# Doping (semiconductor)

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In semiconductor production, doping intentionally introduces impurities into an extremely pure (also referred to as intrinsic) semiconductor for the purpose of modulating its electrical properties. The impurities are dependent upon the type of semiconductor. Lightly and moderately doped semiconductors are referred to as extrinsic. A semiconductor doped to such high levels that it acts more like a conductor than a semiconductor is referred to as degenerate.

In the context of phosphors and scintillators, doping is better known as activation.

## History

The effects of semiconductor doping were long known empirically in such devices as crystal radio detectors and selenium rectifiers. However, the process was formally first developed by John Robert Woodyard working at Sperry Gyroscope Company during World War II.[1] The demands of his work on radar denied Woodyard the opportunity to pursue research on semiconductor doping. However, after the war ended, his patent proved the grounds of extensive litigation by Sperry Rand.[2] Related work was performed at Bell Labs by Gordon K. Teal and Morgan Sparks.[3]

## Carrier concentration

The quantity of dopant introduced to an intrinsic semiconductor determines its concentration and indirectly affects many of its electrical properties. The most important factor that doping directly affects is the material's carrier concentration. In an intrinsic semiconductor under thermal equilibrium, the concentration of electrons and holes is equivalent. That is,

$n = p = n_i.\$

If we have a non-intrinsic semiconductor in thermal equilibrium the relation becomes (for low doping):

$n_0 \cdot p_0 = n_i^2\$

where n0 is the concentration of conducting electrons, p0 is the electron hole concentration, and ni is the material's intrinsic carrier concentration. Intrinsic carrier concentration varies between materials and is dependent on temperature. Silicon's ni, for example, is roughly 1.08×1010 cm−3 at 300 kelvin (room temperature).[4]

In general, an increase in doping concentration affords an increase in conductivity due to the higher concentration of carriers available for conduction. Degenerate (very highly doped) semiconductors have conductivity levels comparable to metals and are often used in modern integrated circuits as a replacement for metal. Often superscript plus and minus symbols are used to denote relative doping concentration in semiconductors. For example, n+ denotes an n-type semiconductor with a high, often degenerate, doping concentration. Similarly, p would indicate a very lightly doped p-type material. Even degenerate levels of doping imply low concentrations of impurities with respect to the base semiconductor. In crystalline intrinsic silicon, there are approximately 5×1022 atoms/cm³. Doping concentration for silicon semiconductors may range anywhere from 1013 cm−3 to 1018 cm−3. Doping concentration above about 1018 cm−3 is considered degenerate at room temperature. Degenerately doped silicon contains a proportion of impurity to silicon on the order of parts per thousand. This proportion may be reduced to parts per billion in very lightly doped silicon. Typical concentration values fall somewhere in this range and are tailored to produce the desired properties in the device that the semiconductor is intended for.

## Effect on band structure

Band diagram of PN junction operation in forward bias mode showing reducing depletion width. Both p and n junctions are doped at a 1×1015/cm3 doping level, leading to built-in potential of ~0.59 V. Reducing depletion width can be inferred from the shrinking charge profile, as fewer dopants are exposed with increasing forward bias.[5]

Doping a semiconductor crystal introduces allowed energy states within the band gap but very close to the energy band that corresponds to the dopant type. In other words, donor impurities create states near the conduction band while acceptors create states near the valence band. The gap between these energy states and the nearest energy band is usually referred to as dopant-site bonding energy or EB and is relatively small. For example, the EB for boron in silicon bulk is 0.045 eV, compared with silicon's band gap of about 1.12 eV. Because EB is so small, room temperature is hot enough to thermally ionize practically all of the dopant atoms and create free carriers in the conduction or valence bands.

Dopants also have the important effect of shifting the energy bands relative to the Fermi level. The energy band that corresponds with the dopant with the greatest concentration ends up closer to the Fermi level. Since the Fermi level must remain constant in a system in thermodynamic equilibrium, stacking layers of materials with different properties leads to many useful electrical properties induced by band bending, if the interfaces can be made cleanly enough. For example, the p-n junction's properties are due to the band bending that happens as a result of the necessity to line up the bands in contacting regions of p-type and n-type material. This effect is shown in a band diagram. The band diagram typically indicates the variation in the valence band and conduction band edges versus some spatial dimension, often denoted x. The Fermi level is also usually indicated in the diagram. Sometimes the intrinsic Fermi level, Ei, which is the Fermi level in the absence of doping, is shown. These diagrams are useful in explaining the operation of many kinds of semiconductor devices.

### Relationship to carrier concentration (low doping)

For low levels of doping, the relevant energy states are populated sparsely by electrons (conduction band) or holes (valence band). This means it is possible to write simple expressions for the electron and hole carrier concentrations, by ignoring Pauli exclusion (via Maxwell–Boltzmann statistics):

$n_e = N_{\rm C}(T) \exp((E_{\rm F} - E_{\rm C})/kT), \quad n_h = N_{\rm V}(T) \exp((E_{\rm V} - E_{\rm F})/kT),$

where EF is the Fermi level, EC is the minimum energy of the conduction band, and EV is the maximum energy of the valence band. These are related to the value of the intrinsic concentration via[6]

$n_i^2 = n_h n_e = N_{\rm V}(T) N_{\rm C}(T) \exp((E_{\rm V}-E_{\rm C})/kT),$

an expression which is independent of the doping level, since EC - EV (the band gap) does not change with doping.

The concentration factors NC(T) and NV(T) are given by

$N_{\rm C}(T) = 2(2\pi m_e^* kT/h^2)^{3/2} \quad N_{\rm V}(T) = 2(2\pi m_v^* kT/h^2)^{3/2}.$

where me* and mh* are the density of states effective masses of electrons and holes, respectively, quantities that are roughly constant over temperature.[6]

## Techniques of doping and synthesis

The synthesis of n-type semiconductors may involve the use of vapor-phase epitaxy. In vapor-phase epitaxy, a gas containing the negative dopant is passed over the substrate wafer. In the case of n-type GaAs doping, hydrogen sulfide is passed over the gallium arsenide, and sulfur is incorporated into the structure.[7] This process is characterized by a constant concentration of sulfur on the surface.[8] In the case of semiconductors in general, only a very thin layer of the wafer needs to be doped in order to obtain the desired electronic properties.[9] The reaction conditions typically range from 600 to 800 °C for the n-doping with group VI elements,[7] and the time is typically 6–12 hours depending on the temperature.

## Process

Some dopants are added as the (usually silicon) boule is grown, giving each wafer an almost uniform initial doping.[10] To define circuit elements, selected areas — typically controlled by photolithography[11] — are further doped by such processes as diffusion[12] and ion implantation, the latter method being more popular in large production runs because of increased controllability.

Small numbers of dopant atoms can change the ability of a semiconductor to conduct electricity. When on the order of one dopant atom is added per 100 million atoms, the doping is said to be low or light. When many more dopant atoms are added, on the order of one per ten thousand atoms, the doping is referred to as heavy or high. This is often shown as n+ for n-type doping or p+ for p-type doping. (See the article on semiconductors for a more detailed description of the doping mechanism.)

## Dopant elements

### Group IV semiconductors

(Note: When discussing periodic table groups, semiconductor physicists always use an older notation, not the current IUPAC group notation. For example, the carbon group is called "Group IV", not "Group 14".)

For the Group IV semiconductors such as diamond, silicon, germanium, silicon carbide, and silicon germanium, the most common dopants are acceptors from Group III or donors from Group V elements. Boron, arsenic, phosphorus, and occasionally gallium are used to dope silicon. Boron is the p-type dopant of choice for silicon integrated circuit production because it diffuses at a rate that makes junction depths easily controllable. Phosphorus is typically used for bulk-doping of silicon wafers, while arsenic is used to diffuse junctions, because it diffuses more slowly than phosphorus and is thus more controllable.

By doping pure silicon with Group V elements such as phosphorus, extra valence electrons are added that become unbonded from individual atoms and allow the compound to be an electrically conductive n-type semiconductor. Doping with Group III elements, which are missing the fourth valence electron, creates "broken bonds" (holes) in the silicon lattice that are free to move. The result is an electrically conductive p-type semiconductor. In this context, a Group V element is said to behave as an electron donor, and a group III element as an acceptor. This is a key concept in the physics of a diode.

A very heavily doped semiconductor behaves more like a good conductor (metal) and thus exhibits more linear positive thermal coefficient. Such effect is used for instance in sensistors.[13] Lower dosage of doping is used in other types (NTC or PTC) thermistors.

## Compensation

In most cases many types of impurities will be present in the resultant doped semiconductor. If an equal number of donors and acceptors are present in the semiconductor, the extra core electrons provided by the former will be used to satisfy the broken bonds due to the latter, so that doping produces no free carriers of either type. This phenomenon is known as compensation, and occurs at the p-n junction in the vast majority of semiconductor devices. Partial compensation, where donors outnumber acceptors or vice versa, allows device makers to repeatedly reverse (invert) the type of a given portion of the material by applying successively higher doses of dopants, so-called counterdoping. Most modern semiconductors are made by successive selective counterdoping steps to create the necessary P and N type areas.[14]

Although compensation can be used to increase or decrease the number of donors or acceptors, the electron and hole mobility is always decreased by compensation because mobility is affected by the sum of the donor and acceptor ions.

## Doping in organic conductors

Main article: Conductive polymer

Conductive polymers can be doped by adding chemical reactants to oxidize, or sometimes reduce, the system so that electrons are pushed into the conducting orbitals within the already potentially conducting system. There are two primary methods of doping a conductive polymer, both of which use an oxidation-reduction (i.e., redox) process.

1. Chemical doping involves exposing a polymer such as melanin, typically a thin film, to an oxidant such as iodine or bromine. Alternatively, the polymer can be exposed to a reductant; this method is far less common, and typically involves alkali metals.
2. Electrochemical doping involves suspending a polymer-coated, working electrode in an electrolyte solution in which the polymer is insoluble along with separate counter and reference electrodes. An electric potential difference is created between the electrodes that causes a charge and the appropriate counter ion from the electrolyte to enter the polymer in the form of electron addition (i.e., n-doping) or removal (i.e., p-doping).

N-doping is much less common because the Earth's atmosphere is oxygen-rich, thus creating an oxidizing environment. An electron-rich, n-doped polymer will react immediately with elemental oxygen to de-dope (i.e., reoxidize to the neutral state) the polymer. Thus, chemical n-doping must be performed in an environment of inert gas (e.g., argon). Electrochemical n-doping is far more common in research, because it is easier to exclude oxygen from a solvent in a sealed flask. However, it is unlikely that n-doped conductive polymers are available commercially.

## Magnetic doping

Research on magnetic doping has shown that considerable alteration of certain properties such as specific heat may be affected by small concentrations of an impurity; for example, dopant impurities in semiconducting ferromagnetic alloys can generate different properties as first predicted by White, Hogan, Suhl and Nakamura.[15][16]

## Single dopants in semiconductors

The sensitive dependence of a semiconductor's electronic, optical, and magnetic properties on dopants has provided an extensive range of tunable phenomena to explore and apply to devices. Recently it has become possible to move past the tunable properties of an ensemble of dopants and to identify the effects of a solitary dopant on commercial device performance as well as locally on the fundamental properties of a semiconductor. New applications have become available that require the discrete character of a single dopant, such as single-spin devices in the area of quantum information or single-dopant transistors. Dramatic advances in the past decade towards observing, controllably creating and manipulating single dopants, as well as their application in novel devices have allowed opening the new field of solotronics (solitary dopant optoelectronics).[17]

## Neutron transmutation doping

Neutron transmutation doping (NTD) is an unusual doping method for special applications. Most commonly, it is used to dope silicon n-type in high-power electronics. It is based on the conversion of the Si-30 isotope into phosphorus atom by neutron absorption as follows:

$^{30}\mathrm{Si} \, (n,\gamma) \, ^{31}\mathrm{Si} \rightarrow \, ^{31}\mathrm{P} + \beta^- \; (\mathrm{T}_{1/2} = 2.62 h).$

In practice, the silicon is typically placed near a nuclear reactor to receive the neutrons. As neutrons continue to pass through the silicon, more and more phosphorus atoms are produced by transmutation, and therefore the doping becomes more and more strongly n-type. NTD is a far less common doping method than diffusion or ion implantation, but it has the advantage of creating an extremely uniform dopant distribution.[18][19]

## References

1. ^ U.S. Patent 2,530,110 filed, 1944, granted 1950
2. ^ "John Robert Woodyard, Electrical Engineering: Berkeley". University of California: In Memoriam. 1985. Retrieved 2007-08-12.
3. ^ Sparks, Morgan and Teal, Gordon K. "Method of Making P-N Junctions in Semiconductor Materials", U.S. Patent 2,631,356 (Filed June 15, 1950. Issued March 17, 1953)
4. ^ A.B Sproul, M.A Green (1991). "Improved value for the silicon intrinsic carrier concentration from 275 to 375 K". J. Appl. Phys. 70: 846. Bibcode:1991JAP....70..846S. doi:10.1063/1.349645.
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6. ^ a b Green, M. A. (1990). "Intrinsic concentration, effective densities of states, and effective mass in silicon". Journal of Applied Physics 67 (6): 2944–2941. Bibcode:1990JAP....67.2944G. doi:10.1063/1.345414. edit
7. ^ a b Schubert, E. F. (2005). Doping in III-V Semiconductors. pp. 241–243. ISBN 0-521-01784-X.
8. ^ Middleman, S. (1993). Process Engineering Analysis in Semiconductor Device Fabrication. pp. 29, 330–337. ISBN 0-07-041853-5.
9. ^ Deen, William M. (1998). Analysis of Transport Phenomena. pp. 91–94. ISBN 978-0-19-508494-8.
10. ^ Levy, Roland Albert (1989). Microelectronic Materials and Processes. Dordrecht: Kluwer Academic. pp. 6–7. ISBN 0-7923-0154-4. Retrieved 2008-02-23.
11. ^ "Computer History Museum - The Silicon Engine|1955 - Photolithography Techniques Are Used to Make Silicon Devices". Computerhistory.org. Retrieved 2014-06-12.
12. ^ Computer History Museum - The Silicon Engine 1954 - Diffusion Process Developed for Transistors
13. ^ Dharma Raj Cheruku, Battula Tirumala Krishna, Electronic Devices and Circuits, 2nd edition, 2008, Delhi, India, ISBN 978-81-317-0098-3
14. ^ Alan Hastings - The Art of Analog Layout, 2nd ed (2005, ISBN 0131464108)
15. ^ Hogan, C. Michael (1969). "Density of States of an Insulating Ferromagnetic Alloy". Physical Review 188 (2): 870. Bibcode:1969PhRv..188..870H. doi:10.1103/PhysRev.188.870.
16. ^ Zhang, X. Y.; Suhl, H. (1985). "Spin-wave-related period doublings and chaos under transverse pumping". Physical Review A 32 (4): 2530–2533. Bibcode:1985PhRvA..32.2530Z. doi:10.1103/PhysRevA.32.2530. PMID 9896377.
17. ^ Koenraad, Paul M.; Flatté, Michael E. (2011). "Single dopants in semiconductors". Nature Materials 10 (2): 91–100. Bibcode:2011NatMa..10...91K. doi:10.1038/nmat2940. PMID 21258352.
18. ^ B. J. Baliga, Modern Power Devices, p.32, John Wiley & Sons, New York (1987).
19. ^ P.E. Schmidt and J. Vedde, "High Resistivity NTD Production and Applications", Electrochemical Society Proceedings, Vol. 98-13, 3 (1998).