Infrared absorption by pairs of group III and V impurities in silicon

Pokrovskiı̆, Ya. E.; Smirnova, O. I.; Khval’kovskii, N. A.

doi:10.1134/1.1499905

Cited by 3 publications

(7 citation statements)

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“…The variational coupling jumps discontinuously to zero at a temperature T c (see fig. 1) and provides an estimate for the superfluid stiffness, which can be used in the BKT renormalization group flow equations [24][25][26][27].…”

Section: Scha With Non-local Couplings -mentioning

confidence: 99%

“…The SCHA for the short-range Hamiltonian (1) applies in a particularly transparent way. One introduces the quadratic Hamiltonian H 0 = J0 4 i,j (θ i − θ j ) 2 and then variationally determines J0 as a function of J 0 and T , or -equivalently-the dimensionless coupling β J0 as a function of βJ 0 [24][25][26][27]. It is found that J0 is different from zero for T smaller than a temperature, denoted by T c , at which the effective J0 drops to zero [24].…”

mentioning

confidence: 99%

“…One introduces the quadratic Hamiltonian H 0 = J0 4 i,j (θ i − θ j ) 2 and then variationally determines J0 as a function of J 0 and T , or -equivalently-the dimensionless coupling β J0 as a function of βJ 0 [24][25][26][27]. It is found that J0 is different from zero for T smaller than a temperature, denoted by T c , at which the effective J0 drops to zero [24]. An improved determination of the BKT critical temperature T BKT can be obtained inserting J0 (T ) in the Nelson-Kosterlitz condition [16] at the BKT critical point [25,26].…”

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confidence: 99%

“…In particular, we will consider the case of the 2D XY model with power-law couplings J(i, j) decaying asymptotically as J ∼ 1/|i − j| 2+σ . The reason for this choice is three-fold: i) The nearestneighbor 2D XY model has been extensively studied with SCHA [24][25][26][27] providing a benchmark for the short-range limit of the theory. ii) The study of statistical mechanics models with long-range interactions attracted considerable attention along the last few decades (see the reviews [33][34][35]).…”

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confidence: 99%

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Self-consistent harmonic approximation in presence of non-local couplings(a)

Giachetti

Defenu

Ruffo

et al. 2021

EPL

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We derive the self-consistent harmonic approximation for the 2D XY model with non-local interactions. The resulting equation for the variational couplings holds for any form of the spin-spin coupling as well as for any dimension. Our analysis is then specialized to power-law couplings decaying with the distance r as in order to investigate the robustness, at finite σ, of the Berezinskii-Kosterlitz-Thouless (BKT) transition, which occurs in the short-range limit . We propose an ansatz for the functional form of the variational couplings and show that for any the BKT mechanism occurs. The present investigation provides an upper bound for the critical threshold above which the traditional BKT transition persists in spite of the non-local nature of the couplings.

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Section: Scha With Non-local Couplings -mentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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confidence: 99%

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Self-consistent harmonic approximation in presence of non-local couplings(a)

Giachetti

Defenu

Ruffo

et al. 2021

EPL

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“…The Frenkel-Kontorova (FK) model was first introduced in the 1930s and is widely used in condensed matter physics 74,75 . It is a discrete model where a chain of atoms is subject to a rigid periodic potential, from a substrate for example 74,[76][77][78] . The FK model has been used as a 1D representation of twisted bilayer systems 18,47,52 , replacing the rigid substrate with a second chain of atoms which can also deform, see Fig.…”

Section: Parameterization In Configuration Spacementioning

confidence: 99%

Electrically tunable stacking domains and ferroelectricity in moiré superlattices

Bennett,

Remez

2021

Preprint

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Impurity pairs and relaxation of excitation in silicon doped with group III and V impurities

Pokrovskiı̆

Khval’kovskii

2003

phys. stat. sol. (c)

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PACS 71.55.Cn, 72.40.+w In Si doped with group III and V impurities at concentrations of 10 16 -10 18 cm −3 infrared absorption bands of impurity pairs (IPs) appear and there is a slow relaxation of polarization hopping photoconductivity (PC) in a microwave (MCW) electric field. IPs create a broad spectrum of local states with ionization and excitation energies both lower and higher than those of single-impurity atoms. It is shown that ionization of IPs in compensated Si and a slow relaxation of re-charge after extrinsic excitation give a principal contribution to PC, due to hopping transitions of carriers between ionized and neutral impurity atoms in IPs induced by a MCW electric field.It has been established [1] that in Si doped with various group III and V impurities at concentrations N > 10 16 cm −3 at low temperatures (T < 20 K) in an 8 mm microwave (MCW) electric field a slow (10 −5 s) component of extrinsic photoresponse U(MCW) appears. It was concluded that the phenomenon is due to an increase of hopping polarization conductivity σ [2] caused by accumulation of captured charge carriers in long-lived excited 1S states with large orbitals, split from the ground states of donors and acceptors by valley -orbit or spin -orbit interactions. However, some subsequent experiments have contradicted the existence of long-lived excited states. Therefore we suggest a new concept of the polarization hopping photoconductivity (PC) in a MCW electric field.We suppose that extrinsic photoexcitation of doped and compensated Si leads to ionization of impurity pairs (IPs) [3,4], i.e. a group of impurities, localized within some distance r of the order of a few Bohr radii a. Hops of non-equilibrium charge carriers between ionized and neutral impurities in IPs, induced by a MCW electric field, should give a principal contribution to polarization hopping PC.To clarify the situation, consider a system of two electrons and two protons, localized at various distances r/a -one-electron terms of the H 2 molecule (Fig. 1) [5]. The solid curves in Fig. 1 correspond to the ground H(1S) + H(1S), the first excited H(1S) + H(1P) and the ionized H + + H(1S) states. The differences between the dashed and solid lines correspond to decreases of ionization and excitation electron energies E as compared to that for r/a = ∞. It is seen from Fig. 1 that significant differences correspond to r/a = 2 -5. Figure 1 also shows the dependence of the contribution of MCW polarization conductivity dσ(MCW)/d(r/a) on r/a, calculated for an 8 mm MCW field for random distribution of atoms [2]. It is clear that the most important hopping transitions again correspond to r/a = 2 -5. Pairs of group III and V impurities are rather like the H 2 molecule, so it could be expected that the impurity atoms in IPs, localized within r/a ~ 2 -5, give the most important contribution to hopping PC in a MCW field.

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Infrared absorption by pairs of group III and V impurities in silicon

Cited by 3 publications

References 5 publications

Self-consistent harmonic approximation in presence of non-local couplings(a)

Self-consistent harmonic approximation in presence of non-local couplings(a)

Electrically tunable stacking domains and ferroelectricity in moiré superlattices

Impurity pairs and relaxation of excitation in silicon doped with group III and V impurities

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