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Diffusion current Density is a
current Currents, Current or The Current may refer to: Science and technology * Current (fluid), the flow of a liquid or a gas ** Air current, a flow of air ** Ocean current, a current in the ocean *** Rip current, a kind of water current ** Current (stre ...
in a
semiconductor A semiconductor is a material which has an electrical conductivity value falling between that of a conductor, such as copper, and an insulator, such as glass. Its resistivity falls as its temperature rises; metals behave in the opposite way. ...
caused by the
diffusion Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical ...
of charge carriers (
electrons The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no ...
and/or
electron holes In physics, chemistry, and electronic engineering, an electron hole (often simply called a hole) is a quasiparticle which is the lack of an electron at a position where one could exist in an atom or atomic lattice. Since in a normal atom or c ...
). This is the current which is due to the transport of charges occurring because of non-uniform concentration of charged particles in a semiconductor. The drift current, by contrast, is due to the motion of charge carriers due to the force exerted on them by an electric field. Diffusion current can be in the same or opposite direction of a drift current. The diffusion current and drift current together are described by the drift–diffusion equation.McGraw Hill Encyclopaedia of Physics (2nd Edition), C.B. Parker, 1994, It is necessary to consider the part of diffusion current when describing many semiconductor devices. For example, the current near the
depletion region In semiconductor physics, the depletion region, also called depletion layer, depletion zone, junction region, space charge region or space charge layer, is an insulating region within a conductive, doped semiconductor material where the mobile ...
of a
p–n junction A p–n junction is a boundary or interface between two types of semiconductor materials, p-type and n-type, inside a single crystal of semiconductor. The "p" (positive) side contains an excess of holes, while the "n" (negative) side contai ...
is dominated by the diffusion current. Inside the depletion region, both diffusion current and drift current are present. At equilibrium in a p–n junction, the forward diffusion current in the depletion region is balanced with a reverse drift current, so that the net current is zero. The diffusion constant for a doped material can be determined with the Haynes–Shockley experiment. Alternatively, if the carrier mobility is known, the diffusion coefficient may be determined from the Einstein relation on electrical mobility.


Overview


Diffusion current versus drift current

The following table compares the two types of current: :


Carrier actions

No external electric field across the semiconductor is required for a diffusion current to take place. This is because diffusion takes place due to the change in concentration of the carrier particles and not the concentrations themselves. The carrier particles, namely the holes and electrons of a semiconductor, move from a place of higher concentration to a place of lower concentration. Hence, due to the flow of holes and electrons there is a current. This current is called the diffusion current. The drift current and the diffusion current make up the total current in the conductor. The change in the concentration of the carrier particles develops a gradient. Due to this gradient, an electric field is produced in the semiconductor.


Derivation

In a region where n and p vary with distance, a diffusion current is superimposed on that due to conductivity. This diffusion current is governed by
Fick's Law Fick's laws of diffusion describe diffusion and were derived by Adolf Fick in 1855. They can be used to solve for the diffusion coefficient, . Fick's first law can be used to derive his second law which in turn is identical to the diffusion e ...
: :F=-D_\text\nabla n where: :''F'' is flux. :''D''e is the
diffusion coefficient Diffusivity, mass diffusivity or diffusion coefficient is a proportionality constant between the molar flux due to molecular diffusion and the gradient in the concentration of the species (or the driving force for diffusion). Diffusivity is enco ...
or diffusivity :\nabla n is the concentration gradient of electrons : there is a minus sign because the direction of diffusion is opposite to that of the concentration gradient The diffusion coefficient for a charge carrier is related to its mobility by the Einstein relation: :D_\text = \frac where: :''k''B is the
Boltzmann constant The Boltzmann constant ( or ) is the proportionality factor that relates the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas constan ...
:''T'' is the
absolute temperature Thermodynamic temperature is a quantity defined in thermodynamics as distinct from kinetic theory or statistical mechanics. Historically, thermodynamic temperature was defined by Kelvin in terms of a macroscopic relation between thermodynamic wo ...
:''e'' is the electrical charge of an electron Now let's focus on the diffusive current in one-dimension along the x-axis: :F_x=-D_\text\frac The electron current density Je is related to flux, ''F'', by: :J_\text=-eF Thus :J_\text=+eD_\text\frac Similarly for holes: :J_\text=-eD_\text\frac Notice that for electrons the diffusive current is in the same direction as the electron density gradient because the minus sign from the negative charge and
Fick's Law Fick's laws of diffusion describe diffusion and were derived by Adolf Fick in 1855. They can be used to solve for the diffusion coefficient, . Fick's first law can be used to derive his second law which in turn is identical to the diffusion e ...
cancel each other out. However, holes have positive charges and therefore the minus sign from Fick's Law is carried over. Superimpose the diffusive current on the
drift current In condensed matter physics and electrochemistry, drift current is the electric current, or movement of charge carriers, which is due to the applied electric field, often stated as the electromotive force over a given distance. When an electric fi ...
to get :J_\text=e\mu_\textnE+eD_\text\frac for electrons and :J_\text=e\mu_\textpE-eD_\text\frac for holes Consider electrons in a constant electric field ''E''. Electrons will flow (i.e. there is a drift current) until the density gradient builds up enough for the diffusion current to exactly balance the drift current. So at equilibrium there is no net current flow: :e\mu_\textnE+eD_\text\frac=0


Example

To derive the diffusion current in a semiconductor diode, the depletion layer must be large compared to the mean free path. One begins with the equation for the net
current density In electromagnetism, current density is the amount of charge per unit time that flows through a unit area of a chosen cross section. The current density vector is defined as a vector whose magnitude is the electric current per cross-sectional ar ...
''J'' in a semiconductor diode, where ''D'' is the
diffusion coefficient Diffusivity, mass diffusivity or diffusion coefficient is a proportionality constant between the molar flux due to molecular diffusion and the gradient in the concentration of the species (or the driving force for diffusion). Diffusivity is enco ...
for the electron in the considered medium, ''n'' is the number of electrons per unit volume (i.e. number density), ''q'' is the magnitude of charge of an electron, ''μ'' is electron mobility in the medium, and ''E'' = −''d''Φ/''dx'' (Φ potential difference) is the
electric field An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field ...
as the
potential gradient In physics, chemistry and biology, a potential gradient is the local rate of change of the potential with respect to displacement, i.e. spatial derivative, or gradient. This quantity frequently occurs in equations of physical processes because ...
of the
electric potential The electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is defined as the amount of work energy needed to move a unit of electric charge from a reference point to the specific point in ...
. According to the Einstein relation on electrical mobility D = \mu V_t and V_t = k T / q. Thus, substituting ''E'' for the potential gradient in the above equation () and multiplying both sides with exp(−Φ/Vt), () becomes: Integrating equation () over the depletion region gives :J = \frac which can be written as where :\Phi^* = \Phi_B + \Phi_i - V_a The denominator in equation () can be solved by using the following equation: :\Phi = - \frac Therefore, Φ* can be written as: Since the ''x'' ≪ ''xd'', the term (''xd'' − ''x''/2) ≈ ''xd'', using this approximation equation () is solved as follows: :\int_0^ e^dx = x_d \frac, since (Φ''i'' − ''Va'') > ''Vt''. One obtains the equation of current caused due to diffusion: From equation (), one can observe that the current depends exponentially on the input voltage ''Va'', also the barrier height Φ''B''. From equation (), ''Va'' can be written as the function of electric field intensity, which is as follows: Substituting equation () in equation () gives: From equation (), one can observe that when a zero voltage is applied to the semi-conductor diode, the drift current totally balances the diffusion current. Hence, the net current in a semiconductor diode at zero potential is always zero. The equation above can be applied to model semiconductor devices. When the density of electrons is not in equilibrium, diffusion of electrons will occur. For example, when a bias is applied to two ends of a chunk of semiconductor, or a light is shining in one place (see right figure), electrons will diffuse from high density regions (center) to low density regions (two ends), forming a gradient of electron density. This process generates diffusion current.


See also

*
Alternating current Alternating current (AC) is an electric current which periodically reverses direction and changes its magnitude continuously with time in contrast to direct current (DC) which flows only in one direction. Alternating current is the form in whic ...
*
Conduction band In solid-state physics, the valence band and conduction band are the bands closest to the Fermi level, and thus determine the electrical conductivity of the solid. In nonmetals, the valence band is the highest range of electron energies in ...
*
Convection–diffusion equation The convection–diffusion equation is a combination of the diffusion and convection (advection) equations, and describes physical phenomena where particles, energy, or other physical quantities are transferred inside a physical system due to two p ...
*
Direct current Direct current (DC) is one-directional flow of electric charge. An electrochemical cell is a prime example of DC power. Direct current may flow through a conductor such as a wire, but can also flow through semiconductors, insulators, or e ...
*
Drift current In condensed matter physics and electrochemistry, drift current is the electric current, or movement of charge carriers, which is due to the applied electric field, often stated as the electromotive force over a given distance. When an electric fi ...
*
Free electron model In solid-state physics, the free electron model is a quantum mechanical model for the behaviour of charge carriers in a metallic solid. It was developed in 1927, principally by Arnold Sommerfeld, who combined the classical Drude model with quantu ...
*
Random walk In mathematics, a random walk is a random process that describes a path that consists of a succession of random steps on some Space (mathematics), mathematical space. An elementary example of a random walk is the random walk on the integer n ...
*
Maximal Entropy Random Walk Maximal entropy random walk (MERW) is a popular type of biased random walk on a graph, in which transition probabilities are chosen accordingly to the principle of maximum entropy, which says that the probability distribution which best represents ...
– diffusion in agreement with quantum predictions


References

* ''Encyclopaedia of Physics'' (2nd Edition), R.G. Lerner, G.L. Trigg, VHC publishers, 1991, ISBN (Verlagsgesellschaft) 3-527-26954-1, ISBN (VHC Inc.) 0-89573-752-3 * ''Concepts of Modern Physics'' (4th Edition), A. Beiser, Physics, McGraw-Hill (International), 1987, * ''Solid State Physics'' (2nd Edition), J.R. Hook, H.E. Hall, Manchester Physics Series, John Wiley & Sons, 2010, * Ben G. Streetman, Santay Kumar Banerjee; ''Solid State Electronic Devices'' (6th Edition), Pearson International Edition; pp. 126–135. * * *{{cite web, title=derivation of difusion current , url=http://www.ee.ui.ac.id/~astha/courses/ts/teksem/msdiffus.htm , accessdate=15 October 2011 , url-status=dead , archiveurl=https://web.archive.org/web/20111214105649/http://www.ee.ui.ac.id/~astha/courses/ts/teksem/msdiffus.htm , archivedate=14 December 2011 Semiconductors Electric current Charge carriers