A Quasi-Classical Model of the Hubbard Gap in Lightly Compensated Semiconductors

A quasi-classical method for calculating the narrowing of the Hubbard gap between the A⁰ and A⁺ acceptor bands in a hole semiconductor or the D⁰ and D^– donor bands in an electron semiconductor is suggested. This narrowing gives rise to the phenomenon of a semiconductor transition from the insulator to metal state with an increase in doping level. The major (doping) impurity can be in one of three charge states (–1, 0, or +1), while the compensating impurity can be in states (+1) or (–1). The impurity distribution over the crystal is assumed to be random and the width of Hubbard bands (levels), to be much smaller than the gap between them. It is shown that narrowing of the Hubbard gap is due to the formation of electrically neutral acceptor (donor) states of the quasicontinuous band of allowed energies for holes (electrons) from excited states. This quasicontinuous band merges with the top of the valence band (v band) for acceptors or with the bottom of the conduction band (c band) for donors. In other words, the top of the v band for a p-type semiconductor or the bottom of the c band for an n-type semiconductor is shifted into the band gap. The value of this shift is determined by the maximum radius of the Bohr orbit of the excited state of an electrically neutral major impurity atom, which is no larger than half the average distance between nearest impurity atoms. As a result of the increasing dopant concentration, the both Hubbard energy levels become shallower and the gap between them narrows. Analytical formulas are derived to describe the thermally activated hopping transition of holes (electrons) between Hubbard bands. The calculated gap narrowing with increasing doping level, which manifests itself in a reduction in the activation energy ε₂ is consistent with available experimental data for lightly compensated p-Si crystals doped with boron and n-Ge crystals doped with antimony.     

Local vibrational modes of the oxygen-vacancy complex in germanium

Infrared absorption of n-and p-Ge crystals enriched with ¹⁶O and/or ¹⁸O isotopes was studied after irradiation with 6-MeV electrons. Absorption spectra were measured at 10 and 300 K. Along with known bands characteristic of oxygen-containing defects, new lines at 669, 944, and 990 cm^?1 were detected. These bands are annealed at temperatures of 120–140°C; the band at 621 cm^?1, previously related to the vacancy-oxygen complex in Ge, is simultaneously annealed. The bands at 621 and 669 cm^?1 showed identical temperatures (10 → 300 K) and oxygen isotope (¹⁶O → ¹⁸O) shifts. These bands were found to correspond to various charge states of a defect with an energy level near E_v=0.25±0.03 eV. It is assumed that such a defect is the vacancy-oxygen complex (A center). The weak bands at 944 and 990 cm^?1 were identified as combinations of asymmetric stretching modes at 621 and 669 cm^?1 with a symmetric one at 320 cm^?1 for neutral and negative charge states of the A center, respectively.     

Evaluation of mobility gaps and density of localized hole states in p-Ge/Ge1−x Six heterostructures in the quantum Hall effect mode

The temperature (0.1 K?T?20 K) and magnetic field (0 T?B?12 T) dependences of the longitudinal (ρ_xx) and Hall (ρ_xy) resistivities have been studied in detail for p-Ge/Ge_1?x Si_x (x=0.07) multilayer heterostructures with hole density p=(2.4–2.6)×10¹¹ cm^?2 and mobility μ=(1.1–1.7)×10⁴ cm² V^?1 s^?1. The energy spectrum parameters of two-dimensional (2D) hole gas in the quantum Hall effect mode have been determined. The mobility gap W=(2–2.5) meV and the background density of localized states g _c =(5–7)×10¹⁰ cm^?2 meV^?1 for the filling factors ν=1 and 2. The results are discussed in terms of long-range impurity potential models for selectively doped 2D systems.     

Quasi-local impurity states in uniaxially compressed p-type Ge

The main characteristics of quasi-local levels produced by shallow-level impurity centers (with a screened Coulomb potential) in uniaxially compressed p-Ge were studied theoretically. Stress dependences of positions and widths of the quasi-local impurity states were calculated. Results of the numerical computations for the Ga impurity are presented.     

Electrostatic model of the energy gap between Hubbard bands for boron atoms in silicon

Electrostatics is used to model the narrowing of the energy gap ɛ ₂ between Hubbard bands (the A ⁰-and A ⁺-bands) in a p-doped semiconductor with increasing acceptor concentration N + N ₀ + N _-1 + N ₊₁ and with increasing degree of compensation K by donors for N ₋₁≈KN. The screening of impurity ions by holes hopping from acceptor to acceptor is taken into account. It is shown that this effect leads to a shift of the A ₀-band towards the valence band and the A ⁺-band towards the conduction band. The concentration of holes hopping in the A ⁺-band N ₊₁ N ₀/N is determined by the energy of their thermal generation ɛ ₂ from the A ⁰-band. The values of ɛ ₂ calculated for Si: B are in agreement with experimental data. Fiz. Tekh. Poluprovodn. 33, 402–404 (April 1999)     

Photoluminescence measurements on undoped CdZnTe grown by the high-pressure bridgman method

The low temperature photoluminescence of Cd_0.91Zn_0.09Te grown by the high-pressure Bridgman (HPB) method exhibits a neutral donor bound exciton emission (D⁰X) at 1.65603 eV with its excited state (D⁰X^*) at 1.65798 eV and neutral acceptor bound exciton emissions (A⁰X) at 1.64566 eV and 1.65201 eV. Assuming a direct generation and subsequent relaxation of excitons at the D⁰X^* state, we demonstrate that the temporal evolution of the above emission bands is well reproduced by a set of rate equations. The resultant radiative-lifetime of 1.4 ns for the D⁰X and 1.5 and 2.0 ns for the A⁰Xs are compared with various CdZnTe's (CZTs) grown by the other methods to demonstrate the particular nature of the HPB CZT.     

Energy spectrum and optical properties of the quantum dot-impurity center complex

The impurity absorption of light in the quantum dot (QD) with a spherically symmetric potential has been considered within the framework of the zero-range potential model in the effective mass approximation. The dynamics of formation of the localized D ^? state as a superposition of QD states with different orbital quantum number values is demonstrated. The impurity absorption coefficient is calculated taking into account the QD size dispersion, which leads to broadening of discrete impurity absorption lines. Numeric estimates of the D ^? state binding energy and the impurity absorption coefficient are presented for the heterophase QD system 〈CdS〉-〈transparent silicate glass matrix〉. The sensitivity of the impurity absorption edge to the impurity level depth and to the mean QD radius was studied.     

Electrical and optical properties of Mn-doped Hg3In2Te6 crystals

The effect of Mn impurities on the properties of Hg₃In₂Te₆ crystals is studied by electrical and optical measurements. It is shown that, despite the high dopant concentration (1 × 10¹⁹ cm^?3), the electron concentration remains the same as that in an undoped crystal (～10¹³ cm^?3 at 300 K). At the same time, narrowing of the band gap from 0.74 to 0.7 eV is observed. From an analysis of the absorption spectra, it is found that the absorption edge is formed by optical transitions involving density-of-states (DoS) tails and that two acceptor- and donor-type impurity bands are formed in the band gap. The two bands are described by a Gaussian distribution of the DoS, with an energy gap between the peaks of E ₀ = E _d ⁰ ? E _a ⁰ = 0.4 eV. The total donor and acceptor concentration N _d + N _a and the degree of compensation K = N _a /N _d → 1 are determined. Such compensation is responsible for pinning of the Fermi level near the middle of the band gap and for quasi-intrinsic conductivity at temperatures T ≥ 300 K.     

Electron levels and luminescence of dislocation networks formed by the hydrophilic bonding of silicon wafers

Local energy levels produced by dislocations at the interface between bonded n- and p-Si wafers are studied by deep level transient spectroscopy and by a new technique for the detection of impurity luminescence, induced by the occupation of electron states upon the application of electric pulses (the pulsed trap-refilling-enhanced luminescence technique). It is established that only the shallow levels of the dislocation network, with activation energies of about 0.1 eV, are responsible for the D1 dislocation-related luminescence band in both n- and p-type samples. The occupation of deep levels has no effect on the D1-band intensity. A model of coupled neutral trapping centers for charge carriers is proposed. In this model, the difference between the energy position of the D1 band (0.8 eV) and the corresponding interlevel energy spacing (0.97 eV) is attributed to the Coulomb interaction between charge carriers trapped at the levels.     

Metallic conductivity over an acceptor band of lightly compensated copper-doped p-Hg0.78Cd0.22Te crystals

The conductivity and Hall effect of heavily doped p-Hg_0.78Cd_0.22Te:Cu crystals were studied in the temperature range of 4.2–125 K. The conductivity over the impurity band is of a metallic type for the acceptor concentration N _A>3.8×10¹⁷ cm^?3. The conductivity and the Hall coefficient governed by the delocalized charge carriers in the impurity band are independent of temperature. The sign of the Hall effect is positive in the metallic conductivity range. Near the metal-insulator transition point, the Hall mobility increases linearly with the acceptor concentration and is independent of the acceptor concentration at N _A>1.6×10¹⁸ cm^?3. The metallic conductivity is proportional to N _A in the concentration range under study at N _A<3.1×10¹⁸ cm^?3. The Anderson transition occurs at the Cu concentration N _A=1.4×10¹⁷ cm^?3 in the A ⁺ impurity band, which is formed by positively charged acceptors. Minimum metallic conductivity corresponding to this transition equals 5.1 Ω^?1 cm^?1. It is shown that ?₂ conductivity in the subthreshold region is defined by delocalized carriers in the upper Hubbard band only for fairly heavy doping (N _A>1.4×10¹⁷ cm^?3). For N _A<1.4×10¹⁷ cm^?3, the hopping conductivity is observed.     

Hydrogen-containing donors in silicon: Centers with negative effective correlation energy

The reconstruction of shallow-level hydrogen-containing donors in Si is studied. The donors are formed by implantation of low-energy (300 keV) hydrogen ions into the experimental samples and subsequent heat treatment at 450°C. The experiments are carried out for Ag-Mo-Si Schottky diodes and diodes with a shallow (～1 μm) p⁺-n junction. The concentration and distribution of the donors are determined by applying the method of C–V characteristics at a frequency of 1.2 MHz. An analysis of the temperature dependence of the equilibrium electron concentration shows that the reconstruction of the hydrogen-containing donors can be described under the assumption of recharging of a center with negative effective correlation energy (U < 0). The transformation between two equilibrium configurations of a double hydrogen donor (D _B ⁺⁺ ? D _A ⁰ ) proceeds with the Fermi level position E_F = E _c ? 0.30 eV. The reconstruction of the donors from a neutral to a doubly charged state (D _A ⁰ → D _B ⁺⁺ ) which is stimulated by the capture of minority carriers, is observed at room temperature.     

Quasi-static capacitance of a weakly compensated semiconductor with hopping conduction (on the example of <Emphasis Type="Italic">p</Emphasis>-Si:B)

A moderately doped semiconductor is considered on the insulator side of the insulator-metal phase transition, where the acceptors in (?1), (0), and (+1) charge states form A ⁰ and A ⁺ bands. The expressions are derived for the Debye-Hückel and Schottky-Mott screening lengths of an external electrostatic field for the case of hopping transport of holes via acceptors. The quasistatic capacitance of a semiconductor is calculated in the temperature region where hopping hole conductances in the A ⁰ and A ⁺ bands are approximately equal. It is shown that the Debye-Hückel screening length can be determined using the measurements of quasistatic capacitance even in the high-field regime, i.e., in the Schottky-Mott approximation. The frequency of an electric signal in the measurements of quasistatic semiconductor capacitance in a metal-insulator-semiconductor structure must be much lower than the average frequency of hole hopping via acceptors (boron atoms in silicon).     

Ionization energy of copper in Hg0.8Cd0.2Te crystals under conditions of light and intermediate doping

Resistivity and the Hall effect were studied in copper-doped p-Hg _0.8 Cd _0.2 Te crystals in the temperature range of 4.2–125 K and the range of Cu concentrations from 2.6×10¹⁵ to 2×10¹⁸ cm^?3. It is shown that the conventional method for determining the ionization energy of impurities from the slope of the dependence R _H (T) is inapplicable in this case. In order to obtain the correct results, it is necessary to take into account the structure of the impurity band and the screening of the impurity charge with free charge carriers. A simplified model of the impurity band is suggested; this model makes it possible to calculate the ionization energy of acceptors under conditions of light doping and a small degree of compensation. This approach is used to find that ionization energy of copper depends only slightly on the copper concentration at T=0 and is equal to E _A =7.6 meV for an isolated acceptor, which coincides with the theoretical value. At finite temperatures, the ionization energy of acceptors decreases appreciably as a result of screening.     

Theoretical analysis of a novel MPN gallium arsenide Schottky barrier solar cell

Theoretical analysis for a novel Au-p-n GaAs Schottky barrier solar cell has been made in this note. It is shown that barrier height equal to the energy band gap of GaAs can be obtained in the proposed cell structure if the thickness and dopant density of the p-GaAs layer are properly chosen. Calculations of the barrier height as function of the thickness and dopant density of the p-layer have been carried out for a Au-p-n GaAs Schottky barrier cell. It is shown that AMO efficiency around 22% can be achieved in the proposed solar cell when N_D = 10¹⁶ cm^?3, N_A = 8 × 10¹⁸ cm^?3 and $\text{W}{}_{\mathrm{p}}\text{= 100}\text{A}\text{?}$ are chosen.     

Special features of conductivity mechanisms in heavily doped n-ZrNiSn intermetallic semiconductors

The effect of high concentrations of acceptor dopants (N _A = 10²⁰ cm^?3) on the electronic structure, Fermi level, electrical conductivity, Seebeck coefficient, and magnetic susceptibility of n-ZrNiSn intermetallic semiconductors is studied. The role of impurity bands produced by donors and acceptors in the conductivity of the heavily doped n-ZrNiSn compound is clarified. The transition from activated conductivity to metal conductivity under variations in the concentration of acceptor dopants is observed.     

Magnetooptical properties of quantum wells with D (−) centers

The D ^(?) states in a quantum well under the magnetic field longitudinal with respect to the axis of growth of the structure are considered. In the context of the model of the zero-radius potential, an equation that defines the dependence of the binding energy of the D ^(?) state on the parameters of the potential of the structure, the coordinates of the D ^(?) center, and the strength of the magnetic field is derived. The results are compared with the experimental data on the dependence of the binding energy of the D ^(?) state on the magnetic field. There is satisfactory agreement between the theoretical calculations and experimental data in the range of magnetic fields B < 10 T. The role of dimensionality in the modification of the coordinate dependence of the binding energy on the 2D → 1D → 0D transition is clarified. The impurity magnetooptical absorption coefficient in a multiple quantum well structure is calculated, and the spectral dependence of the coefficient is studied. It is shown that a substantial contribution to the broadening of the absorption lines is made by the dispersion of quantum well widths in the structure.     

Novel diarylborane–phenanthroimidazole hybrid bipolar host materials for high-performance red,yellow and green electrophosphorescent devices

In this work, two novel bipolar host materials p-BPPI and m-BPPI containing phenanthroimidazole/dimesitylborane (Mes₂B) with para- and meta-linkage have been designed, synthesized and characterized. The appending Mes₂B moiety improves the thermal stability, electrochemical stability and carrier injection/transport ability of both target compounds. The test results of time-of-flight (TOF) and single-carrier devices show that both the new hosts possess bipolar charge-transporting characteristics. As a result, series of highly efficient green (66.3 cd A⁻¹, 63.1 lm W⁻¹, 18.2%), yellow (55.2 cd A⁻¹, 66.6 lm W⁻¹, 14.5%) and red (20.1 cd A⁻¹, 20.4 lm W⁻¹, 13.5%) PhOLEDs are achieved by using them as the universal host materials. The results indicate that bipolar host p-BPPI and m-BPPI have high potential in fabricating various color OLEDs for displays and lighting applications. Our study further enriches the selection of D and A group for phosphorescent host materials. The relationship between molecular structures and optoelectronic properties is discussed experimentally and theoretically.     

Energy Spectra of the Local States in the Forbidden Gap of Monoclinic TlInS 2x Se 2(1−x) Crystals

Near IR properties of the mixed TlInS_2xSe_2(1?x) have been studied previously by the present authors. In this work the temperature and frequency dependence's of the conductivity and the current-voltage characteristics (in relatively weak electric field), have been investigated for monoclinic TlInS_2xSe_2(1?x) crystals, which are perspective materials for IR applications. From the temperature dependence's of conductivity in the direction perpendicular to c- axis the band gap E^g = 2.22 eV was determined for β--TlInS₂ crystals. The impurity centres were determined located at 0.43, 0.73 eV and 0.35, 0.48, 1.12 eV for the direction of current i//c and i ⊥ c, respectively. The concentration of the centres located at 0.48 and 1.12 eV were calculated to be N_A ? N_D = 4.8 · 10⁹ cm^?3 and 1.9 · 10¹¹ cm^?3, respectively. It was found that in the solid solutions TlInS_2xSe_2(1?x) for 0.3 ≤ x ≤ 1, the conductivity follows the dependence σ (v) = σ₀·υ^s in the temperature range between 100 to 600 K. In the temperature range of 80-400 K charge bounce plays an important role in the conductivity mechanism. Occurrence of the deep and low-levels impurity centres and a “tail” of the density of energy states in TlInS_2xSe_2(1?x) crystals make them perspective for practical applications: switching and memory effects, N-type current-voltage characteristics, induced conductivity etc.     

Influence of an impurity profile on the determination of interface states

In order to determine the density of interface states from C(V) curves for high test frequencies, a comparison is made with a computed curve for uniform impurity concentration but identical minimum capacitance. The curves calculated for a doping profile (due, say, to acceptor depletion near the surface of a p-type semiconductor) are assumed to represent the measured C(V) curves of MOS diodes. A number of “charges in interface states” (8 × 10¹⁰ cm^?2 in the given example) are simulated by the impurity profile. This shows that it is not sufficient to introduce a mean effective substrate impurity concentration by adapting the minimum capacitance in the inversion region.The same accordingly applies for the C(V) curves for low test frequencies. The error due to “simulated interface states” is reduced somewhat, but it remains the altered relation between the applied voltage and the surface potential.     

The concentration dependence of acceptor-state radii in p-Hg0.78Cd0.22Te crystals

Hopping conduction in undoped p-Hg_0.78Cd_0.22Te crystals containing native double-charged acceptors (Hg vacancies) with concentrations of 10¹⁶–10¹⁸cm^?3 was studied. Electrical conduction with a variable hopping range is dominant in the entire concentration range at temperatures below 6–16 K. The measured parameters of this conduction were used to calculate the acceptor-state radius as a function of vacancy concentration N _A . It is shown that, for N _A <4×10¹⁷ cm^?3, the low-temperature conduction occurs via the vacancy states whose radius is independent of N _A . For N _A >5×10¹⁷ cm^?3, the hopping conduction is governed by the states of uncontrolled shallow-level impurity acceptors. The radius of the state for these defects increases with increasing N _A owing to an increase in the effective permittivity of the medium.