Analysis of Variable-Range Hopping Conductivity in Si : P

Hornung, M.; Iqbal, Mahdi; Waffenschmidt, S.; Löhneysen, H. v.

doi:10.1002/(sici)1521-3951(200003)218:1<75::aid-pssb75>3.0.co;2-z

Cited by 12 publications

(34 citation statements)

References 12 publications

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“…The best scaling is achieved with y = 0.33, or z v = 3.0. With v= 1.1 as obtained from a variablerange hopping analysis of the conductivity in the insulating region [57] one obtains z = 2.75. The value # = x / y = 1.3 agrees fully with that derived from the a(0) extrapolation [52].…”

Section: Metallic Sip: Formation Of Local Magnetic Moments and Kondo supporting

confidence: 49%

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Disorder, electron-electron interactions and the metal-insulator transition in heavily doped Si:P

Löhneysen

2000

Advances in Solid State Physics

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Electron localization in a metal, ultimately leadingto a metalinsulator (MI) transition, can occur because of disorder (Anderson transition) or electron-electron interactions (Mott-Hubbard transition). Both effects play a role in heavily doped semiconductors which have become prototype systems for the study of MI transitions. In this review we focus on phosphorus-doped Si. The statistical distribution of donor atoms on an atomic scale as the origin of random disorder can be checked by scanning tunneling microscopy. Long-range Coulomb interactions lead to AltshulerAronov corrections to the density of states N(EF) at the Fermi level and the electrical conductivity a(T) on the metallic side of the MI transition, and to a soft Coulomb gap at EF and Efros-Shklovskii variable-range hopping on the insulating side. On-site Coulomb interactions, on the other hand, lead to the formation of localized magnetic moments and the Kondo effect on the metallic side, and to a Hubbard splitting of thedonor band on the insulating side. The MI transition in Si:P can be tuned by varying the P concentration or -for barely insulating samples -by application of uniaxial stress S. The continuous stress tuning allows the observation of dynamic scaling of a(T,S) and hence a reliable determination of the critical exponent # of the extrapolated zero-temperature conductivity a(0)~l S -S¢ Iv, i.e. # --1, and of the dynamical exponent z --3. IntroductionThe problem of the metal-insulator (MI) transition in heavily doped semiconductors has come of age. Although these materials have become prototype systems for the study of a MI transition driven by the combined effects of disorder (Anderson transition) and electron-electron interactions (Mott-Hubbard transition), these effects are only beginning to be disentangled experimentally. In a strict sense, the MI transition viewed as a transition from extended to localized states at the Fermi level, occurs only at T = 0 because at finite temperature T thermally activated charge transport may occur. Hence a metal is defined by a finite dc conductivity a(T) for T --~0, while for an insulator a(0) = 0. Zero-point quantum fluctuations become important at a quantum phase transition between these two groundstates [1]. The determination of the critical exponent # describing how a(0) vanishes at T = 0 as a function of a control parameter 5 at a critical value 5c, i.e. a(0)~1 5 -5c I", has been a subject of considerable controversy, as will be discussed below. However, using both carrier concentration N and uniaxial stress S to

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Section: Metallic Sip: Formation Of Local Magnetic Moments and Kondo supporting

confidence: 49%

“…From an analysis of a(T) of Si:P for different P concentrations N we had previously inferred # = 1.3 from a(0) vs. N [52] and F i g u r e 15 Scaling plot of o/ac vs. I N -N~I~NoT~for SliP with different P concentrations N, with Nc = 3.52 • 1018cm-a and y = 0.33 [57], data after Ref. [52].…”

Section: Metallic Sip: Formation Of Local Magnetic Moments and Kondo mentioning

confidence: 99%

Disorder, electron-electron interactions and the metal-insulator transition in heavily doped Si:P

Löhneysen

2000

Advances in Solid State Physics

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“…29. Our DC conductivity results extended to 4.2 K. As indicated in Figure 3 a kink in the curve is clearly evident, which occurs at or somewhat below the lowest temperature indicated in the work from Hornung et al 27 . The change in functional form that we observe is inconsistent with the presence of a hard gap which would result in a single activated process as the conduction mechanism.…”

Section: A DC Conductivitymentioning

confidence: 97%

“…The characteristic Mott temperatures, T 0 , determined for our Si:P samples is of the order 10 7 K, a ridiculously large value. The ES characteristic temperatures, T ′ 0 , deter- mined by fitting the lower temperature data are more reasonable but still extremely large, of the order 10 3 K. Compared to the characteristic Mott and ES temperatures measured by Dai et al 26 and Hornung et al 27 , our values seem extremely high and unphysical, even though their materials were of a different composition, or fell in a different range of dopant concentrations.…”

Section: A DC Conductivitymentioning

confidence: 99%

“…In fact such a prediction that deep in the insulating regime an alternate method of charge transfer should exist is exactly what Hornung et al 27 claim to have observed in their DC conductivity measurements of Si:P. Among other findings, these authors claim that below a majority dopant concentration of 2.78×10 18 cm −3 , (recall that x c = 3.52 × 10 18 cm −3 ) the conductivity was better described by an activation process with an activation energy E 2 which was interpreted as a "hard" Hubbard gap.…”

Section: A DC Conductivitymentioning

confidence: 99%

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Frequency-dependent conductivity of electron glasses

2004

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Results of DC and frequency dependent conductivity in the quantum limit, i.e.hω > kBT , for a broad range of dopant concentrations in nominally uncompensated, crystalline phosphorous doped silicon and amorphous niobium-silicon alloys are reported. These materials fall under the general category of disordered insulating systems, which are referred to as electron glasses. Using microwave resonant cavities and quasi-optical millimeter wave spectroscopy we are able to study the frequency dependent response on the insulating side of the metal-insulator transition. We identify a quantum critical regime, a Fermi glass regime and a Coulomb glass regime. Our phenomenological results lead to a phase diagram description, or taxonomy, of the electrodynamic response of electron glass systems.

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Electron‐electron interactions and the metal‐insulator transition in heavily doped silicon

Löhneysen

2011

Annalen der Physik

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This article is dedicated to Dieter Vollhardt on the occasion of his 60th birthday.The metal-insulator (MI) transition in Si:P can be tuned by varying the P concentration or -for barely insulating samples -by application of uniaxial stress S. On-site Coulomb interactions lead to the formation of localized magnetic moments and the Kondo effect on the metallic side, and to a Hubbard splitting of the donor band on the insulating side. Continuous stress tuning allows the observation of finite-temperature dynamic scaling of σ(T, S) and hence a reliable determination of the critical exponent μ of the extrapolated zero-temperature conductivity σ(0) ∼ |S − Sc| µ , i.e., μ = 1, and of the dynamical exponent z = 3. The issue of half-filling vs. away from half-filling of the donor band (i.e., uncompensated vs. compensated semiconductors) is discussed in detail.

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Analysis of Variable-Range Hopping Conductivity in Si : P

Cited by 12 publications

References 12 publications

Disorder, electron-electron interactions and the metal-insulator transition in heavily doped Si:P

Disorder, electron-electron interactions and the metal-insulator transition in heavily doped Si:P

Frequency-dependent conductivity of electron glasses

Electron‐electron interactions and the metal‐insulator transition in heavily doped silicon

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