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J. Semicond. > 2021, Volume 42 > Issue 5 > 052001

ARTICLES

A crossover from Efros–Shklovskii hopping to activated transport in a GaAs two-dimensional hole system at low temperatures

S. Dlimi1, , A. El kaaouachi1, 2, L. Limouny1 and B. A. Hammou2

+ Author Affiliations

 Corresponding author: S. Dlimi, dlimi1975@gmail.com

DOI: 10.1088/1674-4926/42/5/052001

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Abstract: In this paper, we discuss low-temperature hopping-conductivity behavior in the insulating phase, in the absence of a magnetic field. We conduct a theoretical study of the crossover from hopping to activated transport in a GaAs two-dimensional hole system at low temperatures, finding that a crossover takes place from the Efros-Shklovskii variable-range hopping (VRH) regime to an activated regime in this system. This conductivity behavior in p-GaAs quantum wells is qualitatively consistent with the laws laid down in theories of localized electron interactions. Given sufficiently strong interactions, the holes in the localized states are able to hop collectively.

Key words: quantum wells2D GaAs heterostructuestransport propertiesvariable range hopping

At low temperatures, electrical transport in two-dimensional (2D) disordered systems, for which energy states are generally located near the Fermi level, is dominated by the variable-range hopping (VRH) transport mechanism, where the density of N(E) states is assumed to be constant near the Fermi level[1-6]. Based on this mechanism, several studies have confirmed the existence of a Coulomb pseudo-gap in 2D systems, where the density of the N(E) states is linear in the vicinity of the Fermi level, EF, and vanishes at E = EF (N (E) =A(E EF))[7]. This theoretical formalism has been experimentally verified by other researchers[8].

When the temperature is sufficiently low, Mott demonstrated that the resistance between two close neighbors is no higher than the lowest resistance, but that it is necessary to take into account remoter neighbors[9]. In the insulating phase, transport can be activated by a similarity in temperature between localized states which are spatially distant but close in terms of energy.

In two dimensions, conductivity can be described by the following equation[1, 2, 10-12]:

σ(T)σ0exp[(T0/T)p], (1)

where σ0 is the pre-factor, T0 is the charactersitic temperature, p = 1/3 for 2D Mott VRH, p = 1/2 for Efros–Shklovskii (E–S) VRH, and p = 1 for the activated regime.

The pre-exponential factor, σ0, can be either temperature independent[13] or temperature dependent[14, 15], based on the type of scattering[16] and the interaction mechanism.

In this paper, we present the behavior of hopping conductivity in a strongly localized state, where the metal–insulator transition (MIT) is approached from the insulating side.

The experimental data which we theoretically analyzed was obtained from a 2D hole gas in GaAs by Hamilton and co-workers[17]. The samples had a peak mobility of µ = 2.5 × 105 cm2V–1s–1

Fig. 1, shows a plot of conductivity dependence on temperature for carrier densities, np, ranging from 3.2 × 1010 to 4.4 × 1010 cm–2.

Figure  1.  Adjustment of conductivity dependence of temperature for 2D p-GaAs system sample for different carrier densities.

The conductivity on the insulating side of the MIT (where dσ/dT > 0 ) varies according to the law represented by Eq. (1), and cannot be interpreted within the transport framework of localized independent electrons.

The theory of transport between localized states via VRH gives precise predictions concerning expected temperature dependencies. These theories provide for a temperature-dependent pre-factor according to the power law σ0 Tm. However, as this dependence is weaker than the exponential law, one might seek to adjust the conductivity curves as a function of temperature for densities np < nc = 4.6 × 1010 cm–2, using Eq. (1).

The most important parameter of this law is the exponent p, which permits the determination of carrier transport mechanisms. Here, we assumed an independent temperature pre-factor, and adjusted the curves, σ(T), based on Eq. (1), with σ0, T0, and p as parameters.

In Fig. 2, we have plotted ln(σ) as a function of T−1/2, T−1/3, and T–1 for different densities. Here, we observe that the data are a close fit for E–S VRH (p = 1/2), Mott VRH (p = 1/3), and activated hopping (p = 1) at temperatures below a critical temperature (Tc = 0.27 K); however, we were not able to determine the best exponent, due to the small range of conductivities under examination. To make an exact determination of the dominant transport-regime type in this investigation, we used the resistance-curve derivative-analysis method, (RCDA)[11, 18, 19].

Figure  2.  ln(σ) as (a) T–1/2, (b) T–1/3 and (c) T–1 of the sample and linear fits where the prefactor σ0 is independent on temperature.

Using Eq. (1), we can define the logarithmic derivative W, as follows:

W=dlnσdlnT=p(T0T)p. (2)

This expression can be written in the following form:

lnW=A+plnT. (3)

We can then determine the values of the exponent p from the slope:

p=dlnWdlnT. (4)

The results are shown in Figs. 3 and 4. This approach leads to an exponent, p, which varies with density. Fig. 5 summarizes the exponent p obtained at various densities. The standard error for the exponent p is indicated by the error bars in Fig. 5.

Figure  3.  Function lnW versus lnT for various densities.
Figure  4.  lnW as a function lnT and linear fits for both cases: T < Tc and T > Tc.
Figure  5.  The exponent p as a function of carrier densities.

At temperatures T < Tc, the average value of the exponent p was found to be 0.52 ± 0.08, which is close to the theoretical value p = 1/2. Therefore, E–S VRH is the dominant hopping regime in the sample studied in this paper. However, the value of the exponent p at temperatures T > Tc, was found to be equal to 1.23 ± 0.12. This result is consistent with the theoretical value p = 1, which is characteristic of the activated regime. We therefore confirm that there is a crossover from E–S VRH to hopping, which is activated by a change of temperature.

The activated behavior can be interpreted as the opening of a "hard" gap at the Fermi level, EF, due to a Coulomb interaction, as suggested by Kim et al.[20]. In particular, this gap can characterize the formation of a Wigner crystal type of ordered electronic phase, for which a simple activated law can be expected to apply[21]. In Fig. 6, the activation energy, KBT0, and the characteristic temperatures (TES and TMott) decrease linearly at low temperatures when the density increases, and tend towards zero at a density of npc = 4.5 × 1010 cm–2.

Figure  6.  (a) Activation energy versus np in the insulating phase. (b) Characteristic temperature for case of Efros-Shklovskii and Mott hopping.

The activated law can also be ascribed to transport in a percolating system: when a system consists of metal islands separated by insulating zones, the transport of carriers occurs by activated hopping from one island to another. This type of analysis has already been performed in the context of transitions in the quantum Hall-effect regime[22, 23], which is now recognized to have percolation transitions[24, 25]. The percolation model gives a good description of the disorder, but it neglects interactions, which play an essential role in electronic transport. In fact, electron–electron interactions are important in 2D-semiconductor systems, since they can form new phases, such as Wigner crystals, Mott insulators, and excitonic insulators[26, 27].

When we take into account the correlated hopping between several electrons, the result is a decrease in activation energy, as is the case here. The authors of Refs. [14, 28] have shown that the electrons in n-GaAs heterostructures hop collectively, but that the correlations between electrons do not modify the density of states (DOS) calculated for independent electrons (in other words, the DOS remains linear).

With regard to the pre-factor, we obtained values of the pre-factor σ0 1.01 e2/h (For p = 1), which is very close to the universal value e2/h found in Refs. [2931]. The universal character of the pre-factor in the non-screened regime seems to be due to the interactions between holes, which allows us to envisage a hopping mechanism generated by the interactions between holes. The E–S pre-factor σES was found to be between 1.23 and 2.16 e2/h; however, the Mott pre-factor was found to be equal to σMott 2.8 e2/h, and independent of both temperature and density. These observations are incompatible with a mechanism where hopping is generated by an electron–phonon interaction, for which a dependence in temperature and density could be expected, and therefore these observations are attributed to a different hopping mechanism, related to the interactions between carriers.

For disordered electronic systems at low temperatures, the interaction parameter rs, defined by rs=me24π2επnp, is high, the electron–electron collision time is much lower than the electron–phonon collision time, and the hopping mechanism is assisted by electron–electron interactions. In this case, the energy required to make a hop does not come from phonons, but emanates instead from another electron, coupled to the electron making the hop.

Our theoretical investigation of the 2D p-GaAs system shows the existence of a crossover from the Efros–Shklovskii variable-range hopping regime (E–S VRH), where a soft gap is created (because the state density is only canceled at a single point, and not at an energy interval), to the activated regime, where a “hard” gap opens at the Fermi level, EF, due to a Coulomb interaction.

At lower carrier densities, conductivity dependencies support a law that is simply activated at low temperatures, and which is not supported by localization theories relating to independent electrons. These characteristics are typical of transport in a collective disordered hung phase, but can also be interpreted in the context of a percolating system.

We are grateful to Professor A. R. Hamilton for allowing us to use the experimental results from his dilute 2D GaAs hole system sample.



[1]
Mott N F. Conduction in glasses containing transition metal ions. J Non-Cryst Solids, 1968, 1, 1 doi: 10.1016/0022-3093(68)90002-1
[2]
Ferrus T, George R, Barnes C W, et al. Activation mechanisms in sodium-doped silicon MOSFETs. J Phys: Condens Matter, 2007, 19, 226216 doi: 10.1088/0953-8984/19/22/226216
[3]
Arshad M, Abushad M, Husain S, et al. Investigation of structural, optical and electrical transport properties of yttrium doped La0.7Ca0.3MnO3 perovskites. Electron Mater Lett, 2020, 16, 321 doi: 10.1007/s13391-020-00216-1
[4]
Dhankhar S, Kundu R S, Rani S, et al. Zinc chloride modified electronic transport and relaxation studies in barium-tellurite glasses. Electron Mater Lett, 2017, 13, 412 doi: 10.1007/s13391-017-6138-1
[5]
Bourim E M, Han J I. Electrical characterization and thermal admittance spectroscopy analysis of InGaN/GaN MQW blue LED structure. Electron Mater Lett, 2015, 11, 982 doi: 10.1007/s13391-015-5180-0
[6]
Dlimi S, Limouny L, Hemine J, et al. Efros–Shklovskii hopping in the electronic transport in 2D p-GaAs. Lith J Phys, 2020, 60, 167 doi: 10.3952/physics.v60i3.4303
[7]
Abrahams E, Anderson P W, Licciardello D C, et al. Scaling theory of localization: Absence of quantum diffusion in two dimensions. Phys Rev Lett, 1979, 42, 673 doi: 10.1103/PhysRevLett.42.673
[8]
Efros A L, Shklovskii B I. Coulomb gap and low temperature conductivity of disordered systems. J Phys C, 1975, 8, L49 doi: 10.1088/0022-3719/8/4/003
[9]
Ono Y, Morizur J F, Nishiguchi K, et al. Impurity conduction in phosphorus-doped buried-channel silicon-on-insulator field-effect transistors at temperatures between 10 and 295 K. Phys Rev B, 2006, 74, 235317 doi: 10.1103/PhysRevB.74.235317
[10]
Liu H, Pourret A, Guyot-Sionnest P. Mott and Efros-Shklovskii variable range hopping in CdSe quantum dots films. ACS Nano, 2010, 4, 5211 doi: 10.1021/nn101376u
[11]
Narjis A, El kaaouachi A, Limouny L, et al. Study of insulating electrical conductivity in hydrogenated amorphous silicon-nickel alloys at very low temperature. Physica B, 2011, 406, 4155 doi: 10.1016/j.physb.2011.08.021
[12]
Narjis A, Biskupski G, Daoudi E, et al. Low temperature electrical resistivity of polycrystalline La0.67Sr0.33MnO3 thin films. Mater Sci Semicond Process, 2013, 16, 1257 doi: 10.1016/j.mssp.2013.01.004
[13]
Shklovskii B I, Efros A L. Percolation theory. In: Electronic Properties of Doped Semiconductors. Berlin, Heidelberg: Springer Berlin Heidelberg, 1984, 94
[14]
van Keuls F W, Hu X L, Jiang H W, et al. Screening of the Coulomb interaction in two-dimensional variable-range hopping. Phys Rev B, 1997, 56, 1161 doi: 10.1103/PhysRevB.56.1161
[15]
Dlimi S, El Kaaouachi A, Narjis A, et al. Evidence for the correlated hopping mechanism in p-GaAs near the 2D MIT at B = 0 T. J Optoelectron Adv Mater, 2013, 15, 1222
[16]
Briggs A, Guldner Y, Vieren J P, et al. Low-temperature investigations of the quantum Hall effect in InxGa1– xAs–InP heterojunctions. Phys Rev B, 1983, 27, 6549 doi: 10.1103/PhysRevB.27.6549
[17]
Hamilton A R, Simmons M Y, Pepper M, et al. Localisation and the metal-insulator transition in two dimensions. Physica B, 2001, 296, 21 doi: 10.1016/S0921-4526(00)00773-0
[18]
Minkov G M, Germanenko A V, Gornyi I V. Magnetoresistance and dephasing in a two-dimensional electron gas at intermediate conductances. Phys Rev B, 2004, 70, 245423 doi: 10.1103/PhysRevB.70.245423
[19]
Lee Y C, Liu C I, Yang Y F, et al. Crossover from Efros-Shklovskii to Mott variable range hopping in monolayer epitaxial graphene grown on SiC. Chin J Phys, 2017, 55, 1235 doi: 10.1016/j.cjph.2017.06.007
[20]
Kim J J, Lee H J. Observation of a nonmagnetic hard gap in amorphous In/InO x films in the hopping regime. Phys Rev Lett, 1993, 70, 2798 doi: 10.1103/PhysRevLett.70.2798
[21]
Chauve P, Giamarchi T, Le Doussal P. Creep and depinning in disordered media. Phys Rev B, 2000, 62, 6241 doi: 10.1103/PhysRevB.62.6241
[22]
Shashkin A A, Dolgopolov V T, Kravchenko G V, et al. Percolation metal-insulator transitions in the two-dimensional electron system of AlGaAs/GaAs heterostructures. Phys Rev Lett, 1994, 73, 3141 doi: 10.1103/PhysRevLett.73.3141
[23]
Arapov Y G, Gudina S V, Klepikova A S, et al. Quantum Hall plateau-plateau transitions in n-InGaAs/GaAs heterostructures before and after IR illumination. Low Temp Phys, 2015, 41, 106 doi: 10.1063/1.4908192
[24]
Das Sarma S, Lilly M P, Hwang E H, et al. Two-dimensional metal-insulator transition as a percolation transition in a high-mobility electron system. Phys Rev Lett, 2005, 94, 136401 doi: 10.1103/PhysRevLett.94.136401
[25]
Dlimi S, El kaaouachi A, Narjis A. Density inhomogeneity driven metal-insulator transition in 2D p-GaAs. Phys E, 2013, 54, 181 doi: 10.1016/j.physe.2013.07.001
[26]
van Keuls F W, Hu X L, Dahm A J, et al. The Coulomb gap and the transition to Mott hopping. Surf Sci, 1996, 361/362, 945 doi: 10.1016/0039-6028(96)00570-5
[27]
Du L J, Li X W, Lou W K, et al. Evidence for a topological excitonic insulator in InAs/GaSb bilayers. Nat Commun, 2017, 8, 1971 doi: 10.1038/s41467-017-01988-1
[28]
Jiang Z Y, Lou W K, Liu Y, et al. Spin-triplet excitonic insulator: The case of semihydrogenated graphene. Phys Rev Lett, 2020, 124, 166401 doi: 10.1103/PhysRevLett.124.166401
[29]
Mason W, Kravchenko S V, Bowker G E, et al. Experimental evidence for a Coulomb gap in two dimensions. Phys Rev B, 1995, 52, 7857 doi: 10.1103/PhysRevB.52.7857
[30]
Dlimi S, El kaaouachi A, Narjis A, et al. Hopping energy and percolation-type transport in p-GaAs low densities near the 2D metal-insulator transition at zero magnetic field. J Phys Chem Solids, 2013, 74, 1349 doi: 10.1016/j.jpcs.2013.05.004
[31]
Khondaker S I, Shlimak I S, Nicholls J T, et al. Two-dimensional hopping conductivity in a δ-doped GaAs/AlxGa1– xAs heterostructure. Phys Rev B, 1999, 59, 4580 doi: 10.1103/PhysRevB.59.4580
Fig. 1.  Adjustment of conductivity dependence of temperature for 2D p-GaAs system sample for different carrier densities.

Fig. 2.  ln(σ) as (a) T–1/2, (b) T–1/3 and (c) T–1 of the sample and linear fits where the prefactor σ0 is independent on temperature.

Fig. 3.  Function lnW versus lnT for various densities.

Fig. 4.  lnW as a function lnT and linear fits for both cases: T < Tc and T > Tc.

Fig. 5.  The exponent p as a function of carrier densities.

Fig. 6.  (a) Activation energy versus np in the insulating phase. (b) Characteristic temperature for case of Efros-Shklovskii and Mott hopping.

[1]
Mott N F. Conduction in glasses containing transition metal ions. J Non-Cryst Solids, 1968, 1, 1 doi: 10.1016/0022-3093(68)90002-1
[2]
Ferrus T, George R, Barnes C W, et al. Activation mechanisms in sodium-doped silicon MOSFETs. J Phys: Condens Matter, 2007, 19, 226216 doi: 10.1088/0953-8984/19/22/226216
[3]
Arshad M, Abushad M, Husain S, et al. Investigation of structural, optical and electrical transport properties of yttrium doped La0.7Ca0.3MnO3 perovskites. Electron Mater Lett, 2020, 16, 321 doi: 10.1007/s13391-020-00216-1
[4]
Dhankhar S, Kundu R S, Rani S, et al. Zinc chloride modified electronic transport and relaxation studies in barium-tellurite glasses. Electron Mater Lett, 2017, 13, 412 doi: 10.1007/s13391-017-6138-1
[5]
Bourim E M, Han J I. Electrical characterization and thermal admittance spectroscopy analysis of InGaN/GaN MQW blue LED structure. Electron Mater Lett, 2015, 11, 982 doi: 10.1007/s13391-015-5180-0
[6]
Dlimi S, Limouny L, Hemine J, et al. Efros–Shklovskii hopping in the electronic transport in 2D p-GaAs. Lith J Phys, 2020, 60, 167 doi: 10.3952/physics.v60i3.4303
[7]
Abrahams E, Anderson P W, Licciardello D C, et al. Scaling theory of localization: Absence of quantum diffusion in two dimensions. Phys Rev Lett, 1979, 42, 673 doi: 10.1103/PhysRevLett.42.673
[8]
Efros A L, Shklovskii B I. Coulomb gap and low temperature conductivity of disordered systems. J Phys C, 1975, 8, L49 doi: 10.1088/0022-3719/8/4/003
[9]
Ono Y, Morizur J F, Nishiguchi K, et al. Impurity conduction in phosphorus-doped buried-channel silicon-on-insulator field-effect transistors at temperatures between 10 and 295 K. Phys Rev B, 2006, 74, 235317 doi: 10.1103/PhysRevB.74.235317
[10]
Liu H, Pourret A, Guyot-Sionnest P. Mott and Efros-Shklovskii variable range hopping in CdSe quantum dots films. ACS Nano, 2010, 4, 5211 doi: 10.1021/nn101376u
[11]
Narjis A, El kaaouachi A, Limouny L, et al. Study of insulating electrical conductivity in hydrogenated amorphous silicon-nickel alloys at very low temperature. Physica B, 2011, 406, 4155 doi: 10.1016/j.physb.2011.08.021
[12]
Narjis A, Biskupski G, Daoudi E, et al. Low temperature electrical resistivity of polycrystalline La0.67Sr0.33MnO3 thin films. Mater Sci Semicond Process, 2013, 16, 1257 doi: 10.1016/j.mssp.2013.01.004
[13]
Shklovskii B I, Efros A L. Percolation theory. In: Electronic Properties of Doped Semiconductors. Berlin, Heidelberg: Springer Berlin Heidelberg, 1984, 94
[14]
van Keuls F W, Hu X L, Jiang H W, et al. Screening of the Coulomb interaction in two-dimensional variable-range hopping. Phys Rev B, 1997, 56, 1161 doi: 10.1103/PhysRevB.56.1161
[15]
Dlimi S, El Kaaouachi A, Narjis A, et al. Evidence for the correlated hopping mechanism in p-GaAs near the 2D MIT at B = 0 T. J Optoelectron Adv Mater, 2013, 15, 1222
[16]
Briggs A, Guldner Y, Vieren J P, et al. Low-temperature investigations of the quantum Hall effect in InxGa1– xAs–InP heterojunctions. Phys Rev B, 1983, 27, 6549 doi: 10.1103/PhysRevB.27.6549
[17]
Hamilton A R, Simmons M Y, Pepper M, et al. Localisation and the metal-insulator transition in two dimensions. Physica B, 2001, 296, 21 doi: 10.1016/S0921-4526(00)00773-0
[18]
Minkov G M, Germanenko A V, Gornyi I V. Magnetoresistance and dephasing in a two-dimensional electron gas at intermediate conductances. Phys Rev B, 2004, 70, 245423 doi: 10.1103/PhysRevB.70.245423
[19]
Lee Y C, Liu C I, Yang Y F, et al. Crossover from Efros-Shklovskii to Mott variable range hopping in monolayer epitaxial graphene grown on SiC. Chin J Phys, 2017, 55, 1235 doi: 10.1016/j.cjph.2017.06.007
[20]
Kim J J, Lee H J. Observation of a nonmagnetic hard gap in amorphous In/InO x films in the hopping regime. Phys Rev Lett, 1993, 70, 2798 doi: 10.1103/PhysRevLett.70.2798
[21]
Chauve P, Giamarchi T, Le Doussal P. Creep and depinning in disordered media. Phys Rev B, 2000, 62, 6241 doi: 10.1103/PhysRevB.62.6241
[22]
Shashkin A A, Dolgopolov V T, Kravchenko G V, et al. Percolation metal-insulator transitions in the two-dimensional electron system of AlGaAs/GaAs heterostructures. Phys Rev Lett, 1994, 73, 3141 doi: 10.1103/PhysRevLett.73.3141
[23]
Arapov Y G, Gudina S V, Klepikova A S, et al. Quantum Hall plateau-plateau transitions in n-InGaAs/GaAs heterostructures before and after IR illumination. Low Temp Phys, 2015, 41, 106 doi: 10.1063/1.4908192
[24]
Das Sarma S, Lilly M P, Hwang E H, et al. Two-dimensional metal-insulator transition as a percolation transition in a high-mobility electron system. Phys Rev Lett, 2005, 94, 136401 doi: 10.1103/PhysRevLett.94.136401
[25]
Dlimi S, El kaaouachi A, Narjis A. Density inhomogeneity driven metal-insulator transition in 2D p-GaAs. Phys E, 2013, 54, 181 doi: 10.1016/j.physe.2013.07.001
[26]
van Keuls F W, Hu X L, Dahm A J, et al. The Coulomb gap and the transition to Mott hopping. Surf Sci, 1996, 361/362, 945 doi: 10.1016/0039-6028(96)00570-5
[27]
Du L J, Li X W, Lou W K, et al. Evidence for a topological excitonic insulator in InAs/GaSb bilayers. Nat Commun, 2017, 8, 1971 doi: 10.1038/s41467-017-01988-1
[28]
Jiang Z Y, Lou W K, Liu Y, et al. Spin-triplet excitonic insulator: The case of semihydrogenated graphene. Phys Rev Lett, 2020, 124, 166401 doi: 10.1103/PhysRevLett.124.166401
[29]
Mason W, Kravchenko S V, Bowker G E, et al. Experimental evidence for a Coulomb gap in two dimensions. Phys Rev B, 1995, 52, 7857 doi: 10.1103/PhysRevB.52.7857
[30]
Dlimi S, El kaaouachi A, Narjis A, et al. Hopping energy and percolation-type transport in p-GaAs low densities near the 2D metal-insulator transition at zero magnetic field. J Phys Chem Solids, 2013, 74, 1349 doi: 10.1016/j.jpcs.2013.05.004
[31]
Khondaker S I, Shlimak I S, Nicholls J T, et al. Two-dimensional hopping conductivity in a δ-doped GaAs/AlxGa1– xAs heterostructure. Phys Rev B, 1999, 59, 4580 doi: 10.1103/PhysRevB.59.4580
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    S. Dlimi, A. El kaaouachi, L. Limouny, B. A. Hammou. A crossover from Efros–Shklovskii hopping to activated transport in a GaAs two-dimensional hole system at low temperatures[J]. Journal of Semiconductors, 2021, 42(5): 052001. doi: 10.1088/1674-4926/42/5/052001
    S Dlimi, A El kaaouachi, L Limouny, B A Hammou, A crossover from Efros–Shklovskii hopping to activated transport in a GaAs two-dimensional hole system at low temperatures[J]. J. Semicond., 2021, 42(5): 052001. doi: 10.1088/1674-4926/42/5/052001.
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    Received: 01 September 2020 Revised: 16 September 2020 Online: Accepted Manuscript: 22 October 2020Uncorrected proof: 26 October 2020Published: 01 May 2021

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      S. Dlimi, A. El kaaouachi, L. Limouny, B. A. Hammou. A crossover from Efros–Shklovskii hopping to activated transport in a GaAs two-dimensional hole system at low temperatures[J]. Journal of Semiconductors, 2021, 42(5): 052001. doi: 10.1088/1674-4926/42/5/052001 ****S Dlimi, A El kaaouachi, L Limouny, B A Hammou, A crossover from Efros–Shklovskii hopping to activated transport in a GaAs two-dimensional hole system at low temperatures[J]. J. Semicond., 2021, 42(5): 052001. doi: 10.1088/1674-4926/42/5/052001.
      Citation:
      S. Dlimi, A. El kaaouachi, L. Limouny, B. A. Hammou. A crossover from Efros–Shklovskii hopping to activated transport in a GaAs two-dimensional hole system at low temperatures[J]. Journal of Semiconductors, 2021, 42(5): 052001. doi: 10.1088/1674-4926/42/5/052001 ****
      S Dlimi, A El kaaouachi, L Limouny, B A Hammou, A crossover from Efros–Shklovskii hopping to activated transport in a GaAs two-dimensional hole system at low temperatures[J]. J. Semicond., 2021, 42(5): 052001. doi: 10.1088/1674-4926/42/5/052001.

      A crossover from Efros–Shklovskii hopping to activated transport in a GaAs two-dimensional hole system at low temperatures

      DOI: 10.1088/1674-4926/42/5/052001
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      • S. Dlimi:got his Master degree in 2009 and his PhD in 2017 at Ibn Zohr University. His researches focus in condensed matter physics, electronics, optoelectronics, photonics and renewable energies. His current project is 'semiconductors' and 'modeling of photovoltaic cells'
      • Corresponding author: dlimi1975@gmail.com
      • Received Date: 2020-09-01
      • Revised Date: 2020-09-16
      • Published Date: 2021-05-10

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