Ohmic contact
Encyclopedia
An ohmic contact is a region on a semiconductor
Semiconductor
A semiconductor is a material with electrical conductivity due to electron flow intermediate in magnitude between that of a conductor and an insulator. This means a conductivity roughly in the range of 103 to 10−8 siemens per centimeter...

 device that has been prepared so that the current-voltage
Current-voltage characteristic
A current–voltage characteristic is a relationship, typically represented as a chart or graph, between an electric current and a corresponding voltage, or potential difference.-In electronics:...

 (I-V) curve of the device is linear and symmetric. If the I-V characteristic is non-linear and asymmetric, the contact is not ohmic, but is a blocking or Schottky
Schottky diode
The Schottky diode is a semiconductor diode with a low forward voltage drop and a very fast switching action...

 contact. Typical ohmic contacts on semiconductors are sputtered
Sputter deposition
Sputter deposition is a physical vapor deposition method of depositing thin films by sputtering, that is ejecting, material from a "target," that is source, which then deposits onto a "substrate," such as a silicon wafer...

 or evaporated
Evaporation (deposition)
Evaporation is a common method of thin film deposition. The source material is evaporated in a vacuum. The vacuum allows vapor particles to travel directly to the target object , where they condense back to a solid state...

 metal pads that are patterned using photolithography
Photolithography
Photolithography is a process used in microfabrication to selectively remove parts of a thin film or the bulk of a substrate. It uses light to transfer a geometric pattern from a photomask to a light-sensitive chemical "photoresist", or simply "resist," on the substrate...

. Low-resistance, stable contacts are critical for the performance and reliability of integrated circuits and their preparation and characterization are major efforts in circuit fabrication. As a rule, ohmic contacts on semiconductors form when the semiconductor is highly doped. A high doping would narrow the depletion region at the interface and allow electrons to flow in both directions easily at any potential by tunneling through the barrier.

Theory

The Fermi level
Fermi energy
The Fermi energy is a concept in quantum mechanics usually referring to the energy of the highest occupied quantum state in a system of fermions at absolute zero temperature....

 (or strictly speaking, electrochemical potential) of any two solids in contact must be equal in thermal equilibrium. The difference between the Fermi energy and the vacuum level is termed the work function
Work function
In solid-state physics, the work function is the minimum energy needed to remove an electron from a solid to a point immediately outside the solid surface...

. A contact metal and a semiconductor can have different work functions, denoted and respectively. If so, when the two materials are placed in contact, electrons will flow from the one with the lower work function until the Fermi levels equilibrate. As a result, the material with the lower work function will take on a slight positive charge while that with the higher work function will become slightly negative. The resulting electrostatic potential is termed the built-in potential designated by . This contact potential will occur between any two solids and is the underlying cause of phenomena such as rectification in diode
Diode
In electronics, a diode is a type of two-terminal electronic component with a nonlinear current–voltage characteristic. A semiconductor diode, the most common type today, is a crystalline piece of semiconductor material connected to two electrical terminals...

s. The built-in field is the cause of band-bending in the semiconductor near the junction. Noticeable band-bending does not occur in most metals since their very short screening length
Electric field screening
Screening is the damping of electric fields caused by the presence of mobile charge carriers. It is an important part of the behavior of charge-carrying fluids, such as ionized gases and conduction electrons in semiconductors and metals....

 means that any electrical field extends only a short distance beyond the interface.

In a classical physics picture, in order to surmount the barrier, a carrier in the semiconductor must gain enough energy to jump from the Fermi level to the top of the bent conduction band. The needed barrier-surmounting energy is the sum of the built-in potential and the offset between the Fermi level and the conduction band. Equivalently for n-type semiconductor
N-type semiconductor
N-type semiconductors are a type of extrinsic semiconductor where the dopant atoms are capable of providing extra conduction electrons to the host material . This creates an excess of negative electron charge carriers....

s, where is the semiconductor's electron affinity
Electron affinity
The Electron affinity of an atom or molecule is defined as the amount of energy released when an electron is added to a neutral atom or molecule to form a negative ion....

, defined to be the difference between the vacuum level and the conduction band
Conduction band
In the solid-state physics field of semiconductors and insulators, the conduction band is the range of electron energies, higher than that of the valence band, sufficient to free an electron from binding with its individual atom and allow it to move freely within the atomic lattice of the material...

 (CB) level. For p-type
P-type semiconductor
A P-type semiconductor is obtained by carrying out a process of doping: that is, adding a certain type of atoms to the semiconductor in order to increase the number of free charge carriers ....

 materials, where is the bandgap. When the excitation over the barrier is thermal, the process is called thermionic emission
Thermionic emission
Thermionic emission is the heat-induced flow of charge carriers from a surface or over a potential-energy barrier. This occurs because the thermal energy given to the carrier overcomes the binding potential, also known as work function of the metal. The charge carriers can be electrons or ions, and...

. An equally important process in real contacts is quantum mechanical
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

 tunneling
Quantum tunnelling
Quantum tunnelling refers to the quantum mechanical phenomenon where a particle tunnels through a barrier that it classically could not surmount. This plays an essential role in several physical phenomena, such as the nuclear fusion that occurs in main sequence stars like the sun, and has important...

. The WKB approximation
WKB approximation
In mathematical physics, the WKB approximation or WKB method is a method for finding approximate solutions to linear partial differential equations with spatially varying coefficients...

 describes the simplest picture of tunnelling in which the probability of barrier penetration is exponentially dependent on the product of the barrier height and thickness. In the case of contacts, the thickness is given by the depletion width, which is the length scale that the built-in field penetrates into the semiconductor. The width of the depletion layer can be calculated by solving Poisson's equation
Poisson's equation
In mathematics, Poisson's equation is a partial differential equation of elliptic type with broad utility in electrostatics, mechanical engineering and theoretical physics...

 and considering the presence of dopant
Dopant
A dopant, also called a doping agent, is a trace impurity element that is inserted into a substance in order to alter the electrical properties or the optical properties of the substance. In the case of crystalline substances, the atoms of the dopant very commonly take the place of elements that...

s in the semiconductor:


where in MKS units
Mks system of units
The MKS system of units is a physical system of units that expresses any given measurement using fundamental units of the metre, kilogram, and/or second ....

  is the net charge density and is the dielectric constant
Dielectric constant
The relative permittivity of a material under given conditions reflects the extent to which it concentrates electrostatic lines of flux. In technical terms, it is the ratio of the amount of electrical energy stored in a material by an applied voltage, relative to that stored in a vacuum...

. The geometry is one-dimensional since the interface is assumed to be planar. Integrating the equation once, approximating the charge density as being constant over the depletion width, we get


The constant of integration  due to the definition of the depletion width as the length over which the interface is fully screened. Then


where the fact that has been used to fix the remaining integration constant. This equation for describes the dashed blue curves in the right-hand panels of the figures. The depletion width can then be determined by setting which results in


For 0 < x < W, is the net charge density of ionized donor or acceptors in the completely depleted semiconductor and is the electronic charge
Elementary charge
The elementary charge, usually denoted as e, is the electric charge carried by a single proton, or equivalently, the absolute value of the electric charge carried by a single electron. This elementary charge is a fundamental physical constant. To avoid confusion over its sign, e is sometimes called...

. and have positive signs for n-type semiconductors and negative signs for p-type semiconductors giving the positive curvature for n-type and negative curvature for p-type as shown in the figures.

Note from this crude derivation that the barrier height (dependent on electron affinity and built-in field) and barrier thickness (dependent on built-in field, semiconductor dielectric constant and doping density) can only be modified by changing the metal or changing the doping density. In general an engineer will choose a contact metal to be conductive, non-reactive, thermally stable, electrically stable and low-stress, and then will increase the doping density below the contact to narrow the width of the barrier region. The highly doped regions are termed or depending on the carrier type. Since the transmission coefficient
Transmission coefficient
The transmission coefficient is used in physics and electrical engineering when wave propagation in a medium containing discontinuities is considered...

 in tunneling depends exponentially on particle mass, semiconductors with lower effective masses are more easily contacted. In addition, semiconductors with smaller bandgaps more readily form ohmic contacts because their electron affinities (and thus barrier heights) tend to be lower.

The simple theory presented above predicts that , so naively metals whose work functions are close to the semiconductor's electron affinity should most easily form ohmic contacts. In fact, metals with high work functions form the best contacts to p-type semiconductors while those with low work functions form the best contacts to n-type semiconductors. Unfortunately experiments have shown that the predictive power of the model doesn't extend much beyond this statement. Under realistic conditions, contact metals may react with semiconductor surfaces to form a compound with new electronic properties. A contamination layer at the interface may effectively widen the barrier. The surface of the semiconductor may reconstruct
Surface reconstruction
Surface reconstruction refers to the process by which atoms at the surface of a crystal assume a different structure than that of the bulk. Surface reconstructions are important in that they help in the understanding of surface chemistry for various materials, especially in the case where another...

 leading to a new electronic state. The dependence of contact resistance on the details of the interfacial chemistry is what makes the reproducible fabrication of ohmic contacts such a manufacturing challenge.

Preparation and characterization of ohmic contacts

The fabrication of ohmic contacts is a much-studied part of materials engineering that nonetheless remains something of an art. The reproducible, reliable fabrication of contacts relies on extreme cleanliness of the semiconductor surface. Since a native oxide rapidly forms on the surface of silicon
Silicon
Silicon is a chemical element with the symbol Si and atomic number 14. A tetravalent metalloid, it is less reactive than its chemical analog carbon, the nonmetal directly above it in the periodic table, but more reactive than germanium, the metalloid directly below it in the table...

, for example, the performance of a contact can depend sensitively on the details of preparation.

The fundamental steps in contact fabrication are semiconductor surface cleaning, contact metal deposition, patterning and annealing. Surface cleaning may be performed by sputter-etching, chemical etching, reactive gas etching or ion milling. For example, the native oxide of silicon may be removed with an HF dip, while GaAs
Gaas
Gaas is a commune in the Landes department in Aquitaine in south-western France....

 is more typically cleaned by a bromine-methanol dip. After cleaning, metals are deposited via sputter deposition
Sputter deposition
Sputter deposition is a physical vapor deposition method of depositing thin films by sputtering, that is ejecting, material from a "target," that is source, which then deposits onto a "substrate," such as a silicon wafer...

, evaporation
Evaporation (deposition)
Evaporation is a common method of thin film deposition. The source material is evaporated in a vacuum. The vacuum allows vapor particles to travel directly to the target object , where they condense back to a solid state...

 or chemical vapor deposition
Chemical vapor deposition
Chemical vapor deposition is a chemical process used to produce high-purity, high-performance solid materials. The process is often used in the semiconductor industry to produce thin films. In a typical CVD process, the wafer is exposed to one or more volatile precursors, which react and/or...

 (CVD). Sputtering is a faster and more convenient method of metal deposition than evaporation but the ion bombardment from the plasma may induce surface states or even invert the charge carrier type at the surface. For this reason the gentler but still rapid CVD is increasingly preferred. Patterning of contacts is accomplished with standard photolithographic methods such as lift-off, where contact metal is deposited through holes in a photoresist layer that is later dissolved away. Post-deposition annealing of contacts is useful for relieving stress as well as for inducing any desirable reactions between the metal and the semiconductor.

The measurement of contact resistance
Contact resistance
The term contact resistance refers to the contribution to the total resistance of a material which comes from the electrical leads and connections as opposed to the intrinsic resistance, which is an inherent property, independent of the measurement method...

 is most simply performed using a four-point probe
Four-terminal sensing
Four-terminal sensing , 4-wire sensing, or 4-point probes method is an electrical impedance measuring technique that uses separate pairs of current-carrying and voltage-sensing electrodes to make more accurate measurements than traditional two-terminal sensing...

 although for more accurate determination, use of the transmission line method
Transmission line measurement
Transmission line measurement or Transfer Length Measurement is a technique used in semiconductor physics and engineering to determine the contact resistance between a metal and a semiconductor. The technique involves making a series of metal-semiconductor contacts separated by various distances...

 is typical.

Technologically important kinds of contacts

Modern ohmic contacts to silicon such as titanium-tungsten disilicide are usually silicide
Silicide
A silicide is a compound that has silicon with more electropositive elements.Silicon is more electropositive than carbon. Silicides are structurally closer to borides than to carbides....

s made by CVD. Contacts are often made by depositing the transition metal and forming the silicide by annealing
Annealing (metallurgy)
Annealing, in metallurgy and materials science, is a heat treatment wherein a material is altered, causing changes in its properties such as strength and hardness. It is a process that produces conditions by heating to above the recrystallization temperature, maintaining a suitable temperature, and...

 with the result that the silicide may be non-stoichiometric. Silicide contacts can also be deposited by direct sputtering of the compound or by ion implantation of the transition metal followed by annealing. Aluminum is another important contact metal for silicon which can be used with either the n-type or p-type semiconductor. As with other reactive metals, Al contributes to contact formation by consuming the oxygen
Oxygen
Oxygen is the element with atomic number 8 and represented by the symbol O. Its name derives from the Greek roots ὀξύς and -γενής , because at the time of naming, it was mistakenly thought that all acids required oxygen in their composition...

 in the native oxide. Silicides have largely replaced Al in part because the more refractory materials are less prone to diffuse into unintended areas especially during subsequent high-temperature processing.

Formation of contacts to compound semiconductors is considerably more difficult than with silicon. For example, GaAs surfaces tend to lose arsenic
Arsenic
Arsenic is a chemical element with the symbol As, atomic number 33 and relative atomic mass 74.92. Arsenic occurs in many minerals, usually in conjunction with sulfur and metals, and also as a pure elemental crystal. It was first documented by Albertus Magnus in 1250.Arsenic is a metalloid...

 and the trend towards As loss can be considerably exacerbated by the deposition of metal. In addition, the volatility of As limits the amount of post-deposition annealing that GaAs devices will tolerate. One solution for GaAs and other compound semiconductors is to deposit a low-bandgap alloy
Alloy
An alloy is a mixture or metallic solid solution composed of two or more elements. Complete solid solution alloys give single solid phase microstructure, while partial solutions give two or more phases that may or may not be homogeneous in distribution, depending on thermal history...

 contact layer as opposed to a heavily doped layer. For example, GaAs itself has a smaller bandgap than AlGaAs and so a layer of GaAs near its surface can promote ohmic behavior. In general the technology of ohmic contacts for III-V and II-VI semiconductors is much less developed than for Si.
Material Contact materials
Si
Silicon
Silicon is a chemical element with the symbol Si and atomic number 14. A tetravalent metalloid, it is less reactive than its chemical analog carbon, the nonmetal directly above it in the periodic table, but more reactive than germanium, the metalloid directly below it in the table...

Al, Al-Si, TiSi2, TiN
Titanium nitride
Titanium nitride is an extremely hard ceramic material, often used as a coating on titanium alloys, steel, carbide, and aluminium components to improve the substrate's surface properties....

, W
Tungsten
Tungsten , also known as wolfram , is a chemical element with the chemical symbol W and atomic number 74.A hard, rare metal under standard conditions when uncombined, tungsten is found naturally on Earth only in chemical compounds. It was identified as a new element in 1781, and first isolated as...

, MoSi2, PtSi, CoSi2, WSi2
Ge
Germanium
Germanium is a chemical element with the symbol Ge and atomic number 32. It is a lustrous, hard, grayish-white metalloid in the carbon group, chemically similar to its group neighbors tin and silicon. The isolated element is a semiconductor, with an appearance most similar to elemental silicon....

In
Indium
Indium is a chemical element with the symbol In and atomic number 49. This rare, very soft, malleable and easily fusible post-transition metal is chemically similar to gallium and thallium, and shows the intermediate properties between these two...

, AuGa, AuSb
GaAs AuGe, PdGe, Ti/Pt/Au
GaN Ti/Al/Ti/Au, Pd/Au
InSb  In
Indium
Indium is a chemical element with the symbol In and atomic number 49. This rare, very soft, malleable and easily fusible post-transition metal is chemically similar to gallium and thallium, and shows the intermediate properties between these two...

ZnO InSnO2
Indium tin oxide
Indium tin oxide is a solid solution of indium oxide and tin oxide , typically 90% In2O3, 10% SnO2 by weight. It is transparent and colorless in thin layers while in bulk form it is yellowish to grey...

, Al
CuIn1-xGaxSe2
Copper indium gallium selenide
Copper indium gallium selenide is a I-III-VI2 semiconductor material composed of copper, indium, gallium, and selenium. The material is a solid solution of copper indium selenide and copper gallium selenide...

Mo
Molybdenum
Molybdenum , is a Group 6 chemical element with the symbol Mo and atomic number 42. The name is from Neo-Latin Molybdaenum, from Ancient Greek , meaning lead, itself proposed as a loanword from Anatolian Luvian and Lydian languages, since its ores were confused with lead ores...

, InSnO2
Indium tin oxide
Indium tin oxide is a solid solution of indium oxide and tin oxide , typically 90% In2O3, 10% SnO2 by weight. It is transparent and colorless in thin layers while in bulk form it is yellowish to grey...

HgCdTe  In
Indium
Indium is a chemical element with the symbol In and atomic number 49. This rare, very soft, malleable and easily fusible post-transition metal is chemically similar to gallium and thallium, and shows the intermediate properties between these two...



Transparent or semi-transparent contacts are necessary for active matrix LCD displays, optoelectronic devices such as laser diode
Laser diode
The laser diode is a laser where the active medium is a semiconductor similar to that found in a light-emitting diode. The most common type of laser diode is formed from a p-n junction and powered by injected electric current...

s and photovoltaics
Photovoltaics
Photovoltaics is a method of generating electrical power by converting solar radiation into direct current electricity using semiconductors that exhibit the photovoltaic effect. Photovoltaic power generation employs solar panels composed of a number of solar cells containing a photovoltaic material...

. The most popular choice is indium tin oxide
Indium tin oxide
Indium tin oxide is a solid solution of indium oxide and tin oxide , typically 90% In2O3, 10% SnO2 by weight. It is transparent and colorless in thin layers while in bulk form it is yellowish to grey...

, a metal that is formed by reactive sputtering of an In-Sn target in an oxide atmosphere.

Significance

The RC time constant
RC time constant
In an RC circuit, the value of the time constant is equal to the product of the circuit resistance and the circuit capacitance , i.e. \tau = R × C. It is the time required to charge the capacitor, through the resistor, to 63.2 percent of full charge; or to discharge it to 36.8 percent of its...

 associated with contact resistance can limit the frequency response
Frequency response
Frequency response is the quantitative measure of the output spectrum of a system or device in response to a stimulus, and is used to characterize the dynamics of the system. It is a measure of magnitude and phase of the output as a function of frequency, in comparison to the input...

 of devices. The charging and discharging of the leads resistance is a major cause of power dissipation in high clock rate
Clock rate
The clock rate typically refers to the frequency that a CPU is running at.For example, a crystal oscillator frequency reference typically is synonymous with a fixed sinusoidal waveform, a clock rate is that frequency reference translated by electronic circuitry into a corresponding square wave...

 digital electronics. Contact resistance causes power dissipation via Joule heating
Joule heating
Joule heating, also known as ohmic heating and resistive heating, is the process by which the passage of an electric current through a conductor releases heat. It was first studied by James Prescott Joule in 1841. Joule immersed a length of wire in a fixed mass of water and measured the temperature...

 in low frequency and analog circuits (for example, solar cells) made from less common semiconductors. The establishment of a contact fabrication methodology is a critical part of the technological development of any new semiconductor. Electromigration
Electromigration
Electromigration is the transport of material caused by the gradual movement of the ions in a conductor due to the momentum transfer between conducting electrons and diffusing metal atoms. The effect is important in applications where high direct current densities are used, such as in...

 and delamination
Delamination
Delamination is a mode of failure for composite materials. Modes of failure are also known as 'failure mechanisms'. In laminated materials, repeated cyclic stresses, impact, and so on can cause layers to separate, forming a mica-like structure of separate layers, with significant loss of mechanical...

at contacts are also a limitation on the lifetime of electronic devices.

See also

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