Uncompensated Si Research Articles

Photoluminescence due to impurity-cluster-bound exciton in highly doped and highly compensated Si

We have investigated photoluminescence (PL) at 4.2 K in highly doped and highly compensated Si with donor and acceptor impurities in the intermediate concentration range from 1 × 1016 to 3 × 1018 cm−3. PL spectra were dominated by the radiative recombination of excitons bound by impurity clusters and the donor–acceptor pair emission. The peak position of the exciton emission shifts to the lower energy side monotonically with an increase in the sum of the donor and acceptor concentrations, where the relationship between the position and the concentration is universal regardless of the species of impurities and is valid also for uncompensated Si. This allowed us to suggest that the cluster consists of multiple species of donor and acceptor impurities and that the difference in the species does not cause a detectable variation in the binding energy of an exciton. A possible method for quantifying the donor and acceptor impurities is proposed.

Donor-acceptor pair luminescence in B and P compensated Si co-doped with Ga

The electrical activity of Ga impurities in a high concentration range in B and P highly compensated Si co-doped with Ga for photovoltaic applications has been investigated through the analysis of donor-acceptor pair luminescence. We have identified the fine structure due to the pair luminescence between P-donors and Ga-acceptors based on a comparison with a theoretical spectrum using their generally accepted ionization energies in low concentration ranges in uncompensated Si. The fine structure showed no dependence on dopant concentrations in the P and Ga concentration ranges from 7 × 1016 to 4 × 1017 cm−3 and from 5 × 1016 to 3 × 1017 cm−3, respectively, which leads us to suggest that both P and Ga impurities act as isolated donors and acceptors without noticeable reduction of ionization energies due to high doping.

Incomplete Ionization and Carrier Mobility in Compensated p -Type and n-Type Silicon

In this paper, we show through both calculations and Hall effect measurements that incomplete ionization of dopants has a greater influence on the majority-carrier density in p-type and n-type compensated Si than in uncompensated Si with the same net doping. The factors influencing incomplete ionization at room temperature are shown to be the majority-dopant concentration, its ionization energy and type, and the compensation level. We show that both the majority- and the minority-carrier mobilities are lower in compensated Si than expected by Klaassen's model and that the discrepancy increases with the compensation level at room temperature. The study of the temperature dependence of themajority-carrier mobility shows that there is no compensation-specific mechanism and that the reduction of the screening in compensated Si cannot explain alone the observed gap between experimental and theoretical mobility.

Impact of incomplete ionization of dopants on the electrical properties of compensated p-type silicon

This paper investigates the importance of incomplete ionization of dopants in compensated p-type Si and its impact on the majority-carrier density and mobility and thus on the resistivity. Both theoretical calculations and temperature-dependent Hall-effect measurements demonstrate that the carrier density is more strongly affected by incomplete ionization in compensated Si than in uncompensated Si with the same net doping. The previously suggested existence of a compensation-specific scattering mechanism to explain the reduction of mobility in compensated Si is shown not to be consistent with the T-dependence of the measured carrier mobility. The experiment also shows that, in the vicinity of 300 K, the resistivity of compensated Si has a much weaker dependence on temperature than that of uncompensated silicon.

Path integral treatment for relativistic particles in external fields and quantized plane wave

Barely insulating, uncompensated Si:P samples have been tuned through the metal-insulator transition applying uniaxial stress along the [100] direction. We find a critical exponent μ ≈︂ 1 of the electrical conductivity extrapolated to temperature T = 0, i.e. σ(T → 0,S) ∼ |S — Sc|μ, in disagreement with earlier stress tuning studies along [123-] where μ ≈︂ 0.5 was reported. Varying the stress or the concentration leads to a different T dependence of σ(T). Our stress-tuning measurements obey finite-T scaling with a dynamic exponent z = 3.

Conductivity of heavily doped Si:P under uniaxial stress

AbstractBarely insulating, uncompensated Si:P samples have been tuned through the metal‐insulator transition applying uniaxial stress along the [100] direction. We find a critical exponent μ ≈︂ 1 of the electrical conductivity extrapolated to temperature T = 0, i.e. σ(T → 0,S) ∼ |S — Sc|μ, in disagreement with earlier stress tuning studies along [123‐] where μ ≈︂ 0.5 was reported. Varying the stress or the concentration leads to a different T dependence of σ(T). Our stress‐tuning measurements obey finite‐T scaling with a dynamic exponent z = 3.

Current issues in the physics of heavily doped semiconductors at the metal–insulator transition

WWHeavily doped semiconductors, in particular Si:P and Si:B, have been prototype materials for the study of the metal–insulator (MI) transition at low temperature, T . Because of the statistical distribution of donors or acceptors in the (usually single–crystalline) host, disorder plays a crucial role for the MI transition. In addition, electron–electron interactions are important as evidenced by the rather large corrections to the Boltzmann conductivity already far above the MI transition. Usually, the MI transition is investigated by studying samples of varying dopant concentrations, N , although stress tuning and magnetic–field tuning have also been employed. An issue of considerable importance which we will discuss in this review is the critical behaviour of the electrical conductivity, σ ( T →0)∼( N − N c ) μ , close to the critical dopant concentration N c , i.e. the exponent puzzle of μ ≈0.5 versus μ ≈1. The question of critical behaviour of the Hall constant will also be addressed. We further discuss the role of magnetic moments on thermodynamic and transport properties close to the MI transition. It has been known for some time that localized moments which of course are present on the insulating side of the MI transition, exist also on the metallic side. Only recently, however, was their influence detected on a transport property, namely the thermoelectric power. We review some of the salient features of local magnetic moments at the MI transition and report on measurements of the specific heat and magnetization on the same samples . The direct comparison of thermodynamic quantities allows a test of models for local moments at the MI transition. Finally, thermoelectric–power measurements together with electrical resistivity reveal strong differences between uncompensated Si:P and compensated Si:(P,B) on the insulating side of the MI transition, with evidence of opening of a Hubbard gap in Si:P only considerably below N c .

Observation of a shift of the mobility threshold in the D − band of silicon in an electric field according to the photoconductivity spectra

We have discovered that the extrinsic photoconductivity spectrum of doped, uncompensated crystalline Si at liquid-helium temperatures is qualitatively different in electric fields E above a critical value E c . Specifically, the red edge of the photoconductivity, associated with photoionization of a neutral impurity, is shifted strongly to lower frequencies. This result is explained by the appearance of a mobility threshold in the D−-band (upper Hubbard band) and the shift of this threshold as E increases.

Disorder induced local moment enhancement in compensated Si:P,B

The recently observed magnetic properties of the compensated Si:P,B and uncompensated Si:P are discussed in the light of a statistical mean field approach to the disordered Hubbard Hamiltonian. Besides giving an explanation for the observed enhancement of the local moment formation in the compensated materials, the model predicts the correct behaviour for the susceptibility as a function of the impurity density. In agreement with the experimental findings a larger persistence of the magnetic properties at high density is expected for larger compensation values.

Specific heat of neutron-compensated heavily doped Si:P near the metal-insulator transition

The specific heat of neutron-irradiated heavily doped Si:P (3.3·1018 cm−3≦Nd≦7.3·1018 cm−3) was measured between 0.07 and 3K and in magnetic fields between 0 and 6T. The compensation ratio was varied systematically by isochronal annealing. Characterization was done by temperature dependent measurements of Hall coefficient and electrical resistivity. The specific heat displays a minimum of the linear coefficient γ at the carrier concentration where the P impurity band is starting to be occupied. The concentration dependence of localized moments inferred from Schottky anomalies can be interpreted in terms of localized magnetic moments arising from the defect structure introduced by the irradiation and from P-derived electrons. As in uncompensated Si:P, local moments survive on the metallic side of the transition.

Thermoelectric power of a disordered metal near the metal-insulator transition.

The thermoelectric power S of uncompensated Si:P with P concentration N near the metal-insulator transition occurring at ${\mathit{N}}_{\mathit{c}}$ has been measured at very low temperatures (0.04\ensuremath{\le}T\ensuremath{\le}3 K). For N\ensuremath{\gg}${\mathit{N}}_{\mathit{c}}$, S is negative and shows the linear T dependence of a metal, whereas close to ${\mathit{N}}_{\mathit{c}}$ an anomalous behavior with a sign change of S at low T is observed. The strong dependence of S on magnetic fields up to 6 T relates the anomaly to magnetic scattering, thus giving the first experimental evidence for localized moments near the metal-insulator transition in a transport property.

NON-BORN CALCULATION OF ZERO TEMPERATURE CONDUCTIVITY OF A DOPED SEMICONDUCTOR UNDER VARIOUS SCREENING MODELS

The zero temperature conductivity of a doped semiconductor is calculated by numerically solving the integral equation which is given as a formal solution of the impurity scattering problem. Here the free-carrier screening of the impurity potential is also discussed, giving a tentative model of the screening. Then the critical exponent for the relation between conductivity and carrier concentration is found to be 0.8 for uncompensated Si:P. The critical carrier concentration for the metal-insulator transition is also calculated for the model of Mott localization as compared with that of Anderson localization, showing largely different results.

Metal-insulator transition in the compensated semiconductor Si:(P,B).

The results of a continuing investigation of the effects of impurity compensation on the characteristics of the metal-insulator (M-I) transition in Si:P are reported. The system used is Si:(P,B). Most of the information is derived from measurements and analysis of the dc electrical conductivity \ensuremath{\sigma} in the temperature range 50 mK T4 K. The form of the temperature dependence of \ensuremath{\sigma} in this range is extensively studied. For samples with electron concentration n near ${\mathit{n}}_{\mathit{c}}$, the critical concentration for the M-I transition, the temperature dependence of \ensuremath{\sigma} departs significantly from the form \ensuremath{\sigma}=\ensuremath{\sigma}(0)+${\mathit{mT}}^{1/2}$+${\mathit{BT}}^{3/4}$, which describes samples at higher values of n. As K, the ratio of acceptor to donor concentration, is increased from zero, the value of ${\mathit{n}}_{\mathit{c}}$ first decreases slightly before rising sharply at larger values of K. Measurements of \ensuremath{\sigma}(0) as a function of n in uncompensated Si:P agree with data in the literature. The applicability of the scaling theory to a description of our measurements of \ensuremath{\sigma}(0) as a function of n in compensated samples is questioned. Attention is given to establishing the most reliable methods for determining values of impurity concentrations.

ESR studies of compensated Si:P,B near the metal-insulator transition.

We have studied the ESR properties of three compensated n-type Si:P,B samples near the metal-insulator transition covering the low-temperature regime from 30 mK to 10 K. We find that both the susceptibility and the ESR linewidth increase dramatically as the temperature is lowered, and in the metallic Si:P,B samples the susceptibility increase is more than in similar uncompensated Si:P samples. We compare results for the insulating phase with numerical calculations, then discuss the metallic region in light of various theoretical models for the low-temperature thermodynamic behavior

Electrical conductivity of metallic Si:B near the metal-insulator transition.

The conductivity has been measured between 55 mK and 4.2 K in zero field and in magnetic fields up to 7.5 T of a series of uncompensated p-type Si:B samples with dopant concentrations near the critical concentration for the metal-insulator transition. Acceptor wave functions, which are derived in silicon from the degenerate light- and heavy-hole J=3/2 valence-band maxima at k=0 and a spin-orbit-split J=1/2 band, are quite different from donor wave functions associated with the six degenerate conduction-band minima at different equivalent points in the Brillouin zone. Despite this, the conductivity of Si:B is found to be quite similar in many ways to that of Si:P. The critical conductivity exponent for Si:B is close to 1/2 as in Si:P and Si:As, rather than having the expected value of 1. The correction to the zero-temperature conductivity arising from electron-electron interactions is comparable in size, and the temperature dependence of the conductivity in various fixed magnetic fields is also found to be quite similar. For the range of dopant concentrations and experimental parameters of these investigations, the only important experimental difference between the two materials is the sign and size of the magnetoresistance. In contrast with Si:P, which has both positive and negative components, the magnetoresistance of Si:B is positive for all temperatures and magnetic fields studied. We attribute this to the strong spin-orbit scattering in p-type silicon associated with the degenerate valence bands.

Critical conductivity exponent for Si:B.

We have determined the critical exponent which characterizes the approach of the zero-temperature conductivity to the insulating phase from measurements down to 60 mK of the resistivity of a series of just-metallic uncompensated p-type Si:B samples with dopant concentrations near the critical concentration for the metal-insulator transition. Our results indicate a critical exponent for Si:B of 0.${65}_{\mathrm{\ensuremath{-}}0.14}^{+0.05}$, which is close to the ``anomalous'' values near 1/2 found for the uncompensated n-type silicon-based semiconductors Si:P, Si:As, and Si:Sb. This implies that, despite strong spin-orbit scattering, Si:B belongs to the same universality class as other silicon-based systems.

Magnetic field dependence of the specific heat of Si:P near the metal-insulator transition

the specific heat of uncompensated Si:P with P concenration 0.79 and 4.5· 10 18 cm −3, i.e. in the vicinity of the critical concentration N c = 3.2 · 10 18 cm −3, has been measured between 0.05 and 3 K and in fields up to 5.7 T. A magnetic-field induced increase of the number of localized electrons exhibiting a Schottky anomaly is observed together with a concomitant decrease of the contribution from delocalized electrons.

Studies of the Correlation Effect on the Anderson-Localized States in Si:P by the MCSCF Method. I. Uncompensated Case

We study the correlation effect on the electronic states in the uncompensated Si:P system from the intermediate to the critical concentration region, by the Multi-Configuration Self Consistent Field (MCSCF) method recently developed by the present authors. By simulating the Si:P system by a cluster model, we clarify the features of the Anderson-localized states and the nature of the metal-insulator transition from a new standpoint. It is shown that most of electrons form spin-singlet pairs and remaining pairs are spin-triplet. Near the metal-insulator transition, MCSCF one-electron orbitals near the Fermi level are extended and the correlation becomes weak by screening. This suggests the Mott-type transition.

Dc conductivity of arsenic-doped silicon near the metal-insulator transition.

dc conductivity measurements have been made on uncompensated Si:As in the concentration range 6.85\ifmmode\times\else\texttimes\fi{}${10}^{18}$32.8\ifmmode\times\else\texttimes\fi{}1${0}^{18}$R ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ for 0.5T77 K, although three samples were studied in a dilution refrigerator. Insulating samples exhibited variable-range hopping (VRH) behavior of the form \ensuremath{\sigma}(T)=${\ensuremath{\sigma}}_{0}$(1/T${)}^{s}$ exp[-(${T}_{0}$/T${)}^{p}$] for 0.86${N}_{c}$0.99${N}_{c}$ for T8 K. The most satisfactory overall fit to the data is p\ensuremath{\sim}(1/4 and s\ensuremath{\sim}0, namely Mott VRH. A new criterion is given to decide the temperature regimes where Mott or Efros-Shklovskii VRH (p=(1/2) should be observed. The characteristic Mott temperature ${T}_{0}$\ensuremath{\propto}(1-N/${N}_{c}$${)}^{3\ensuremath{\nu}}$ yielded 0.77\ensuremath{\nu}0.97. Strong deviations from VRH behavior were observed for N0.84${N}_{c}$. Metallic samples showed a \ensuremath{\sigma}(n,T)=\ensuremath{\sigma}(n,0)+m(n)${T}^{1/2}$ dependence at sufficiently low temperatures. The results yield \ensuremath{\sigma}(n,0)=${\ensuremath{\sigma}}_{0}$(n/${n}_{c}$${\mathrm{\ensuremath{-}}1)}^{\ensuremath{\mu}}$ with ${\ensuremath{\sigma}}_{0}$=376 S/cm, 8.55${n}_{c}$8.60\ifmmode\times\else\texttimes\fi{}${10}^{18}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$, and \ensuremath{\mu}=0.60\ifmmode\pm\else\textpm\fi{}0.05. The coefficient m(n) shows behavior similar to that for Si:P, but shows a second sign crossing for n/${n}_{c}$\ensuremath{\sim}2.4. The m(n) results seem to confirm the dominance of the Hartree interaction for the many-valley case.

Ionized-impurity scattering in the strong-screening limit.

We have developed a self-consistent multi-ion screening formalism which, unlike conventional treatments, explicitly assures that no electron state should contribute more than -e to the net charge screening the donors. A key finding is that formal consistency can be achieved only when neighboring ion potentials overlap somewhat. Ionized-impurity scattering in a semiconductor is therefore intrinsically a multi-ion process, and the tightly screened, isolated-impurity regime is unphysical. Temperature- and doping-dependent majority-carrier mobilities for uncompensated n-type Si, Ge, GaAs, and InP are recalculated using the ``multi-ion'' screening length. The correction to the mobility is often substantial (as much as a factor of 4), and in some regimes the agreement between theory and experiment is considerably improved.