Hydrogen-like Acceptors Research Articles

Maximum hopping direct current conductivity via hydrogen-like impurities in semiconductors

A quasi-classical model for calculating DC (direct current) electrical conductivity in crystalline semiconductors with hydrogen-like impurities is developed at the transition from band conduction to impurity hopping conduction with decreasing temperature. This transition from the minimum band conductivity to the maximum hopping conductivity via impurities has the form of a characteristic "kink" in the temperature dependence of the electrical resistivity. The idea of the calculation is to preliminarily determine the transition temperature Tj using the standard approach within the framework of the two-band model. The shift of the top of the v-band (the bottom of the c-band) into the depth of the band gap due to the formation of a quasi-continuous band of allowed energy values from the excited states of acceptors (donors) is taken into account. This leads to a decrease in the value of a thermal ionization energy of the majority shallow impurities due to a decrease in the maximum localization radius of a hole on an acceptor (an electron on a donor) with increasing impurity concentration. The values of the observed maximum hopping conductivity and drift hopping mobility corresponding to the temperature Tj are calculated. The numerical calculation within the framework of the proposed model is consistent with the known experimental data on the electrical conductivity and Hall coefficient of moderately compensated p-Ge crystals doped by neutron transmutation and non-intentionally compensated metallurgically doped n-Ge, as well as n- and p-Si crystals on the insulator side of the Mott insulator--metal concentration phase transition. Keywords: bulk crystals of germanium and silicon, hydrogen-like acceptors and donors, holes and electrons, band and hopping motion of charge carriers.

Resonant boron acceptor states in semiconducting diamond

High-excited discrete states of boron hydrogenlike acceptors in crystalline diamond have been measured by temperature-dependent infrared absorption spectroscopy. We distinguish the boron resonant states in diamond crystals from the localized boron states in the band gap by differentiating the impurity transitions within state continua of the valence light- and heavy-hole subbands on the basis of their relative oscillator strengths, specific selection rules, and temperature dependences. Constraints on the boron binding energy and spin-orbit splitting of the valence band have been derived by analysis of the structure of the infrared absorption spectra of boron-doped diamond, in particular by a comparison with boron spectra in other semiconductors with a diamond lattice.

Design of Peltier Element Based on Semiconductors with Hopping Electron Transfer via Defects

The study of thermoelectric properties of crystalline semiconductors with structural defects is of practical interest in the development of radiation-resistant Peltier elements. In this case, the spectrum of energy levels of hydrogen-like impurities and intrinsic point defects in the band gap (energy gap) of crystal plays an important role.The purpose of this work is to analyze the features of the single-electron band model of semiconductors with hopping electron migration both via atoms of hydrogen-like impurities and via their own point triplecharged intrinsic defects in the c- and v-bands, as well as to search for the possibility of their use in the Peltier element in the temperature range, when the transitions of electrons and holes from impurity atoms and/or intrinsic defects to the c- and v-bands can be neglected.For Peltier elements with electron hopping migration we propose: (i) an h-diode containing |d1)and |d2)-regions with hydrogen-like donors of two types in the charge states (0) and (+1) and compensating them hydrogen-like acceptors in the charge state (−1); (ii) a homogeneous semiconductor containing intrinsic t-defects in the charge states (−1, 0, +1), as well as ions of donors and acceptors to control the distribution of t-defects over the charge states. The band diagrams of the proposed Peltier elements in equilibrium and upon excitation of a stationary hopping electric current are analyzed.A model of the h-diode containing hydrogen-like donors of two types |d1) and |d2) with hopping migration of electrons between them for 50 % compensation by acceptors is considered. It is shown that in the case of the reverse (forward) electrical bias of the diode, the cooling (heating) of the region of the electric double layer between |d1)and |d2)-regions is possible.A Peltier element based on a semiconductor with point t-defects is considered. It is assumed that the temperature and the concentration of ions of hydrogen-like acceptors and donors are to assure all t-defects to be in the charge state (0). It is shown that in such an element it is possible to cool down the metal-semiconductor contact under a negative electric potential and to heat up the opposite contact under a positive potential.

Model of stationary migration of free and hopping via acceptors holes in a crystalline semiconductor

In the diffusion-drift approximation, we have constructed a phenomenological theory of the coexisting migration of v-band holes and holes by means of hopping from hydrogen-like acceptors in the charge state (0) to acceptors in the charge state (−1). A p-type crystalline semiconductor is considered at a constant temperature, to which an external stationary electric field is applied. In the linear approximation, analytical expressions for the screening length of the static electric field and the length of the diffusion of v-band holes and the holes quasilocalized on acceptors are obtained for the first time. The presented relations, as special cases, contain well-known expressions. It is shown that the hopping migration of holes via acceptors leads to a decrease in the screening length and in the diffusion length.

CALCULATION OF STATIC PARAMETERS OF SILICON DIODE CONTAINING δ-LAYER OF TRIPLE-CHARGED POINT DEFECTS IN SYMMETRIC p–n-JUNCTION

The study of semiconductor materials and devices containing a narrow layer of impurity atoms and/or intrinsic point defects of the crystal lattice is of fundamental and practical interest. The aim of the study is to calculate the electric parameters of a symmetric silicon diode, in the flat p–n-junction of which a δ-layer of point triple-charged t-defects is formed. Such a diode is called p–t–n-diode, similarly to p–i–n-diode.Each t-defect can be in one of the three charge states (−1, 0, and +1; in the units of the elementary charge). It is assumed that at room temperature all hydrogen-like acceptors in p-region and hydrogen-like donors in n-region are ionized. It was assumed that the cross-section for v-band hole capture on t-defects is greater than the cross-section for c-band electron capture on t-defects.The system of stationary nonlinear differential equations, which describe in the drift-diffusion approximation a migration of electrons and holes in semiconductors, is solved numerically. The static capacityvoltage and current-voltage characteristics of the silicon diode with nondegenerate regions of pand n-type of electrical conductivity are calculated for forward and reverse electric bias voltage.It is shown by calculation that in the p–t–n-diode containing the δ-layer of t-defects, at the forward bias a region of current density stabilization occurs. At the reverse bias the current density in such a diode is much greater than the one in a p–n-diode without t-defects. With the reverse bias the capacitance of the p–t–n-diode, in contrast to the p–n-diode, increases at first and then decreases.

Drift-diffusion model of hole migration in diamond crystals via states of valence and acceptor bands

Ionization equilibrium and dc electrical conductivity of crystalline diamond are considered, for the temperature in the vicinity of which valence band (v-band) conductivity is approximately equal to hopping conductivity via acceptors. For the first time, we find explicitly (in the form of definite integrals) the fundamental ratio of diffusion coefficient to drift mobility for both v-band holes and holes hopping via hydrogen-like acceptors for the temperature . The known ratios follow from the obtained ones as particular cases. The densities of the spatial distributions of acceptors and hydrogen-like donors as well as of holes are considered to be Poissonian and the fluctuations of electrostatic potential energy are considered to be Gaussian. The dependence of exchange energy of v-band holes on temperature is taken into account. The thermal activation energy of hopping conduction as a function of the concentration of boron atoms (as acceptors) is calculated for temperature . Without the use of any adjustable parameters, the results of calculations quantitatively agree with data obtained from the measurements of hopping conductivity of diamond with boron concentration from to cm−3, i.e. on the insulating side of the Mott phase transition.

Ionization equilibrium at the transition from valence-band to acceptor-band migration of holes in boron-doped diamond

A quasi-classical model of ionization equilibrium in the p-type diamond between hydrogen-like acceptors (boron atoms which substitute carbon atoms in the crystal lattice) and holes in the valence band (v-band) is proposed. The model is applicable on the insulator side of the insulator–metal concentration phase transition (Mott transition) in p-Dia:B crystals. The densities of the spatial distributions of impurity atoms (acceptors and donors) and of holes in the crystal are considered to be Poissonian, and the fluctuations of their electrostatic potential energy are considered to be Gaussian. The model accounts for the decrease in thermal ionization energy of boron atoms with increasing concentration, as well as for electrostatic fluctuations due to the Coulomb interaction limited to two nearest point charges (impurity ions and holes). The mobility edge of holes in the v-band is assumed to be equal to the sum of the threshold energy for diffusion percolation and the exchange energy of the holes. On the basis of the virial theorem, the temperature Tj is determined, in the vicinity of which the dc band-like conductivity of holes in the v-band is approximately equal to the hopping conductivity of holes via the boron atoms. For compensation ratio (hydrogen-like donor to acceptor concentration ratio) K ≈ 0.15 and temperature Tj, the concentration of “free” holes in the v-band and their jumping (turbulent) drift mobility are calculated. Dependence of the differential energy of thermal ionization of boron atoms (at the temperature 3Tj/2) as a function of their concentration N is calculated. The estimates of the extrapolated into the temperature region close to Tj hopping drift mobility of holes hopping from the boron atoms in the charge states (0) to the boron atoms in the charge states (−1) are given. Calculations based on the model show good agreement with electrical conductivity and Hall effect measurements for p-type diamond with boron atom concentrations in the range from 3 × 1017 to 3 × 1020 cm−3, i.e., up to the Mott transition. The model uses no fitting parameters.

Role of electrostatic fluctuations in doped semiconductors upon the transition from band to hopping conduction (by the example of p-Ge:Ga)

The electrostatic model of ionization equilibrium between hydrogen-like acceptors and v-band holes in crystalline covalent p-type semiconductors is developed. The range of applicability of the model is the entire insulator side of the insulator–metal (Mott) phase transition. The density of the spatial distribution of acceptor- and donor-impurity atoms and holes over a crystal was assumed to be Poissonian and the fluctuations of their electrostatic potential energy, to be Gaussian. The model takes into account the effect of a decrease in the energy of affinity of an ionized acceptor to a v-band hole due to Debye–Huckel ion screening by both free v-band holes and localized holes hopping over charge states (0) and (–1) of acceptors in the acceptor band. All donors are in charge state (+1) and are not directly involved in the screening, but ensure the total electroneutrality of a sample. In the quasiclassical approximation, analytical expressions for the root-mean-square fluctuation of the v-band hole energy Wp and effective acceptor bandwidth Wa are obtained. In calculating Wa, only fluctuations caused by the Coulomb interaction between two nearest point charges (impurity ions and holes) are taken into account. It is shown that Wp is lower than Wa, since electrostatic fluctuations do not manifest themselves on scales smaller than the average de Broglie wavelength of a free hole. The delocalization threshold for v-band holes is determined as the sum of the diffusive-percolation threshold and exchange energy of holes. The concentration of free v-band holes is calculated at the temperature Tj of the transition from dc band conductivity to conductivity implemented via hopping over acceptor states, which is determined from the virial theorem. The dependence of the differential energy of the thermal ionization of acceptors at the temperature 3Tj/2 on their concentration N and degree of compensation K (the ratio between the donor and acceptor concentrations) is determined. Good quantitative agreement between the results of the calculation and data on the series of neutron transmutation doped p-Ge samples is obtained up to the Mott transition without using any fitting parameters.

Terahertz Stimulated Emission from Silicon Doped by Hydrogenlike Acceptors

Silicon-based laser sources could bring tremendous advances to science and technology. But, laser generation in pure silicon is fundamentally forbidden. Now scientists demonstrate experimentally the feasibility of laser generation in boron-doped silicon.

Impurity centers in ZnSe:Na crystals

The influence of sodium impurity on photoluminescence (PL) spectra of ZnSe crystals doped in a growth process from a Se+Na melt is investigated. It is shown that the introduction of the impurity results in emergence of emission bands in the PL spectra due to the recombination of exciton impurity complexes associated with both donors and hydrogen-like acceptors. Apart from that, four bands generated by donor–acceptor pairs recombination and a band produced by electronic transitions from the conduction band to a shallow acceptor are discussed. As a result of the analysis it is concluded that Na impurity forms in ZnSe lattice Na Zn hydrogen-like acceptors with activation energy of 105±3 meV, Na i donor centers with activation energy of 18±3 meV, as well as Na ZnV Se and Na i Na Zn associative donors with activation energy of 35±3 and 52±9 meV, respectively.

Imperfection photoconductivity peak related to the Urbach's absorption edge in Cd 1− xMn xTe and CdTe

The narrow photoconductivity (PC) peak observed as the main feature of the PC spectrum in many Cd 1− x Mn x Te and CdTe crystals is ascribed to the transitions between ionized shallow hydrogen-like acceptors and the conduction band. The shape and the position of this large extrinsic PC peak is determined by a steep Urbach's edge of the intrinsic absorption which plays a parasitic role.

Determination of trace constituents of high-purity gallium arsenide

Various schemes for the determination of unintentionally introduced impurities in high-purity GaAs are discussed. The identification of acceptor species is accomplished by measuring the 1s/sub 3/2/-2s/sub 3/2/ splitting of hydrogen-like acceptors. This measurement is made possible by an excited final state relaxation process which is manifested in the luminescence spectrum by a red-shifted replica of the acceptor bound exciton doublet. A technique is described for enhancing this process with respect to the free to bound transitions which make up the background. It involves selectively exciting only those initial states which can give rise to the desired process. Laser excitation wavelength and power density affect the emission intensities of various bound exciton peaks. The implications of these results for quantitative determinations of acceptors are discussed. 20 references, 8 figures.