### Abstract

We have measured the temperature- and field-dependent longitudinal conductivity, σ_{xx}, in the Landau level tails of two modulation-doped Si/Si_{1-x}Ge_{x} two-dimensional electron gas samples at temperatures below 1 K. The temperature dependence of σ_{xx} at the minima of the Shubnikov-de Haas oscillations obeyed a relation of the form σ_{xx}
^{min} (T) ∝ (1/T) exp[-(T_{0}T)^{ 1/2 }], in agreement with published models of variable-range hopping between localized states by Ono and by Polyakov and Shklovskii. However, the value and magnetic field dependence of the characteristic temperature, T_{0}, cannot be explained quantitatively on Ono's model, which is based on Gaussian localization of the electron wavefunction on a scale given by the magnetic length. Polyakov and Shklovskii used exponential wavefunctions to derive an alternative expression for the characteristic temperature, and to model the conductivity in the vicinity of the peaks between adjacent quantum Hall plateaux. Our results have been analysed according to this theory, and show good agreement: the magnetic field dependence of the corresponding characteristic temperature, T_{1} (v), obeys the power law relation. T_{1} ∝ (Δv)^{γ}, as expected from theory, while the experimental value of γ, 0.90 ± 0.07, agreed with that determined from a half-width analysis of the σ_{xx} peaks; however, this value differs from the theoretically predicted figure of approx. 2.3.

Original language | English (US) |
---|---|

Pages (from-to) | 762-767 |

Number of pages | 6 |

Journal | Semiconductor Science and Technology |

Volume | 14 |

Issue number | 9 |

DOIs | |

State | Published - Sep 1999 |

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### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Materials Science(all)
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics

### Cite this

_{1-x}Ge

_{x}quantum well structures.

*Semiconductor Science and Technology*,

*14*(9), 762-767. https://doi.org/10.1088/0268-1242/14/9/304

**Variable-range hopping transport in modulation-doped n-channel Si/Si _{1-x}Ge_{x} quantum well structures.** / Shin, D. H.; Becker, C. E.; Harris, J. J.; Fernández, J. M.; Woods, N. J.; Thornton, Trevor; Maude, D. K.; Portal, J. C.

Research output: Contribution to journal › Article

_{1-x}Ge

_{x}quantum well structures',

*Semiconductor Science and Technology*, vol. 14, no. 9, pp. 762-767. https://doi.org/10.1088/0268-1242/14/9/304

_{1-x}Ge

_{x}quantum well structures. Semiconductor Science and Technology. 1999 Sep;14(9):762-767. https://doi.org/10.1088/0268-1242/14/9/304

}

TY - JOUR

T1 - Variable-range hopping transport in modulation-doped n-channel Si/Si1-xGex quantum well structures

AU - Shin, D. H.

AU - Becker, C. E.

AU - Harris, J. J.

AU - Fernández, J. M.

AU - Woods, N. J.

AU - Thornton, Trevor

AU - Maude, D. K.

AU - Portal, J. C.

PY - 1999/9

Y1 - 1999/9

N2 - We have measured the temperature- and field-dependent longitudinal conductivity, σxx, in the Landau level tails of two modulation-doped Si/Si1-xGex two-dimensional electron gas samples at temperatures below 1 K. The temperature dependence of σxx at the minima of the Shubnikov-de Haas oscillations obeyed a relation of the form σxx min (T) ∝ (1/T) exp[-(T0T) 1/2 ], in agreement with published models of variable-range hopping between localized states by Ono and by Polyakov and Shklovskii. However, the value and magnetic field dependence of the characteristic temperature, T0, cannot be explained quantitatively on Ono's model, which is based on Gaussian localization of the electron wavefunction on a scale given by the magnetic length. Polyakov and Shklovskii used exponential wavefunctions to derive an alternative expression for the characteristic temperature, and to model the conductivity in the vicinity of the peaks between adjacent quantum Hall plateaux. Our results have been analysed according to this theory, and show good agreement: the magnetic field dependence of the corresponding characteristic temperature, T1 (v), obeys the power law relation. T1 ∝ (Δv)γ, as expected from theory, while the experimental value of γ, 0.90 ± 0.07, agreed with that determined from a half-width analysis of the σxx peaks; however, this value differs from the theoretically predicted figure of approx. 2.3.

AB - We have measured the temperature- and field-dependent longitudinal conductivity, σxx, in the Landau level tails of two modulation-doped Si/Si1-xGex two-dimensional electron gas samples at temperatures below 1 K. The temperature dependence of σxx at the minima of the Shubnikov-de Haas oscillations obeyed a relation of the form σxx min (T) ∝ (1/T) exp[-(T0T) 1/2 ], in agreement with published models of variable-range hopping between localized states by Ono and by Polyakov and Shklovskii. However, the value and magnetic field dependence of the characteristic temperature, T0, cannot be explained quantitatively on Ono's model, which is based on Gaussian localization of the electron wavefunction on a scale given by the magnetic length. Polyakov and Shklovskii used exponential wavefunctions to derive an alternative expression for the characteristic temperature, and to model the conductivity in the vicinity of the peaks between adjacent quantum Hall plateaux. Our results have been analysed according to this theory, and show good agreement: the magnetic field dependence of the corresponding characteristic temperature, T1 (v), obeys the power law relation. T1 ∝ (Δv)γ, as expected from theory, while the experimental value of γ, 0.90 ± 0.07, agreed with that determined from a half-width analysis of the σxx peaks; however, this value differs from the theoretically predicted figure of approx. 2.3.

UR - http://www.scopus.com/inward/record.url?scp=0033190057&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033190057&partnerID=8YFLogxK

U2 - 10.1088/0268-1242/14/9/304

DO - 10.1088/0268-1242/14/9/304

M3 - Article

AN - SCOPUS:0033190057

VL - 14

SP - 762

EP - 767

JO - Semiconductor Science and Technology

JF - Semiconductor Science and Technology

SN - 0268-1242

IS - 9

ER -