the semiconductor are referred to as n-doped .

Similarly, (electron) acceptors (Latin: accipere = to accept) are the foreign atoms that have one electron less in the valence band. This electron is missing for the bond to the neighboring atom. They act as an additional defect electron (hole), which can easily be occupied by valence band electrons - this is why the term hole donors is also used in some considerations. In the band scheme, such an impurity level is close to the valence band edge (acceptor level). Correspondingly doped areas of the semiconductor are referred to as p-doped .

Even if both types of doping increase the conductivity (almost equally), the underlying mechanisms are quite different. With donors, as the temperature rises, electrons from the donor level ( ) are increasingly excited into the conduction band (here the energy difference is the smallest “energy gap”). In the conduction band, they are now available for charge transport. Fixed positively charged traps remain ( so to speak, fixed defect electrons ). In contrast to this, in acceptors electrons from the valence band are excited and bound into the fixed acceptor levels (here the energy difference is the smallest “energy gap”). What remains are “free-moving” positive charges (defect electrons), which are responsible for charge transport in the valence band (so-called majority charge carriers). ${\displaystyle E_{\mathrm {D} }}$ ${\displaystyle \Delta E_{\mathrm {D} }=E_{\mathrm {C} }-E_{\mathrm {D} }}$ ${\displaystyle \Delta E_{\mathrm {A} }=E_{\mathrm {A} }-E_{\mathrm {V} }}$

In addition to this previously described distinction, defects are also divided into shallow and deep defects with regard to the energy level. Flat impurities have a low energy difference, so they are located in the vicinity of the valence or conduction band, depending on the type of impurity. In contrast, deep imperfections, also called deep centers, have a relatively large energy difference; they lie in the region of the middle of the band gap.

Depending on the material composition, an imperfection can also create more than one trapping point in the energy band. These can act as both donor and acceptor levels. For example, in a silicon crystal, sulfur creates a donor level at E _D  = 260 meV and an acceptor level at E _A  = 480 meV.

Energetic distance and for selected semiconductors ${\displaystyle \Delta E_{\mathrm {D} }}$ ${\displaystyle \Delta E_{\mathrm {A} }}$

Crystal material	Band gap in eV	(Donors) in meV ${\displaystyle E_{\mathrm {D} }}$			(Acceptors) in meV ${\displaystyle E_{\mathrm {A} }}$
		P	As	Sb	B.	Al	Ga	In
Si	1.12	45	54	39	45	67	74	160
Ge	0.67	12	12.7	9.6	10	10	10	11
		S.	Te	Si	Be	Zn	CD	Si
GaAs	1.42	6th	30th	5.8	28	31	35	35

Effects on the energy band model

Density of states (colored) in an n-doped semiconductor with a direct band transition . Energy level of the dopant atoms E _D .

The additional energy levels result in a shift in the density of states and thus in the Fermi level , which according to the Fermi-Dirac statistics is occupied by the occupation probability ½. For n-doped semiconductors, the Fermi level is between the intrinsic Fermi level and the higher effective donor level : ${\displaystyle E_{\mathrm {F} }}$ ${\displaystyle E_{\mathrm {i} }}$ ${\displaystyle {E_{\mathrm {D} }}^{*}}$

${\displaystyle E_{\mathrm {i} }\leq E_{\mathrm {F} }\leq {E_{\mathrm {D} }}^{*}}$

analogously, the Fermi level for p-doped semiconductors shifts to lower energies, because the unoccupied acceptor levels are below the Fermi level. The new Fermi level is therefore between the effective acceptor level and the intrinsic Fermi level : ${\displaystyle {E_{\mathrm {A} }}^{*}}$ ${\displaystyle E_{\mathrm {i} }}$

${\displaystyle {E_{\mathrm {A} }}^{*}\leq E_{\mathrm {F} }\leq E_{\mathrm {i} }}$

Isoelectronic defects

In addition to foreign atoms with a different number of external electrons, foreign atoms with the same number of external electrons as the atom they replace can be introduced into a semiconductor. These imperfections are called isoelectronic (or isovalent) imperfections, for example imperfections that arise from the germanium doping of a silicon crystal. Particularly in the case of tetravalent materials, two levels of impurity are often formed, for example, germanium generates two donor levels in the silicon energy band, they are at +0.5 eV (measured from the valence band edge) and −0.27 eV (measured from the conduction band edge ). However, since all valence electrons are required for the bond in the crystal, isoelectronic impurities are neutrally charged.

Since they influence the optical properties of semiconductors, isoelectronic impurities are mainly used for optical applications. A well-known example are gallium phosphide crystals (GaP), in which the doping with nitrogen enables the production of luminescent diodes with an intense green glow .

application

In semiconductor technology , foreign atoms with a different valence are technically interesting impurities, for example boron or phosphorus for silicon crystals. The targeted introduction of foreign atoms is called doping . Usual concentrations are in the range from 10 ¹⁴ to 10 ¹⁷  cm ⁻³ (the concentration of the Si atoms themselves is 5 · 10 ²²  cm ⁻³ ). Due to the relatively low concentrations, the chemical and crystallographic properties are changed only insignificantly (seen on the entire crystal). Electrically, however, these imperfections (of a different value) are of great importance. They produce so-called traps (Engl. Trans ), localized energy levels in the energy gap (band gap) of semiconductor , thus not be occupied by electrons of energy between the valence and conduction band . In this way, the conductivity behavior of the semiconductors can be specifically influenced. Due to the impurities, more free charge carriers are present even at lower temperatures (than with high-purity semiconductors), which leads to a higher electrical conductivity . The associated mechanism is called impurity conduction  - in contrast to this, intrinsic (pure) semiconductors are self-conduction at higher temperatures.

literature

• Frank Thuselt: Physics of Semiconductor Components: Introductory textbook for engineers and physicists . Springer, Berlin 2004, ISBN 3-540-22316-9 .
• Werner Schatt, Hartmut Worch: Materials Science . 9th edition. Wiley-VCH, 2003, ISBN 3-527-30535-1 .

Individual evidence

1. ↑ Dieter Sautter, Hans Weinerth (Ed.): Lexicon Electronics And Microelectronics . Springer, 1993, ISBN 3-642-58006-8 , impurities , S. 1011 .
2. ↑ ^{a b c} S. M. Sze: Physics of Semiconductor Devices . 2nd Edition. Wiley & Sons, 1981, ISBN 0-471-09837-X , pp. 21 (Newer editions do not contain an overview for germanium).
3. ↑ Werner Schatt, Hartmut Worch: Material Science . 9th edition. Wiley-VCH, 2003, ISBN 3-527-30535-1 , pp. 439 .
4. ↑ ^{a b} Frank Thuselt: Physics of semiconductor components: Introductory textbook for engineers and physicists . Springer, 2005, ISBN 978-3-540-22316-0 , pp. 65 .
5. ↑ ^{a b} Rolf Sauer: Semiconductor physics: textbook for physicists and engineers . Oldenbourg Wissenschaftsverlag, 2008, ISBN 978-3-486-58863-7 , p. 336 .