Electron mobility - Knowledge (XXG)

3663: 8252:"Extracting the field-effect mobility directly from the linear region of the output characteristic may yield larger values for the field-effect mobility than the actual one, since the drain current is linear only for very small VDS and large VG. In contrast, extracting the field-effect mobility from the saturated region might yield rather conservative values for the field-effect mobility, since the drain-current dependence from the gate-voltage becomes sub-quadratic for large VG as well as for small VDS." 2393:

charge, the defect becomes charged and therefore starts interacting with free carriers. If scattered carriers are in the inversion layer at the interface, the reduced dimensionality of the carriers makes the case differ from the case of bulk impurity scattering as carriers move only in two dimensions. Interfacial roughness also causes short-range scattering limiting the mobility of quasi-two-dimensional electrons at the interface.

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30-50 meV, for comparison energies of acoustic phonon are typically less than 1 meV but some might have energy in order of 10 meV. There is significant change in carrier energy during the scattering process. Optical or high-energy acoustic phonons can also cause intervalley or interband scattering, which means that scattering is not limited within single valley.

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and therefore the relaxation time is inversely proportional to the scattering probability. For example, lattice scattering alters the average electron velocity (in the electric-field direction), which in turn alters the tendency to scatter off impurities. There are more complicated formulas that attempt to take these effects into account.

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their crystal structure forms by randomly replacing some atoms in one of the sublattices (sublattice) of the crystal structure. Generally, this phenomenon is quite weak but in certain materials or circumstances, it can become dominant effect limiting conductivity. In bulk materials, interface scattering is usually ignored.

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A proxy for charge carrier mobility can be evaluated using time-resolved microwave conductivity (TRMC). A pulsed optical laser is used to create electrons and holes in a semiconductor, which are then detected as an increase in photoconductance. With knowledge of the sample absorbance, dimensions, and

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is a thermal average (Boltzmann statistics) over all electron or hole velocities in the lower conduction band or upper valence band, temperature dependence of the mobility can be determined. In here, the following definition for the scattering cross section is used: number of particles scattered into

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Matthiessen's rule is an approximation and is not universally valid. This rule is not valid if the factors affecting the mobility depend on each other, because individual scattering probabilities cannot be summed unless they are independent of each other. The average free time of flight of a carrier

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A simple model gives the approximate relation between scattering time (average time between scattering events) and mobility. It is assumed that after each scattering event, the carrier's motion is randomized, so it has zero average velocity. After that, it accelerates uniformly in the electric field,

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In compound (alloy) semiconductors, which many thermoelectric materials are, scattering caused by the perturbation of crystal potential due to the random positioning of substituting atom species in a relevant sublattice is known as alloy scattering. This can only happen in ternary or higher alloys as

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Piezoelectric effect can occur only in compound semiconductor due to their polar nature. It is small in most semiconductors but may lead to local electric fields that cause scattering of carriers by deflecting them, this effect is important mainly at low temperatures where other scattering mechanisms

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by the electric field until it scatters (collides) with something that changes its direction and/or energy. The most important sources of scattering in typical semiconductor materials, discussed below, are ionized impurity scattering and acoustic phonon scattering (also called lattice scattering). In

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During inelastic scattering processes, significant energy exchange happens. As with elastic phonon scattering also in the inelastic case, the potential arises from energy band deformations caused by atomic vibrations. Optical phonons causing inelastic scattering usually have the energy in the range

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If these scatterers are near the interface, the complexity of the problem increases due to the existence of crystal defects and disorders. Charge trapping centers that scatter free carriers form in many cases due to defects associated with dangling bonds. Scattering happens because after trapping a

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Surface roughness scattering caused by interfacial disorder is short range scattering limiting the mobility of quasi-two-dimensional electrons at the interface. From high-resolution transmission electron micrographs, it has been determined that the interface is not abrupt on the atomic level, but

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Usually, the electron drift velocity in a material is directly proportional to the electric field, which means that the electron mobility is a constant (independent of the electric field). When this is not true (for example, in very large electric fields), mobility depends on the electric field.

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and other devices can be very different depending on whether there are many electrons with low mobility or few electrons with high mobility. Therefore mobility is a very important parameter for semiconductor materials. Almost always, higher mobility leads to better device performance, with other

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Due to the Pauli exclusion principle, electrons can be considered as non-interacting if their density does not exceed the value 10~10 cm or electric field value 10 V/cm. However, significantly above these limits electron–electron scattering starts to dominate. Long range and nonlinearity of the

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between collisions, and the smaller the mobility. When determining the strength of these interactions due to the long-range nature of the Coulomb potential, other impurities and free carriers cause the range of interaction with the carriers to reduce significantly compared to bare Coulomb

3655:, electrons are only able to travel when in extended states, and are constantly being trapped in, and re-released from, the lower energy localized states. Because the probability of an electron being released from a trap depends on its thermal energy, mobility can be described by an 3546:

These two effects operate simultaneously on the carriers through Matthiessen's rule. At lower temperatures, ionized impurity scattering dominates, while at higher temperatures, phonon scattering dominates, and the actual mobility reaches a maximum at an intermediate temperature.

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is proportional to the product of mobility and carrier concentration. For example, the same conductivity could come from a small number of electrons with high mobility for each, or a large number of electrons with a small mobility for each. For semiconductors, the behavior of

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Elastic scattering means that energy is (almost) conserved during the scattering event. Some elastic scattering processes are scattering from acoustic phonons, impurity scattering, piezoelectric scattering, etc. In acoustic phonon scattering, electrons scatter from state

1985:(Si) the electron mobility is of the order of 1,000, in germanium around 4,000, and in gallium arsenide up to 10,000 cm/(V⋅s). Hole mobilities are generally lower and range from around 100 cm/(V⋅s) in gallium arsenide, to 450 in silicon, and 2,000 in germanium. 6201:

measurements. A series of photo-reflectance measurements are made as the sample is stepped through focus. The electron diffusion length and recombination time are determined by a regressive fit to the data. Then the Einstein relation is used to calculate the mobility.

2369:. This phenomenon is usually modeled by assuming that lattice vibrations cause small shifts in energy bands. The additional potential causing the scattering process is generated by the deviations of bands due to these small transitions from frozen lattice positions. 5341: 8399:

Evers, Wiel H.; Schins, Juleon M.; Aerts, Michiel; Kulkarni, Aditya; Capiod, Pierre; Berthe, Maxime; Grandidier, Bruno; Delerue, Christophe; van der Zant, Herre S. J.; van Overbeek, Carlo; Peters, Joep L.; Vanmaekelbergh, Daniel; Siebbeles, Laurens D. A. (2015).

3613:, and not contributing to transport. Extended states are spread over the extent of the material, not normalizable, and contribute to transport. Unlike crystalline semiconductors, mobility generally increases with temperature in disordered semiconductors. 2409:. Like electrons, phonons can be considered to be particles. A phonon can interact (collide) with an electron (or hole) and scatter it. At higher temperature, there are more phonons, and thus increased electron scattering, which tends to reduce mobility. 210:

Semiconductor mobility depends on the impurity concentrations (including donor and acceptor concentrations), defect concentration, temperature, and electron and hole concentrations. It also depends on the electric field, particularly at high fields when

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Mobility is usually a strong function of material impurities and temperature, and is determined empirically. Mobility values are typically presented in table or chart form. Mobility is also different for electrons and holes in a given material.

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The drift current density resulting from an electric field can be calculated from the drift velocity. Consider a sample with cross-sectional area A, length l and an electron concentration of n. The current carried by each electron must be

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Shin, Jungwoo; Gamage, Geethal Amila; Ding, Zhiwei; Chen, Ke; Tian, Fei; Qian, Xin; Zhou, Jiawei; Lee, Hwijong; Zhou, Jianshi; Shi, Li; Nguyen, Thanh; Han, Fei; Li, Mingda; Broido, David; Schmidt, Aaron; Ren, Zhifeng; Chen, Gang (2022).

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With increasing temperature, phonon concentration increases and causes increased scattering. Thus lattice scattering lowers the carrier mobility more and more at higher temperature. Theoretical calculations reveal that the mobility in

2384:. The amount of deflection depends on the speed of the carrier and its proximity to the ion. The more heavily a material is doped, the higher the probability that a carrier will collide with an ion in a given time, and the smaller the 2786: 2327:

In the regime of velocity saturation (or other high-field effects), mobility is a strong function of electric field. This means that mobility is a somewhat less useful concept, compared to simply discussing drift velocity directly.

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Normally, more than one source of scattering is present, for example both impurities and lattice phonons. It is normally a very good approximation to combine their influences using "Matthiessen's Rule" (developed from work by

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For a metal, described by a Fermi gas (Fermi liquid), quantum version of the Einstein relation should be used. Typically, temperature is much smaller than the Fermi energy, in this case one should use the following formula:

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with increasing temperature because the average thermal speeds of the carriers are increased. Thus, the carriers spend less time near an ionized impurity as they pass and the scattering effect of the ions is thus reduced.

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actual position of the interfacial plane varies one or two atomic layers along the surface. These variations are random and cause fluctuations of the energy levels at the interface, which then causes scattering.

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Semiconductors are doped with donors and/or acceptors, which are typically ionized, and are thus charged. The Coulombic forces will deflect an electron or hole approaching the ionized impurity. This is known as

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in semiconductors are electrons and holes. Their numbers are controlled by the concentrations of impurity elements, i.e. doping concentration. Thus doping concentration has great influence on carrier mobility.

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At low temperature, or in system with a large degree of structural disorder (such as fully amorphous systems), electrons cannot access delocalized states. In such a system, electrons can only travel by

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or impurity levels and temperature. It is one of the key material and semiconductor device properties that determine a device such as a transistor's ultimate limit of speed of response and frequency.

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However, when an electric field is applied, each electron or hole is accelerated by the electric field. If the electron were in a vacuum, it would be accelerated to ever-increasing velocity (called

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solid angle dΩ per unit time divided by number of particles per area per time (incident intensity), which comes from classical mechanics. As Boltzmann statistics are valid for semiconductors

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Chung, Y. J., Wang, C., Singh, S. K., Gupta, A., Baldwin, K. W., West, K. W., Shayegan, M., Pfeiffer, L. N., Winkler, R. (14 March 2022). "Record-quality GaAs two-dimensional hole systems".

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Ibach, Harald.; Luth, Hans. Solid-state physics : an introduction to principles of materials science / Harald Ibach, Hans Luth. New York: Springer, 2009. -(Advanced texts in physics)

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is the mobility that the material would have if there was lattice phonon scattering but no other source of scattering. Other terms may be added for other scattering sources, for example

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Y. Takeda and T.P. Pearsall, "Failure of Mattheissen's Rule in the Calculation of Carrier Mobility and Alloy Scattering Effects in Ga0.47In0.53As", Electronics Lett. 17, 573-574 (1981).

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While in crystalline materials electrons can be described by wavefunctions extended over the entire solid, this is not the case in systems with appreciable structural disorder, such as

706: 6461: 3483: 2217: 5119: 3398:. This formula is the scattering cross section for "Rutherford scattering", where a point charge (carrier) moves past another point charge (defect) experiencing Coulomb interaction. 2734: 1739: 5519:{\displaystyle {\begin{aligned}\mu _{n}&=\left(-nq\right)\mu _{n}\left(-{\frac {1}{nq}}\right)\\&=-\sigma _{n}R_{Hn}\\&=-{\frac {\sigma _{n}V_{Hn}t}{IB}}\end{aligned}}} 2214:

between collisions to emit an optical phonon, and they do so very quickly, before being accelerated once again. The velocity that the electron reaches before emitting a phonon is:

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is on the order of 1×10 cm/s for both electrons and holes in Si. It is on the order of 6×10 cm/s for Ge. This velocity is a characteristic of the material and a strong function of

4012: 2781: 5950: 4873: 1291: 1242: 879: 6396: 2316:, where a sufficiently high electric field can cause intervalley electron transfer, which reduces drift velocity. This is unusual; increasing the electric field almost always 991: 501: 410: 5962: 4005: 594: 4941: 3831: 3804: 3672: 163: 1547: 824: 641: 6370: 6343: 4315: 3777: 1784: 1318: 4177: 3263: 1567: 1097: 3972: 3902: 8631: 7107:

Umansky, V.; Heiblum, M.; Levinson, Y.; Smet, J.; Nübler, J.; Dolev, M. (2009). "MBE growth of ultra-low disorder 2DEG with mobility exceeding 35×106 cm2 V−1 s−1".

6316: 5782: 4392: 4342: 4157: 3649: 3587: 1193: 120: 4564: 4488: 8066: 4384: 4362: 3942: 3922: 3851: 1797: 330:, impurities, etc., so that it loses some energy and changes direction. The final result is that the electron moves with a finite average velocity, called the 7577:

Heremans, Paul (2015). "Mechanical and Electronic Properties of Thin-Film Transistors on Plastic, and Their Integration in Flexible Electronic Applications".

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As the electric field is increased, however, the carrier velocity increases sublinearly and asymptotically towards a maximum possible value, called the

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A similar set of equations applies to the holes, (noting that the charge on a hole is positive). Therefore the current density due to holes is given by

8580: 3346: 3106:{\displaystyle {\frac {1}{\tau }}={\frac {1}{\tau _{\rm {impurities}}}}+{\frac {1}{\tau _{\rm {lattice}}}}+{\frac {1}{\tau _{\rm {defects}}}}+\cdots .} 4184: 1695:

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

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Note that both electron mobility and hole mobility are positive. A minus sign is added for electron drift velocity to account for the minus charge.

5172: 2941:{\displaystyle {\frac {1}{\mu }}={\frac {1}{\mu _{\rm {impurities}}}}+{\frac {1}{\mu _{\rm {lattice}}}}+{\frac {1}{\mu _{\rm {defects}}}}+\cdots .} 5258: 198: 7188:

Bolotin, K; Sikes, K; Jiang, Z; Klima, M; Fudenberg, G; Hone, J; Kim, P; Stormer, H (2008). "Ultrahigh electron mobility in suspended graphene".

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some cases other sources of scattering may be important, such as neutral impurity scattering, optical phonon scattering, surface scattering, and

2466: 5531: 3204: 2012:) developed thus far have carrier mobilities below 50 cm/(V⋅s), and typically below 1, with well performing materials measured below 10. 8238: 8147: 8076: 8047: 7934: 7875: 7841: 7745: 7671: 7634: 7906: 2418:

are weak. These electric fields arise from the distortion of the basic unit cell as strain is applied in certain directions in the lattice.

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Nawrocki, Robert (2016). "300-nm Imperceptible, Ultraflexible, and Biocompatible e-Skin Fit with Tactile Sensors and Organic Transistors".

6231: 2526: 2337: 644: 5658:(FET). The result of the measurement is called the "field-effect mobility" (meaning "mobility inferred from a field-effect measurement"). 4759: 4650: 1102: 6211: 3401:

The temperature dependencies of these two scattering mechanism in semiconductors can be determined by combining formulas for τ, Σ and

1791: 254: 7805: 7721: 7713: 7481:"Air-Stable n-Channel Organic Single Crystal Field-Effect Transistors Based on Microribbons of Core-Chlorinated Naphthalene Diimide" 5779:

is the gate insulator capacitance per unit area. This equation comes from the approximate equation for a MOSFET in saturation mode:

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Bhattacharya, Pallab. Semiconductor optoelectronic devices / Pallab Bhattacharya. Upper Saddle River (NJ): Prentice-Hall, 1997.

658: 8467:"Revealing the Dynamics of Charge Carriers in Polymer:Fullerene Blends Using Photoinduced Time-Resolved Microwave Conductivity" 6240: 2336:

Recall that by definition, mobility is dependent on the drift velocity. The main factor determining drift velocity (other than

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is the optical-phonon angular frequency and m* the carrier effective mass in the direction of the electric field. The value of

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Dürkop, T.; Getty, S. A.; Cobas, Enrique; Fuhrer, M. S. (2004). "Extraordinary Mobility in Semiconducting Carbon Nanotubes".

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Dürkop, T.; Getty, S. A.; Cobas, Enrique; Fuhrer, M. S. (2004). "Extraordinary Mobility in Semiconducting Carbon Nanotubes".

5073: 1702: 258: 4403:. The result of the measurement is called the "Hall mobility" (meaning "mobility inferred from a Hall-effect measurement"). 832:

Since we only care about how the drift velocity changes with the electric field, we lump the loose terms together to get

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The two charge carriers, electrons and holes, will typically have different drift velocities for the same electric field.

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Very high mobility has been found in several ultrapure low-dimensional systems, such as two-dimensional electron gases (

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is the wavefunction overlap parameter. The mobility in a system governed by variable range hopping can be shown to be:

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Consider a semiconductor sample with a rectangular cross section as shown in the figures, a current is flowing in the

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This article is about the mobility for electrons and holes in metals and semiconductors. For the general concept, see

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is temperature. The activation energy is typically evaluated by measuring mobility as a function of temperature. The

3488: 3198: . Experimentally, values of the temperature dependence of the mobility in Si, Ge and GaAs are listed in table. 2736:

is the mobility that the material would have if there was impurity scattering but no other source of scattering, and

243: 8289: 8621: 4391: 553: 7889: 5897:(channel length modulation), among other things. In practice, this technique may underestimate the true mobility. 3404: 3335:

For scattering from acoustic phonons, for temperatures well above Debye temperature, the estimated cross section Σ

3268: 315:. Therefore, on average there will be no overall motion of charge carriers in any particular direction over time. 262: 247: 129: 8274:

W. Chism, "Z-scanning Laser Photoreflectance as a Tool for Characterization of Electronic Transport Properties,"

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Lloyd-Hughes, James; Jeon, Tae-In (2012). "A Review of the Terahertz Conductivity of Bulk and Nano-Materials".

6421: 3651:, above which electrons undergo a transition from localized to delocalized states. In this description, termed 5685:

saturates. Next, the square root of this saturated current is plotted against the gate voltage, and the slope

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Caughey, D.M.; Thomas, R.E. (1967). "Carrier mobilities in silicon empirically related to doping and field".

8402:"High charge mobility in two-dimensional percolative networks of PbSe quantum dots connected by atomic bonds" 5661:

The measurement can work in two ways: From saturation-mode measurements, or linear-region measurements. (See

2683: 8626: 8577: 5655: 2350: 323: 6696:{\displaystyle \mu _{n}(N_{D})=65+{\frac {1265}{1+\left({\frac {N_{D}}{8.5\times 10^{16}}}\right)^{0.72}}}} 2454:

Coulomb potential governing interactions between electrons make these interactions difficult to deal with.

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is applied across a piece of material, the electrons respond by moving with an average velocity called the

7530:"Ultra-high mobility transparent organic thin film transistors grown by an off-centre spin-coating method" 6809:{\displaystyle \mu _{p}(N_{A})=48+{\frac {447}{1+\left({\frac {N_{A}}{6.3\times 10^{16}}}\right)^{0.76}}}} 6464: 3656: 2739: 2197: 547: 7038:{\displaystyle \mu _{p}(N_{D})=130+{\frac {370}{1+\left({\frac {N_{D}}{8\times 10^{17}}}\right)^{1.25}}}} 6925:{\displaystyle \mu _{n}(N_{A})=232+{\frac {1180}{1+\left({\frac {N_{A}}{8\times 10^{16}}}\right)^{0.9}}}} 5912: 2669:{\displaystyle {\frac {1}{\mu }}={\frac {1}{\mu _{\rm {impurities}}}}+{\frac {1}{\mu _{\rm {lattice}}}}.} 8071:. Oxford Classic Texts in the Physical Sciences. Oxford, New York: Oxford University Press. 2012-03-24. 2001: 1758: 8261:

W. Chism, "Precise Optical Measurement of Carrier Mobilities Using Z-scanning Laser Photoreflectance,"

8168: 6174:{\displaystyle I_{D}=\mu C_{i}{\frac {W}{L}}\left((V_{GS}-V_{th})V_{DS}-{\frac {V_{DS}^{2}}{2}}\right)} 6550:{\displaystyle \mu =\mu _{o}+{\frac {\mu _{1}}{1+\left({\frac {N}{N_{\text{ref}}}}\right)^{\alpha }}}} 6375: 8549: 8413: 8357: 8304: 8190: 8169:"Influence of the gate dielectric on the mobility of rubrene single-crystal field-effect transistors" 8105: 8002: 7963: 7769: 7541: 7492: 7437: 7385: 7338: 7295: 7207: 7151: 7116: 7056: 3610: 3339:

is determined from the square of the average vibrational amplitude of a phonon to be proportional to

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is possible in solids if the electrons are accelerated across a very small distance (as small as the

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In steady state this force is balanced by the force set up by the Hall voltage, so that there is no

3874:. In the original theory of variable range hopping, as developed by Mott and Davis, the probability 8540:

Del Alamo, J (1985). "Measuring and modeling minority carrier transport in heavily doped silicon".

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is a parameter (with dimensions of temperature) that quantifies the width of localized states, and

3977: 3621: 3194: , while the mobility due to optical phonon scattering only is expected to be proportional to 2345: 2146: 361: 341: 319: 212: 81: 38: 31: 4898: 3809: 3782: 8381: 8206: 8180: 7903: 7602: 7461: 7354: 7285: 7258: 7223: 7197: 7167: 3867: 3602: 2274:{\displaystyle {\frac {m^{*}v_{\text{emit}}^{2}}{2}}\approx \hbar \omega _{\text{phonon (opt.)}}} 1869: 3121:

is the scattering time if there was impurity scattering but no other source of scattering, etc.

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B. L. Anderson and R. L. Anderson, "Fundamentals of Semiconductor Devices, " Mc Graw Hill, 2005

7831: 3343:. The scattering from charged defects (ionized donors or acceptors) leads to the cross section 802: 614: 8486: 8447: 8429: 8373: 8330: 8234: 8143: 8072: 8043: 8018: 7930: 7871: 7837: 7801: 7741: 7717: 7709: 7667: 7630: 7624: 7623:

Vladimir Vasilʹevich Mitin; Vi︠a︡cheslav Aleksandrovich Kochelap; Michael A. Stroscio (1999).

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This is the acceleration on the electron between collisions. The drift velocity is therefore:

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In this technique, the transistor is operated in the linear region (or "ohmic mode"), where V

4162: 4123:{\displaystyle P_{ij}=P_{0}\exp \left(-2\alpha r_{ij}-{\frac {\Delta E_{ij}}{k_{B}T}}\right)} 3248: 2295:

is 0.063 eV for Si and 0.034 eV for GaAs and Ge. The saturation velocity is only one-half of

1552: 1069: 334:. This net electron motion is usually much slower than the normally occurring random motion. 8636: 8557: 8522: 8478: 8437: 8421: 8365: 8320: 8312: 8198: 8113: 8010: 7971: 7777: 7586: 7549: 7500: 7445: 7393: 7346: 7303: 7250: 7215: 7159: 7124: 6583: 6222:

is measured using a terahertz probe, which detects changes in the terahertz electric field.

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We have previously derived the relationship between electron mobility and current density

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Bulusu, A. (2008). "Review of electronic transport models for thermoelectric materials".

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suggested that beyond a critical value of structural disorder, electron states would be

2405:, the vibrating atoms create pressure (acoustic) waves in the crystal, which are termed 8442: 8401: 6407: 6035:{\displaystyle \mu =m_{\text{lin}}{\frac {L}{W}}{\frac {1}{V_{DS}}}{\frac {1}{C_{i}}}.} 4442: 4411: 4347: 3927: 3907: 3836: 2385: 2211: 2205: 827: 424: 349: 345: 331: 299: 92: 58: 8465:

Savenije, Tom J.; Ferguson, Andrew J.; Kopidakis, Nikos; Rumbles, Garry (2013-11-21).

8290:"Carrier dynamics in semiconductors studied with time-resolved terahertz spectroscopy" 8093: 7425: 7307: 6398:

has the same dimensions as mobility, but carrier type (electron or hole) is obscured.

8605: 8561: 8210: 7465: 7262: 7227: 6418:, for noncompensated material (no counter doping) for heavily doped substrates (i.e. 6042:

This equation comes from the approximate equation for a MOSFET in the linear region:

4475: 3854: 3743:{\displaystyle \mu =\mu _{0}\exp \left(-{\frac {E_{\text{A}}}{k_{\text{B}}T}}\right)} 3666:

Energy band diagram depicting electron transport under multiple trapping and release.

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is the scattering cross section for electrons and holes at a scattering center and

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is 30–50 cm/(V⋅s). Carrier mobility in semiconductors is doping dependent. In

523: 184: 77: 7409: 1517: 8037: 7924: 7865: 4441:. As a result there is a voltage across the sample, which can be measured with a 3391:{\displaystyle {\Sigma }_{\text{def}}\propto {\left\langle v\right\rangle }^{-4}} 2312:

Velocity saturation is not the only possible high-field behavior. Another is the

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The diffusion coefficient for a charge carrier is related to its mobility by the

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Ulbricht, Ronald; Hendry, Euan; Shan, Jie; Heinz, Tony F.; Bonn, Mischa (2011).

5648: 4453: 4400: 4378: 3594: 2313: 232: 216: 8117: 7781: 534:). However, mobility is much more commonly expressed in cm/(V⋅s) = 10 m/(V⋅s). 8369: 8316: 8014: 7374:"High-mobility carbon-nanotube thin-film transistors on a polymeric substrate" 7219: 5879:{\displaystyle I_{D}={\frac {\mu C_{i}}{2}}{\frac {W}{L}}(V_{GS}-V_{th})^{2}.} 2341: 203: 8490: 8433: 8377: 8334: 8022: 7975: 7708:

Ferry, David K. Semiconductor transport. London: Taylor & Francis, 2000.

7405: 7315: 4628:{\displaystyle \mathbf {F} _{Hp}=+q(\mathbf {v} _{p}\times \mathbf {B} _{z})} 4552:{\displaystyle \mathbf {F} _{Hn}=-q(\mathbf {v} _{n}\times \mathbf {B} _{z})} 7990: 7449: 6181:

In practice, this technique may overestimate the true mobility, because if V

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in eqn (2.11). The correct version of that equation can be found, e.g., in

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From the Hall coefficient, we can obtain the carrier mobility as follows:

3238:{\textstyle {\frac {1}{\tau }}\propto \left\langle v\right\rangle \Sigma } 1851:{\displaystyle D_{\text{e}}={\frac {\mu _{\text{e}}k_{\mathrm {B} }T}{e}}} 1323:

The total current density is the sum of the electron and hole components:

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Stassen, A. F.; De Boer, R. W. I.; Iosad, N. N.; Morpurgo, A. F. (2004).

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is a prefactor associated with the phonon frequency in the material, and

2009: 1997: 305: 46: 5755:{\displaystyle \mu =m_{\text{sat}}^{2}{\frac {2L}{W}}{\frac {1}{C_{i}}}} 8425: 8325: 7554: 7529: 4418:-direction. The resulting Lorentz force will accelerate the electrons ( 2948:

Matthiessen's rule can also be stated in terms of the scattering time:

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interaction. The resulting mobility is expected to be proportional to

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Introduction to Thin Film Transistors: Physics and Technology of TFTs

5662: 5642: 3187: 2406: 2302:, because the electron starts at zero velocity and accelerates up to 2210:. At high fields, carriers are accelerated enough to gain sufficient 1978: 1974: 1969:

Typical electron mobility at room temperature (300 K) in metals like

531: 192: 176: 8595: 8466: 5633:

are either known or can be obtained from measuring the resistivity.

5054:{\displaystyle \xi _{y}=-{\frac {IB}{nqtW}}=+{\frac {R_{Hn}IB}{tW}}} 8275: 8262: 7290: 6189:

is not large enough, the MOSFET may not stay in the linear region.

5665:

for a description of the different modes or regions of operation.)

792:{\displaystyle v_{d}=a\tau _{c}=-{\frac {e\tau _{c}}{m_{e}^{*}}}E,} 440:

of the electron drift velocity (in other words, the electron drift

352:). In these cases, drift velocity and mobility are not meaningful. 7372:

Snow, E. S.; Campbell, P. M.; Ancona, M. G.; Novak, J. P. (2005).

7202: 5619:(magnetic field) can be measured directly, and the conductivities 4390: 4382: 3661: 3624:

later developed the concept of a mobility edge. This is an energy

3554: 2463:

until it scatters again. The resulting average drift mobility is:

2203:

This velocity saturation phenomenon results from a process called

1099:, so that the total current density due to electrons is given by: 519: 441: 50: 7047:

These equations apply only to silicon, and only under low field.

84:

of charged particles in a fluid under an applied electric field.

7833:

Fundamentals of Semiconductors: Physics and Materials Properties

4281:{\displaystyle \mu =\mu _{0}\exp \left(-\left^{-1/(d+1)}\right)} 2542:* is the effective mass in the direction of the electric field. 2309:

in each cycle. (This is a somewhat oversimplified description.)

1989: 1970: 527: 515: 188: 172: 6463:

and up), the mobility in silicon is often characterized by the

3186:

semiconductors, such as silicon and germanium, is dominated by

2320:

the drift velocity, or else leaves it unchanged. The result is

7626:

Quantum heterostructures: microelectronics and optoelectronics

3857:

can be used as a proxy for activation energy in some systems.

1943:{\displaystyle D_{\text{e}}={\frac {\mu _{\text{e}}E_{F}}{e}}} 503:

Both electron and hole mobilities are positive by definition.

226: 8230:

Ambipolar and Light-Emitting Organic Field-Effect Transistors

8139:

Ambipolar and Light-Emitting Organic Field-Effect Transistors

5246:{\displaystyle R_{Hn}=-{\frac {1}{nq}}={\frac {V_{Hn}t}{IB}}} 1996:(100,000 cm/(V⋅s) at room temperature) and freestanding 1569:

is defined as the conductivity. Therefore we can write down:

322:). However, in a solid, the electron repeatedly scatters off 5329:{\displaystyle R_{Hp}={\frac {1}{pq}}={\frac {V_{Hp}t}{IB}}} 3325:{\displaystyle \left\langle v\right\rangle \sim {\sqrt {T}}} 2538:

If the effective mass is anisotropic (direction-dependent),

6197:

Electron mobility may be determined from non-contact laser

180: 8590:

Resistivity and Mobility Calculator from the BYU Cleanroom

2506:{\displaystyle \mu ={\frac {q}{m^{*}}}{\overline {\tau }}} 7479:

He, Tao; Stolte, Matthias; Würthner, Frank (2013-12-23).

7080: 6291:{\displaystyle \phi \Sigma \mu =\phi (\mu _{e}+\mu _{h})} 5893:

is the threshold voltage. This approximation ignores the

5591:{\displaystyle \mu _{p}={\frac {\sigma _{p}V_{Hp}t}{IB}}} 1794:. For a classical system (e.g. Boltzmann gas), it reads: 167:

Electron mobility is almost always specified in units of

6402:

Doping concentration dependence in heavily-doped silicon

5070:

is the Hall coefficient for electron, and is defined as

1050:{\displaystyle \mu _{h}={\frac {e\tau _{c}}{m_{h}^{*}}}} 938:{\displaystyle \mu _{e}={\frac {e\tau _{c}}{m_{e}^{*}}}} 609:

is the electric force exerted by the electric field, and

6210:

Electron mobility can be calculated from time-resolved

8161:. This reference mistakenly leaves out a factor of 1/V 3207: 2365:, while emitting or absorbing a phonon of wave vector 1509:{\displaystyle J=J_{e}+J_{h}=(en\mu _{e}+ep\mu _{h})E} 1409:{\displaystyle J=J_{e}+J_{h}=(en\mu _{e}+ep\mu _{h})E} 73:

refers in general to both electron and hole mobility.

7081:"NSM Archive - Physical Properties of Semiconductors" 6937: 6824: 6708: 6595: 6473: 6424: 6378: 6351: 6324: 6304: 6243: 6048: 5965: 5915: 5785: 5698: 5534: 5344: 5261: 5175: 5129: 5076: 4969: 4901: 4831: 4762: 4653: 4567: 4491: 4399:

Carrier mobility is most commonly measured using the

4350: 4323: 4296: 4187: 4165: 4138: 4015: 3980: 3950: 3930: 3910: 3880: 3839: 3812: 3785: 3758: 3675: 3630: 3568: 3491: 3435: 3407: 3349: 3300: 3271: 3251: 2954: 2789: 2742: 2686: 2563: 2469: 2220: 1897: 1800: 1769: 1705: 1633: 1575: 1555: 1526: 1429: 1329: 1299: 1250: 1201: 1174: 1105: 1072: 999: 953: 887: 838: 805: 716: 661: 617: 556: 522:. Therefore the SI unit of mobility is (m/s)/(V/m) = 463: 457:

The hole mobility is defined by a similar equation:

372: 132: 101: 8350:

Journal of Infrared, Millimeter, and Terahertz Waves

8094:"Phonon-Assisted Jump Rate in Noncrystalline Solids" 4817:{\displaystyle \Rightarrow -q\xi _{y}+qv_{x}B_{z}=0} 4748:{\displaystyle \mathbf {F} _{y}=(-q)\xi _{y}+(-q)=0} 3538:

The effect of ionized impurity scattering, however,

6318:is the carrier generation yield (between 0 and 1), 8578:semiconductor glossary entry for electron mobility 8042:. Springer International Publishing. p. 143. 7037: 6924: 6808: 6695: 6549: 6455: 6390: 6364: 6337: 6310: 6290: 6218:pulses excite the semiconductor and the resulting 6173: 6034: 5944: 5878: 5754: 5590: 5518: 5328: 5245: 5162: 5113: 5053: 4935: 4867: 4816: 4747: 4627: 4551: 4356: 4336: 4309: 4280: 4171: 4151: 4122: 3999: 3966: 3936: 3916: 3896: 3845: 3825: 3798: 3771: 3742: 3643: 3581: 3527: 3477: 3421: 3390: 3324: 3285: 3257: 3237: 3105: 2940: 2775: 2728: 2668: 2505: 2273: 1942: 1850: 1778: 1733: 1680: 1619: 1561: 1541: 1508: 1408: 1312: 1285: 1236: 1187: 1160: 1091: 1049: 985: 937: 873: 818: 791: 700: 635: 588: 495: 404: 366:The electron mobility is defined by the equation: 157: 114: 8068:Electronic Processes in Non-Crystalline Materials 7952:"Absence of Diffusion in Certain Random Lattices" 7426:"High ambipolar mobility in cubic boron arsenide" 2141:Electric field dependence and velocity saturation 1992:) (35,000,000 cm/(V⋅s) at low temperature), 1161:{\displaystyle J_{e}={\frac {I_{n}}{A}}=-env_{d}} 7867:Handbook of photovoltaic science and engineering 5673:In this technique, for each fixed gate voltage V 304:Without any applied electric field, in a solid, 195:). They are related by 1 m/(V⋅s) = 10 cm/(V⋅s). 3528:{\displaystyle {\mu }_{\text{def}}\sim T^{3/2}} 7629:. Cambridge University Press. pp. 307–9. 1681:{\displaystyle \sigma =e(n\mu _{e}+p\mu _{h})} 7870:. John Wiley and Sons. p. 79, eq. 3.58. 7864:Antonio Luque; Steven Hegedus (9 June 2003). 3870:for one site to another, in a process called 3429:, to be for scattering from acoustic phonons 2458:Relation between mobility and scattering time 1620:{\displaystyle \sigma =en\mu _{e}+ep\mu _{h}} 348:), or for a very short time (as short as the 8: 5770:are the length and width of the channel and 4881:direction, and for holes, it points in the + 3422:{\displaystyle \left\langle v\right\rangle } 3286:{\displaystyle \left\langle v\right\rangle } 2000:(200,000 cm/(V⋅s) at low temperature). 7830:Peter Y. Yu; Manuel Cardona (30 May 2010). 6414:While there is considerable scatter in the 6226:Time resolved microwave conductivity (TRMC) 5163:{\displaystyle \xi _{y}={\frac {V_{H}}{W}}} 4395:Hall effect measurement setup for electrons 3134:Typical temperature dependence of mobility 261:. Unsourced material may be challenged and 7663:Electronic Devices And Integrated Circuits 5654:The mobility can also be measured using a 2016:List of highest measured mobilities 2014: 1786:is the concentration gradient of electrons 701:{\displaystyle a=-{\frac {eE}{m_{e}^{*}}}} 8441: 8324: 8184: 7816: 7814: 7796: 7794: 7792: 7755: 7753: 7553: 7504: 7289: 7201: 7026: 7013: 6996: 6990: 6973: 6955: 6942: 6936: 6913: 6900: 6883: 6877: 6860: 6842: 6829: 6823: 6797: 6784: 6767: 6761: 6744: 6726: 6713: 6707: 6684: 6671: 6654: 6648: 6631: 6613: 6600: 6594: 6538: 6526: 6517: 6499: 6493: 6484: 6472: 6456:{\displaystyle 10^{18}\mathrm {cm} ^{-3}} 6444: 6436: 6429: 6423: 6377: 6356: 6350: 6329: 6323: 6303: 6279: 6266: 6242: 6155: 6147: 6141: 6129: 6113: 6097: 6075: 6069: 6053: 6047: 6021: 6012: 6001: 5992: 5982: 5976: 5964: 5933: 5920: 5914: 5867: 5854: 5838: 5821: 5809: 5799: 5790: 5784: 5744: 5735: 5720: 5714: 5709: 5697: 5565: 5555: 5548: 5539: 5533: 5489: 5479: 5472: 5450: 5440: 5403: 5389: 5353: 5345: 5343: 5303: 5296: 5278: 5266: 5260: 5220: 5213: 5195: 5180: 5174: 5149: 5143: 5134: 5128: 5096: 5081: 5075: 5025: 5018: 4986: 4974: 4968: 4921: 4900: 4859: 4849: 4836: 4830: 4802: 4792: 4776: 4761: 4730: 4725: 4715: 4710: 4685: 4660: 4655: 4652: 4616: 4611: 4601: 4596: 4574: 4569: 4566: 4540: 4535: 4525: 4520: 4498: 4493: 4490: 4349: 4328: 4322: 4301: 4295: 4251: 4244: 4229: 4223: 4198: 4186: 4164: 4143: 4137: 4103: 4088: 4078: 4066: 4036: 4020: 4014: 3988: 3979: 3955: 3949: 3929: 3909: 3885: 3879: 3838: 3817: 3811: 3790: 3784: 3763: 3757: 3723: 3712: 3706: 3686: 3674: 3635: 3629: 3573: 3567: 3515: 3511: 3498: 3493: 3490: 3465: 3458: 3442: 3437: 3434: 3406: 3379: 3366: 3356: 3351: 3348: 3315: 3299: 3270: 3250: 3208: 3206: 3117:is the true average scattering time and τ 3067: 3066: 3057: 3027: 3026: 3017: 2978: 2977: 2968: 2955: 2953: 2902: 2901: 2892: 2862: 2861: 2852: 2813: 2812: 2803: 2790: 2788: 2748: 2747: 2741: 2692: 2691: 2685: 2636: 2635: 2626: 2587: 2586: 2577: 2564: 2562: 2493: 2485: 2476: 2468: 2265: 2243: 2238: 2228: 2221: 2219: 1928: 1918: 1911: 1902: 1896: 1832: 1831: 1821: 1814: 1805: 1799: 1768: 1719: 1704: 1669: 1653: 1632: 1611: 1592: 1574: 1554: 1525: 1494: 1475: 1453: 1440: 1428: 1394: 1375: 1353: 1340: 1328: 1304: 1298: 1274: 1255: 1249: 1225: 1206: 1200: 1179: 1173: 1152: 1125: 1119: 1110: 1104: 1083: 1071: 1039: 1034: 1023: 1013: 1004: 998: 971: 958: 952: 927: 922: 911: 901: 892: 886: 859: 843: 837: 810: 804: 775: 770: 759: 749: 737: 721: 715: 690: 685: 671: 660: 627: 622: 616: 580: 575: 566: 555: 481: 468: 462: 390: 377: 371: 281:Learn how and when to remove this message 137: 131: 106: 100: 8222: 8220: 7655: 7653: 7618: 7616: 4877:For electrons, the field points in the − 3478:{\displaystyle {\mu }_{ph}\sim T^{-3/2}} 3132: 2332:Relation between scattering and mobility 219:, or inferred from transistor behavior. 8131: 8129: 8127: 7923:Hook, J. R.; Hall, H. E. (1991-09-05). 7913:. Online textbook by B. Van Zeghbroeck] 7666:. PHI Learning Pvt. Ltd. pp. 77–. 7067: 5114:{\displaystyle R_{Hn}=-{\frac {1}{nq}}} 4387:Hall effect measurement setup for holes 3944:, depends on their separation in space 3904:, of an electron hopping from one site 3562:of a solid possessing a mobility edge, 2729:{\displaystyle \mu _{\rm {impurities}}} 2258: 1734:{\displaystyle F=-D_{\text{e}}\nabla n} 603:is the acceleration between collisions. 514:, and the SI unit of electric field is 8632:Electric and magnetic fields in matter 8227:Constance Rost-Bietsch (August 2005). 8136:Constance Rost-Bietsch (August 2005). 7899: 7897: 7736: 7734: 7732: 7730: 7704: 7702: 7700: 7698: 7696: 7694: 7692: 7690: 6237:incident laser fluence, the parameter 2160:is proportional to the electric field 1293:where p is the hole concentration and 8061: 8059: 7904:Chapter 2: Semiconductor Fundamentals 4368:Measurement of semiconductor mobility 4364:is the dimensionality of the system. 1886:is the electric charge of an electron 61:. There is an analogous quantity for 7: 7991:"Electrons in disordered structures" 7183: 7181: 7102: 7100: 7075: 7073: 7071: 6561:is the doping concentration (either 6232:Time resolved microwave conductivity 2776:{\displaystyle \mu _{\rm {lattice}}} 651:Since the force on the electron is − 259:adding citations to reliable sources 215:occurs. It can be determined by the 8471:The Journal of Physical Chemistry C 5945:{\displaystyle I_{D}\propto V_{GS}} 5692:is measured. Then the mobility is: 4868:{\displaystyle \xi _{y}=v_{x}B_{z}} 2344:time, i.e. how long the carrier is 444:) caused by the electric field, and 294:Drift velocity in an electric field 8233:. Cuvillier Verlag. pp. 19–. 8142:. Cuvillier Verlag. pp. 17–. 6440: 6437: 6382: 6247: 4081: 3981: 3352: 3252: 3232: 3129:Temperature dependence of mobility 3086: 3083: 3080: 3077: 3074: 3071: 3068: 3046: 3043: 3040: 3037: 3034: 3031: 3028: 3006: 3003: 3000: 2997: 2994: 2991: 2988: 2985: 2982: 2979: 2921: 2918: 2915: 2912: 2909: 2906: 2903: 2881: 2878: 2875: 2872: 2869: 2866: 2863: 2841: 2838: 2835: 2832: 2829: 2826: 2823: 2820: 2817: 2814: 2767: 2764: 2761: 2758: 2755: 2752: 2749: 2720: 2717: 2714: 2711: 2708: 2705: 2702: 2699: 2696: 2693: 2655: 2652: 2649: 2646: 2643: 2640: 2637: 2615: 2612: 2609: 2606: 2603: 2600: 2597: 2594: 2591: 2588: 2151:At low fields, the drift velocity 1833: 1770: 1725: 25: 7762:Superlattices and Microstructures 7308:10.1103/PhysRevMaterials.6.034005 6582:and α are fitting parameters. At 3974:, and their separation in energy 1286:{\displaystyle J_{h}=ep\mu _{h}E} 1237:{\displaystyle J_{e}=en\mu _{e}E} 874:{\displaystyle v_{d}=-\mu _{e}E,} 6391:{\displaystyle \phi \Sigma \mu } 5681:is increased until the current I 4726: 4711: 4656: 4612: 4597: 4570: 4536: 4521: 4494: 4467:-type material and positive for 2535:is the average scattering time. 2322:negative differential resistance 986:{\displaystyle v_{d}=\mu _{h}E,} 496:{\displaystyle v_{d}=\mu _{h}E.} 405:{\displaystyle v_{d}=\mu _{e}E.} 231: 8598:from an atomistic point of view 3833:is the Boltzmann constant, and 76:Electron and hole mobility are 27:Quantity in solid-state physics 7950:Anderson, P. W. (1958-03-01). 7129:10.1016/j.jcrysgro.2008.09.151 6961: 6948: 6848: 6835: 6732: 6719: 6619: 6606: 6586:, the above equation becomes: 6285: 6259: 6122: 6090: 5864: 5831: 4763: 4736: 4706: 4703: 4694: 4678: 4669: 4622: 4592: 4546: 4516: 4430:) direction, according to the 4268: 4256: 1691:Relation to electron diffusion 1675: 1643: 1500: 1462: 1400: 1362: 947:Similarly, for holes we have 179:). This is different from the 1: 7243:Advanced Electronic Materials 6345:is the electron mobility and 4434:and set up an electric field 4000:{\displaystyle \Delta E_{ij}} 3653:multiple trapping and release 3617:Multiple trapping and release 2063:Cubic boron arsenide (c-BAs) 2032:AlGaAs/GaAs heterostructures 589:{\displaystyle a=F/m_{e}^{*}} 122:. Then the electron mobility 45:characterises how quickly an 8562:10.1016/0038-1101(85)90209-6 5677:, the drain-source voltage V 4936:{\displaystyle I=-qnv_{x}tW} 3826:{\displaystyle k_{\text{B}}} 3799:{\displaystyle E_{\text{A}}} 2498: 2449:Electron–electron scattering 2422:Surface roughness scattering 2189:. For example, the value of 158:{\displaystyle v_{d}=\mu E.} 57:when pushed or pulled by an 7890:weblink (subscription only) 7836:. Springer. pp. 205–. 6199:photo-reflectance technique 4422:-type materials) or holes ( 2397:Lattice (phonon) scattering 2381:ionized impurity scattering 2373:Ionized impurity scattering 2168:is constant. This value of 1627:which can be factorised to 1520:can be written in the form 1061:Relation to current density 510:The SI unit of velocity is 8653: 8118:10.1103/PhysRevLett.32.303 8092:Emin, David (1974-02-11). 8036:Brotherton, S. D. (2013). 7989:Mott, N. F. (1967-01-01). 7782:10.1016/j.spmi.2008.02.008 7190:Solid State Communications 6229: 5646: 5640: 4645:direction. For electrons, 4426:-type materials) in the (− 4376: 2144: 1542:{\displaystyle J=\sigma E} 359: 297: 29: 8370:10.1007/s10762-012-9905-y 8317:10.1103/RevModPhys.83.543 8297:Reviews of Modern Physics 8015:10.1080/00018736700101265 7278:Physical Review Materials 7220:10.1016/j.ssc.2008.02.024 7109:Journal of Crystal Growth 6185:is not small enough and V 4445:voltmeter. This voltage, 4317:is a mobility prefactor, 3779:is a mobility prefactor, 3551:Disordered Semiconductors 3485:and from charged defects 2401:At any temperature above 2346:ballistically accelerated 1168:Using the expression for 819:{\displaystyle \tau _{c}} 636:{\displaystyle m_{e}^{*}} 453:is the electron mobility. 7976:10.1103/PhysRev.109.1492 6365:{\displaystyle \mu _{h}} 6338:{\displaystyle \mu _{e}} 6298:can be evaluated, where 5959:. Then the mobility is: 5647:Not to be confused with 4952:into the expression for 4310:{\displaystyle \mu _{0}} 3772:{\displaystyle \mu _{0}} 2680:is the actual mobility, 2413:Piezoelectric scattering 2094:Metals (Al, Au, Cu, Ag) 2084:Polycrystalline silicon 1779:{\displaystyle \nabla n} 1419:Relation to conductivity 1313:{\displaystyle \mu _{h}} 8542:Solid-State Electronics 8515:Proceedings of the IEEE 8173:Applied Physics Letters 8098:Physical Review Letters 7450:10.1126/science.abn4290 7378:Applied Physics Letters 5901:Using the linear region 5656:field-effect transistor 4641:on the carriers in the 4172:{\displaystyle \alpha } 3258:{\displaystyle \Sigma } 1562:{\displaystyle \sigma } 1092:{\displaystyle -ev_{d}} 87:When an electric field 8527:10.1109/PROC.1967.6123 7591:10.1002/adma.201504360 7506:10.1002/adma.201303392 7412:on September 24, 2017. 7255:10.1002/aelm.201500452 7039: 6926: 6810: 6697: 6551: 6465:empirical relationship 6457: 6392: 6372:is the hole mobility. 6366: 6339: 6312: 6292: 6175: 6036: 5946: 5880: 5756: 5592: 5520: 5330: 5247: 5164: 5115: 5055: 4937: 4869: 4818: 4749: 4629: 4553: 4396: 4388: 4358: 4338: 4311: 4282: 4173: 4153: 4124: 4001: 3968: 3967:{\displaystyle r_{ij}} 3938: 3918: 3898: 3897:{\displaystyle P_{ij}} 3872:variable range hopping 3861:Variable Range Hopping 3847: 3827: 3806:is activation energy, 3800: 3773: 3744: 3667: 3657:Arrhenius relationship 3645: 3590: 3583: 3529: 3479: 3423: 3392: 3326: 3287: 3259: 3239: 3107: 2942: 2777: 2730: 2670: 2507: 2275: 2043:Freestanding graphene 2002:Organic semiconductors 1944: 1852: 1780: 1735: 1682: 1621: 1563: 1543: 1510: 1410: 1314: 1287: 1238: 1189: 1162: 1093: 1051: 987: 939: 875: 820: 793: 702: 637: 590: 497: 427:applied to a material, 406: 159: 116: 8406:Nature Communications 7534:Nature Communications 7528:Yuan, Yongbo (2014). 7040: 6927: 6811: 6698: 6552: 6458: 6393: 6367: 6340: 6313: 6311:{\displaystyle \phi } 6293: 6176: 6037: 5947: 5881: 5757: 5669:Using saturation mode 5637:Field-effect mobility 5593: 5521: 5331: 5255:Similarly, for holes 5248: 5165: 5116: 5056: 4938: 4870: 4819: 4750: 4630: 4554: 4394: 4386: 4359: 4339: 4337:{\displaystyle T_{0}} 4312: 4283: 4174: 4154: 4152:{\displaystyle P_{0}} 4125: 4002: 3969: 3939: 3919: 3899: 3848: 3828: 3801: 3774: 3745: 3665: 3646: 3644:{\displaystyle E_{C}} 3584: 3582:{\displaystyle E_{C}} 3558: 3530: 3480: 3424: 3393: 3327: 3288: 3260: 3240: 3108: 2943: 2778: 2731: 2671: 2508: 2276: 1945: 1853: 1781: 1759:diffusion coefficient 1736: 1683: 1622: 1564: 1544: 1511: 1411: 1315: 1288: 1239: 1190: 1188:{\displaystyle v_{d}} 1163: 1094: 1052: 988: 940: 876: 821: 794: 703: 638: 591: 498: 407: 160: 117: 115:{\displaystyle v_{d}} 18:Field-effect mobility 7057:Speed of electricity 6935: 6822: 6818:Minority carriers: 6706: 6593: 6589:Majority carriers: 6471: 6422: 6376: 6349: 6322: 6302: 6241: 6046: 5963: 5913: 5783: 5696: 5611:(sample thickness), 5532: 5342: 5259: 5173: 5127: 5074: 4967: 4899: 4829: 4760: 4651: 4565: 4489: 4474:Mathematically, the 4348: 4321: 4294: 4185: 4163: 4136: 4013: 3978: 3948: 3928: 3908: 3878: 3837: 3810: 3783: 3756: 3673: 3628: 3566: 3489: 3433: 3405: 3347: 3298: 3269: 3249: 3205: 2952: 2787: 2740: 2684: 2561: 2553:Augustus Matthiessen 2545: 2467: 2440:Inelastic scattering 2218: 2073:Crystalline silicon 1895: 1879:absolute temperature 1798: 1767: 1703: 1631: 1573: 1553: 1524: 1427: 1327: 1297: 1248: 1199: 1172: 1103: 1070: 997: 951: 885: 836: 803: 714: 659: 615: 554: 461: 370: 356:Definition and units 313:move around randomly 255:improve this section 130: 99: 8612:Physical quantities 8554:1985SSEle..28...47D 8477:(46): 24085–24103. 8418:2015NatCo...6.8195E 8362:2012JIMTW..33..871L 8309:2011RvMP...83..543U 8195:2004ApPhL..85.3899S 8110:1974PhRvL..32..303E 8007:1967AdPhy..16...49M 7995:Advances in Physics 7968:1958PhRv..109.1492A 7926:Solid State Physics 7774:2008SuMi...44....1B 7546:2014NatCo...5.3005Y 7497:2013AdM....25.6951H 7442:2022Sci...377..437S 7390:2005ApPhL..86c3105S 7343:2004NanoL...4...35D 7300:2022PhRvM...6c4005C 7212:2008SSCom.146..351B 7156:2004NanoL...4...35D 7121:2009JCrGr.311.1658U 6160: 5719: 4478:acting on a charge 3135: 2248: 2181:saturation velocity 2147:Velocity saturation 2017: 1960:is the Fermi energy 1320:the hole mobility. 1044: 932: 780: 695: 632: 585: 548:Newton's second law 362:Electrical mobility 342:ballistic transport 320:ballistic transport 213:velocity saturation 82:electrical mobility 49:can move through a 39:solid-state physics 32:Electrical mobility 8583:2009-01-04 at the 8426:10.1038/ncomms9195 7909:2009-01-21 at the 7579:Advanced Materials 7555:10.1038/ncomms4005 7485:Advanced Materials 7035: 6922: 6806: 6693: 6547: 6453: 6388: 6362: 6335: 6308: 6288: 6206:Terahertz mobility 6171: 6143: 6032: 5942: 5876: 5752: 5705: 5600:Here the value of 5588: 5516: 5514: 5326: 5243: 5160: 5111: 5051: 4933: 4865: 4814: 4745: 4625: 4549: 4414:is applied in the 4397: 4389: 4354: 4334: 4307: 4278: 4169: 4149: 4120: 3997: 3964: 3934: 3924:, to another site 3914: 3894: 3843: 3823: 3796: 3769: 3740: 3668: 3659:in such a system: 3641: 3591: 3579: 3525: 3475: 3419: 3388: 3322: 3283: 3255: 3235: 3133: 3103: 2938: 2773: 2726: 2666: 2546:Matthiessen's rule 2503: 2271: 2234: 2174:low-field mobility 2129:Amorphous silicon 2024:Electron mobility 2015: 1940: 1870:Boltzmann constant 1848: 1776: 1731: 1678: 1617: 1559: 1539: 1506: 1406: 1310: 1283: 1234: 1185: 1158: 1089: 1047: 1030: 983: 935: 918: 871: 816: 789: 766: 698: 681: 633: 618: 586: 571: 493: 402: 183:unit of mobility, 155: 112: 8622:Materials science 8521:(12): 2192–2193. 8483:10.1021/jp406706u 8240:978-3-86537-535-3 8203:10.1063/1.1812368 8179:(17): 3899–3901. 8149:978-3-86537-535-3 8078:978-0-19-964533-6 8049:978-3-319-00001-5 7936:978-0-471-92804-1 7877:978-0-471-49196-5 7843:978-3-642-00709-5 7746:978-3-540-93803-3 7673:978-81-203-3192-1 7636:978-0-521-63635-3 7585:(22): 4266–4282. 7491:(48): 6951–6955. 7436:(6604): 437–440. 7398:10.1063/1.1854721 7351:10.1021/nl034841q 7164:10.1021/nl034841q 7033: 7020: 6920: 6907: 6804: 6791: 6691: 6678: 6545: 6532: 6529: 6416:experimental data 6220:photoconductivity 6216:Femtosecond laser 6164: 6083: 6027: 6010: 5990: 5979: 5829: 5819: 5750: 5733: 5712: 5586: 5510: 5416: 5324: 5291: 5241: 5208: 5158: 5109: 5049: 5010: 4410:-direction and a 4357:{\displaystyle d} 4238: 4113: 3937:{\displaystyle j} 3917:{\displaystyle i} 3846:{\displaystyle T} 3820: 3793: 3733: 3726: 3715: 3560:Density of states 3501: 3359: 3320: 3216: 3179: 3178: 3092: 3052: 3012: 2963: 2927: 2887: 2847: 2798: 2661: 2621: 2572: 2525:* is the carrier 2519:elementary charge 2501: 2491: 2268: 2253: 2241: 2138: 2137: 2053:Carbon nanotubes 1938: 1921: 1905: 1846: 1824: 1808: 1792:Einstein relation 1722: 1134: 1045: 933: 781: 696: 291: 290: 283: 43:electron mobility 16:(Redirected from 8644: 8594:Online lecture- 8566: 8565: 8537: 8531: 8530: 8510: 8504: 8501: 8495: 8494: 8462: 8456: 8455: 8445: 8396: 8390: 8389: 8345: 8339: 8338: 8328: 8294: 8285: 8279: 8276:arXiv:1808.01897 8272: 8266: 8263:arXiv:1711.01138 8259: 8253: 8251: 8249: 8247: 8224: 8215: 8214: 8188: 8186:cond-mat/0407293 8160: 8158: 8156: 8133: 8122: 8121: 8089: 8083: 8082: 8063: 8054: 8053: 8033: 8027: 8026: 7986: 7980: 7979: 7962:(5): 1492–1505. 7947: 7941: 7940: 7920: 7914: 7901: 7892: 7888: 7886: 7884: 7861: 7855: 7854: 7852: 7850: 7827: 7821: 7818: 7809: 7798: 7787: 7785: 7757: 7748: 7738: 7725: 7706: 7685: 7684: 7682: 7680: 7657: 7648: 7647: 7645: 7643: 7620: 7611: 7610: 7574: 7568: 7567: 7557: 7525: 7519: 7518: 7508: 7476: 7470: 7469: 7420: 7414: 7413: 7408:. Archived from 7369: 7363: 7362: 7326: 7320: 7319: 7293: 7273: 7267: 7266: 7238: 7232: 7231: 7205: 7185: 7176: 7175: 7139: 7133: 7132: 7115:(7): 1658–1661. 7104: 7095: 7094: 7092: 7091: 7077: 7044: 7042: 7041: 7036: 7034: 7032: 7031: 7030: 7025: 7021: 7019: 7018: 7017: 7001: 7000: 6991: 6974: 6960: 6959: 6947: 6946: 6931: 6929: 6928: 6923: 6921: 6919: 6918: 6917: 6912: 6908: 6906: 6905: 6904: 6888: 6887: 6878: 6861: 6847: 6846: 6834: 6833: 6815: 6813: 6812: 6807: 6805: 6803: 6802: 6801: 6796: 6792: 6790: 6789: 6788: 6772: 6771: 6762: 6745: 6731: 6730: 6718: 6717: 6702: 6700: 6699: 6694: 6692: 6690: 6689: 6688: 6683: 6679: 6677: 6676: 6675: 6659: 6658: 6649: 6632: 6618: 6617: 6605: 6604: 6584:room temperature 6556: 6554: 6553: 6548: 6546: 6544: 6543: 6542: 6537: 6533: 6531: 6530: 6527: 6518: 6504: 6503: 6494: 6489: 6488: 6462: 6460: 6459: 6454: 6452: 6451: 6443: 6434: 6433: 6397: 6395: 6394: 6389: 6371: 6369: 6368: 6363: 6361: 6360: 6344: 6342: 6341: 6336: 6334: 6333: 6317: 6315: 6314: 6309: 6297: 6295: 6294: 6289: 6284: 6283: 6271: 6270: 6193:Optical mobility 6180: 6178: 6177: 6172: 6170: 6166: 6165: 6159: 6154: 6142: 6137: 6136: 6121: 6120: 6105: 6104: 6084: 6076: 6074: 6073: 6058: 6057: 6041: 6039: 6038: 6033: 6028: 6026: 6025: 6013: 6011: 6009: 6008: 5993: 5991: 5983: 5981: 5980: 5977: 5951: 5949: 5948: 5943: 5941: 5940: 5925: 5924: 5885: 5883: 5882: 5877: 5872: 5871: 5862: 5861: 5846: 5845: 5830: 5822: 5820: 5815: 5814: 5813: 5800: 5795: 5794: 5761: 5759: 5758: 5753: 5751: 5749: 5748: 5736: 5734: 5729: 5721: 5718: 5713: 5710: 5607:(Hall voltage), 5597: 5595: 5594: 5589: 5587: 5585: 5577: 5573: 5572: 5560: 5559: 5549: 5544: 5543: 5525: 5523: 5522: 5517: 5515: 5511: 5509: 5501: 5497: 5496: 5484: 5483: 5473: 5462: 5458: 5457: 5445: 5444: 5426: 5422: 5418: 5417: 5415: 5404: 5394: 5393: 5384: 5380: 5358: 5357: 5335: 5333: 5332: 5327: 5325: 5323: 5315: 5311: 5310: 5297: 5292: 5290: 5279: 5274: 5273: 5252: 5250: 5249: 5244: 5242: 5240: 5232: 5228: 5227: 5214: 5209: 5207: 5196: 5188: 5187: 5169: 5167: 5166: 5161: 5159: 5154: 5153: 5144: 5139: 5138: 5120: 5118: 5117: 5112: 5110: 5108: 5097: 5089: 5088: 5060: 5058: 5057: 5052: 5050: 5048: 5040: 5033: 5032: 5019: 5011: 5009: 4995: 4987: 4979: 4978: 4942: 4940: 4939: 4934: 4926: 4925: 4890:electron current 4874: 4872: 4871: 4866: 4864: 4863: 4854: 4853: 4841: 4840: 4823: 4821: 4820: 4815: 4807: 4806: 4797: 4796: 4781: 4780: 4754: 4752: 4751: 4746: 4735: 4734: 4729: 4720: 4719: 4714: 4690: 4689: 4665: 4664: 4659: 4634: 4632: 4631: 4626: 4621: 4620: 4615: 4606: 4605: 4600: 4582: 4581: 4573: 4558: 4556: 4555: 4550: 4545: 4544: 4539: 4530: 4529: 4524: 4506: 4505: 4497: 4471:-type material. 4463:is negative for 4452:, is called the 4363: 4361: 4360: 4355: 4343: 4341: 4340: 4335: 4333: 4332: 4316: 4314: 4313: 4308: 4306: 4305: 4287: 4285: 4284: 4279: 4277: 4273: 4272: 4271: 4255: 4243: 4239: 4234: 4233: 4224: 4203: 4202: 4178: 4176: 4175: 4170: 4158: 4156: 4155: 4150: 4148: 4147: 4129: 4127: 4126: 4121: 4119: 4115: 4114: 4112: 4108: 4107: 4097: 4096: 4095: 4079: 4074: 4073: 4041: 4040: 4028: 4027: 4006: 4004: 4003: 3998: 3996: 3995: 3973: 3971: 3970: 3965: 3963: 3962: 3943: 3941: 3940: 3935: 3923: 3921: 3920: 3915: 3903: 3901: 3900: 3895: 3893: 3892: 3852: 3850: 3849: 3844: 3832: 3830: 3829: 3824: 3822: 3821: 3818: 3805: 3803: 3802: 3797: 3795: 3794: 3791: 3778: 3776: 3775: 3770: 3768: 3767: 3749: 3747: 3746: 3741: 3739: 3735: 3734: 3732: 3728: 3727: 3724: 3717: 3716: 3713: 3707: 3691: 3690: 3650: 3648: 3647: 3642: 3640: 3639: 3601:semiconductors. 3588: 3586: 3585: 3580: 3578: 3577: 3534: 3532: 3531: 3526: 3524: 3523: 3519: 3503: 3502: 3499: 3497: 3484: 3482: 3481: 3476: 3474: 3473: 3469: 3450: 3449: 3441: 3428: 3426: 3425: 3420: 3418: 3397: 3395: 3394: 3389: 3387: 3386: 3378: 3377: 3361: 3360: 3357: 3355: 3331: 3329: 3328: 3323: 3321: 3316: 3311: 3292: 3290: 3289: 3284: 3282: 3264: 3262: 3261: 3256: 3244: 3242: 3241: 3236: 3231: 3217: 3209: 3136: 3112: 3110: 3109: 3104: 3093: 3091: 3090: 3089: 3058: 3053: 3051: 3050: 3049: 3018: 3013: 3011: 3010: 3009: 2969: 2964: 2956: 2947: 2945: 2944: 2939: 2928: 2926: 2925: 2924: 2893: 2888: 2886: 2885: 2884: 2853: 2848: 2846: 2845: 2844: 2804: 2799: 2791: 2782: 2780: 2779: 2774: 2772: 2771: 2770: 2735: 2733: 2732: 2727: 2725: 2724: 2723: 2675: 2673: 2672: 2667: 2662: 2660: 2659: 2658: 2627: 2622: 2620: 2619: 2618: 2578: 2573: 2565: 2534: 2512: 2510: 2509: 2504: 2502: 2494: 2492: 2490: 2489: 2477: 2431:Alloy scattering 2280: 2278: 2277: 2272: 2270: 2269: 2266: 2254: 2249: 2247: 2242: 2239: 2233: 2232: 2222: 2104:2D material (MoS 2018: 1994:carbon nanotubes 1949: 1947: 1946: 1941: 1939: 1934: 1933: 1932: 1923: 1922: 1919: 1912: 1907: 1906: 1903: 1857: 1855: 1854: 1849: 1847: 1842: 1838: 1837: 1836: 1826: 1825: 1822: 1815: 1810: 1809: 1806: 1785: 1783: 1782: 1777: 1740: 1738: 1737: 1732: 1724: 1723: 1720: 1687: 1685: 1684: 1679: 1674: 1673: 1658: 1657: 1626: 1624: 1623: 1618: 1616: 1615: 1597: 1596: 1568: 1566: 1565: 1560: 1548: 1546: 1545: 1540: 1515: 1513: 1512: 1507: 1499: 1498: 1480: 1479: 1458: 1457: 1445: 1444: 1415: 1413: 1412: 1407: 1399: 1398: 1380: 1379: 1358: 1357: 1345: 1344: 1319: 1317: 1316: 1311: 1309: 1308: 1292: 1290: 1289: 1284: 1279: 1278: 1260: 1259: 1243: 1241: 1240: 1235: 1230: 1229: 1211: 1210: 1194: 1192: 1191: 1186: 1184: 1183: 1167: 1165: 1164: 1159: 1157: 1156: 1135: 1130: 1129: 1120: 1115: 1114: 1098: 1096: 1095: 1090: 1088: 1087: 1056: 1054: 1053: 1048: 1046: 1043: 1038: 1029: 1028: 1027: 1014: 1009: 1008: 992: 990: 989: 984: 976: 975: 963: 962: 944: 942: 941: 936: 934: 931: 926: 917: 916: 915: 902: 897: 896: 880: 878: 877: 872: 864: 863: 848: 847: 825: 823: 822: 817: 815: 814: 798: 796: 795: 790: 782: 779: 774: 765: 764: 763: 750: 742: 741: 726: 725: 707: 705: 704: 699: 697: 694: 689: 680: 672: 642: 640: 639: 634: 631: 626: 595: 593: 592: 587: 584: 579: 570: 502: 500: 499: 494: 486: 485: 473: 472: 411: 409: 408: 403: 395: 394: 382: 381: 286: 279: 275: 272: 266: 235: 227: 164: 162: 161: 156: 142: 141: 121: 119: 118: 113: 111: 110: 71:carrier mobility 21: 8652: 8651: 8647: 8646: 8645: 8643: 8642: 8641: 8617:Charge carriers 8602: 8601: 8585:Wayback Machine 8574: 8569: 8539: 8538: 8534: 8512: 8511: 8507: 8502: 8498: 8464: 8463: 8459: 8398: 8397: 8393: 8347: 8346: 8342: 8292: 8287: 8286: 8282: 8273: 8269: 8260: 8256: 8245: 8243: 8241: 8226: 8225: 8218: 8166: 8164: 8154: 8152: 8150: 8135: 8134: 8125: 8091: 8090: 8086: 8079: 8065: 8064: 8057: 8050: 8035: 8034: 8030: 7988: 7987: 7983: 7956:Physical Review 7949: 7948: 7944: 7937: 7922: 7921: 7917: 7911:Wayback Machine 7902: 7895: 7882: 7880: 7878: 7863: 7862: 7858: 7848: 7846: 7844: 7829: 7828: 7824: 7819: 7812: 7799: 7790: 7759: 7758: 7751: 7739: 7728: 7707: 7688: 7678: 7676: 7674: 7659: 7658: 7651: 7641: 7639: 7637: 7622: 7621: 7614: 7576: 7575: 7571: 7527: 7526: 7522: 7478: 7477: 7473: 7422: 7421: 7417: 7371: 7370: 7366: 7328: 7327: 7323: 7275: 7274: 7270: 7240: 7239: 7235: 7187: 7186: 7179: 7141: 7140: 7136: 7106: 7105: 7098: 7089: 7087: 7079: 7078: 7069: 7065: 7053: 7009: 7002: 6992: 6986: 6985: 6978: 6951: 6938: 6933: 6932: 6896: 6889: 6879: 6873: 6872: 6865: 6838: 6825: 6820: 6819: 6780: 6773: 6763: 6757: 6756: 6749: 6722: 6709: 6704: 6703: 6667: 6660: 6650: 6644: 6643: 6636: 6609: 6596: 6591: 6590: 6581: 6573: 6566: 6522: 6513: 6512: 6505: 6495: 6480: 6469: 6468: 6435: 6425: 6420: 6419: 6408:charge carriers 6404: 6374: 6373: 6352: 6347: 6346: 6325: 6320: 6319: 6300: 6299: 6275: 6262: 6239: 6238: 6234: 6228: 6212:terahertz probe 6208: 6195: 6188: 6184: 6125: 6109: 6093: 6089: 6085: 6065: 6049: 6044: 6043: 6017: 5997: 5972: 5961: 5960: 5958: 5929: 5916: 5911: 5910: 5908: 5903: 5892: 5863: 5850: 5834: 5805: 5801: 5786: 5781: 5780: 5778: 5740: 5722: 5694: 5693: 5691: 5684: 5680: 5676: 5671: 5652: 5645: 5639: 5632: 5625: 5605: 5578: 5561: 5551: 5550: 5535: 5530: 5529: 5513: 5512: 5502: 5485: 5475: 5474: 5460: 5459: 5446: 5436: 5424: 5423: 5408: 5399: 5395: 5385: 5370: 5366: 5359: 5349: 5340: 5339: 5316: 5299: 5298: 5283: 5262: 5257: 5256: 5233: 5216: 5215: 5200: 5176: 5171: 5170: 5145: 5130: 5125: 5124: 5101: 5077: 5072: 5071: 5068: 5041: 5021: 5020: 4996: 4988: 4970: 4965: 4964: 4960: 4951: 4917: 4897: 4896: 4855: 4845: 4832: 4827: 4826: 4798: 4788: 4772: 4758: 4757: 4724: 4709: 4681: 4654: 4649: 4648: 4610: 4595: 4568: 4563: 4562: 4534: 4519: 4492: 4487: 4486: 4485:For electrons: 4461: 4450: 4439: 4432:right hand rule 4381: 4375: 4370: 4346: 4345: 4324: 4319: 4318: 4297: 4292: 4291: 4225: 4219: 4218: 4214: 4210: 4194: 4183: 4182: 4161: 4160: 4139: 4134: 4133: 4099: 4098: 4084: 4080: 4062: 4052: 4048: 4032: 4016: 4011: 4010: 3984: 3976: 3975: 3951: 3946: 3945: 3926: 3925: 3906: 3905: 3881: 3876: 3875: 3863: 3835: 3834: 3813: 3808: 3807: 3786: 3781: 3780: 3759: 3754: 3753: 3719: 3718: 3708: 3702: 3698: 3682: 3671: 3670: 3631: 3626: 3625: 3619: 3595:polycrystalline 3569: 3564: 3563: 3553: 3507: 3492: 3487: 3486: 3454: 3436: 3431: 3430: 3408: 3403: 3402: 3367: 3365: 3350: 3345: 3344: 3338: 3301: 3296: 3295: 3272: 3267: 3266: 3247: 3246: 3221: 3203: 3202: 3188:acoustic phonon 3131: 3120: 3062: 3022: 2973: 2950: 2949: 2897: 2857: 2808: 2785: 2784: 2743: 2738: 2737: 2687: 2682: 2681: 2631: 2582: 2559: 2558: 2548: 2530: 2481: 2465: 2464: 2460: 2451: 2442: 2433: 2424: 2415: 2399: 2375: 2334: 2308: 2301: 2294: 2287: 2261: 2224: 2223: 2216: 2215: 2195: 2188: 2159: 2149: 2143: 2107: 1967: 1959: 1924: 1914: 1913: 1898: 1893: 1892: 1867: 1827: 1817: 1816: 1801: 1796: 1795: 1765: 1764: 1756: 1715: 1701: 1700: 1693: 1665: 1649: 1629: 1628: 1607: 1588: 1571: 1570: 1551: 1550: 1522: 1521: 1490: 1471: 1449: 1436: 1425: 1424: 1421: 1390: 1371: 1349: 1336: 1325: 1324: 1300: 1295: 1294: 1270: 1251: 1246: 1245: 1221: 1202: 1197: 1196: 1175: 1170: 1169: 1148: 1121: 1106: 1101: 1100: 1079: 1068: 1067: 1063: 1019: 1015: 1000: 995: 994: 967: 954: 949: 948: 907: 903: 888: 883: 882: 855: 839: 834: 833: 806: 801: 800: 755: 751: 733: 717: 712: 711: 673: 657: 656: 647:of an electron. 613: 612: 552: 551: 544: 477: 464: 459: 458: 452: 434: 386: 373: 368: 367: 364: 358: 324:crystal defects 302: 296: 287: 276: 270: 267: 252: 236: 225: 133: 128: 127: 102: 97: 96: 35: 28: 23: 22: 15: 12: 11: 5: 8650: 8648: 8640: 8639: 8634: 8629: 8627:Semiconductors 8624: 8619: 8614: 8604: 8603: 8600: 8599: 8592: 8587: 8573: 8572:External links 8570: 8568: 8567: 8532: 8505: 8496: 8457: 8391: 8356:(9): 871–925. 8340: 8303:(2): 543–586. 8280: 8267: 8254: 8239: 8216: 8162: 8148: 8123: 8104:(6): 303–307. 8084: 8077: 8055: 8048: 8028: 8001:(61): 49–144. 7981: 7942: 7935: 7915: 7893: 7876: 7856: 7842: 7822: 7810: 7788: 7749: 7726: 7686: 7672: 7660:Singh (2008). 7649: 7635: 7612: 7569: 7520: 7471: 7415: 7364: 7321: 7268: 7249:(4): 1500452. 7233: 7196:(9): 351–355. 7177: 7134: 7096: 7085:www.matprop.ru 7066: 7064: 7061: 7060: 7059: 7052: 7049: 7029: 7024: 7016: 7012: 7008: 7005: 6999: 6995: 6989: 6984: 6981: 6977: 6972: 6969: 6966: 6963: 6958: 6954: 6950: 6945: 6941: 6916: 6911: 6903: 6899: 6895: 6892: 6886: 6882: 6876: 6871: 6868: 6864: 6859: 6856: 6853: 6850: 6845: 6841: 6837: 6832: 6828: 6800: 6795: 6787: 6783: 6779: 6776: 6770: 6766: 6760: 6755: 6752: 6748: 6743: 6740: 6737: 6734: 6729: 6725: 6721: 6716: 6712: 6687: 6682: 6674: 6670: 6666: 6663: 6657: 6653: 6647: 6642: 6639: 6635: 6630: 6627: 6624: 6621: 6616: 6612: 6608: 6603: 6599: 6579: 6571: 6564: 6541: 6536: 6525: 6521: 6516: 6511: 6508: 6502: 6498: 6492: 6487: 6483: 6479: 6476: 6450: 6447: 6442: 6439: 6432: 6428: 6403: 6400: 6387: 6384: 6381: 6359: 6355: 6332: 6328: 6307: 6287: 6282: 6278: 6274: 6269: 6265: 6261: 6258: 6255: 6252: 6249: 6246: 6230:Main article: 6227: 6224: 6207: 6204: 6194: 6191: 6186: 6182: 6169: 6163: 6158: 6153: 6150: 6146: 6140: 6135: 6132: 6128: 6124: 6119: 6116: 6112: 6108: 6103: 6100: 6096: 6092: 6088: 6082: 6079: 6072: 6068: 6064: 6061: 6056: 6052: 6031: 6024: 6020: 6016: 6007: 6004: 6000: 5996: 5989: 5986: 5975: 5971: 5968: 5956: 5939: 5936: 5932: 5928: 5923: 5919: 5906: 5902: 5899: 5890: 5875: 5870: 5866: 5860: 5857: 5853: 5849: 5844: 5841: 5837: 5833: 5828: 5825: 5818: 5812: 5808: 5804: 5798: 5793: 5789: 5774: 5747: 5743: 5739: 5732: 5728: 5725: 5717: 5708: 5704: 5701: 5689: 5682: 5678: 5674: 5670: 5667: 5638: 5635: 5630: 5623: 5615:(current) and 5603: 5584: 5581: 5576: 5571: 5568: 5564: 5558: 5554: 5547: 5542: 5538: 5508: 5505: 5500: 5495: 5492: 5488: 5482: 5478: 5471: 5468: 5465: 5463: 5461: 5456: 5453: 5449: 5443: 5439: 5435: 5432: 5429: 5427: 5425: 5421: 5414: 5411: 5407: 5402: 5398: 5392: 5388: 5383: 5379: 5376: 5373: 5369: 5365: 5362: 5360: 5356: 5352: 5348: 5347: 5322: 5319: 5314: 5309: 5306: 5302: 5295: 5289: 5286: 5282: 5277: 5272: 5269: 5265: 5239: 5236: 5231: 5226: 5223: 5219: 5212: 5206: 5203: 5199: 5194: 5191: 5186: 5183: 5179: 5157: 5152: 5148: 5142: 5137: 5133: 5107: 5104: 5100: 5095: 5092: 5087: 5084: 5080: 5066: 5047: 5044: 5039: 5036: 5031: 5028: 5024: 5017: 5014: 5008: 5005: 5002: 4999: 4994: 4991: 4985: 4982: 4977: 4973: 4956: 4947: 4932: 4929: 4924: 4920: 4916: 4913: 4910: 4907: 4904: 4862: 4858: 4852: 4848: 4844: 4839: 4835: 4813: 4810: 4805: 4801: 4795: 4791: 4787: 4784: 4779: 4775: 4771: 4768: 4765: 4744: 4741: 4738: 4733: 4728: 4723: 4718: 4713: 4708: 4705: 4702: 4699: 4696: 4693: 4688: 4684: 4680: 4677: 4674: 4671: 4668: 4663: 4658: 4624: 4619: 4614: 4609: 4604: 4599: 4594: 4591: 4588: 4585: 4580: 4577: 4572: 4548: 4543: 4538: 4533: 4528: 4523: 4518: 4515: 4512: 4509: 4504: 4501: 4496: 4459: 4448: 4443:high-impedance 4437: 4412:magnetic field 4377:Main article: 4374: 4371: 4369: 4366: 4353: 4331: 4327: 4304: 4300: 4276: 4270: 4267: 4264: 4261: 4258: 4254: 4250: 4247: 4242: 4237: 4232: 4228: 4222: 4217: 4213: 4209: 4206: 4201: 4197: 4193: 4190: 4168: 4146: 4142: 4118: 4111: 4106: 4102: 4094: 4091: 4087: 4083: 4077: 4072: 4069: 4065: 4061: 4058: 4055: 4051: 4047: 4044: 4039: 4035: 4031: 4026: 4023: 4019: 3994: 3991: 3987: 3983: 3961: 3958: 3954: 3933: 3913: 3891: 3888: 3884: 3862: 3859: 3842: 3816: 3789: 3766: 3762: 3738: 3731: 3722: 3711: 3705: 3701: 3697: 3694: 3689: 3685: 3681: 3678: 3638: 3634: 3618: 3615: 3576: 3572: 3552: 3549: 3522: 3518: 3514: 3510: 3506: 3496: 3472: 3468: 3464: 3461: 3457: 3453: 3448: 3445: 3440: 3417: 3414: 3411: 3385: 3382: 3376: 3373: 3370: 3364: 3354: 3336: 3319: 3314: 3310: 3307: 3304: 3281: 3278: 3275: 3254: 3234: 3230: 3227: 3224: 3220: 3215: 3212: 3177: 3176: 3173: 3170: 3167: 3163: 3162: 3159: 3156: 3153: 3149: 3148: 3145: 3142: 3139: 3130: 3127: 3118: 3102: 3099: 3096: 3088: 3085: 3082: 3079: 3076: 3073: 3070: 3065: 3061: 3056: 3048: 3045: 3042: 3039: 3036: 3033: 3030: 3025: 3021: 3016: 3008: 3005: 3002: 2999: 2996: 2993: 2990: 2987: 2984: 2981: 2976: 2972: 2967: 2962: 2959: 2937: 2934: 2931: 2923: 2920: 2917: 2914: 2911: 2908: 2905: 2900: 2896: 2891: 2883: 2880: 2877: 2874: 2871: 2868: 2865: 2860: 2856: 2851: 2843: 2840: 2837: 2834: 2831: 2828: 2825: 2822: 2819: 2816: 2811: 2807: 2802: 2797: 2794: 2769: 2766: 2763: 2760: 2757: 2754: 2751: 2746: 2722: 2719: 2716: 2713: 2710: 2707: 2704: 2701: 2698: 2695: 2690: 2665: 2657: 2654: 2651: 2648: 2645: 2642: 2639: 2634: 2630: 2625: 2617: 2614: 2611: 2608: 2605: 2602: 2599: 2596: 2593: 2590: 2585: 2581: 2576: 2571: 2568: 2547: 2544: 2527:effective mass 2500: 2497: 2488: 2484: 2480: 2475: 2472: 2459: 2456: 2450: 2447: 2441: 2438: 2432: 2429: 2423: 2420: 2414: 2411: 2398: 2395: 2386:mean free time 2374: 2371: 2338:effective mass 2333: 2330: 2306: 2299: 2292: 2285: 2264: 2260: 2257: 2252: 2246: 2237: 2231: 2227: 2212:kinetic energy 2206:optical phonon 2193: 2186: 2172:is called the 2164:, so mobility 2155: 2145:Main article: 2142: 2139: 2136: 2135: 2133: 2130: 2126: 2125: 2122: 2119: 2115: 2114: 2112: 2109: 2105: 2101: 2100: 2098: 2095: 2091: 2090: 2088: 2085: 2081: 2080: 2077: 2074: 2070: 2069: 2067: 2064: 2060: 2059: 2057: 2054: 2050: 2049: 2047: 2044: 2040: 2039: 2036: 2033: 2029: 2028: 2027:Hole mobility 2025: 2022: 1966: 1963: 1962: 1961: 1957: 1937: 1931: 1927: 1917: 1910: 1901: 1888: 1887: 1881: 1872: 1865: 1845: 1841: 1835: 1830: 1820: 1813: 1804: 1788: 1787: 1775: 1772: 1762: 1761:or diffusivity 1754: 1749: 1730: 1727: 1718: 1714: 1711: 1708: 1692: 1689: 1677: 1672: 1668: 1664: 1661: 1656: 1652: 1648: 1645: 1642: 1639: 1636: 1614: 1610: 1606: 1603: 1600: 1595: 1591: 1587: 1584: 1581: 1578: 1558: 1538: 1535: 1532: 1529: 1505: 1502: 1497: 1493: 1489: 1486: 1483: 1478: 1474: 1470: 1467: 1464: 1461: 1456: 1452: 1448: 1443: 1439: 1435: 1432: 1420: 1417: 1405: 1402: 1397: 1393: 1389: 1386: 1383: 1378: 1374: 1370: 1367: 1364: 1361: 1356: 1352: 1348: 1343: 1339: 1335: 1332: 1307: 1303: 1282: 1277: 1273: 1269: 1266: 1263: 1258: 1254: 1233: 1228: 1224: 1220: 1217: 1214: 1209: 1205: 1182: 1178: 1155: 1151: 1147: 1144: 1141: 1138: 1133: 1128: 1124: 1118: 1113: 1109: 1086: 1082: 1078: 1075: 1062: 1059: 1042: 1037: 1033: 1026: 1022: 1018: 1012: 1007: 1003: 982: 979: 974: 970: 966: 961: 957: 930: 925: 921: 914: 910: 906: 900: 895: 891: 870: 867: 862: 858: 854: 851: 846: 842: 828:mean free time 813: 809: 788: 785: 778: 773: 769: 762: 758: 754: 748: 745: 740: 736: 732: 729: 724: 720: 693: 688: 684: 679: 676: 670: 667: 664: 649: 648: 645:effective mass 630: 625: 621: 610: 604: 583: 578: 574: 569: 565: 562: 559: 546:Starting with 543: 540: 492: 489: 484: 480: 476: 471: 467: 455: 454: 450: 445: 432: 428: 425:electric field 401: 398: 393: 389: 385: 380: 376: 357: 354: 350:mean free time 346:mean free path 332:drift velocity 300:Drift velocity 298:Main article: 295: 292: 289: 288: 239: 237: 230: 224: 221: 207:things equal. 154: 151: 148: 145: 140: 136: 126:is defined as 109: 105: 93:drift velocity 59:electric field 26: 24: 14: 13: 10: 9: 6: 4: 3: 2: 8649: 8638: 8635: 8633: 8630: 8628: 8625: 8623: 8620: 8618: 8615: 8613: 8610: 8609: 8607: 8597: 8593: 8591: 8588: 8586: 8582: 8579: 8576: 8575: 8571: 8563: 8559: 8555: 8551: 8547: 8543: 8536: 8533: 8528: 8524: 8520: 8516: 8509: 8506: 8500: 8497: 8492: 8488: 8484: 8480: 8476: 8472: 8468: 8461: 8458: 8453: 8449: 8444: 8439: 8435: 8431: 8427: 8423: 8419: 8415: 8411: 8407: 8403: 8395: 8392: 8387: 8383: 8379: 8375: 8371: 8367: 8363: 8359: 8355: 8351: 8344: 8341: 8336: 8332: 8327: 8322: 8318: 8314: 8310: 8306: 8302: 8298: 8291: 8284: 8281: 8277: 8271: 8268: 8264: 8258: 8255: 8242: 8236: 8232: 8231: 8223: 8221: 8217: 8212: 8208: 8204: 8200: 8196: 8192: 8187: 8182: 8178: 8174: 8170: 8151: 8145: 8141: 8140: 8132: 8130: 8128: 8124: 8119: 8115: 8111: 8107: 8103: 8099: 8095: 8088: 8085: 8080: 8074: 8070: 8069: 8062: 8060: 8056: 8051: 8045: 8041: 8040: 8032: 8029: 8024: 8020: 8016: 8012: 8008: 8004: 8000: 7996: 7992: 7985: 7982: 7977: 7973: 7969: 7965: 7961: 7957: 7953: 7946: 7943: 7938: 7932: 7928: 7927: 7919: 7916: 7912: 7908: 7905: 7900: 7898: 7894: 7891: 7879: 7873: 7869: 7868: 7860: 7857: 7845: 7839: 7835: 7834: 7826: 7823: 7817: 7815: 7811: 7807: 7806:0-13-495656-7 7803: 7797: 7795: 7793: 7789: 7783: 7779: 7775: 7771: 7767: 7763: 7756: 7754: 7750: 7747: 7743: 7737: 7735: 7733: 7731: 7727: 7723: 7722:0-7484-0866-5 7719: 7715: 7714:0-7484-0865-7 7711: 7705: 7703: 7701: 7699: 7697: 7695: 7693: 7691: 7687: 7675: 7669: 7665: 7664: 7656: 7654: 7650: 7638: 7632: 7628: 7627: 7619: 7617: 7613: 7608: 7604: 7600: 7596: 7592: 7588: 7584: 7580: 7573: 7570: 7565: 7561: 7556: 7551: 7547: 7543: 7539: 7535: 7531: 7524: 7521: 7516: 7512: 7507: 7502: 7498: 7494: 7490: 7486: 7482: 7475: 7472: 7467: 7463: 7459: 7455: 7451: 7447: 7443: 7439: 7435: 7431: 7427: 7419: 7416: 7411: 7407: 7403: 7399: 7395: 7391: 7387: 7384:(3): 033105. 7383: 7379: 7375: 7368: 7365: 7360: 7356: 7352: 7348: 7344: 7340: 7336: 7332: 7325: 7322: 7317: 7313: 7309: 7305: 7301: 7297: 7292: 7287: 7284:(3): 034005. 7283: 7279: 7272: 7269: 7264: 7260: 7256: 7252: 7248: 7244: 7237: 7234: 7229: 7225: 7221: 7217: 7213: 7209: 7204: 7199: 7195: 7191: 7184: 7182: 7178: 7173: 7169: 7165: 7161: 7157: 7153: 7149: 7145: 7138: 7135: 7130: 7126: 7122: 7118: 7114: 7110: 7103: 7101: 7097: 7086: 7082: 7076: 7074: 7072: 7068: 7062: 7058: 7055: 7054: 7050: 7048: 7045: 7027: 7022: 7014: 7010: 7006: 7003: 6997: 6993: 6987: 6982: 6979: 6975: 6970: 6967: 6964: 6956: 6952: 6943: 6939: 6914: 6909: 6901: 6897: 6893: 6890: 6884: 6880: 6874: 6869: 6866: 6862: 6857: 6854: 6851: 6843: 6839: 6830: 6826: 6816: 6798: 6793: 6785: 6781: 6777: 6774: 6768: 6764: 6758: 6753: 6750: 6746: 6741: 6738: 6735: 6727: 6723: 6714: 6710: 6685: 6680: 6672: 6668: 6664: 6661: 6655: 6651: 6645: 6640: 6637: 6633: 6628: 6625: 6622: 6614: 6610: 6601: 6597: 6587: 6585: 6578: 6574: 6567: 6560: 6539: 6534: 6523: 6519: 6514: 6509: 6506: 6500: 6496: 6490: 6485: 6481: 6477: 6474: 6466: 6448: 6445: 6430: 6426: 6417: 6412: 6409: 6401: 6399: 6385: 6379: 6357: 6353: 6330: 6326: 6305: 6280: 6276: 6272: 6267: 6263: 6256: 6253: 6250: 6244: 6233: 6225: 6223: 6221: 6217: 6214:measurement. 6213: 6205: 6203: 6200: 6192: 6190: 6167: 6161: 6156: 6151: 6148: 6144: 6138: 6133: 6130: 6126: 6117: 6114: 6110: 6106: 6101: 6098: 6094: 6086: 6080: 6077: 6070: 6066: 6062: 6059: 6054: 6050: 6029: 6022: 6018: 6014: 6005: 6002: 5998: 5994: 5987: 5984: 5973: 5969: 5966: 5955: 5937: 5934: 5930: 5926: 5921: 5917: 5909:is small and 5900: 5898: 5896: 5889: 5873: 5868: 5858: 5855: 5851: 5847: 5842: 5839: 5835: 5826: 5823: 5816: 5810: 5806: 5802: 5796: 5791: 5787: 5777: 5773: 5769: 5765: 5745: 5741: 5737: 5730: 5726: 5723: 5715: 5706: 5702: 5699: 5688: 5668: 5666: 5664: 5659: 5657: 5650: 5644: 5636: 5634: 5629: 5622: 5618: 5614: 5610: 5606: 5598: 5582: 5579: 5574: 5569: 5566: 5562: 5556: 5552: 5545: 5540: 5536: 5526: 5506: 5503: 5498: 5493: 5490: 5486: 5480: 5476: 5469: 5466: 5464: 5454: 5451: 5447: 5441: 5437: 5433: 5430: 5428: 5419: 5412: 5409: 5405: 5400: 5396: 5390: 5386: 5381: 5377: 5374: 5371: 5367: 5363: 5361: 5354: 5350: 5336: 5320: 5317: 5312: 5307: 5304: 5300: 5293: 5287: 5284: 5280: 5275: 5270: 5267: 5263: 5253: 5237: 5234: 5229: 5224: 5221: 5217: 5210: 5204: 5201: 5197: 5192: 5189: 5184: 5181: 5177: 5155: 5150: 5146: 5140: 5135: 5131: 5121: 5105: 5102: 5098: 5093: 5090: 5085: 5082: 5078: 5069: 5061: 5045: 5042: 5037: 5034: 5029: 5026: 5022: 5015: 5012: 5006: 5003: 5000: 4997: 4992: 4989: 4983: 4980: 4975: 4971: 4962: 4959: 4955: 4950: 4946: 4930: 4927: 4922: 4918: 4914: 4911: 4908: 4905: 4902: 4894: 4891: 4886: 4884: 4880: 4875: 4860: 4856: 4850: 4846: 4842: 4837: 4833: 4824: 4811: 4808: 4803: 4799: 4793: 4789: 4785: 4782: 4777: 4773: 4769: 4766: 4755: 4742: 4739: 4731: 4721: 4716: 4700: 4697: 4691: 4686: 4682: 4675: 4672: 4666: 4661: 4646: 4644: 4640: 4635: 4617: 4607: 4602: 4589: 4586: 4583: 4578: 4575: 4559: 4541: 4531: 4526: 4513: 4510: 4507: 4502: 4499: 4483: 4481: 4477: 4476:Lorentz force 4472: 4470: 4466: 4462: 4455: 4451: 4444: 4440: 4433: 4429: 4425: 4421: 4417: 4413: 4409: 4404: 4402: 4393: 4385: 4380: 4373:Hall mobility 4372: 4367: 4365: 4351: 4329: 4325: 4302: 4298: 4288: 4274: 4265: 4262: 4259: 4252: 4248: 4245: 4240: 4235: 4230: 4226: 4220: 4215: 4211: 4207: 4204: 4199: 4195: 4191: 4188: 4180: 4166: 4144: 4140: 4130: 4116: 4109: 4104: 4100: 4092: 4089: 4085: 4075: 4070: 4067: 4063: 4059: 4056: 4053: 4049: 4045: 4042: 4037: 4033: 4029: 4024: 4021: 4017: 4008: 3992: 3989: 3985: 3959: 3956: 3952: 3931: 3911: 3889: 3886: 3882: 3873: 3869: 3860: 3858: 3856: 3855:Urbach Energy 3840: 3814: 3787: 3764: 3760: 3750: 3736: 3729: 3720: 3709: 3703: 3699: 3695: 3692: 3687: 3683: 3679: 3676: 3664: 3660: 3658: 3654: 3636: 3632: 3623: 3616: 3614: 3612: 3608: 3604: 3600: 3596: 3574: 3570: 3561: 3557: 3550: 3548: 3544: 3541: 3536: 3520: 3516: 3512: 3508: 3504: 3494: 3470: 3466: 3462: 3459: 3455: 3451: 3446: 3443: 3438: 3415: 3412: 3409: 3399: 3383: 3380: 3374: 3371: 3368: 3362: 3342: 3333: 3317: 3312: 3308: 3305: 3302: 3279: 3276: 3273: 3228: 3225: 3222: 3218: 3213: 3210: 3199: 3197: 3193: 3189: 3185: 3174: 3171: 3168: 3165: 3164: 3160: 3157: 3154: 3151: 3150: 3146: 3143: 3140: 3138: 3137: 3128: 3126: 3122: 3116: 3100: 3097: 3094: 3063: 3059: 3054: 3023: 3019: 3014: 2974: 2970: 2965: 2960: 2957: 2935: 2932: 2929: 2898: 2894: 2889: 2858: 2854: 2849: 2809: 2805: 2800: 2795: 2792: 2744: 2688: 2679: 2663: 2632: 2628: 2623: 2583: 2579: 2574: 2569: 2566: 2556: 2554: 2543: 2541: 2536: 2533: 2528: 2524: 2520: 2516: 2495: 2486: 2482: 2478: 2473: 2470: 2457: 2455: 2448: 2446: 2439: 2437: 2430: 2428: 2421: 2419: 2412: 2410: 2408: 2404: 2403:absolute zero 2396: 2394: 2390: 2389:interaction. 2387: 2383: 2382: 2372: 2370: 2368: 2364: 2360: 2354: 2352: 2347: 2343: 2339: 2331: 2329: 2325: 2323: 2319: 2315: 2310: 2305: 2298: 2293:phonon (opt.) 2291: 2284: 2267:phonon (opt.) 2262: 2255: 2250: 2244: 2235: 2229: 2225: 2213: 2209: 2207: 2201: 2199: 2192: 2185: 2182: 2177: 2175: 2171: 2167: 2163: 2158: 2154: 2148: 2140: 2134: 2131: 2128: 2127: 2123: 2120: 2117: 2116: 2113: 2110: 2103: 2102: 2099: 2096: 2093: 2092: 2089: 2086: 2083: 2082: 2078: 2075: 2072: 2071: 2068: 2065: 2062: 2061: 2058: 2055: 2052: 2051: 2048: 2045: 2042: 2041: 2037: 2034: 2031: 2030: 2026: 2023: 2020: 2019: 2013: 2011: 2007: 2003: 1999: 1995: 1991: 1986: 1984: 1980: 1976: 1972: 1964: 1956: 1953: 1952: 1951: 1935: 1929: 1925: 1915: 1908: 1899: 1885: 1882: 1880: 1876: 1873: 1871: 1864: 1861: 1860: 1859: 1843: 1839: 1828: 1818: 1811: 1802: 1793: 1773: 1763: 1760: 1753: 1750: 1747: 1744: 1743: 1742: 1728: 1716: 1712: 1709: 1706: 1698: 1690: 1688: 1670: 1666: 1662: 1659: 1654: 1650: 1646: 1640: 1637: 1634: 1612: 1608: 1604: 1601: 1598: 1593: 1589: 1585: 1582: 1579: 1576: 1556: 1536: 1533: 1530: 1527: 1519: 1503: 1495: 1491: 1487: 1484: 1481: 1476: 1472: 1468: 1465: 1459: 1454: 1450: 1446: 1441: 1437: 1433: 1430: 1418: 1416: 1403: 1395: 1391: 1387: 1384: 1381: 1376: 1372: 1368: 1365: 1359: 1354: 1350: 1346: 1341: 1337: 1333: 1330: 1321: 1305: 1301: 1280: 1275: 1271: 1267: 1264: 1261: 1256: 1252: 1231: 1226: 1222: 1218: 1215: 1212: 1207: 1203: 1180: 1176: 1153: 1149: 1145: 1142: 1139: 1136: 1131: 1126: 1122: 1116: 1111: 1107: 1084: 1080: 1076: 1073: 1060: 1058: 1040: 1035: 1031: 1024: 1020: 1016: 1010: 1005: 1001: 980: 977: 972: 968: 964: 959: 955: 945: 928: 923: 919: 912: 908: 904: 898: 893: 889: 868: 865: 860: 856: 852: 849: 844: 840: 830: 829: 811: 807: 786: 783: 776: 771: 767: 760: 756: 752: 746: 743: 738: 734: 730: 727: 722: 718: 708: 691: 686: 682: 677: 674: 668: 665: 662: 654: 646: 628: 623: 619: 611: 608: 605: 602: 599: 598: 597: 581: 576: 572: 567: 563: 560: 557: 549: 541: 539: 535: 533: 529: 525: 521: 517: 513: 508: 504: 490: 487: 482: 478: 474: 469: 465: 449: 446: 443: 439: 435: 429: 426: 422: 418: 415: 414: 413: 399: 396: 391: 387: 383: 378: 374: 363: 355: 353: 351: 347: 343: 338: 335: 333: 329: 325: 321: 316: 314: 311: 307: 301: 293: 285: 282: 274: 264: 260: 256: 250: 249: 245: 240:This section 238: 234: 229: 228: 222: 220: 218: 214: 208: 205: 200: 196: 194: 190: 186: 182: 178: 174: 170: 165: 152: 149: 146: 143: 138: 134: 125: 107: 103: 94: 90: 85: 83: 79: 78:special cases 74: 72: 68: 67:hole mobility 64: 60: 56: 55:semiconductor 52: 48: 44: 40: 33: 19: 8548:(1): 47–54. 8545: 8541: 8535: 8518: 8514: 8508: 8499: 8474: 8470: 8460: 8409: 8405: 8394: 8353: 8349: 8343: 8300: 8296: 8283: 8278:, Aug. 2018. 8270: 8265:, Oct. 2017. 8257: 8244:. Retrieved 8229: 8176: 8172: 8153:. Retrieved 8138: 8101: 8097: 8087: 8067: 8038: 8031: 7998: 7994: 7984: 7959: 7955: 7945: 7925: 7918: 7881:. Retrieved 7866: 7859: 7847:. Retrieved 7832: 7825: 7765: 7761: 7677:. Retrieved 7662: 7640:. Retrieved 7625: 7582: 7578: 7572: 7537: 7533: 7523: 7488: 7484: 7474: 7433: 7429: 7418: 7410:the original 7381: 7377: 7367: 7337:(1): 35–39. 7334: 7331:Nano Letters 7330: 7324: 7281: 7277: 7271: 7246: 7242: 7236: 7193: 7189: 7147: 7144:Nano Letters 7143: 7137: 7112: 7108: 7088:. Retrieved 7084: 7046: 6817: 6588: 6576: 6569: 6562: 6558: 6413: 6405: 6235: 6209: 6196: 5953: 5904: 5895:Early effect 5887: 5775: 5771: 5767: 5763: 5686: 5672: 5660: 5653: 5627: 5620: 5616: 5612: 5608: 5601: 5599: 5527: 5337: 5254: 5122: 5064: 5062: 4963: 4957: 4953: 4948: 4944: 4895:is given by 4892: 4887: 4882: 4878: 4876: 4825: 4756: 4647: 4642: 4636: 4560: 4484: 4482:is given by 4479: 4473: 4468: 4464: 4457: 4454:Hall voltage 4446: 4435: 4427: 4423: 4419: 4415: 4407: 4405: 4398: 4289: 4181: 4131: 4009: 3871: 3864: 3751: 3669: 3652: 3620: 3611:normalizable 3606: 3592: 3545: 3539: 3537: 3400: 3340: 3334: 3200: 3195: 3191: 3180: 3123: 3114: 2677: 2557: 2549: 2539: 2537: 2531: 2522: 2514: 2461: 2452: 2443: 2434: 2425: 2416: 2400: 2391: 2379: 2376: 2366: 2362: 2358: 2355: 2353:scattering. 2335: 2326: 2317: 2311: 2303: 2296: 2289: 2286:phonon(opt.) 2282: 2204: 2202: 2190: 2183: 2180: 2178: 2173: 2169: 2165: 2161: 2156: 2152: 2150: 1987: 1968: 1954: 1889: 1883: 1874: 1862: 1789: 1751: 1745: 1694: 1422: 1322: 1064: 946: 831: 709: 652: 650: 606: 600: 545: 536: 509: 505: 456: 447: 430: 416: 365: 339: 336: 317: 303: 277: 268: 253:Please help 241: 223:Introduction 209: 199:Conductivity 197: 166: 123: 88: 86: 75: 70: 66: 42: 36: 8326:10871/15671 7768:(1): 1–36. 5952:with slope 5649:Wien effect 5528:Similarly, 4885:direction. 4561:For holes: 4401:Hall effect 4379:Hall effect 2314:Gunn effect 2035:35,000,000 217:Hall effect 204:transistors 69:. The term 8606:Categories 7291:2203.10713 7090:2020-07-25 7063:References 5641:See also: 3868:tunnelling 3152:Electrons 3119:impurities 2555:in 1864): 2342:scattering 2208:scattering 2038:5,800,000 1697:Fick's law 542:Derivation 360:See also: 271:March 2021 8491:1932-7447 8434:2041-1723 8378:1866-6892 8335:0034-6861 8211:119532427 8023:0001-8732 7929:. Wiley. 7466:250952849 7406:0003-6951 7316:2475-9953 7263:138355533 7228:118392999 7203:0802.2389 7150:(1): 35. 7007:× 6940:μ 6894:× 6827:μ 6778:× 6711:μ 6665:× 6598:μ 6540:α 6497:μ 6482:μ 6475:μ 6446:− 6386:μ 6383:Σ 6380:ϕ 6354:μ 6327:μ 6306:ϕ 6277:μ 6264:μ 6257:ϕ 6251:μ 6248:Σ 6245:ϕ 6139:− 6107:− 6063:μ 5967:μ 5927:∝ 5848:− 5803:μ 5700:μ 5553:σ 5537:μ 5477:σ 5470:− 5438:σ 5434:− 5401:− 5387:μ 5372:− 5351:μ 5193:− 5132:ξ 5094:− 4984:− 4972:ξ 4909:− 4834:ξ 4774:ξ 4767:− 4764:⇒ 4722:× 4698:− 4683:ξ 4673:− 4639:net force 4608:× 4532:× 4511:− 4299:μ 4246:− 4216:− 4208:⁡ 4196:μ 4189:μ 4167:α 4082:Δ 4076:− 4060:α 4054:− 4046:⁡ 3982:Δ 3761:μ 3704:− 3696:⁡ 3684:μ 3677:μ 3607:localized 3599:amorphous 3540:decreases 3505:∼ 3495:μ 3460:− 3452:∼ 3439:μ 3381:− 3363:∝ 3353:Σ 3313:∼ 3253:Σ 3233:Σ 3219:∝ 3214:τ 3184:non-polar 3098:⋯ 3064:τ 3024:τ 2975:τ 2961:τ 2933:⋯ 2899:μ 2859:μ 2810:μ 2796:μ 2745:μ 2689:μ 2633:μ 2584:μ 2570:μ 2499:¯ 2496:τ 2487:∗ 2471:μ 2318:increases 2263:ω 2259:ℏ 2256:≈ 2230:∗ 2118:Organics 2021:Material 1916:μ 1819:μ 1771:∇ 1726:∇ 1713:− 1667:μ 1651:μ 1635:σ 1609:μ 1590:μ 1577:σ 1557:σ 1534:σ 1518:Ohm's law 1492:μ 1473:μ 1392:μ 1373:μ 1302:μ 1272:μ 1223:μ 1140:− 1074:− 1041:∗ 1021:τ 1002:μ 969:μ 929:∗ 909:τ 890:μ 857:μ 853:− 808:τ 777:∗ 757:τ 747:− 735:τ 692:∗ 669:− 629:∗ 582:∗ 479:μ 438:magnitude 421:magnitude 388:μ 306:electrons 242:does not 147:μ 65:, called 8596:Mobility 8581:Archived 8452:26400049 8412:: 8195. 8386:13849900 8246:20 April 7907:Archived 7716:(hbk.), 7607:25457390 7599:26707947 7564:24398476 7540:: 3005. 7515:24105872 7458:35862526 7359:45010238 7172:45010238 7051:See also 3603:Anderson 3416:⟩ 3410:⟨ 3375:⟩ 3369:⟨ 3309:⟩ 3303:⟨ 3280:⟩ 3274:⟨ 3245:, where 3229:⟩ 3223:⟨ 2046:200,000 2010:oligomer 1998:graphene 1965:Examples 1748:is flux. 47:electron 8637:MOSFETs 8550:Bibcode 8443:4598357 8414:Bibcode 8358:Bibcode 8305:Bibcode 8191:Bibcode 8155:1 March 8106:Bibcode 8003:Bibcode 7964:Bibcode 7883:2 March 7849:1 March 7770:Bibcode 7679:1 March 7642:2 March 7542:Bibcode 7493:Bibcode 7438:Bibcode 7430:Science 7386:Bibcode 7339:Bibcode 7296:Bibcode 7208:Bibcode 7152:Bibcode 7117:Bibcode 6575:), and 2517:is the 2407:phonons 2056:79,000 2006:polymer 1983:silicon 1950:where: 1877:is the 1868:is the 1858:where: 1757:is the 1741:where: 826:is the 643:is the 596:where: 436:is the 423:of the 419:is the 412:where: 328:phonons 263:removed 248:sources 8489: 8450: 8440: 8432: 8384: 8376: 8333: 8237: 8209: 8146: 8075: 8046: 8021: 7933: 7874: 7840: 7808:(nid.) 7804: 7744: 7724:(pbk.) 7720: 7712: 7670: 7633: 7605: 7597: 7562: 7513: 7464: 7456: 7404: 7357: 7314: 7261: 7226: 7170: 6557:where 5886:where 5762:where 5663:MOSFET 5643:MOSFET 5123:Since 5063:where 4943:. Sub 4290:where 3752:where 3166:Holes 3113:where 2676:where 2529:, and 2513:where 2351:defect 2281:where 2198:doping 2111:10–50 2097:10–50 2076:1,400 2066:1,600 1979:silver 1975:copper 1549:where 1195:gives 993:where 881:where 799:where 340:Quasi- 41:, the 8382:S2CID 8293:(PDF) 8207:S2CID 8181:arXiv 7603:S2CID 7462:S2CID 7355:S2CID 7286:arXiv 7259:S2CID 7224:S2CID 7198:arXiv 7168:S2CID 4132:Here 3147:GaAs 2340:) is 442:speed 310:holes 63:holes 51:metal 8487:ISSN 8448:PMID 8430:ISSN 8374:ISSN 8331:ISSN 8248:2011 8235:ISBN 8157:2011 8144:ISBN 8073:ISBN 8044:ISBN 8019:ISSN 7931:ISBN 7885:2011 7872:ISBN 7851:2011 7838:ISBN 7802:ISBN 7742:ISBN 7718:ISBN 7710:ISBN 7681:2011 7668:ISBN 7644:2011 7631:ISBN 7595:PMID 7560:PMID 7511:PMID 7454:PMID 7402:ISSN 7312:ISSN 7028:1.25 6863:1180 6799:0.76 6686:0.72 6634:1265 6406:The 5766:and 4888:The 3622:Mott 3175:∝T 3172:∝T 3169:∝T 3161:∝T 3158:∝T 3155:∝T 2307:emit 2300:emit 2240:emit 2121:8.6 2087:100 2079:450 1990:2DEG 1977:and 1971:gold 1516:Now 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4993:B 4990:I 4981:= 4976:y 4958:y 4954:ξ 4949:x 4945:v 4931:W 4928:t 4923:x 4919:v 4915:n 4912:q 4906:= 4903:I 4893:I 4883:y 4879:y 4861:z 4857:B 4851:x 4847:v 4843:= 4838:y 4812:0 4809:= 4804:z 4800:B 4794:x 4790:v 4786:q 4783:+ 4778:y 4770:q 4743:0 4740:= 4737:] 4732:z 4727:B 4717:n 4712:v 4707:[ 4704:) 4701:q 4695:( 4692:+ 4687:y 4679:) 4676:q 4670:( 4667:= 4662:y 4657:F 4643:y 4623:) 4618:z 4613:B 4603:p 4598:v 4593:( 4590:q 4587:+ 4584:= 4579:p 4576:H 4571:F 4547:) 4542:z 4537:B 4527:n 4522:v 4517:( 4514:q 4508:= 4503:n 4500:H 4495:F 4480:q 4469:p 4465:n 4460:H 4458:V 4449:H 4447:V 4438:y 4436:ξ 4428:y 4424:p 4420:n 4416:z 4408:x 4352:d 4330:0 4326:T 4303:0 4275:) 4269:) 4266:1 4263:+ 4260:d 4257:( 4253:/ 4249:1 4241:] 4236:T 4231:0 4227:T 4221:[ 4212:( 4200:0 4192:= 4145:0 4141:P 4117:) 4110:T 4105:B 4101:k 4093:j 4090:i 4086:E 4071:j 4068:i 4064:r 4057:2 4050:( 4038:0 4034:P 4030:= 4025:j 4022:i 4018:P 3993:j 3990:i 3986:E 3960:j 3957:i 3953:r 3932:j 3912:i 3890:j 3887:i 3883:P 3841:T 3819:B 3815:k 3792:A 3788:E 3765:0 3737:) 3730:T 3725:B 3721:k 3714:A 3710:E 3700:( 3688:0 3680:= 3637:C 3633:E 3589:. 3575:C 3571:E 3521:2 3517:/ 3513:3 3509:T 3471:2 3467:/ 3463:3 3456:T 3447:h 3444:p 3413:v 3384:4 3372:v 3341:T 3318:T 3306:v 3277:v 3226:v 3211:1 3196:T 3192:T 3115:τ 3101:. 3095:+ 3087:s 3084:t 3081:c 3078:e 3075:f 3072:e 3069:d 3060:1 3055:+ 3047:e 3044:c 3041:i 3038:t 3035:t 3032:a 3029:l 3020:1 3015:+ 3007:s 3004:e 3001:i 2998:t 2995:i 2992:r 2989:u 2986:p 2983:m 2980:i 2971:1 2966:= 2958:1 2936:. 2930:+ 2922:s 2919:t 2916:c 2913:e 2910:f 2907:e 2904:d 2895:1 2890:+ 2882:e 2879:c 2876:i 2873:t 2870:t 2867:a 2864:l 2855:1 2850:+ 2842:s 2839:e 2836:i 2833:t 2830:i 2827:r 2824:u 2821:p 2818:m 2815:i 2806:1 2801:= 2793:1 2768:e 2765:c 2762:i 2759:t 2756:t 2753:a 2750:l 2721:s 2718:e 2715:i 2712:t 2709:i 2706:r 2703:u 2700:p 2697:m 2694:i 2678:μ 2664:. 2656:e 2653:c 2650:i 2647:t 2644:t 2641:a 2638:l 2629:1 2624:+ 2616:s 2613:e 2610:i 2607:t 2604:i 2601:r 2598:u 2595:p 2592:m 2589:i 2580:1 2575:= 2567:1 2540:m 2532:τ 2523:m 2515:q 2483:m 2479:q 2474:= 2367:q 2359:k 2304:v 2297:v 2290:E 2283:ω 2251:2 2245:2 2236:v 2226:m 2191:v 2184:v 2170:μ 2166:μ 2162:E 2157:d 2153:v 2106:2 2004:( 1958:F 1955:E 1936:e 1930:F 1926:E 1920:e 1909:= 1904:e 1900:D 1884:e 1875:T 1866:B 1863:k 1844:e 1840:T 1834:B 1829:k 1823:e 1812:= 1807:e 1803:D 1774:n 1755:e 1752:D 1746:F 1729:n 1721:e 1717:D 1710:= 1707:F 1676:) 1671:h 1663:p 1660:+ 1655:e 1647:n 1644:( 1641:e 1638:= 1613:h 1605:p 1602:e 1599:+ 1594:e 1586:n 1583:e 1580:= 1537:E 1531:= 1528:J 1504:E 1501:) 1496:h 1488:p 1485:e 1482:+ 1477:e 1469:n 1466:e 1463:( 1460:= 1455:h 1451:J 1447:+ 1442:e 1438:J 1434:= 1431:J 1404:E 1401:) 1396:h 1388:p 1385:e 1382:+ 1377:e 1369:n 1366:e 1363:( 1360:= 1355:h 1351:J 1347:+ 1342:e 1338:J 1334:= 1331:J 1306:h 1281:E 1276:h 1268:p 1265:e 1262:= 1257:h 1253:J 1232:E 1227:e 1219:n 1216:e 1213:= 1208:e 1204:J 1181:d 1177:v 1154:d 1150:v 1146:n 1143:e 1137:= 1132:A 1127:n 1123:I 1117:= 1112:e 1108:J 1085:d 1081:v 1077:e 1036:h 1032:m 1025:c 1017:e 1011:= 1006:h 981:, 978:E 973:h 965:= 960:d 956:v 924:e 920:m 913:c 905:e 899:= 894:e 869:, 866:E 861:e 850:= 845:d 841:v 812:c 787:, 784:E 772:e 768:m 761:c 753:e 744:= 739:c 731:a 728:= 723:d 719:v 687:e 683:m 678:E 675:e 666:= 663:a 624:e 620:m 607:F 601:a 577:e 573:m 568:/ 564:F 561:= 558:a 532:s 530:⋅ 528:V 524:m 520:m 518:/ 516:V 491:. 488:E 483:h 475:= 470:d 466:v 451:e 448:μ 433:d 431:v 417:E 400:. 397:E 392:e 384:= 379:d 375:v 284:) 278:( 273:) 269:( 265:. 251:. 193:s 191:⋅ 189:V 185:m 177:s 175:⋅ 173:V 153:. 150:E 144:= 139:d 135:v 124:μ 108:d 104:v 89:E 34:. 20:)

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