Electron mobility - Knowledge

3652: 8241:"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." 222: 2382:

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.

3545: 2434:

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.

3114:

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.

2425:

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.

5513: 6225:

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

3282:

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

3113:

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

2451:

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,

2424:

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

2406:

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

2337:

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

2433:

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

2381:

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

2415:

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

495:

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.

195:

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

2442:

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

3100: 2935: 2377:

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

3644:, 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 3535:

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.

190:

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

2345:

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

1974:(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. 6190:

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.

2358:. 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. 5330: 8388:

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).

3602:, 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. 2398:. 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. 199:

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

6690: 6803: 7032: 6919: 2663: 6168: 6544: 526:

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.

2268: 1054:

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

7412:

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).

2940: 4117: 3170:

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

2373:. 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 2775: 2316:

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.

6029: 3737: 2539:

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

3385: 1879:

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:

3531:

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.

5873: 4622: 4546: 3232: 1845: 5749: 2416:

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.

5048: 2366:

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

6399:

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.

786: 4381: 4275: 4373: 1937: 5240: 5323: 3319: 3854:

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

2500: 6285: 5585: 2189:

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.

1044: 932: 307:

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

1503: 1403: 4811: 4742: 5335: 6581: 6694: 1155: 6923: 6810: 3283:

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

2549: 7265:

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".

3522: 6034: 1675: 7729:

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)

6459: 1614: 3416: 3280: 5157: 2772:

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

7809:

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).

3582:

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

695: 6450: 3472: 2206: 5108: 3387:. This formula is the scattering cross section for "Rutherford scattering", where a point charge (carrier) moves past another point charge (defect) experiencing Coulomb interaction. 2723: 1728: 5508:{\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}}} 2203:

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:

2185:

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

4001: 2770: 5939: 4862: 1280: 1231: 868: 6385: 2305:, where a sufficiently high electric field can cause intervalley electron transfer, which reduces drift velocity. This is unusual; increasing the electric field almost always 980: 490: 399: 6187: 5951: 3994: 583: 4930: 3820: 3793: 3661: 152: 1536: 813: 630: 6359: 6332: 4304: 3766: 1773: 1307: 4166: 3252: 1556: 1086: 3961: 3891: 7096:

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".

6305: 5771: 4331: 4146: 3638: 3576: 1182: 109: 4553: 4477: 8055: 4351: 3931: 3911: 3840: 1786: 319:, 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 7566:

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

5684: 4955: 702: 2168:

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

1233:

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

8569: 3335: 3095:{\displaystyle {\frac {1}{\tau }}={\frac {1}{\tau _{\rm {impurities}}}}+{\frac {1}{\tau _{\rm {lattice}}}}+{\frac {1}{\tau _{\rm {defects}}}}+\cdots .} 4173: 1684:

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

1883: 1046:

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.

5161: 2930:{\displaystyle {\frac {1}{\mu }}={\frac {1}{\mu _{\rm {impurities}}}}+{\frac {1}{\mu _{\rm {lattice}}}}+{\frac {1}{\mu _{\rm {defects}}}}+\cdots .} 5247: 8620: 7177:

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

2338:

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

2455: 5520: 3193: 2001:) developed thus far have carrier mobilities below 50 cm/(V⋅s), and typically below 1, with well performing materials measured below 10. 7895: 2407:

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

1415: 1315: 7230:

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

5647:(FET). The result of the measurement is called the "field-effect mobility" (meaning "mobility inferred from a field-effect measurement"). 4748: 4639: 1091: 3390:

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

7470:"Air-Stable n-Channel Organic Single Crystal Field-Effect Transistors Based on Microribbons of Core-Chlorinated Naphthalene Diimide" 5768:

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

1619: 1561: 3286: 187: 7789:

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

647: 8456:"Revealing the Dynamics of Charge Carriers in Polymer:Fullerene Blends Using Photoinduced Time-Resolved Microwave Conductivity" 6229: 2325:

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

2277:

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

8578: 985: 873: 8227: 8136: 8065: 8036: 7923: 7864: 7830: 7734: 7660: 7623: 7362: 7318:

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

7131:

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

5062: 1691: 4392:. The result of the measurement is called the "Hall mobility" (meaning "mobility inferred from a Hall-effect measurement"). 6220: 2515: 2326: 633: 821:

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

326:

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

4817: 1977:

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

6200: 4168:

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

1780: 1236: 1187: 824: 243: 4395:

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

939: 449: 358: 19:

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

7794: 7710: 7702: 3842:

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

3477: 3187: . Experimentally, values of the temperature dependence of the mobility in Si, Ge and GaAs are listed in table. 2725:

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

269: 8278: 251: 2310: 542: 7878: 5886:(channel length modulation), among other things. In practice, this technique may underestimate the true mobility. 3393: 3324:

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

3257: 304:. Therefore, on average there will be no overall motion of charge carriers in any particular direction over time. 118: 8263:

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

7611: 5115: 1512: 8337:

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

6410: 3640:, above which electrons undergo a transition from localized to delocalized states. In this description, termed 247: 5674:

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

3421: 8502:

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

8391:"High charge mobility in two-dimensional percolative networks of PbSe quantum dots connected by atomic bonds" 5650:

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

2672: 8566: 8600: 6685:{\displaystyle \mu _{n}(N_{D})=65+{\frac {1265}{1+\left({\frac {N_{D}}{8.5\times 10^{16}}}\right)^{0.72}}}} 2443:

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

80:

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

7519:"Ultra-high mobility transparent organic thin film transistors grown by an off-centre spin-coating method" 6798:{\displaystyle \mu _{p}(N_{A})=48+{\frac {447}{1+\left({\frac {N_{A}}{6.3\times 10^{16}}}\right)^{0.76}}}} 2728: 7027:{\displaystyle \mu _{p}(N_{D})=130+{\frac {370}{1+\left({\frac {N_{D}}{8\times 10^{17}}}\right)^{1.25}}}} 6914:{\displaystyle \mu _{n}(N_{A})=232+{\frac {1180}{1+\left({\frac {N_{A}}{8\times 10^{16}}}\right)^{0.9}}}} 5901: 3651: 2658:{\displaystyle {\frac {1}{\mu }}={\frac {1}{\mu _{\rm {impurities}}}}+{\frac {1}{\mu _{\rm {lattice}}}}.} 2369: 8060:. Oxford Classic Texts in the Physical Sciences. Oxford, New York: Oxford University Press. 2012-03-24. 8610: 8250:

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

8157: 6163:{\displaystyle I_{D}=\mu C_{i}{\frac {W}{L}}\left((V_{GS}-V_{th})V_{DS}-{\frac {V_{DS}^{2}}{2}}\right)} 6539:{\displaystyle \mu =\mu _{o}+{\frac {\mu _{1}}{1+\left({\frac {N}{N_{\text{ref}}}}\right)^{\alpha }}}} 6364: 8158:"Influence of the gate dielectric on the mobility of rubrene single-crystal field-effect transistors" 3328:

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

333:

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

4626:

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

3863:. In the original theory of variable range hopping, as developed by Mott and Davis, the probability 8605: 8529:

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

4333:

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

3966: 3183: , while the mobility due to optical phonon scattering only is expected to be proportional to 232: 4887: 3798: 3771: 8615: 7892: 5644: 2339: 2263:{\displaystyle {\frac {m^{*}v_{\text{emit}}^{2}}{2}}\approx \hbar \omega _{\text{phonon (opt.)}}} 312: 236: 3110:

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

8492:

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

7820: 6453: 3645: 3332:. The scattering from charged defects (ionized donors or acceptors) leads to the cross section 2186: 791: 603: 536: 7613: 7612:

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

6337: 6310: 4380: 4282: 3744: 1755: 1285: 699:

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

8217: 8126: 7650: 5894:

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

4151: 4112:{\displaystyle P_{ij}=P_{0}\exp \left(-2\alpha r_{ij}-{\frac {\Delta E_{ij}}{k_{B}T}}\right)} 3237: 2284:

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

1990: 1747: 1541: 1058: 323:. This net electron motion is usually much slower than the normally occurring random motion. 6211:

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

3936: 3866: 8538: 8402: 8346: 8293: 8179: 8094: 7991: 7952: 7758: 7530: 7481: 7426: 7374: 7327: 7284: 7196: 7140: 7105: 7045: 6290: 4309: 4124: 3616: 3599: 3554: 2541: 1867: 1412:

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

1160: 87: 4372: 8: 7749:

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

3610: 2334: 2135: 350: 330: 308: 201: 70: 27: 20: 8542: 8406: 8350: 8297: 8183: 8098: 7995: 7956: 7762: 7534: 7485: 7430: 7378: 7331: 7288: 7200: 7144: 7109: 3594:

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

2394:, the vibrating atoms create pressure (acoustic) waves in the crystal, which are termed 8431: 8390: 8370: 8195: 8169: 7591: 7450: 7343: 7274: 7247: 7212: 7186: 7156: 6024:{\displaystyle \mu =m_{\text{lin}}{\frac {L}{W}}{\frac {1}{V_{DS}}}{\frac {1}{C_{i}}}.} 4336: 3916: 3896: 3856: 3825: 3591: 1858: 8454:

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

8279:"Carrier dynamics in semiconductors studied with time-resolved terahertz spectroscopy" 8082: 7414: 7296: 6387:

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

8550: 8475: 8436: 8418: 8362: 8319: 8223: 8199: 8132: 8061: 8032: 8007: 7919: 7860: 7826: 7790: 7730: 7706: 7698: 7656: 7619: 7583: 7548: 7499: 7454: 7442: 7390: 7300: 7251: 7216: 6407:, for noncompensated material (no counter doping) for heavily doped substrates (i.e. 6404: 6208: 6204: 6031:

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

3732:{\displaystyle \mu =\mu _{0}\exp \left(-{\frac {E_{\text{A}}}{k_{\text{B}}T}}\right)} 3655:

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

3548: 3172: 2507: 157: 8374: 7940: 7595: 7347: 7160: 8625: 8546: 8511: 8467: 8426: 8410: 8354: 8309: 8301: 8187: 8102: 7999: 7960: 7766: 7575: 7538: 7489: 7434: 7382: 7335: 7292: 7239: 7204: 7148: 7117: 7113: 6572: 4878: 3598:. Localized states are described as being confined to finite region of real space, 3254:

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

1982: 1970:

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

500: 426: 409: 7398: 8573: 8026: 7913: 7899: 7854: 4430:. As a result there is a voltage across the sample, which can be measured with a 4420: 3587: 3380:{\displaystyle {\Sigma }_{\text{def}}\propto {\left\langle v\right\rangle }^{-4}} 2301:

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

1779:

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

301: 8277:

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

8106: 7770: 6396: 4431: 4400: 2374: 2200: 2194: 816: 523:). However, mobility is much more commonly expressed in cm/(V⋅s) = 10 m/(V⋅s). 413: 338: 334: 320: 288: 81: 47: 8358: 8305: 8003: 7363:"High-mobility carbon-nanotube thin-film transistors on a polymeric substrate" 7208: 5868:{\displaystyle I_{D}={\frac {\mu C_{i}}{2}}{\frac {W}{L}}(V_{GS}-V_{th})^{2}.} 8594: 8479: 8422: 8366: 8323: 8011: 7964: 7697:

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

7394: 7304: 4617:{\displaystyle \mathbf {F} _{Hp}=+q(\mathbf {v} _{p}\times \mathbf {B} _{z})} 4541:{\displaystyle \mathbf {F} _{Hn}=-q(\mathbf {v} _{n}\times \mathbf {B} _{z})} 4464: 3843: 2391: 1685: 298: 51: 43: 7979: 7438: 6170:

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

8515: 8440: 8154:

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

7587: 7579: 7552: 7503: 7494: 7469: 7446: 7243: 6390: 5883: 1506: 512: 173: 66: 5327:

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

3227:{\textstyle {\frac {1}{\tau }}\propto \left\langle v\right\rangle \Sigma } 1840:{\displaystyle D_{\text{e}}={\frac {\mu _{\text{e}}k_{\mathrm {B} }T}{e}}} 1312:

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

8174: 8156:

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

7264: 5637: 4442: 4389: 4367: 4148:

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

3583: 2302: 205: 5744:{\displaystyle \mu =m_{\text{sat}}^{2}{\frac {2L}{W}}{\frac {1}{C_{i}}}} 8414: 8314: 7543: 7518: 4407:-direction. The resulting Lorentz force will accelerate the electrons ( 2937:

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

2330: 192: 8471: 8191: 7386: 7339: 7152: 3179:

interaction. The resulting mobility is expected to be proportional to

8028:

Introduction to Thin Film Transistors: Physics and Technology of TFTs

4627: 2291:, because the electron starts at zero velocity and accelerates up to 2199:. At high fields, carriers are accelerated enough to gain sufficient 1958:

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

8584: 8455: 5622:

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

5043:{\displaystyle \xi _{y}=-{\frac {IB}{nqtW}}=+{\frac {R_{Hn}IB}{tW}}} 2129: 221: 8264: 8251: 7279: 6178:

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

5654:

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

1998: 1986: 781:{\displaystyle v_{d}=a\tau _{c}=-{\frac {e\tau _{c}}{m_{e}^{*}}}E,} 429:

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

341:). In these cases, drift velocity and mobility are not meaningful. 294: 35: 7361:

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

7191: 5608:(magnetic field) can be measured directly, and the conductivities 3613:

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

2452:

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

2192:

This velocity saturation phenomenon results from a process called

1088:, so that the total current density due to electrons is given by: 7036:

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

1994: 1971: 316: 73:

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

8453: 7822:

Fundamentals of Semiconductors: Physics and Materials Properties

4270:{\displaystyle \mu =\mu _{0}\exp \left(-\left^{-1/(d+1)}\right)} 3544: 2531:* is the effective mass in the direction of the electric field. 2446: 2298:

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

6452:

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

5651: 5631: 3176: 3175:

semiconductors, such as silicon and germanium, is dominated by

2395: 2309:

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

1967: 1963: 520: 181: 165: 7615:

Quantum heterostructures: microelectronics and optoelectronics

6214: 3846:

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

1932:{\displaystyle D_{\text{e}}={\frac {\mu _{\text{e}}E_{F}}{e}}} 492:

Both electron and hole mobilities are positive by definition.

8219:

Ambipolar and Light-Emitting Organic Field-Effect Transistors

8128:

Ambipolar and Light-Emitting Organic Field-Effect Transistors

5235:{\displaystyle R_{Hn}=-{\frac {1}{nq}}={\frac {V_{Hn}t}{IB}}} 1985:(100,000 cm/(V⋅s) at room temperature) and freestanding 1558:

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

508: 430: 311:). However, in a solid, the electron repeatedly scatters off 39: 5318:{\displaystyle R_{Hp}={\frac {1}{pq}}={\frac {V_{Hp}t}{IB}}} 3314:{\displaystyle \left\langle v\right\rangle \sim {\sqrt {T}}} 2527:

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

8155: 7852: 6186:

Electron mobility may be determined from non-contact laser

2320: 1978: 1959: 516: 504: 177: 161: 8579:

Resistivity and Mobility Calculator from the BYU Cleanroom

7095: 2495:{\displaystyle \mu ={\frac {q}{m^{*}}}{\overline {\tau }}} 7818: 7468:

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

7069: 6280:{\displaystyle \phi \Sigma \mu =\phi (\mu _{e}+\mu _{h})} 5882:

is the threshold voltage. This approximation ignores the

5580:{\displaystyle \mu _{p}={\frac {\sigma _{p}V_{Hp}t}{IB}}} 1783:. For a classical system (e.g. Boltzmann gas), it reads: 156:

Electron mobility is almost always specified in units of

8387: 6391:

Doping concentration dependence in heavily-doped silicon

5059:

is the Hall coefficient for electron, and is defined as

4356: 1039:{\displaystyle \mu _{h}={\frac {e\tau _{c}}{m_{h}^{*}}}} 927:{\displaystyle \mu _{e}={\frac {e\tau _{c}}{m_{e}^{*}}}} 598:

is the electric force exerted by the electric field, and

8276: 7360: 6199:

Electron mobility can be calculated from time-resolved

169: 8215: 8150:. This reference mistakenly leaves out a factor of 1/V 8124: 7317: 7176: 7130: 3196: 2354:, while emitting or absorbing a phonon of wave vector 1498:{\displaystyle J=J_{e}+J_{h}=(en\mu _{e}+ep\mu _{h})E} 1398:{\displaystyle J=J_{e}+J_{h}=(en\mu _{e}+ep\mu _{h})E} 282: 62:

refers in general to both electron and hole mobility.

7070:"NSM Archive - Physical Properties of Semiconductors" 6926: 6813: 6697: 6584: 6462: 6413: 6367: 6340: 6313: 6293: 6232: 6037: 5954: 5904: 5774: 5687: 5523: 5333: 5250: 5164: 5118: 5065: 4958: 4890: 4820: 4751: 4642: 4556: 4480: 4388:

Carrier mobility is most commonly measured using the

4339: 4312: 4285: 4176: 4154: 4127: 4004: 3969: 3939: 3919: 3899: 3869: 3828: 3801: 3774: 3747: 3664: 3619: 3557: 3480: 3424: 3396: 3338: 3289: 3260: 3240: 3117: 2943: 2778: 2731: 2675: 2552: 2458: 2209: 1886: 1789: 1758: 1694: 1622: 1564: 1544: 1515: 1418: 1318: 1288: 1239: 1190: 1163: 1094: 1061: 988: 942: 876: 827: 794: 705: 650: 606: 545: 511:. Therefore the SI unit of mobility is (m/s)/(V/m) = 452: 446:

The hole mobility is defined by a similar equation:

361: 121: 90: 8339:

Journal of Infrared, Millimeter, and Terahertz Waves

8330: 8083:"Phonon-Assisted Jump Rate in Noncrystalline Solids" 4806:{\displaystyle \Rightarrow -q\xi _{y}+qv_{x}B_{z}=0} 4737:{\displaystyle \mathbf {F} _{y}=(-q)\xi _{y}+(-q)=0} 3527:

The effect of ionized impurity scattering, however,

6307:is the carrier generation yield (between 0 and 1), 8567:semiconductor glossary entry for electron mobility 8270: 8031:. Springer International Publishing. p. 143. 7411: 7026: 6913: 6797: 6684: 6538: 6444: 6379: 6353: 6326: 6299: 6279: 6207:pulses excite the semiconductor and the resulting 6162: 6023: 5933: 5867: 5743: 5579: 5507: 5317: 5234: 5151: 5102: 5042: 4924: 4856: 4805: 4736: 4616: 4540: 4345: 4325: 4298: 4269: 4160: 4140: 4111: 3988: 3955: 3925: 3905: 3885: 3834: 3814: 3787: 3760: 3731: 3632: 3570: 3516: 3466: 3410: 3379: 3313: 3274: 3246: 3226: 3094: 2929: 2764: 2717: 2657: 2494: 2262: 1931: 1839: 1767: 1722: 1669: 1608: 1550: 1530: 1497: 1397: 1301: 1274: 1225: 1176: 1149: 1080: 1038: 974: 926: 862: 807: 780: 689: 624: 577: 484: 393: 355:The electron mobility is defined by the equation: 146: 103: 8057:Electronic Processes in Non-Crystalline Materials 7941:"Absence of Diffusion in Certain Random Lattices" 7415:"High ambipolar mobility in cubic boron arsenide" 2130:Electric field dependence and velocity saturation 1981:) (35,000,000 cm/(V⋅s) at low temperature), 1679: 1150:{\displaystyle J_{e}={\frac {I_{n}}{A}}=-env_{d}} 8592: 8336: 7856:Handbook of photovoltaic science and engineering 7467: 5662:In this technique, for each fixed gate voltage V 3605: 293:Without any applied electric field, in a solid, 184:). They are related by 1 m/(V⋅s) = 10 cm/(V⋅s). 8381: 7354: 3517:{\displaystyle {\mu }_{\text{def}}\sim T^{3/2}} 2437: 2410: 7618:. Cambridge University Press. pp. 307–9. 7311: 2385: 2361: 1670:{\displaystyle \sigma =e(n\mu _{e}+p\mu _{h})} 1049: 8501: 7859:. John Wiley and Sons. p. 79, eq. 3.58. 7853:Antonio Luque; Steven Hegedus (9 June 2003). 3859:for one site to another, in a process called 3418:, to be for scattering from acoustic phonons 2447:Relation between mobility and scattering time 1609:{\displaystyle \sigma =en\mu _{e}+ep\mu _{h}} 337:), or for a very short time (as short as the 5759:are the length and width of the channel and 4870:direction, and for holes, it points in the + 3539: 3411:{\displaystyle \left\langle v\right\rangle } 3275:{\displaystyle \left\langle v\right\rangle } 1989:(200,000 cm/(V⋅s) at low temperature). 7819:Peter Y. Yu; Manuel Cardona (30 May 2010). 6403:While there is considerable scatter in the 6215:Time resolved microwave conductivity (TRMC) 5152:{\displaystyle \xi _{y}={\frac {V_{H}}{W}}} 4384:Hall effect measurement setup for electrons 3123:Typical temperature dependence of mobility 2401: 1407: 250:. Unsourced material may be challenged and 8024: 7652:Electronic Devices And Integrated Circuits 5889: 5643:The mobility can also be measured using a 2005:List of highest measured mobilities 1775:is the concentration gradient of electrons 690:{\displaystyle a=-{\frac {eE}{m_{e}^{*}}}} 8528: 8430: 8313: 8173: 7805: 7803: 7785: 7783: 7781: 7744: 7742: 7542: 7493: 7278: 7190: 6445:{\displaystyle 10^{18}\mathrm {cm} ^{-3}} 3849: 3106:is the true average scattering time and τ 270:Learn how and when to remove this message 8211: 8209: 7938: 7911: 7644: 7642: 7607: 7605: 7565: 7229: 5657: 5625: 4866:For electrons, the field points in the − 4379: 4371: 3650: 3543: 3467:{\displaystyle {\mu }_{ph}\sim T^{-3/2}} 2321:Relation between scattering and mobility 208:, or inferred from transistor behavior. 8120: 8118: 8116: 7912:Hook, J. R.; Hall, H. E. (1991-09-05). 7902:. Online textbook by B. Van Zeghbroeck] 7655:. PHI Learning Pvt. Ltd. pp. 77–. 5103:{\displaystyle R_{Hn}=-{\frac {1}{nq}}} 4376:Hall effect measurement setup for holes 3933:, depends on their separation in space 3893:, of an electron hopping from one site 3551:of a solid possessing a mobility edge, 2718:{\displaystyle \mu _{\rm {impurities}}} 2428: 1723:{\displaystyle F=-D_{\text{e}}\nabla n} 592:is the acceleration between collisions. 503:, and the SI unit of electric field is 344: 8621:Electric and magnetic fields in matter 8593: 8216:Constance Rost-Bietsch (August 2005). 8125:Constance Rost-Bietsch (August 2005). 7888: 7886: 7800: 7778: 7748: 7739: 7725: 7723: 7721: 7719: 7693: 7691: 7689: 7687: 7685: 7683: 7681: 7679: 6226:incident laser fluence, the parameter 2149:is proportional to the electric field 1282:where p is the hole concentration and 8206: 8050: 8048: 7893:Chapter 2: Semiconductor Fundamentals 7648: 7639: 7602: 6194: 4357:Measurement of semiconductor mobility 4353:is the dimensionality of the system. 2534: 1875:is the electric charge of an electron 50:. There is an analogous quantity for 8113: 8080: 7980:"Electrons in disordered structures" 7977: 7516: 7172: 7170: 7091: 7089: 7064: 7062: 7060: 6550:is the doping concentration (either 6221:Time resolved microwave conductivity 2765:{\displaystyle \mu _{\rm {lattice}}} 640:Since the force on the electron is − 248:adding citations to reliable sources 215: 204:occurs. It can be determined by the 8460:The Journal of Physical Chemistry C 7883: 7716: 7676: 6181: 5934:{\displaystyle I_{D}\propto V_{GS}} 5681:is measured. Then the mobility is: 4857:{\displaystyle \xi _{y}=v_{x}B_{z}} 2419: 2333:time, i.e. how long the carrier is 433:) caused by the electric field, and 283:Drift velocity in an electric field 13: 8222:. Cuvillier Verlag. pp. 19–. 8131:. Cuvillier Verlag. pp. 17–. 8045: 6429: 6426: 6371: 6236: 4070: 3970: 3341: 3241: 3221: 3118:Temperature dependence of mobility 3075: 3072: 3069: 3066: 3063: 3060: 3057: 3035: 3032: 3029: 3026: 3023: 3020: 3017: 2995: 2992: 2989: 2986: 2983: 2980: 2977: 2974: 2971: 2968: 2910: 2907: 2904: 2901: 2898: 2895: 2892: 2870: 2867: 2864: 2861: 2858: 2855: 2852: 2830: 2827: 2824: 2821: 2818: 2815: 2812: 2809: 2806: 2803: 2756: 2753: 2750: 2747: 2744: 2741: 2738: 2709: 2706: 2703: 2700: 2697: 2694: 2691: 2688: 2685: 2682: 2644: 2641: 2638: 2635: 2632: 2629: 2626: 2604: 2601: 2598: 2595: 2592: 2589: 2586: 2583: 2580: 2577: 2140:At low fields, the drift velocity 1822: 1759: 1714: 14: 8637: 8560: 7751:Superlattices and Microstructures 7297:10.1103/PhysRevMaterials.6.034005 7167: 7086: 7057: 6571:and α are fitting parameters. At 3963:, and their separation in energy 2247: 1275:{\displaystyle J_{h}=ep\mu _{h}E} 1226:{\displaystyle J_{e}=en\mu _{e}E} 863:{\displaystyle v_{d}=-\mu _{e}E,} 6380:{\displaystyle \phi \Sigma \mu } 5670:is increased until the current I 4715: 4700: 4645: 4601: 4586: 4559: 4525: 4510: 4483: 4456:-type material and positive for 4361: 2524:is the average scattering time. 2311:negative differential resistance 975:{\displaystyle v_{d}=\mu _{h}E,} 485:{\displaystyle v_{d}=\mu _{h}E.} 394:{\displaystyle v_{d}=\mu _{e}E.} 220: 8587:from an atomistic point of view 8522: 8495: 8486: 8447: 8257: 8244: 8074: 8018: 7971: 7932: 7905: 7846: 7812: 7559: 7510: 7461: 3822:is the Boltzmann constant, and 211: 65:Electron and hole mobility are 16:Quantity in solid-state physics 7939:Anderson, P. W. (1958-03-01). 7405: 7258: 7223: 7124: 7118:10.1016/j.jcrysgro.2008.09.151 6950: 6937: 6837: 6824: 6721: 6708: 6608: 6595: 6575:, the above equation becomes: 6274: 6248: 6111: 6079: 5853: 5820: 4752: 4725: 4695: 4692: 4683: 4667: 4658: 4611: 4581: 4535: 4505: 4419:) direction, according to the 4257: 4245: 1680:Relation to electron diffusion 1664: 1632: 1489: 1451: 1389: 1351: 936:Similarly, for holes we have 168:). This is different from the 1: 7232:Advanced Electronic Materials 7051: 6334:is the electron mobility and 4423:and set up an electric field 3989:{\displaystyle \Delta E_{ij}} 3642:multiple trapping and release 3606:Multiple trapping and release 2052:Cubic boron arsenide (c-BAs) 2021:AlGaAs/GaAs heterostructures 578:{\displaystyle a=F/m_{e}^{*}} 530: 111:. Then the electron mobility 34:characterises how quickly an 8551:10.1016/0038-1101(85)90209-6 5666:, the drain-source voltage V 4925:{\displaystyle I=-qnv_{x}tW} 3815:{\displaystyle k_{\text{B}}} 3788:{\displaystyle E_{\text{A}}} 2487: 2438:Electron–electron scattering 2411:Surface roughness scattering 2178:. For example, the value of 147:{\displaystyle v_{d}=\mu E.} 46:when pushed or pulled by an 7: 7879:weblink (subscription only) 7825:. Springer. pp. 205–. 7039: 6188:photo-reflectance technique 4411:-type materials) or holes ( 2386:Lattice (phonon) scattering 2370:ionized impurity scattering 2362:Ionized impurity scattering 2157:is constant. This value of 1953: 1616:which can be factorised to 1509:can be written in the form 1050:Relation to current density 499:The SI unit of velocity is 10: 8642: 8107:10.1103/PhysRevLett.32.303 8081:Emin, David (1974-02-11). 8025:Brotherton, S. D. (2013). 7978:Mott, N. F. (1967-01-01). 7771:10.1016/j.spmi.2008.02.008 7179:Solid State Communications 6218: 5635: 5629: 4634:direction. For electrons, 4415:-type materials) in the (− 4365: 2133: 1531:{\displaystyle J=\sigma E} 348: 286: 18: 8359:10.1007/s10762-012-9905-y 8306:10.1103/RevModPhys.83.543 8286:Reviews of Modern Physics 8004:10.1080/00018736700101265 7267:Physical Review Materials 7209:10.1016/j.ssc.2008.02.024 7098:Journal of Crystal Growth 6174:is not small enough and V 4434:voltmeter. This voltage, 4306:is a mobility prefactor, 3768:is a mobility prefactor, 3540:Disordered Semiconductors 3474:and from charged defects 2390:At any temperature above 2335:ballistically accelerated 1157:Using the expression for 808:{\displaystyle \tau _{c}} 625:{\displaystyle m_{e}^{*}} 442:is the electron mobility. 7965:10.1103/PhysRev.109.1492 6354:{\displaystyle \mu _{h}} 6327:{\displaystyle \mu _{e}} 6287:can be evaluated, where 5948:. Then the mobility is: 5636:Not to be confused with 4941:into the expression for 4299:{\displaystyle \mu _{0}} 3761:{\displaystyle \mu _{0}} 2669:is the actual mobility, 2402:Piezoelectric scattering 2083:Metals (Al, Au, Cu, Ag) 2073:Polycrystalline silicon 1768:{\displaystyle \nabla n} 1408:Relation to conductivity 1302:{\displaystyle \mu _{h}} 8531:Solid-State Electronics 8504:Proceedings of the IEEE 8162:Applied Physics Letters 8087:Physical Review Letters 7439:10.1126/science.abn4290 7367:Applied Physics Letters 5890:Using the linear region 5645:field-effect transistor 4630:on the carriers in the 4161:{\displaystyle \alpha } 3247:{\displaystyle \Sigma } 1551:{\displaystyle \sigma } 1081:{\displaystyle -ev_{d}} 76:When an electric field 8516:10.1109/PROC.1967.6123 7580:10.1002/adma.201504360 7495:10.1002/adma.201303392 7401:on September 24, 2017. 7244:10.1002/aelm.201500452 7028: 6915: 6799: 6686: 6540: 6454:empirical relationship 6446: 6381: 6361:is the hole mobility. 6355: 6328: 6301: 6281: 6164: 6025: 5935: 5869: 5745: 5581: 5509: 5319: 5236: 5153: 5104: 5044: 4926: 4858: 4807: 4738: 4618: 4542: 4385: 4377: 4347: 4327: 4300: 4271: 4162: 4142: 4113: 3990: 3957: 3956:{\displaystyle r_{ij}} 3927: 3907: 3887: 3886:{\displaystyle P_{ij}} 3861:variable range hopping 3850:Variable Range Hopping 3836: 3816: 3795:is activation energy, 3789: 3762: 3733: 3656: 3646:Arrhenius relationship 3634: 3579: 3572: 3518: 3468: 3412: 3381: 3315: 3276: 3248: 3228: 3096: 2931: 2766: 2719: 2659: 2496: 2264: 2032:Freestanding graphene 1991:Organic semiconductors 1933: 1841: 1769: 1724: 1671: 1610: 1552: 1532: 1499: 1399: 1303: 1276: 1227: 1178: 1151: 1082: 1040: 976: 928: 864: 809: 782: 691: 626: 579: 486: 416:applied to a material, 395: 148: 105: 8395:Nature Communications 7523:Nature Communications 7517:Yuan, Yongbo (2014). 7029: 6916: 6800: 6687: 6541: 6447: 6382: 6356: 6329: 6302: 6300:{\displaystyle \phi } 6282: 6165: 6026: 5936: 5870: 5746: 5658:Using saturation mode 5626:Field-effect mobility 5582: 5510: 5320: 5244:Similarly, for holes 5237: 5154: 5105: 5045: 4927: 4859: 4808: 4739: 4619: 4543: 4383: 4375: 4348: 4328: 4326:{\displaystyle T_{0}} 4301: 4272: 4163: 4143: 4141:{\displaystyle P_{0}} 4114: 3991: 3958: 3928: 3908: 3888: 3837: 3817: 3790: 3763: 3734: 3654: 3635: 3633:{\displaystyle E_{C}} 3573: 3571:{\displaystyle E_{C}} 3547: 3519: 3469: 3413: 3382: 3316: 3277: 3249: 3229: 3097: 2932: 2767: 2720: 2660: 2497: 2265: 1934: 1842: 1770: 1748:diffusion coefficient 1725: 1672: 1611: 1553: 1533: 1500: 1400: 1304: 1277: 1228: 1179: 1177:{\displaystyle v_{d}} 1152: 1083: 1041: 977: 929: 865: 810: 783: 692: 627: 580: 487: 396: 149: 106: 104:{\displaystyle v_{d}} 7046:Speed of electricity 6924: 6811: 6807:Minority carriers: 6695: 6582: 6578:Majority carriers: 6460: 6411: 6365: 6338: 6311: 6291: 6230: 6035: 5952: 5902: 5772: 5685: 5600:(sample thickness), 5521: 5331: 5248: 5162: 5116: 5063: 4956: 4888: 4818: 4749: 4640: 4554: 4478: 4463:Mathematically, the 4337: 4310: 4283: 4174: 4152: 4125: 4002: 3967: 3937: 3917: 3897: 3867: 3826: 3799: 3772: 3745: 3662: 3617: 3555: 3478: 3422: 3394: 3336: 3287: 3258: 3238: 3194: 2941: 2776: 2729: 2673: 2550: 2542:Augustus Matthiessen 2456: 2429:Inelastic scattering 2207: 2062:Crystalline silicon 1884: 1868:absolute temperature 1787: 1756: 1692: 1620: 1562: 1542: 1513: 1416: 1316: 1286: 1237: 1188: 1161: 1092: 1059: 986: 940: 874: 825: 792: 703: 648: 604: 543: 450: 359: 345:Definition and units 302:move around randomly 244:improve this section 119: 88: 8601:Physical quantities 8543:1985SSEle..28...47D 8466:(46): 24085–24103. 8407:2015NatCo...6.8195E 8351:2012JIMTW..33..871L 8298:2011RvMP...83..543U 8184:2004ApPhL..85.3899S 8099:1974PhRvL..32..303E 7996:1967AdPhy..16...49M 7984:Advances in Physics 7957:1958PhRv..109.1492A 7915:Solid State Physics 7763:2008SuMi...44....1B 7535:2014NatCo...5.3005Y 7486:2013AdM....25.6951H 7431:2022Sci...377..437S 7379:2005ApPhL..86c3105S 7332:2004NanoL...4...35D 7289:2022PhRvM...6c4005C 7201:2008SSCom.146..351B 7145:2004NanoL...4...35D 7110:2009JCrGr.311.1658U 6149: 5708: 4467:acting on a charge 3124: 2237: 2170:saturation velocity 2136:Velocity saturation 2006: 1949:is the Fermi energy 1309:the hole mobility. 1033: 921: 769: 684: 621: 574: 537:Newton's Second Law 351:Electrical mobility 331:ballistic transport 309:ballistic transport 202:velocity saturation 71:electrical mobility 38:can move through a 28:solid-state physics 21:Electrical mobility 8572:2009-01-04 at the 8415:10.1038/ncomms9195 7898:2009-01-21 at the 7568:Advanced Materials 7544:10.1038/ncomms4005 7474:Advanced Materials 7024: 6911: 6795: 6682: 6536: 6442: 6377: 6351: 6324: 6297: 6277: 6195:Terahertz mobility 6160: 6132: 6021: 5931: 5865: 5741: 5694: 5589:Here the value of 5577: 5505: 5503: 5315: 5232: 5149: 5100: 5040: 4922: 4854: 4803: 4734: 4614: 4538: 4403:is applied in the 4386: 4378: 4343: 4323: 4296: 4267: 4158: 4138: 4109: 3986: 3953: 3923: 3913:, to another site 3903: 3883: 3832: 3812: 3785: 3758: 3729: 3657: 3648:in such a system: 3630: 3580: 3568: 3514: 3464: 3408: 3377: 3311: 3272: 3244: 3224: 3122: 3092: 2927: 2762: 2715: 2655: 2535:Matthiessen's rule 2492: 2260: 2223: 2163:low-field mobility 2118:Amorphous silicon 2013:Electron mobility 2004: 1929: 1859:Boltzmann constant 1837: 1765: 1720: 1667: 1606: 1548: 1528: 1495: 1395: 1299: 1272: 1223: 1174: 1147: 1078: 1036: 1019: 972: 924: 907: 860: 805: 778: 755: 687: 670: 622: 607: 575: 560: 482: 391: 172:unit of mobility, 144: 101: 8611:Materials science 8510:(12): 2192–2193. 8472:10.1021/jp406706u 8229:978-3-86537-535-3 8192:10.1063/1.1812368 8168:(17): 3899–3901. 8138:978-3-86537-535-3 8067:978-0-19-964533-6 8038:978-3-319-00001-5 7925:978-0-471-92804-1 7866:978-0-471-49196-5 7832:978-3-642-00709-5 7735:978-3-540-93803-3 7662:978-81-203-3192-1 7625:978-0-521-63635-3 7574:(22): 4266–4282. 7480:(48): 6951–6955. 7425:(6604): 437–440. 7387:10.1063/1.1854721 7340:10.1021/nl034841q 7153:10.1021/nl034841q 7022: 7009: 6909: 6896: 6793: 6780: 6680: 6667: 6534: 6521: 6518: 6405:experimental data 6209:photoconductivity 6205:Femtosecond laser 6153: 6072: 6016: 5999: 5979: 5968: 5818: 5808: 5739: 5722: 5701: 5575: 5499: 5405: 5313: 5280: 5230: 5197: 5147: 5098: 5038: 4999: 4399:-direction and a 4346:{\displaystyle d} 4227: 4102: 3926:{\displaystyle j} 3906:{\displaystyle i} 3835:{\displaystyle T} 3809: 3782: 3722: 3715: 3704: 3549:Density of states 3490: 3348: 3309: 3205: 3168: 3167: 3081: 3041: 3001: 2952: 2916: 2876: 2836: 2787: 2650: 2610: 2561: 2514:* is the carrier 2508:elementary charge 2490: 2480: 2257: 2242: 2230: 2127: 2126: 2042:Carbon nanotubes 1927: 1910: 1894: 1835: 1813: 1797: 1781:Einstein relation 1711: 1123: 1034: 922: 770: 685: 280: 279: 272: 32:electron mobility 8633: 8583:Online lecture- 8555: 8554: 8526: 8520: 8519: 8499: 8493: 8490: 8484: 8483: 8451: 8445: 8444: 8434: 8385: 8379: 8378: 8334: 8328: 8327: 8317: 8283: 8274: 8268: 8265:arXiv:1808.01897 8261: 8255: 8252:arXiv:1711.01138 8248: 8242: 8240: 8238: 8236: 8213: 8204: 8203: 8177: 8175:cond-mat/0407293 8149: 8147: 8145: 8122: 8111: 8110: 8078: 8072: 8071: 8052: 8043: 8042: 8022: 8016: 8015: 7975: 7969: 7968: 7951:(5): 1492–1505. 7936: 7930: 7929: 7909: 7903: 7890: 7881: 7877: 7875: 7873: 7850: 7844: 7843: 7841: 7839: 7816: 7810: 7807: 7798: 7787: 7776: 7774: 7746: 7737: 7727: 7714: 7695: 7674: 7673: 7671: 7669: 7646: 7637: 7636: 7634: 7632: 7609: 7600: 7599: 7563: 7557: 7556: 7546: 7514: 7508: 7507: 7497: 7465: 7459: 7458: 7409: 7403: 7402: 7397:. Archived from 7358: 7352: 7351: 7315: 7309: 7308: 7282: 7262: 7256: 7255: 7227: 7221: 7220: 7194: 7174: 7165: 7164: 7128: 7122: 7121: 7104:(7): 1658–1661. 7093: 7084: 7083: 7081: 7080: 7066: 7033: 7031: 7030: 7025: 7023: 7021: 7020: 7019: 7014: 7010: 7008: 7007: 7006: 6990: 6989: 6980: 6963: 6949: 6948: 6936: 6935: 6920: 6918: 6917: 6912: 6910: 6908: 6907: 6906: 6901: 6897: 6895: 6894: 6893: 6877: 6876: 6867: 6850: 6836: 6835: 6823: 6822: 6804: 6802: 6801: 6796: 6794: 6792: 6791: 6790: 6785: 6781: 6779: 6778: 6777: 6761: 6760: 6751: 6734: 6720: 6719: 6707: 6706: 6691: 6689: 6688: 6683: 6681: 6679: 6678: 6677: 6672: 6668: 6666: 6665: 6664: 6648: 6647: 6638: 6621: 6607: 6606: 6594: 6593: 6573:room temperature 6545: 6543: 6542: 6537: 6535: 6533: 6532: 6531: 6526: 6522: 6520: 6519: 6516: 6507: 6493: 6492: 6483: 6478: 6477: 6451: 6449: 6448: 6443: 6441: 6440: 6432: 6423: 6422: 6386: 6384: 6383: 6378: 6360: 6358: 6357: 6352: 6350: 6349: 6333: 6331: 6330: 6325: 6323: 6322: 6306: 6304: 6303: 6298: 6286: 6284: 6283: 6278: 6273: 6272: 6260: 6259: 6182:Optical mobility 6169: 6167: 6166: 6161: 6159: 6155: 6154: 6148: 6143: 6131: 6126: 6125: 6110: 6109: 6094: 6093: 6073: 6065: 6063: 6062: 6047: 6046: 6030: 6028: 6027: 6022: 6017: 6015: 6014: 6002: 6000: 5998: 5997: 5982: 5980: 5972: 5970: 5969: 5966: 5940: 5938: 5937: 5932: 5930: 5929: 5914: 5913: 5874: 5872: 5871: 5866: 5861: 5860: 5851: 5850: 5835: 5834: 5819: 5811: 5809: 5804: 5803: 5802: 5789: 5784: 5783: 5750: 5748: 5747: 5742: 5740: 5738: 5737: 5725: 5723: 5718: 5710: 5707: 5702: 5699: 5596:(Hall voltage), 5586: 5584: 5583: 5578: 5576: 5574: 5566: 5562: 5561: 5549: 5548: 5538: 5533: 5532: 5514: 5512: 5511: 5506: 5504: 5500: 5498: 5490: 5486: 5485: 5473: 5472: 5462: 5451: 5447: 5446: 5434: 5433: 5415: 5411: 5407: 5406: 5404: 5393: 5383: 5382: 5373: 5369: 5347: 5346: 5324: 5322: 5321: 5316: 5314: 5312: 5304: 5300: 5299: 5286: 5281: 5279: 5268: 5263: 5262: 5241: 5239: 5238: 5233: 5231: 5229: 5221: 5217: 5216: 5203: 5198: 5196: 5185: 5177: 5176: 5158: 5156: 5155: 5150: 5148: 5143: 5142: 5133: 5128: 5127: 5109: 5107: 5106: 5101: 5099: 5097: 5086: 5078: 5077: 5049: 5047: 5046: 5041: 5039: 5037: 5029: 5022: 5021: 5008: 5000: 4998: 4984: 4976: 4968: 4967: 4931: 4929: 4928: 4923: 4915: 4914: 4879:electron current 4863: 4861: 4860: 4855: 4853: 4852: 4843: 4842: 4830: 4829: 4812: 4810: 4809: 4804: 4796: 4795: 4786: 4785: 4770: 4769: 4743: 4741: 4740: 4735: 4724: 4723: 4718: 4709: 4708: 4703: 4679: 4678: 4654: 4653: 4648: 4623: 4621: 4620: 4615: 4610: 4609: 4604: 4595: 4594: 4589: 4571: 4570: 4562: 4547: 4545: 4544: 4539: 4534: 4533: 4528: 4519: 4518: 4513: 4495: 4494: 4486: 4460:-type material. 4452:is negative for 4441:, is called the 4352: 4350: 4349: 4344: 4332: 4330: 4329: 4324: 4322: 4321: 4305: 4303: 4302: 4297: 4295: 4294: 4276: 4274: 4273: 4268: 4266: 4262: 4261: 4260: 4244: 4232: 4228: 4223: 4222: 4213: 4192: 4191: 4167: 4165: 4164: 4159: 4147: 4145: 4144: 4139: 4137: 4136: 4118: 4116: 4115: 4110: 4108: 4104: 4103: 4101: 4097: 4096: 4086: 4085: 4084: 4068: 4063: 4062: 4030: 4029: 4017: 4016: 3995: 3993: 3992: 3987: 3985: 3984: 3962: 3960: 3959: 3954: 3952: 3951: 3932: 3930: 3929: 3924: 3912: 3910: 3909: 3904: 3892: 3890: 3889: 3884: 3882: 3881: 3841: 3839: 3838: 3833: 3821: 3819: 3818: 3813: 3811: 3810: 3807: 3794: 3792: 3791: 3786: 3784: 3783: 3780: 3767: 3765: 3764: 3759: 3757: 3756: 3738: 3736: 3735: 3730: 3728: 3724: 3723: 3721: 3717: 3716: 3713: 3706: 3705: 3702: 3696: 3680: 3679: 3639: 3637: 3636: 3631: 3629: 3628: 3590:semiconductors. 3577: 3575: 3574: 3569: 3567: 3566: 3523: 3521: 3520: 3515: 3513: 3512: 3508: 3492: 3491: 3488: 3486: 3473: 3471: 3470: 3465: 3463: 3462: 3458: 3439: 3438: 3430: 3417: 3415: 3414: 3409: 3407: 3386: 3384: 3383: 3378: 3376: 3375: 3367: 3366: 3350: 3349: 3346: 3344: 3320: 3318: 3317: 3312: 3310: 3305: 3300: 3281: 3279: 3278: 3273: 3271: 3253: 3251: 3250: 3245: 3233: 3231: 3230: 3225: 3220: 3206: 3198: 3125: 3121: 3101: 3099: 3098: 3093: 3082: 3080: 3079: 3078: 3047: 3042: 3040: 3039: 3038: 3007: 3002: 3000: 2999: 2998: 2958: 2953: 2945: 2936: 2934: 2933: 2928: 2917: 2915: 2914: 2913: 2882: 2877: 2875: 2874: 2873: 2842: 2837: 2835: 2834: 2833: 2793: 2788: 2780: 2771: 2769: 2768: 2763: 2761: 2760: 2759: 2724: 2722: 2721: 2716: 2714: 2713: 2712: 2664: 2662: 2661: 2656: 2651: 2649: 2648: 2647: 2616: 2611: 2609: 2608: 2607: 2567: 2562: 2554: 2523: 2501: 2499: 2498: 2493: 2491: 2483: 2481: 2479: 2478: 2466: 2420:Alloy scattering 2269: 2267: 2266: 2261: 2259: 2258: 2255: 2243: 2238: 2236: 2231: 2228: 2222: 2221: 2211: 2093:2D material (MoS 2007: 2003: 1983:carbon nanotubes 1938: 1936: 1935: 1930: 1928: 1923: 1922: 1921: 1912: 1911: 1908: 1901: 1896: 1895: 1892: 1846: 1844: 1843: 1838: 1836: 1831: 1827: 1826: 1825: 1815: 1814: 1811: 1804: 1799: 1798: 1795: 1774: 1772: 1771: 1766: 1729: 1727: 1726: 1721: 1713: 1712: 1709: 1676: 1674: 1673: 1668: 1663: 1662: 1647: 1646: 1615: 1613: 1612: 1607: 1605: 1604: 1586: 1585: 1557: 1555: 1554: 1549: 1537: 1535: 1534: 1529: 1504: 1502: 1501: 1496: 1488: 1487: 1469: 1468: 1447: 1446: 1434: 1433: 1404: 1402: 1401: 1396: 1388: 1387: 1369: 1368: 1347: 1346: 1334: 1333: 1308: 1306: 1305: 1300: 1298: 1297: 1281: 1279: 1278: 1273: 1268: 1267: 1249: 1248: 1232: 1230: 1229: 1224: 1219: 1218: 1200: 1199: 1183: 1181: 1180: 1175: 1173: 1172: 1156: 1154: 1153: 1148: 1146: 1145: 1124: 1119: 1118: 1109: 1104: 1103: 1087: 1085: 1084: 1079: 1077: 1076: 1045: 1043: 1042: 1037: 1035: 1032: 1027: 1018: 1017: 1016: 1003: 998: 997: 981: 979: 978: 973: 965: 964: 952: 951: 933: 931: 930: 925: 923: 920: 915: 906: 905: 904: 891: 886: 885: 869: 867: 866: 861: 853: 852: 837: 836: 814: 812: 811: 806: 804: 803: 787: 785: 784: 779: 771: 768: 763: 754: 753: 752: 739: 731: 730: 715: 714: 696: 694: 693: 688: 686: 683: 678: 669: 661: 631: 629: 628: 623: 620: 615: 584: 582: 581: 576: 573: 568: 559: 491: 489: 488: 483: 475: 474: 462: 461: 400: 398: 397: 392: 384: 383: 371: 370: 275: 268: 264: 261: 255: 224: 216: 153: 151: 150: 145: 131: 130: 110: 108: 107: 102: 100: 99: 60:carrier mobility 8641: 8640: 8636: 8635: 8634: 8632: 8631: 8630: 8606:Charge carriers 8591: 8590: 8574:Wayback Machine 8563: 8558: 8527: 8523: 8500: 8496: 8491: 8487: 8452: 8448: 8386: 8382: 8335: 8331: 8281: 8275: 8271: 8262: 8258: 8249: 8245: 8234: 8232: 8230: 8214: 8207: 8153: 8143: 8141: 8139: 8123: 8114: 8079: 8075: 8068: 8054: 8053: 8046: 8039: 8023: 8019: 7976: 7972: 7945:Physical Review 7937: 7933: 7926: 7910: 7906: 7900:Wayback Machine 7891: 7884: 7871: 7869: 7867: 7851: 7847: 7837: 7835: 7833: 7817: 7813: 7808: 7801: 7788: 7779: 7747: 7740: 7728: 7717: 7696: 7677: 7667: 7665: 7663: 7647: 7640: 7630: 7628: 7626: 7610: 7603: 7564: 7560: 7515: 7511: 7466: 7462: 7410: 7406: 7359: 7355: 7316: 7312: 7263: 7259: 7228: 7224: 7175: 7168: 7129: 7125: 7094: 7087: 7078: 7076: 7068: 7067: 7058: 7054: 7042: 7015: 7002: 6998: 6991: 6985: 6981: 6979: 6975: 6974: 6967: 6962: 6944: 6940: 6931: 6927: 6925: 6922: 6921: 6902: 6889: 6885: 6878: 6872: 6868: 6866: 6862: 6861: 6854: 6849: 6831: 6827: 6818: 6814: 6812: 6809: 6808: 6786: 6773: 6769: 6762: 6756: 6752: 6750: 6746: 6745: 6738: 6733: 6715: 6711: 6702: 6698: 6696: 6693: 6692: 6673: 6660: 6656: 6649: 6643: 6639: 6637: 6633: 6632: 6625: 6620: 6602: 6598: 6589: 6585: 6583: 6580: 6579: 6570: 6562: 6555: 6527: 6515: 6511: 6506: 6502: 6501: 6494: 6488: 6484: 6482: 6473: 6469: 6461: 6458: 6457: 6433: 6425: 6424: 6418: 6414: 6412: 6409: 6408: 6397:charge carriers 6393: 6366: 6363: 6362: 6345: 6341: 6339: 6336: 6335: 6318: 6314: 6312: 6309: 6308: 6292: 6289: 6288: 6268: 6264: 6255: 6251: 6231: 6228: 6227: 6223: 6217: 6201:terahertz probe 6197: 6184: 6177: 6173: 6144: 6136: 6130: 6118: 6114: 6102: 6098: 6086: 6082: 6078: 6074: 6064: 6058: 6054: 6042: 6038: 6036: 6033: 6032: 6010: 6006: 6001: 5990: 5986: 5981: 5971: 5965: 5961: 5953: 5950: 5949: 5947: 5922: 5918: 5909: 5905: 5903: 5900: 5899: 5897: 5892: 5881: 5856: 5852: 5843: 5839: 5827: 5823: 5810: 5798: 5794: 5790: 5788: 5779: 5775: 5773: 5770: 5769: 5767: 5733: 5729: 5724: 5711: 5709: 5703: 5698: 5686: 5683: 5682: 5680: 5673: 5669: 5665: 5660: 5641: 5634: 5628: 5621: 5614: 5594: 5567: 5554: 5550: 5544: 5540: 5539: 5537: 5528: 5524: 5522: 5519: 5518: 5502: 5501: 5491: 5478: 5474: 5468: 5464: 5463: 5461: 5449: 5448: 5439: 5435: 5429: 5425: 5413: 5412: 5397: 5392: 5388: 5384: 5378: 5374: 5359: 5355: 5348: 5342: 5338: 5334: 5332: 5329: 5328: 5305: 5292: 5288: 5287: 5285: 5272: 5267: 5255: 5251: 5249: 5246: 5245: 5222: 5209: 5205: 5204: 5202: 5189: 5184: 5169: 5165: 5163: 5160: 5159: 5138: 5134: 5132: 5123: 5119: 5117: 5114: 5113: 5090: 5085: 5070: 5066: 5064: 5061: 5060: 5057: 5030: 5014: 5010: 5009: 5007: 4985: 4977: 4975: 4963: 4959: 4957: 4954: 4953: 4949: 4940: 4910: 4906: 4889: 4886: 4885: 4848: 4844: 4838: 4834: 4825: 4821: 4819: 4816: 4815: 4791: 4787: 4781: 4777: 4765: 4761: 4750: 4747: 4746: 4719: 4714: 4713: 4704: 4699: 4698: 4674: 4670: 4649: 4644: 4643: 4641: 4638: 4637: 4605: 4600: 4599: 4590: 4585: 4584: 4563: 4558: 4557: 4555: 4552: 4551: 4529: 4524: 4523: 4514: 4509: 4508: 4487: 4482: 4481: 4479: 4476: 4475: 4474:For electrons: 4450: 4439: 4428: 4421:right hand rule 4370: 4364: 4359: 4338: 4335: 4334: 4317: 4313: 4311: 4308: 4307: 4290: 4286: 4284: 4281: 4280: 4240: 4233: 4218: 4214: 4212: 4208: 4207: 4203: 4199: 4187: 4183: 4175: 4172: 4171: 4153: 4150: 4149: 4132: 4128: 4126: 4123: 4122: 4092: 4088: 4087: 4077: 4073: 4069: 4067: 4055: 4051: 4041: 4037: 4025: 4021: 4009: 4005: 4003: 4000: 3999: 3977: 3973: 3968: 3965: 3964: 3944: 3940: 3938: 3935: 3934: 3918: 3915: 3914: 3898: 3895: 3894: 3874: 3870: 3868: 3865: 3864: 3852: 3827: 3824: 3823: 3806: 3802: 3800: 3797: 3796: 3779: 3775: 3773: 3770: 3769: 3752: 3748: 3746: 3743: 3742: 3712: 3708: 3707: 3701: 3697: 3695: 3691: 3687: 3675: 3671: 3663: 3660: 3659: 3624: 3620: 3618: 3615: 3614: 3608: 3584:polycrystalline 3562: 3558: 3556: 3553: 3552: 3542: 3504: 3500: 3496: 3487: 3482: 3481: 3479: 3476: 3475: 3454: 3447: 3443: 3431: 3426: 3425: 3423: 3420: 3419: 3397: 3395: 3392: 3391: 3368: 3356: 3355: 3354: 3345: 3340: 3339: 3337: 3334: 3333: 3327: 3304: 3290: 3288: 3285: 3284: 3261: 3259: 3256: 3255: 3239: 3236: 3235: 3210: 3197: 3195: 3192: 3191: 3177:acoustic phonon 3120: 3109: 3056: 3055: 3051: 3046: 3016: 3015: 3011: 3006: 2967: 2966: 2962: 2957: 2944: 2942: 2939: 2938: 2891: 2890: 2886: 2881: 2851: 2850: 2846: 2841: 2802: 2801: 2797: 2792: 2779: 2777: 2774: 2773: 2737: 2736: 2732: 2730: 2727: 2726: 2681: 2680: 2676: 2674: 2671: 2670: 2625: 2624: 2620: 2615: 2576: 2575: 2571: 2566: 2553: 2551: 2548: 2547: 2537: 2519: 2482: 2474: 2470: 2465: 2457: 2454: 2453: 2449: 2440: 2431: 2422: 2413: 2404: 2388: 2364: 2323: 2297: 2290: 2283: 2276: 2254: 2250: 2232: 2227: 2217: 2213: 2212: 2210: 2208: 2205: 2204: 2184: 2177: 2148: 2138: 2132: 2096: 1956: 1948: 1917: 1913: 1907: 1903: 1902: 1900: 1891: 1887: 1885: 1882: 1881: 1856: 1821: 1820: 1816: 1810: 1806: 1805: 1803: 1794: 1790: 1788: 1785: 1784: 1757: 1754: 1753: 1745: 1708: 1704: 1693: 1690: 1689: 1682: 1658: 1654: 1642: 1638: 1621: 1618: 1617: 1600: 1596: 1581: 1577: 1563: 1560: 1559: 1543: 1540: 1539: 1514: 1511: 1510: 1483: 1479: 1464: 1460: 1442: 1438: 1429: 1425: 1417: 1414: 1413: 1410: 1383: 1379: 1364: 1360: 1342: 1338: 1329: 1325: 1317: 1314: 1313: 1293: 1289: 1287: 1284: 1283: 1263: 1259: 1244: 1240: 1238: 1235: 1234: 1214: 1210: 1195: 1191: 1189: 1186: 1185: 1168: 1164: 1162: 1159: 1158: 1141: 1137: 1114: 1110: 1108: 1099: 1095: 1093: 1090: 1089: 1072: 1068: 1060: 1057: 1056: 1052: 1028: 1023: 1012: 1008: 1004: 1002: 993: 989: 987: 984: 983: 960: 956: 947: 943: 941: 938: 937: 916: 911: 900: 896: 892: 890: 881: 877: 875: 872: 871: 848: 844: 832: 828: 826: 823: 822: 799: 795: 793: 790: 789: 764: 759: 748: 744: 740: 738: 726: 722: 710: 706: 704: 701: 700: 679: 674: 662: 660: 649: 646: 645: 636:of an electron. 616: 611: 605: 602: 601: 569: 564: 555: 544: 541: 540: 533: 470: 466: 457: 453: 451: 448: 447: 441: 423: 379: 375: 366: 362: 360: 357: 356: 353: 347: 313:crystal defects 291: 285: 276: 265: 259: 256: 241: 225: 214: 126: 122: 120: 117: 116: 95: 91: 89: 86: 85: 24: 17: 12: 11: 5: 8639: 8629: 8628: 8623: 8618: 8616:Semiconductors 8613: 8608: 8603: 8589: 8588: 8581: 8576: 8562: 8561:External links 8559: 8557: 8556: 8521: 8494: 8485: 8446: 8380: 8345:(9): 871–925. 8329: 8292:(2): 543–586. 8269: 8256: 8243: 8228: 8205: 8151: 8137: 8112: 8093:(6): 303–307. 8073: 8066: 8044: 8037: 8017: 7990:(61): 49–144. 7970: 7931: 7924: 7904: 7882: 7865: 7845: 7831: 7811: 7799: 7777: 7738: 7715: 7675: 7661: 7649:Singh (2008). 7638: 7624: 7601: 7558: 7509: 7460: 7404: 7353: 7310: 7257: 7238:(4): 1500452. 7222: 7185:(9): 351–355. 7166: 7123: 7085: 7074:www.matprop.ru 7055: 7053: 7050: 7049: 7048: 7041: 7038: 7018: 7013: 7005: 7001: 6997: 6994: 6988: 6984: 6978: 6973: 6970: 6966: 6961: 6958: 6955: 6952: 6947: 6943: 6939: 6934: 6930: 6905: 6900: 6892: 6888: 6884: 6881: 6875: 6871: 6865: 6860: 6857: 6853: 6848: 6845: 6842: 6839: 6834: 6830: 6826: 6821: 6817: 6789: 6784: 6776: 6772: 6768: 6765: 6759: 6755: 6749: 6744: 6741: 6737: 6732: 6729: 6726: 6723: 6718: 6714: 6710: 6705: 6701: 6676: 6671: 6663: 6659: 6655: 6652: 6646: 6642: 6636: 6631: 6628: 6624: 6619: 6616: 6613: 6610: 6605: 6601: 6597: 6592: 6588: 6568: 6560: 6553: 6530: 6525: 6514: 6510: 6505: 6500: 6497: 6491: 6487: 6481: 6476: 6472: 6468: 6465: 6439: 6436: 6431: 6428: 6421: 6417: 6392: 6389: 6376: 6373: 6370: 6348: 6344: 6321: 6317: 6296: 6276: 6271: 6267: 6263: 6258: 6254: 6250: 6247: 6244: 6241: 6238: 6235: 6219:Main article: 6216: 6213: 6196: 6193: 6183: 6180: 6175: 6171: 6158: 6152: 6147: 6142: 6139: 6135: 6129: 6124: 6121: 6117: 6113: 6108: 6105: 6101: 6097: 6092: 6089: 6085: 6081: 6077: 6071: 6068: 6061: 6057: 6053: 6050: 6045: 6041: 6020: 6013: 6009: 6005: 5996: 5993: 5989: 5985: 5978: 5975: 5964: 5960: 5957: 5945: 5928: 5925: 5921: 5917: 5912: 5908: 5895: 5891: 5888: 5879: 5864: 5859: 5855: 5849: 5846: 5842: 5838: 5833: 5830: 5826: 5822: 5817: 5814: 5807: 5801: 5797: 5793: 5787: 5782: 5778: 5763: 5736: 5732: 5728: 5721: 5717: 5714: 5706: 5697: 5693: 5690: 5678: 5671: 5667: 5663: 5659: 5656: 5627: 5624: 5619: 5612: 5604:(current) and 5592: 5573: 5570: 5565: 5560: 5557: 5553: 5547: 5543: 5536: 5531: 5527: 5497: 5494: 5489: 5484: 5481: 5477: 5471: 5467: 5460: 5457: 5454: 5452: 5450: 5445: 5442: 5438: 5432: 5428: 5424: 5421: 5418: 5416: 5414: 5410: 5403: 5400: 5396: 5391: 5387: 5381: 5377: 5372: 5368: 5365: 5362: 5358: 5354: 5351: 5349: 5345: 5341: 5337: 5336: 5311: 5308: 5303: 5298: 5295: 5291: 5284: 5278: 5275: 5271: 5266: 5261: 5258: 5254: 5228: 5225: 5220: 5215: 5212: 5208: 5201: 5195: 5192: 5188: 5183: 5180: 5175: 5172: 5168: 5146: 5141: 5137: 5131: 5126: 5122: 5096: 5093: 5089: 5084: 5081: 5076: 5073: 5069: 5055: 5036: 5033: 5028: 5025: 5020: 5017: 5013: 5006: 5003: 4997: 4994: 4991: 4988: 4983: 4980: 4974: 4971: 4966: 4962: 4945: 4936: 4921: 4918: 4913: 4909: 4905: 4902: 4899: 4896: 4893: 4851: 4847: 4841: 4837: 4833: 4828: 4824: 4802: 4799: 4794: 4790: 4784: 4780: 4776: 4773: 4768: 4764: 4760: 4757: 4754: 4733: 4730: 4727: 4722: 4717: 4712: 4707: 4702: 4697: 4694: 4691: 4688: 4685: 4682: 4677: 4673: 4669: 4666: 4663: 4660: 4657: 4652: 4647: 4613: 4608: 4603: 4598: 4593: 4588: 4583: 4580: 4577: 4574: 4569: 4566: 4561: 4537: 4532: 4527: 4522: 4517: 4512: 4507: 4504: 4501: 4498: 4493: 4490: 4485: 4448: 4437: 4432:high-impedance 4426: 4401:magnetic field 4366:Main article: 4363: 4360: 4358: 4355: 4342: 4320: 4316: 4293: 4289: 4265: 4259: 4256: 4253: 4250: 4247: 4243: 4239: 4236: 4231: 4226: 4221: 4217: 4211: 4206: 4202: 4198: 4195: 4190: 4186: 4182: 4179: 4157: 4135: 4131: 4107: 4100: 4095: 4091: 4083: 4080: 4076: 4072: 4066: 4061: 4058: 4054: 4050: 4047: 4044: 4040: 4036: 4033: 4028: 4024: 4020: 4015: 4012: 4008: 3983: 3980: 3976: 3972: 3950: 3947: 3943: 3922: 3902: 3880: 3877: 3873: 3851: 3848: 3831: 3805: 3778: 3755: 3751: 3727: 3720: 3711: 3700: 3694: 3690: 3686: 3683: 3678: 3674: 3670: 3667: 3627: 3623: 3607: 3604: 3565: 3561: 3541: 3538: 3511: 3507: 3503: 3499: 3495: 3485: 3461: 3457: 3453: 3450: 3446: 3442: 3437: 3434: 3429: 3406: 3403: 3400: 3374: 3371: 3365: 3362: 3359: 3353: 3343: 3325: 3308: 3303: 3299: 3296: 3293: 3270: 3267: 3264: 3243: 3223: 3219: 3216: 3213: 3209: 3204: 3201: 3166: 3165: 3162: 3159: 3156: 3152: 3151: 3148: 3145: 3142: 3138: 3137: 3134: 3131: 3128: 3119: 3116: 3107: 3091: 3088: 3085: 3077: 3074: 3071: 3068: 3065: 3062: 3059: 3054: 3050: 3045: 3037: 3034: 3031: 3028: 3025: 3022: 3019: 3014: 3010: 3005: 2997: 2994: 2991: 2988: 2985: 2982: 2979: 2976: 2973: 2970: 2965: 2961: 2956: 2951: 2948: 2926: 2923: 2920: 2912: 2909: 2906: 2903: 2900: 2897: 2894: 2889: 2885: 2880: 2872: 2869: 2866: 2863: 2860: 2857: 2854: 2849: 2845: 2840: 2832: 2829: 2826: 2823: 2820: 2817: 2814: 2811: 2808: 2805: 2800: 2796: 2791: 2786: 2783: 2758: 2755: 2752: 2749: 2746: 2743: 2740: 2735: 2711: 2708: 2705: 2702: 2699: 2696: 2693: 2690: 2687: 2684: 2679: 2654: 2646: 2643: 2640: 2637: 2634: 2631: 2628: 2623: 2619: 2614: 2606: 2603: 2600: 2597: 2594: 2591: 2588: 2585: 2582: 2579: 2574: 2570: 2565: 2560: 2557: 2536: 2533: 2516:effective mass 2489: 2486: 2477: 2473: 2469: 2464: 2461: 2448: 2445: 2439: 2436: 2430: 2427: 2421: 2418: 2412: 2409: 2403: 2400: 2387: 2384: 2375:mean free time 2363: 2360: 2327:effective mass 2322: 2319: 2295: 2288: 2281: 2274: 2253: 2249: 2246: 2241: 2235: 2226: 2220: 2216: 2201:kinetic energy 2195:optical phonon 2182: 2175: 2161:is called the 2153:, so mobility 2144: 2134:Main article: 2131: 2128: 2125: 2124: 2122: 2119: 2115: 2114: 2111: 2108: 2104: 2103: 2101: 2098: 2094: 2090: 2089: 2087: 2084: 2080: 2079: 2077: 2074: 2070: 2069: 2066: 2063: 2059: 2058: 2056: 2053: 2049: 2048: 2046: 2043: 2039: 2038: 2036: 2033: 2029: 2028: 2025: 2022: 2018: 2017: 2016:Hole mobility 2014: 2011: 1955: 1952: 1951: 1950: 1946: 1926: 1920: 1916: 1906: 1899: 1890: 1877: 1876: 1870: 1861: 1854: 1834: 1830: 1824: 1819: 1809: 1802: 1793: 1777: 1776: 1764: 1761: 1751: 1750:or diffusivity 1743: 1738: 1719: 1716: 1707: 1703: 1700: 1697: 1681: 1678: 1666: 1661: 1657: 1653: 1650: 1645: 1641: 1637: 1634: 1631: 1628: 1625: 1603: 1599: 1595: 1592: 1589: 1584: 1580: 1576: 1573: 1570: 1567: 1547: 1527: 1524: 1521: 1518: 1494: 1491: 1486: 1482: 1478: 1475: 1472: 1467: 1463: 1459: 1456: 1453: 1450: 1445: 1441: 1437: 1432: 1428: 1424: 1421: 1409: 1406: 1394: 1391: 1386: 1382: 1378: 1375: 1372: 1367: 1363: 1359: 1356: 1353: 1350: 1345: 1341: 1337: 1332: 1328: 1324: 1321: 1296: 1292: 1271: 1266: 1262: 1258: 1255: 1252: 1247: 1243: 1222: 1217: 1213: 1209: 1206: 1203: 1198: 1194: 1171: 1167: 1144: 1140: 1136: 1133: 1130: 1127: 1122: 1117: 1113: 1107: 1102: 1098: 1075: 1071: 1067: 1064: 1051: 1048: 1031: 1026: 1022: 1015: 1011: 1007: 1001: 996: 992: 971: 968: 963: 959: 955: 950: 946: 919: 914: 910: 903: 899: 895: 889: 884: 880: 859: 856: 851: 847: 843: 840: 835: 831: 817:mean free time 802: 798: 777: 774: 767: 762: 758: 751: 747: 743: 737: 734: 729: 725: 721: 718: 713: 709: 682: 677: 673: 668: 665: 659: 656: 653: 638: 637: 634:effective mass 619: 614: 610: 599: 593: 572: 567: 563: 558: 554: 551: 548: 535:Starting with 532: 529: 481: 478: 473: 469: 465: 460: 456: 444: 443: 439: 434: 421: 417: 414:electric field 390: 387: 382: 378: 374: 369: 365: 346: 343: 339:mean free time 335:mean free path 321:drift velocity 289:Drift velocity 287:Main article: 284: 281: 278: 277: 228: 226: 219: 213: 210: 196:things equal. 143: 140: 137: 134: 129: 125: 115:is defined as 98: 94: 82:drift velocity 48:electric field 15: 9: 6: 4: 3: 2: 8638: 8627: 8624: 8622: 8619: 8617: 8614: 8612: 8609: 8607: 8604: 8602: 8599: 8598: 8596: 8586: 8582: 8580: 8577: 8575: 8571: 8568: 8565: 8564: 8552: 8548: 8544: 8540: 8536: 8532: 8525: 8517: 8513: 8509: 8505: 8498: 8489: 8481: 8477: 8473: 8469: 8465: 8461: 8457: 8450: 8442: 8438: 8433: 8428: 8424: 8420: 8416: 8412: 8408: 8404: 8400: 8396: 8392: 8384: 8376: 8372: 8368: 8364: 8360: 8356: 8352: 8348: 8344: 8340: 8333: 8325: 8321: 8316: 8311: 8307: 8303: 8299: 8295: 8291: 8287: 8280: 8273: 8266: 8260: 8253: 8247: 8231: 8225: 8221: 8220: 8212: 8210: 8201: 8197: 8193: 8189: 8185: 8181: 8176: 8171: 8167: 8163: 8159: 8140: 8134: 8130: 8129: 8121: 8119: 8117: 8108: 8104: 8100: 8096: 8092: 8088: 8084: 8077: 8069: 8063: 8059: 8058: 8051: 8049: 8040: 8034: 8030: 8029: 8021: 8013: 8009: 8005: 8001: 7997: 7993: 7989: 7985: 7981: 7974: 7966: 7962: 7958: 7954: 7950: 7946: 7942: 7935: 7927: 7921: 7917: 7916: 7908: 7901: 7897: 7894: 7889: 7887: 7880: 7868: 7862: 7858: 7857: 7849: 7834: 7828: 7824: 7823: 7815: 7806: 7804: 7796: 7795:0-13-495656-7 7792: 7786: 7784: 7782: 7772: 7768: 7764: 7760: 7756: 7752: 7745: 7743: 7736: 7732: 7726: 7724: 7722: 7720: 7712: 7711:0-7484-0866-5 7708: 7704: 7703:0-7484-0865-7 7700: 7694: 7692: 7690: 7688: 7686: 7684: 7682: 7680: 7664: 7658: 7654: 7653: 7645: 7643: 7627: 7621: 7617: 7616: 7608: 7606: 7597: 7593: 7589: 7585: 7581: 7577: 7573: 7569: 7562: 7554: 7550: 7545: 7540: 7536: 7532: 7528: 7524: 7520: 7513: 7505: 7501: 7496: 7491: 7487: 7483: 7479: 7475: 7471: 7464: 7456: 7452: 7448: 7444: 7440: 7436: 7432: 7428: 7424: 7420: 7416: 7408: 7400: 7396: 7392: 7388: 7384: 7380: 7376: 7373:(3): 033105. 7372: 7368: 7364: 7357: 7349: 7345: 7341: 7337: 7333: 7329: 7325: 7321: 7314: 7306: 7302: 7298: 7294: 7290: 7286: 7281: 7276: 7273:(3): 034005. 7272: 7268: 7261: 7253: 7249: 7245: 7241: 7237: 7233: 7226: 7218: 7214: 7210: 7206: 7202: 7198: 7193: 7188: 7184: 7180: 7173: 7171: 7162: 7158: 7154: 7150: 7146: 7142: 7138: 7134: 7127: 7119: 7115: 7111: 7107: 7103: 7099: 7092: 7090: 7075: 7071: 7065: 7063: 7061: 7056: 7047: 7044: 7043: 7037: 7034: 7016: 7011: 7003: 6999: 6995: 6992: 6986: 6982: 6976: 6971: 6968: 6964: 6959: 6956: 6953: 6945: 6941: 6932: 6928: 6903: 6898: 6890: 6886: 6882: 6879: 6873: 6869: 6863: 6858: 6855: 6851: 6846: 6843: 6840: 6832: 6828: 6819: 6815: 6805: 6787: 6782: 6774: 6770: 6766: 6763: 6757: 6753: 6747: 6742: 6739: 6735: 6730: 6727: 6724: 6716: 6712: 6703: 6699: 6674: 6669: 6661: 6657: 6653: 6650: 6644: 6640: 6634: 6629: 6626: 6622: 6617: 6614: 6611: 6603: 6599: 6590: 6586: 6576: 6574: 6567: 6563: 6556: 6549: 6528: 6523: 6512: 6508: 6503: 6498: 6495: 6489: 6485: 6479: 6474: 6470: 6466: 6463: 6455: 6437: 6434: 6419: 6415: 6406: 6401: 6398: 6388: 6374: 6368: 6346: 6342: 6319: 6315: 6294: 6269: 6265: 6261: 6256: 6252: 6245: 6242: 6239: 6233: 6222: 6212: 6210: 6206: 6203:measurement. 6202: 6192: 6189: 6179: 6156: 6150: 6145: 6140: 6137: 6133: 6127: 6122: 6119: 6115: 6106: 6103: 6099: 6095: 6090: 6087: 6083: 6075: 6069: 6066: 6059: 6055: 6051: 6048: 6043: 6039: 6018: 6011: 6007: 6003: 5994: 5991: 5987: 5983: 5976: 5973: 5962: 5958: 5955: 5944: 5926: 5923: 5919: 5915: 5910: 5906: 5898:is small and 5887: 5885: 5878: 5862: 5857: 5847: 5844: 5840: 5836: 5831: 5828: 5824: 5815: 5812: 5805: 5799: 5795: 5791: 5785: 5780: 5776: 5766: 5762: 5758: 5754: 5734: 5730: 5726: 5719: 5715: 5712: 5704: 5695: 5691: 5688: 5677: 5655: 5653: 5648: 5646: 5639: 5633: 5623: 5618: 5611: 5607: 5603: 5599: 5595: 5587: 5571: 5568: 5563: 5558: 5555: 5551: 5545: 5541: 5534: 5529: 5525: 5515: 5495: 5492: 5487: 5482: 5479: 5475: 5469: 5465: 5458: 5455: 5453: 5443: 5440: 5436: 5430: 5426: 5422: 5419: 5417: 5408: 5401: 5398: 5394: 5389: 5385: 5379: 5375: 5370: 5366: 5363: 5360: 5356: 5352: 5350: 5343: 5339: 5325: 5309: 5306: 5301: 5296: 5293: 5289: 5282: 5276: 5273: 5269: 5264: 5259: 5256: 5252: 5242: 5226: 5223: 5218: 5213: 5210: 5206: 5199: 5193: 5190: 5186: 5181: 5178: 5173: 5170: 5166: 5144: 5139: 5135: 5129: 5124: 5120: 5110: 5094: 5091: 5087: 5082: 5079: 5074: 5071: 5067: 5058: 5050: 5034: 5031: 5026: 5023: 5018: 5015: 5011: 5004: 5001: 4995: 4992: 4989: 4986: 4981: 4978: 4972: 4969: 4964: 4960: 4951: 4948: 4944: 4939: 4935: 4919: 4916: 4911: 4907: 4903: 4900: 4897: 4894: 4891: 4883: 4880: 4875: 4873: 4869: 4864: 4849: 4845: 4839: 4835: 4831: 4826: 4822: 4813: 4800: 4797: 4792: 4788: 4782: 4778: 4774: 4771: 4766: 4762: 4758: 4755: 4744: 4731: 4728: 4720: 4710: 4705: 4689: 4686: 4680: 4675: 4671: 4664: 4661: 4655: 4650: 4635: 4633: 4629: 4624: 4606: 4596: 4591: 4578: 4575: 4572: 4567: 4564: 4548: 4530: 4520: 4515: 4502: 4499: 4496: 4491: 4488: 4472: 4470: 4466: 4465:Lorentz force 4461: 4459: 4455: 4451: 4444: 4440: 4433: 4429: 4422: 4418: 4414: 4410: 4406: 4402: 4398: 4393: 4391: 4382: 4374: 4369: 4362:Hall mobility 4354: 4340: 4318: 4314: 4291: 4287: 4277: 4263: 4254: 4251: 4248: 4241: 4237: 4234: 4229: 4224: 4219: 4215: 4209: 4204: 4200: 4196: 4193: 4188: 4184: 4180: 4177: 4169: 4155: 4133: 4129: 4119: 4105: 4098: 4093: 4089: 4081: 4078: 4074: 4064: 4059: 4056: 4052: 4048: 4045: 4042: 4038: 4034: 4031: 4026: 4022: 4018: 4013: 4010: 4006: 3997: 3981: 3978: 3974: 3948: 3945: 3941: 3920: 3900: 3878: 3875: 3871: 3862: 3858: 3847: 3845: 3844:Urbach Energy 3829: 3803: 3776: 3753: 3749: 3739: 3725: 3718: 3709: 3698: 3692: 3688: 3684: 3681: 3676: 3672: 3668: 3665: 3653: 3649: 3647: 3643: 3625: 3621: 3612: 3603: 3601: 3597: 3593: 3589: 3585: 3563: 3559: 3550: 3546: 3537: 3533: 3530: 3525: 3509: 3505: 3501: 3497: 3493: 3483: 3459: 3455: 3451: 3448: 3444: 3440: 3435: 3432: 3427: 3404: 3401: 3398: 3388: 3372: 3369: 3363: 3360: 3357: 3351: 3331: 3322: 3306: 3301: 3297: 3294: 3291: 3268: 3265: 3262: 3217: 3214: 3211: 3207: 3202: 3199: 3188: 3186: 3182: 3178: 3174: 3163: 3160: 3157: 3154: 3153: 3149: 3146: 3143: 3140: 3139: 3135: 3132: 3129: 3127: 3126: 3115: 3111: 3105: 3089: 3086: 3083: 3052: 3048: 3043: 3012: 3008: 3003: 2963: 2959: 2954: 2949: 2946: 2924: 2921: 2918: 2887: 2883: 2878: 2847: 2843: 2838: 2798: 2794: 2789: 2784: 2781: 2733: 2677: 2668: 2652: 2621: 2617: 2612: 2572: 2568: 2563: 2558: 2555: 2545: 2543: 2532: 2530: 2525: 2522: 2517: 2513: 2509: 2505: 2484: 2475: 2471: 2467: 2462: 2459: 2444: 2435: 2426: 2417: 2408: 2399: 2397: 2393: 2392:absolute zero 2383: 2379: 2378:interaction. 2376: 2372: 2371: 2359: 2357: 2353: 2349: 2343: 2341: 2336: 2332: 2328: 2318: 2314: 2312: 2308: 2304: 2299: 2294: 2287: 2282:phonon (opt.) 2280: 2273: 2256:phonon (opt.) 2251: 2244: 2239: 2233: 2224: 2218: 2214: 2202: 2198: 2196: 2190: 2188: 2181: 2174: 2171: 2166: 2164: 2160: 2156: 2152: 2147: 2143: 2137: 2123: 2120: 2117: 2116: 2112: 2109: 2106: 2105: 2102: 2099: 2092: 2091: 2088: 2085: 2082: 2081: 2078: 2075: 2072: 2071: 2067: 2064: 2061: 2060: 2057: 2054: 2051: 2050: 2047: 2044: 2041: 2040: 2037: 2034: 2031: 2030: 2026: 2023: 2020: 2019: 2015: 2012: 2009: 2008: 2002: 2000: 1996: 1992: 1988: 1984: 1980: 1975: 1973: 1969: 1965: 1961: 1945: 1942: 1941: 1940: 1924: 1918: 1914: 1904: 1897: 1888: 1874: 1871: 1869: 1865: 1862: 1860: 1853: 1850: 1849: 1848: 1832: 1828: 1817: 1807: 1800: 1791: 1782: 1762: 1752: 1749: 1742: 1739: 1736: 1733: 1732: 1731: 1717: 1705: 1701: 1698: 1695: 1687: 1677: 1659: 1655: 1651: 1648: 1643: 1639: 1635: 1629: 1626: 1623: 1601: 1597: 1593: 1590: 1587: 1582: 1578: 1574: 1571: 1568: 1565: 1545: 1525: 1522: 1519: 1516: 1508: 1492: 1484: 1480: 1476: 1473: 1470: 1465: 1461: 1457: 1454: 1448: 1443: 1439: 1435: 1430: 1426: 1422: 1419: 1405: 1392: 1384: 1380: 1376: 1373: 1370: 1365: 1361: 1357: 1354: 1348: 1343: 1339: 1335: 1330: 1326: 1322: 1319: 1310: 1294: 1290: 1269: 1264: 1260: 1256: 1253: 1250: 1245: 1241: 1220: 1215: 1211: 1207: 1204: 1201: 1196: 1192: 1169: 1165: 1142: 1138: 1134: 1131: 1128: 1125: 1120: 1115: 1111: 1105: 1100: 1096: 1073: 1069: 1065: 1062: 1047: 1029: 1024: 1020: 1013: 1009: 1005: 999: 994: 990: 969: 966: 961: 957: 953: 948: 944: 934: 917: 912: 908: 901: 897: 893: 887: 882: 878: 857: 854: 849: 845: 841: 838: 833: 829: 819: 818: 800: 796: 775: 772: 765: 760: 756: 749: 745: 741: 735: 732: 727: 723: 719: 716: 711: 707: 697: 680: 675: 671: 666: 663: 657: 654: 651: 643: 635: 617: 612: 608: 600: 597: 594: 591: 588: 587: 586: 570: 565: 561: 556: 552: 549: 546: 538: 528: 524: 522: 518: 514: 510: 506: 502: 497: 493: 479: 476: 471: 467: 463: 458: 454: 438: 435: 432: 428: 424: 418: 415: 411: 407: 404: 403: 402: 388: 385: 380: 376: 372: 367: 363: 352: 342: 340: 336: 332: 327: 324: 322: 318: 314: 310: 305: 303: 300: 296: 290: 274: 271: 263: 253: 249: 245: 239: 238: 234: 229:This section 227: 223: 218: 217: 209: 207: 203: 197: 194: 189: 185: 183: 179: 175: 171: 167: 163: 159: 154: 141: 138: 135: 132: 127: 123: 114: 96: 92: 83: 79: 74: 72: 68: 67:special cases 63: 61: 57: 56:hole mobility 53: 49: 45: 44:semiconductor 41: 37: 33: 29: 22: 8537:(1): 47–54. 8534: 8530: 8524: 8507: 8503: 8497: 8488: 8463: 8459: 8449: 8398: 8394: 8383: 8342: 8338: 8332: 8289: 8285: 8272: 8267:, Aug. 2018. 8259: 8254:, Oct. 2017. 8246: 8233:. Retrieved 8218: 8165: 8161: 8142:. Retrieved 8127: 8090: 8086: 8076: 8056: 8027: 8020: 7987: 7983: 7973: 7948: 7944: 7934: 7914: 7907: 7870:. Retrieved 7855: 7848: 7836:. Retrieved 7821: 7814: 7754: 7750: 7666:. Retrieved 7651: 7629:. Retrieved 7614: 7571: 7567: 7561: 7526: 7522: 7512: 7477: 7473: 7463: 7422: 7418: 7407: 7399:the original 7370: 7366: 7356: 7326:(1): 35–39. 7323: 7320:Nano Letters 7319: 7313: 7270: 7266: 7260: 7235: 7231: 7225: 7182: 7178: 7136: 7133:Nano Letters 7132: 7126: 7101: 7097: 7077:. Retrieved 7073: 7035: 6806: 6577: 6565: 6558: 6551: 6547: 6402: 6394: 6224: 6198: 6185: 5942: 5893: 5884:Early effect 5876: 5764: 5760: 5756: 5752: 5675: 5661: 5649: 5642: 5616: 5609: 5605: 5601: 5597: 5590: 5588: 5516: 5326: 5243: 5111: 5053: 5051: 4952: 4946: 4942: 4937: 4933: 4884:is given by 4881: 4876: 4871: 4867: 4865: 4814: 4745: 4636: 4631: 4625: 4549: 4473: 4471:is given by 4468: 4462: 4457: 4453: 4446: 4443:Hall voltage 4435: 4424: 4416: 4412: 4408: 4404: 4396: 4394: 4387: 4278: 4170: 4120: 3998: 3860: 3853: 3740: 3658: 3641: 3609: 3600:normalizable 3595: 3581: 3534: 3528: 3526: 3389: 3329: 3323: 3189: 3184: 3180: 3169: 3112: 3103: 2666: 2546: 2538: 2528: 2526: 2520: 2511: 2503: 2450: 2441: 2432: 2423: 2414: 2405: 2389: 2380: 2368: 2365: 2355: 2351: 2347: 2344: 2342:scattering. 2324: 2315: 2306: 2300: 2292: 2285: 2278: 2275:phonon(opt.) 2271: 2193: 2191: 2179: 2172: 2169: 2167: 2162: 2158: 2154: 2150: 2145: 2141: 2139: 1976: 1957: 1943: 1878: 1872: 1863: 1851: 1778: 1740: 1734: 1683: 1411: 1311: 1053: 935: 820: 698: 641: 639: 595: 589: 534: 525: 498: 494: 445: 436: 419: 405: 354: 328: 325: 306: 292: 266: 257: 242:Please help 230: 212:Introduction 198: 188:Conductivity 186: 155: 112: 77: 75: 64: 59: 55: 31: 25: 8315:10871/15671 7757:(1): 1–36. 5941:with slope 5638:Wien effect 5517:Similarly, 4874:direction. 4550:For holes: 4390:Hall effect 4368:Hall effect 2303:Gunn effect 2024:35,000,000 206:Hall effect 193:transistors 58:. The term 8595:Categories 7280:2203.10713 7079:2020-07-25 7052:References 5630:See also: 3857:tunnelling 3141:Electrons 3108:impurities 2544:in 1864): 2331:scattering 2197:scattering 2027:5,800,000 1686:Fick's Law 531:Derivation 349:See also: 260:March 2021 8480:1932-7447 8423:2041-1723 8367:1866-6892 8324:0034-6861 8200:119532427 8012:0001-8732 7918:. Wiley. 7455:250952849 7395:0003-6951 7305:2475-9953 7252:138355533 7217:118392999 7192:0802.2389 7139:(1): 35. 6996:× 6929:μ 6883:× 6816:μ 6767:× 6700:μ 6654:× 6587:μ 6529:α 6486:μ 6471:μ 6464:μ 6435:− 6375:μ 6372:Σ 6369:ϕ 6343:μ 6316:μ 6295:ϕ 6266:μ 6253:μ 6246:ϕ 6240:μ 6237:Σ 6234:ϕ 6128:− 6096:− 6052:μ 5956:μ 5916:∝ 5837:− 5792:μ 5689:μ 5542:σ 5526:μ 5466:σ 5459:− 5427:σ 5423:− 5390:− 5376:μ 5361:− 5340:μ 5182:− 5121:ξ 5083:− 4973:− 4961:ξ 4898:− 4823:ξ 4763:ξ 4756:− 4753:⇒ 4711:× 4687:− 4672:ξ 4662:− 4628:net force 4597:× 4521:× 4500:− 4288:μ 4235:− 4205:− 4197:⁡ 4185:μ 4178:μ 4156:α 4071:Δ 4065:− 4049:α 4043:− 4035:⁡ 3971:Δ 3750:μ 3693:− 3685:⁡ 3673:μ 3666:μ 3596:localized 3588:amorphous 3529:decreases 3494:∼ 3484:μ 3449:− 3441:∼ 3428:μ 3370:− 3352:∝ 3342:Σ 3302:∼ 3242:Σ 3222:Σ 3208:∝ 3203:τ 3173:non-polar 3087:⋯ 3053:τ 3013:τ 2964:τ 2950:τ 2922:⋯ 2888:μ 2848:μ 2799:μ 2785:μ 2734:μ 2678:μ 2622:μ 2573:μ 2559:μ 2488:¯ 2485:τ 2476:∗ 2460:μ 2307:increases 2252:ω 2248:ℏ 2245:≈ 2219:∗ 2107:Organics 2010:Material 1905:μ 1808:μ 1760:∇ 1715:∇ 1702:− 1656:μ 1640:μ 1624:σ 1598:μ 1579:μ 1566:σ 1546:σ 1523:σ 1507:Ohm's law 1481:μ 1462:μ 1381:μ 1362:μ 1291:μ 1261:μ 1212:μ 1129:− 1063:− 1030:∗ 1010:τ 991:μ 958:μ 918:∗ 898:τ 879:μ 846:μ 842:− 797:τ 766:∗ 746:τ 736:− 724:τ 681:∗ 658:− 618:∗ 571:∗ 468:μ 427:magnitude 410:magnitude 377:μ 295:electrons 231:does not 136:μ 54:, called 8585:Mobility 8570:Archived 8441:26400049 8401:: 8195. 8375:13849900 8235:20 April 7896:Archived 7705:(hbk.), 7596:25457390 7588:26707947 7553:24398476 7529:: 3005. 7504:24105872 7447:35862526 7348:45010238 7161:45010238 7040:See also 3592:Anderson 3405:⟩ 3399:⟨ 3364:⟩ 3358:⟨ 3298:⟩ 3292:⟨ 3269:⟩ 3263:⟨ 3234:, where 3218:⟩ 3212:⟨ 2035:200,000 1999:oligomer 1987:graphene 1954:Examples 1737:is flux. 36:electron 8626:MOSFETs 8539:Bibcode 8432:4598357 8403:Bibcode 8347:Bibcode 8294:Bibcode 8180:Bibcode 8144:1 March 8095:Bibcode 7992:Bibcode 7953:Bibcode 7872:2 March 7838:1 March 7759:Bibcode 7668:1 March 7631:2 March 7531:Bibcode 7482:Bibcode 7427:Bibcode 7419:Science 7375:Bibcode 7328:Bibcode 7285:Bibcode 7197:Bibcode 7141:Bibcode 7106:Bibcode 6564:), and 2506:is the 2396:phonons 2045:79,000 1995:polymer 1972:silicon 1939:where: 1866:is the 1857:is the 1847:where: 1746:is the 1730:where: 815:is the 632:is the 585:where: 425:is the 412:of the 408:is the 401:where: 317:phonons 252:removed 237:sources 8478: 8439: 8429: 8421: 8373: 8365: 8322: 8226: 8198: 8135: 8064: 8035: 8010: 7922: 7863: 7829: 7797:(nid.) 7793: 7733: 7713:(pbk.) 7709: 7701: 7659: 7622: 7594: 7586: 7551: 7502: 7453: 7445: 7393: 7346: 7303: 7250: 7215: 7159: 6546:where 5875:where 5751:where 5652:MOSFET 5632:MOSFET 5112:Since 5052:where 4932:. Sub 4279:where 3741:where 3155:Holes 3102:where 2665:where 2518:, and 2502:where 2340:defect 2270:where 2187:doping 2100:10–50 2086:10–50 2065:1,400 2055:1,600 1968:silver 1964:copper 1538:where 1184:gives 982:where 870:where 788:where 329:Quasi- 30:, the 8371:S2CID 8282:(PDF) 8196:S2CID 8170:arXiv 7592:S2CID 7451:S2CID 7344:S2CID 7275:arXiv 7248:S2CID 7213:S2CID 7187:arXiv 7157:S2CID 4121:Here 3136:GaAs 2329:) is 431:speed 299:holes 52:holes 40:metal 8476:ISSN 8437:PMID 8419:ISSN 8363:ISSN 8320:ISSN 8237:2011 8224:ISBN 8146:2011 8133:ISBN 8062:ISBN 8033:ISBN 8008:ISSN 7920:ISBN 7874:2011 7861:ISBN 7840:2011 7827:ISBN 7791:ISBN 7731:ISBN 7707:ISBN 7699:ISBN 7670:2011 7657:ISBN 7633:2011 7620:ISBN 7584:PMID 7549:PMID 7500:PMID 7443:PMID 7391:ISSN 7301:ISSN 7017:1.25 6852:1180 6788:0.76 6675:0.72 6623:1265 6395:The 5755:and 4877:The 3611:Mott 3164:∝T 3161:∝T 3158:∝T 3150:∝T 3147:∝T 3144:∝T 2296:emit 2289:emit 2229:emit 2110:8.6 2076:100 2068:450 1979:2DEG 1966:and 1960:gold 1505:Now 297:and 235:any 233:cite 8547:doi 8512:doi 8468:doi 8464:117 8427:PMC 8411:doi 8355:doi 8310:hdl 8302:doi 8188:doi 8103:doi 8000:doi 7961:doi 7949:109 7767:doi 7576:doi 7539:doi 7490:doi 7435:doi 7423:377 7383:doi 7336:doi 7293:doi 7240:doi 7205:doi 7183:146 7149:doi 7114:doi 7102:311 6965:370 6957:130 6904:0.9 6844:232 6764:6.3 6736:447 6651:8.5 6569:ref 6557:or 6517:ref 6456:: 5967:lin 5946:lin 5700:sat 5679:sat 5615:or 4194:exp 4032:exp 3682:exp 3586:or 3489:def 3347:def 3190:As 3133:Ge 3130:Si 2183:sat 2176:sat 2121:~1 2113:43 501:m/s 246:by 69:of 42:or 26:In 8597:: 8545:. 8535:28 8533:. 8508:55 8506:. 8474:. 8462:. 8458:. 8435:. 8425:. 8417:. 8409:. 8397:. 8393:. 8369:. 8361:. 8353:. 8343:33 8341:. 8318:. 8308:. 8300:. 8290:83 8288:. 8284:. 8208:^ 8194:. 8186:. 8178:. 8166:85 8164:. 8160:. 8152:DS 8115:^ 8101:. 8091:32 8089:. 8085:. 8047:^ 8006:. 7998:. 7988:16 7986:. 7982:. 7959:. 7947:. 7943:. 7885:^ 7802:^ 7780:^ 7765:. 7755:44 7753:. 7741:^ 7718:^ 7678:^ 7641:^ 7604:^ 7590:. 7582:. 7572:28 7570:. 7547:. 7537:. 7525:. 7521:. 7498:. 7488:. 7478:25 7476:. 7472:. 7449:. 7441:. 7433:. 7421:. 7417:. 7389:. 7381:. 7371:86 7369:. 7365:. 7342:. 7334:. 7322:. 7299:. 7291:. 7283:. 7269:. 7246:. 7234:. 7211:. 7203:. 7195:. 7181:. 7169:^ 7155:. 7147:. 7135:. 7112:. 7100:. 7088:^ 7072:. 7059:^ 7004:17 7000:10 6891:16 6887:10 6775:16 6771:10 6728:48 6662:16 6658:10 6615:65 6420:18 6416:10 6172:DS 5896:DS 5880:th 5668:DS 5664:GS 5593:Hp 5056:Hn 4950:, 4445:. 3996:. 3524:. 3326:ph 3321:. 2510:, 2352:k' 2350:to 2313:. 2165:. 2097:) 1997:, 1962:, 1688:: 644:: 642:eE 539:: 515:/( 315:, 176:/( 170:SI 160:/( 158:cm 84:, 8553:. 8549:: 8541:: 8518:. 8514:: 8482:. 8470:: 8443:. 8413:: 8405:: 8399:6 8377:. 8357:: 8349:: 8326:. 8312:: 8304:: 8296:: 8239:. 8202:. 8190:: 8182:: 8172:: 8148:. 8109:. 8105:: 8097:: 8070:. 8041:. 8014:. 8002:: 7994:: 7967:. 7963:: 7955:: 7928:. 7876:. 7842:. 7775:. 7773:. 7769:: 7761:: 7672:. 7635:. 7598:. 7578:: 7555:. 7541:: 7533:: 7527:5 7506:. 7492:: 7484:: 7457:. 7437:: 7429:: 7385:: 7377:: 7350:. 7338:: 7330:: 7324:4 7307:. 7295:: 7287:: 7277:: 7271:6 7254:. 7242:: 7236:2 7219:. 7207:: 7199:: 7189:: 7163:. 7151:: 7143:: 7137:4 7120:. 7116:: 7108:: 7082:. 7012:) 6993:8 6987:D 6983:N 6977:( 6972:+ 6969:1 6960:+ 6954:= 6951:) 6946:D 6942:N 6938:( 6933:p 6899:) 6880:8 6874:A 6870:N 6864:( 6859:+ 6856:1 6847:+ 6841:= 6838:) 6833:A 6829:N 6825:( 6820:n 6783:) 6758:A 6754:N 6748:( 6743:+ 6740:1 6731:+ 6725:= 6722:) 6717:A 6713:N 6709:( 6704:p 6670:) 6645:D 6641:N 6635:( 6630:+ 6627:1 6618:+ 6612:= 6609:) 6604:D 6600:N 6596:( 6591:n 6566:N 6561:A 6559:N 6554:D 6552:N 6548:N 6524:) 6513:N 6509:N 6504:( 6499:+ 6496:1 6490:1 6480:+ 6475:o 6467:= 6438:3 6430:m 6427:c 6347:h 6320:e 6275:) 6270:h 6262:+ 6257:e 6249:( 6243:= 6176:G 6157:) 6151:2 6146:2 6141:S 6138:D 6134:V 6123:S 6120:D 6116:V 6112:) 6107:h 6104:t 6100:V 6091:S 6088:G 6084:V 6080:( 6076:( 6070:L 6067:W 6060:i 6056:C 6049:= 6044:D 6040:I 6019:. 6012:i 6008:C 6004:1 5995:S 5992:D 5988:V 5984:1 5977:W 5974:L 5963:m 5959:= 5943:m 5927:S 5924:G 5920:V 5911:D 5907:I 5877:V 5863:. 5858:2 5854:) 5848:h 5845:t 5841:V 5832:S 5829:G 5825:V 5821:( 5816:L 5813:W 5806:2 5800:i 5796:C 5786:= 5781:D 5777:I 5765:i 5761:C 5757:W 5753:L 5735:i 5731:C 5727:1 5720:W 5716:L 5713:2 5705:2 5696:m 5692:= 5676:m 5672:D 5640:. 5620:p 5617:σ 5613:n 5610:σ 5606:B 5602:I 5598:t 5591:V 5572:B 5569:I 5564:t 5559:p 5556:H 5552:V 5546:p 5535:= 5530:p 5496:B 5493:I 5488:t 5483:n 5480:H 5476:V 5470:n 5456:= 5444:n 5441:H 5437:R 5431:n 5420:= 5409:) 5402:q 5399:n 5395:1 5386:( 5380:n 5371:) 5367:q 5364:n 5357:( 5353:= 5344:n 5310:B 5307:I 5302:t 5297:p 5294:H 5290:V 5283:= 5277:q 5274:p 5270:1 5265:= 5260:p 5257:H 5253:R 5227:B 5224:I 5219:t 5214:n 5211:H 5207:V 5200:= 5194:q 5191:n 5187:1 5179:= 5174:n 5171:H 5167:R 5145:W 5140:H 5136:V 5130:= 5125:y 5095:q 5092:n 5088:1 5080:= 5075:n 5072:H 5068:R 5054:R 5035:W 5032:t 5027:B 5024:I 5019:n 5016:H 5012:R 5005:+ 5002:= 4996:W 4993:t 4990:q 4987:n 4982:B 4979:I 4970:= 4965:y 4947:y 4943:ξ 4938:x 4934:v 4920:W 4917:t 4912:x 4908:v 4904:n 4901:q 4895:= 4892:I 4882:I 4872:y 4868:y 4850:z 4846:B 4840:x 4836:v 4832:= 4827:y 4801:0 4798:= 4793:z 4789:B 4783:x 4779:v 4775:q 4772:+ 4767:y 4759:q 4732:0 4729:= 4726:] 4721:z 4716:B 4706:n 4701:v 4696:[ 4693:) 4690:q 4684:( 4681:+ 4676:y 4668:) 4665:q 4659:( 4656:= 4651:y 4646:F 4632:y 4612:) 4607:z 4602:B 4592:p 4587:v 4582:( 4579:q 4576:+ 4573:= 4568:p 4565:H 4560:F 4536:) 4531:z 4526:B 4516:n 4511:v 4506:( 4503:q 4497:= 4492:n 4489:H 4484:F 4469:q 4458:p 4454:n 4449:H 4447:V 4438:H 4436:V 4427:y 4425:ξ 4417:y 4413:p 4409:n 4405:z 4397:x 4341:d 4319:0 4315:T 4292:0 4264:) 4258:) 4255:1 4252:+ 4249:d 4246:( 4242:/ 4238:1 4230:] 4225:T 4220:0 4216:T 4210:[ 4201:( 4189:0 4181:= 4134:0 4130:P 4106:) 4099:T 4094:B 4090:k 4082:j 4079:i 4075:E 4060:j 4057:i 4053:r 4046:2 4039:( 4027:0 4023:P 4019:= 4014:j 4011:i 4007:P 3982:j 3979:i 3975:E 3949:j 3946:i 3942:r 3921:j 3901:i 3879:j 3876:i 3872:P 3830:T 3808:B 3804:k 3781:A 3777:E 3754:0 3726:) 3719:T 3714:B 3710:k 3703:A 3699:E 3689:( 3677:0 3669:= 3626:C 3622:E 3578:. 3564:C 3560:E 3510:2 3506:/ 3502:3 3498:T 3460:2 3456:/ 3452:3 3445:T 3436:h 3433:p 3402:v 3373:4 3361:v 3330:T 3307:T 3295:v 3266:v 3215:v 3200:1 3185:T 3181:T 3104:τ 3090:. 3084:+ 3076:s 3073:t 3070:c 3067:e 3064:f 3061:e 3058:d 3049:1 3044:+ 3036:e 3033:c 3030:i 3027:t 3024:t 3021:a 3018:l 3009:1 3004:+ 2996:s 2993:e 2990:i 2987:t 2984:i 2981:r 2978:u 2975:p 2972:m 2969:i 2960:1 2955:= 2947:1 2925:. 2919:+ 2911:s 2908:t 2905:c 2902:e 2899:f 2896:e 2893:d 2884:1 2879:+ 2871:e 2868:c 2865:i 2862:t 2859:t 2856:a 2853:l 2844:1 2839:+ 2831:s 2828:e 2825:i 2822:t 2819:i 2816:r 2813:u 2810:p 2807:m 2804:i 2795:1 2790:= 2782:1 2757:e 2754:c 2751:i 2748:t 2745:t 2742:a 2739:l 2710:s 2707:e 2704:i 2701:t 2698:i 2695:r 2692:u 2689:p 2686:m 2683:i 2667:μ 2653:. 2645:e 2642:c 2639:i 2636:t 2633:t 2630:a 2627:l 2618:1 2613:+ 2605:s 2602:e 2599:i 2596:t 2593:i 2590:r 2587:u 2584:p 2581:m 2578:i 2569:1 2564:= 2556:1 2529:m 2521:τ 2512:m 2504:q 2472:m 2468:q 2463:= 2356:q 2348:k 2293:v 2286:v 2279:E 2272:ω 2240:2 2234:2 2225:v 2215:m 2180:v 2173:v 2159:μ 2155:μ 2151:E 2146:d 2142:v 2095:2 1993:( 1947:F 1944:E 1925:e 1919:F 1915:E 1909:e 1898:= 1893:e 1889:D 1873:e 1864:T 1855:B 1852:k 1833:e 1829:T 1823:B 1818:k 1812:e 1801:= 1796:e 1792:D 1763:n 1744:e 1741:D 1735:F 1718:n 1710:e 1706:D 1699:= 1696:F 1665:) 1660:h 1652:p 1649:+ 1644:e 1636:n 1633:( 1630:e 1627:= 1602:h 1594:p 1591:e 1588:+ 1583:e 1575:n 1572:e 1569:= 1526:E 1520:= 1517:J 1493:E 1490:) 1485:h 1477:p 1474:e 1471:+ 1466:e 1458:n 1455:e 1452:( 1449:= 1444:h 1440:J 1436:+ 1431:e 1427:J 1423:= 1420:J 1393:E 1390:) 1385:h 1377:p 1374:e 1371:+ 1366:e 1358:n 1355:e 1352:( 1349:= 1344:h 1340:J 1336:+ 1331:e 1327:J 1323:= 1320:J 1295:h 1270:E 1265:h 1257:p 1254:e 1251:= 1246:h 1242:J 1221:E 1216:e 1208:n 1205:e 1202:= 1197:e 1193:J 1170:d 1166:v 1143:d 1139:v 1135:n 1132:e 1126:= 1121:A 1116:n 1112:I 1106:= 1101:e 1097:J 1074:d 1070:v 1066:e 1025:h 1021:m 1014:c 1006:e 1000:= 995:h 970:, 967:E 962:h 954:= 949:d 945:v 913:e 909:m 902:c 894:e 888:= 883:e 858:, 855:E 850:e 839:= 834:d 830:v 801:c 776:, 773:E 761:e 757:m 750:c 742:e 733:= 728:c 720:a 717:= 712:d 708:v 676:e 672:m 667:E 664:e 655:= 652:a 613:e 609:m 596:F 590:a 566:e 562:m 557:/ 553:F 550:= 547:a 521:s 519:⋅ 517:V 513:m 509:m 507:/ 505:V 480:. 477:E 472:h 464:= 459:d 455:v 440:e 437:μ 422:d 420:v 406:E 389:. 386:E 381:e 373:= 368:d 364:v 273:) 267:( 262:) 258:( 254:. 240:. 182:s 180:⋅ 178:V 174:m 166:s 164:⋅ 162:V 142:. 139:E 133:= 128:d 124:v 113:μ 97:d 93:v 78:E 23:.

Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.

Index