Theory of hopping conduction in arrays of doped semiconductor nanocrystals

Skinner, B. F.; Chen, Tianran; Shklovskiǐ, B. I.

doi:10.1103/physrevb.85.205316

Cited by 70 publications

(111 citation statements)

References 23 publications

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“…Therefore, for efficient charge transport the fluctuations of the site energies should be small. Hopping transport becomes dominant at large disorder 23,24 .…”

Section: A Superlattice Systemsmentioning

confidence: 99%

Tunneling of electrons between Si nanocrystals embedded in a SiO2matrix

2012

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Based on ab initio density functional calculations of Si nanocrystals (NCs) in a SiO2 matrix we study the impact of NC size and separation on electronic properties and present consequences for inter-NC carrier transport. The nanocrystal size and separation significantly influence the electronic structure of three-dimensional superlattice systems with different NC filling. The energy levels for large NC distances are broadened to minibands for small separations due to the wave-function overlap. Their formation is described in terms of inter-NC hopping and carrier tunneling. We find that electron transport in conduction minibands is more likely than hole transport.

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“…Therefore, for efficient charge transport the fluctuations of the site energies should be small. Hopping transport becomes dominant at large disorder 23,24 .…”

Section: A Superlattice Systemsmentioning

confidence: 99%

Tunneling of electrons between Si nanocrystals embedded in a SiO2matrix

2012

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“…This effect can be understood as follows [29]. In ES variable range hopping, when an electron tunnels to a distant, non-neighboring NC at a distance x, its tunneling trajectory involves passing through a chain of intermediate NCs, and the decay of the electron wave function is dominated by passage through gaps between neighboring NCs along the chain.…”

Section: Si4 Oxidationmentioning

confidence: 99%

“…To establish a unique chemical potential of electrons (the Fermi level), electrons move from NCs with larger than average n to ones with smaller than average n. Accordingly, most NCs attain net charges ∼ √ N e. This leads to large fluctuations of the Coulomb potential and moves the NC electron energy levels with respect to the Fermi level. In an insulating NC array (n < n c ), this replaces the global charging energy gap of the density of states by the Coulomb gap which leads to the Efros-Shklovskii variable range hopping [29] (see below).…”

Section: Critical Doping Concentration At Mitmentioning

confidence: 99%

Metal–insulator transition in films of doped semiconductor nanocrystals

Chen¹,

Reich²,

Kramer³

et al. 2015

Nature Mater

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109

134

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To fully deploy the potential of semiconductor nanocrystal films as low-cost electronic materials, a better understanding of the amount of dopants required to make their conductivity metallic is needed. In bulk semiconductors, the critical concentration of electrons at the metal-insulator transition is described by the Mott criterion. Here, we theoretically derive the critical concentration nc for films of heavily doped nanocrystals devoid of ligands at their surface and in direct contact with each other. In the accompanying experiments, we investigate the conduction mechanism in films of phosphorus-doped, ligand-free silicon nanocrystals. At the largest electron concentration achieved in our samples, which is half the predicted nc, we find that the localization length of hopping electrons is close to three times the nanocrystals diameter, indicating that the film approaches the metal-insulator transition.Semiconductor nanocrystals (NCs) have shown great potential in optoelectronics applications such as solar cells [1], light emitting diodes [2], and field-effect transistors [3,4] by virtue of their size-tunable optical and electrical properties [5] and low-cost solution-based processing techniques [6,7]. These applications require conducting NC films and the introduction of extra carriers through doping can enhance the electrical conduction. Several strategies for NC doping have been developed. Remote doping, the use of suitable ligands as donors in the vicinity of NC surface, increased the conductivity of PbSe NC films by 12 orders of magnitude [8]. Electrochemical doping, which tunes the carrier concentration accurately and reversibly, resulted in conducting NC films [9,10]. Lately, stoichiometric control has emerged as a strategy to dope lead chalcogenide NCs [11]. Finally, electronic impurity doping of NCs, originally impeded by synthetic challenges [12], was recently achieved in InAs [13] and CdSe [14] NCs.While many experimental studies have been directed towards increasing the conductivity of NC films, there is still no clear consensus on the fundamental question: what is the condition for the metal-insulator transition (MIT) in NC films [15][16][17]? In a bulk semiconductor, the critical electron concentration n M for the MIT depends on the Bohr radius a B according to the well-known Mott criterion [18] n M a 3 B 0.02, where a B = ε 2 /m * e 2 is the effective Bohr radius (in Gaussian units), ε is the dielectric constant of the semiconductor, and m * is the effective electron mass. It is obvious that a dense film of undoped semiconductor NCs is an insulator, while a film of touching metallic NCs with the same geometry is a conductor. Therefore, the MIT has to occur in semiconductor NC films at some criti-FIG. 1. The origin of the metal-to-insulator transition in semiconductor nanocrystal films. The figure shows the cross section of two nanocrystals in contact through facets with radius ρ. The blue spherical cloud represents an electron wave packet which moves through the contact. Such a compact wave pac...

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“…If the move lowers the Hamiltonian H, then it is accepted, otherwise it is rejected. In this way we arrive to a pseudogrond state, which describes a NC array at low temperatures 6 . As soon as this state is found one can calculate the conductivity of the system σ.…”

Section: Computer Simulationmentioning

confidence: 99%

“…Like in bulk semiconductors, adding charged carriers is critical for NC solids, which would otherwise be electrically insulating. There are a few theoretical works on the conductivity of impurity doped arrays of NCs [6][7][8][9] . However, due to intrinsic difficulties of doping of NCs by impurity atoms 10 , so far there are only a limited number of experimental works with successful bulk doping [11][12][13] .…”

Section: Introductionmentioning

confidence: 99%

Theory of a field-effect transistor based on a semiconductor nanocrystal array

2014

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We study the surface conductivity of a field-effect transistor (FET) made of periodic array of spherical semiconductor nanocrystals (NCs). We show that electrons introduced to NCs by the gate voltage occupy one or two layers of the array. Computer simulations and analytical theory are used to study the array screening and corresponding evolution of electron concentrations of the first and second layers with growing gate voltage. When first layer NCs have two electrons per NC the quantization energy gap between its 1S and 1P levels induces occupation of 1S levels of second layer NCs. Only at a larger gate voltage electrons start leaving 1S levels of second layer NCs and filling 1P levels of first layer NCs. By substantially larger gate voltage, all the electrons vacate the second layer and move to 1P levels of first layer NCs. As a result of this nontrivial evolution of the two layers concentrations, the surface conductivity of FET non-monotonically depends on the gate voltage. The same evolution of electron concentrations leads to non-monotonous behaviour of the differential capacitance.

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Theory of hopping conduction in arrays of doped semiconductor nanocrystals

Cited by 70 publications

References 23 publications

Tunneling of electrons between Si nanocrystals embedded in a SiO2matrix

Tunneling of electrons between Si nanocrystals embedded in a SiO2matrix

Metal–insulator transition in films of doped semiconductor nanocrystals

Theory of a field-effect transistor based on a semiconductor nanocrystal array

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