Extrinsic Carrier Research Articles

Electrical Properties of β-Ag2Te and β-Ag2Se from 4.2° to 300°K

The study of electrical properties of β-Ag2Te and β-Ag2Se has been extended to 4.2°K. The former compound was zone refined without decomposition. Both n- and p-type samples of β-Ag2Te were studied; all samples of β-Ag2Se prepared were n type to 4.2°K. Neither semiconductor showed any indication of extrinsic carrier freeze-out or of impurity banding. Study of oxygen as a possible acceptor in β-Ag2Te showed no significant effect; a selenium-doped sample of β-Ag2Se was n-type to 4.2°K.

THE HALL AND SEEBECK EFFECTS IN NONSTOICHIOMETRIC BISMUTH TELLURIDE

Detailed measurements of electrical conductivity (σ), Hall coefficient (RH), and Seebeck coefficient (α) were made on seven bismuth telluride samples of composition Bi2Te3+x, with x ranging from −0.06 to +0.48. Above room temperature the slope of RHT3/2 gave an apparent energy gap about 50% higher than that from the σ slope, and the Hall mobility decreased steeply with a T−4 dependence. These effects could be explained by an electron-to-hole mobility ratio (b) near unity, but the magnitude of α at higher temperatures appeared to require a b value of about 2. At the highest temperature the Hall mobility was found to increase with increasing tellurium content. The electron effective mass (mn) was found to be less than that of the holes (mp), at least below room temperature. Both mn and mp increased with extrinsic carrier concentration, and to some extent with temperature. These facts may be due to a stronger warping of the valence band at higher energies than the conduction band. The Hall mobility below room temperature could be explained by acoustic lattice scattering and degeneracy. At the Seebeck coefficient maxima, the value of αT was found to be roughly constant. The temperature slopes of α below the maxima were generally greater than expected classically. Anomalies were found in RH, RHσ, and α above room temperature in a near intrinsic n-type sample.

Helicon induced D.C. voltage in InSb

We have observed a d.c. voltage induced in the direction of a Poynting vector when helicon waves propagated in a single-crystal slab of n-type InSb. The experiment was performed at a frequency of 70 Gc/s and 77°K on a sample with an extrinsic carrier concentration of 1 × 10su14 cm -3. The sign of the voltage was independent of the sign of the applied d.c. magnetic field. When the microwaves were amplitude-modulated, it was found that the resulting a.c. voltage in the Poynting vector direction was independent of modulation frequency for frequencies as high as 10 kc/sec. The voltage observed as a function of d.c. magnetic field displayed oscillatory behavior due to standing helicon waves in the sample. The voltage amplitude was proportional to microwave power; a typical value was 10μV for 30 mW of incident microwave power. We have interpreted this voltage as arising from the Lorentz force on a carrier due to the microwave magnetic field.

PHOTOCONDUCTION AND SEMICONDUCTION IN MONOCRYSTALS OF THE CHARGE-TRANSFER COMPLEX, PERYLENE–FLUORANIL

Single crystals of the perylene–fluoranil charge-transfer complex were found to be photoconductive throughout the near ultraviolet, visible, and near infrared spectral regions. The temperature dependence of the semiconduction and photoconduction are characterized by apparent activation energies of 0.73 ev and 0.12 ev, respectively. Conductivity parallel to the c-crystallographic axis (along which the complex units are stacked in columns) was found to be about threefold greater than that in the perpendicular direction. Attempts to measure carrier mobilities proved unsuccessful. The results suggest extrinsic carrier generation accompanied by pronounced carrier trapping processes.

Etude de l'equilibre de phases dans le tellurure de mercure

A study of the solid-vapor equilibrium in HgTe is performed. The experimental ( P H , T, x) diagram is given, where ( P H is the mercury vapor pressure, T the temperature of the solid and x the concentration of extrinsic charge carriers. The results can be interpreted by assuming the presence of one structural defect at low temperatures ( T < 350°C)—probably Frenkel defects—and the occurrence of another defect above 350°C. The energy of formation of Frenkel defects W F = 0.50 eV, and the energy of transfer of an interstitial mercury to the vapor W R = 0.19 eV, are deduced from low-temperature results. These equilibrium constants allow to build a theoretical ( P H , T, x) diagram, which is in agreement with experimental results on n-type samples ; the interpretation of results on p-type samples leads to a determination of the electron-to-hole mobility ratio : b≅ 65 at 77°K. The particular results for T > 350°C and the observed dependence of the Hall constant with magnetic field are also discussed. The intrinsic carrier concentration is determined between 20°K and 350°K.

Internal Friction in Germanium and Silicon II: Oxygen Movement and Dislocation Damping

Measurements of the magnitude of electronic and oxygen impurity relaxation peaks in single crystal silicon yield values for the extrinsic carrier lifetime and the relative oxygen concentration, respectively. This method is used to study the production of recombination centres associated with oxygen impurity, and the internal precipitation of oxygen. Recombination centres are induced when oxygen-containing silicon is cooled rapidly from above 1000°C to 650°C, reducing the lifetime to less than 0.35 μsec, which then recovers at a rate which increases with successive heat treatments. Precipitation onto internal particles at 1025°C occurs in the order of 3 hours for 2.7 Ω cm aluminium-doped silicon, and considerably longer for a purer sample, indicating that aluminium acts as an efficient precipitation nucleus. A 2% plastic deformation of the aluminium-doped specimen does not greatly reduce the precipitation time. Analysis of the precipitation curve form indicates that stresses around the precipitate particles may be important in determining the precipitation rate. Dislocation relaxation produces a rise in internal friction at elevated temperatures, an activation energy of 1.1 ev in germanium and 1.5 ev in silicon being associated with the rise. In silicon and germanium specimens which have been plastically deformed by about 2% the process becomes dominant above 0.6 of the melting temperature. Undistorted (`as-grown') specimens show a rise at higher temperatures, which varies in magnitude between specimens, and which could be due to the same process as that in deformed specimens. Oxygen in silicon appears to inhibit the loss process. Experimental results are discussed in the light of three possible theories, and it is concluded that there is insufficient evidence to indicate which one is applicable.

Magnetic Susceptibility of InSb

The magnetic susceptibility of $n$-InSb has been measured for a range of extrinsic carrier densities extending from ${10}^{16}$ to 6\ifmmode\times\else\texttimes\fi{}${10}^{18}$ ${\mathrm{cm}}^{\ensuremath{-}3}$. Measurements were made in the temperature range 300\ifmmode^\circ\else\textdegree\fi{}K to 1.3\ifmmode^\circ\else\textdegree\fi{}K. The degenerate conduction electron susceptibility was determined from the data. The deviation of the conduction band from parabolic form is clearly exhibited in the susceptibility. A theoretical analysis has been made using Kane's band-structure calculation. The mixing of the conduction and valence bands resulting from the magnetic field has been treated exactly. Consideration of these two bands alone will not explain the dependence on concentration of the observed susceptibility; at the higher carrier densities, higher bands are important and a perturbation-theoretical treatment of these indicates that the observed susceptibility is consistent with Kane's model.

Mobility of Electrons and Holes in PbS, PbSe, and PbTe between Room Temperature and 4.2°K

Hall coefficient and resistivity measurements have been made on 29 single crystals (mostly synthetic) of PbS, PbSe, and PbTe between room temperature and 4.2\ifmmode^\circ\else\textdegree\fi{}K. Almost all of the samples had extrinsic carrier concentrations of the order of ${10}^{18}$ per ${\mathrm{cm}}^{3}$, as deduced from the Hall coefficients which were essentially constant over the entire temperature range investigated. Hall mobilities were calculated from the Hall and resistivity data, and were found to increase rapidly with decreasing temperature. Between room temperature and about 50\ifmmode^\circ\else\textdegree\fi{}K the mobility behavior was essentially intrinsic and varied approximately as ${T}^{\ensuremath{-}2.2}$. Below 50\ifmmode^\circ\else\textdegree\fi{}K the mobility curves turned gradually toward the horizontal in a manner resembling the residual resistance phenomenon observed in metals. Values as high as 800 000 ${\mathrm{cm}}^{2}$/v-sec were attained at 4.2\ifmmode^\circ\else\textdegree\fi{}K despite the large carrier concentrations present in all the samples. A simple experiment was performed which suggests that dislocations are the principal scattering mechanism below 50\ifmmode^\circ\else\textdegree\fi{}K, rather than the charged point defects associated with the extrinsic carriers. The possibility that a high static dielectric constant could explain the large mobilities at low temperatures is discussed.

The Electrical Conductivity and Hall Effect of Silicon

The electrical conductivity and Hall effect have been measured over the temperature range 20°K to 500°K on single crystals of silicon with extrinsic carrier concentrations between 2 and 5 × 1012 cm-3. The Hall mobility for electrons and holes can be represented between 100° and 300°K by the expression 1.2 × 108T-2 and 2.9 × 109T-2.7 respectively. Both these results indicate a higher Hall mobility than has been previously reported, and the result for holes is greater than values reported for the drift mobility. From the results between 350° and 500°K the expression ni = 3.10 × 1016T3/2 exp -0.603/kT was obtained for the intrinsic concentration. Attempts were made to estimate the total impurity concentration in these specimens. The variation of extrinsic carrier concentration with temperature and the effect of impurity scattering at 20°K both indicate that the total concentration of impurities is less than 1014 cm-3.

Electrical and Thermal Properties ofBi2Te3

Samples of both $n$-type and $p$-type ${\mathrm{Bi}}_{2}$${\mathrm{Te}}_{3}$ containing from 3\ifmmode\times\else\texttimes\fi{}${10}^{17}$ to 5\ifmmode\times\else\texttimes\fi{}${10}^{19}$ extrinsic carriers were prepared and the phase diagram in the region about ${\mathrm{Bi}}_{2}$${\mathrm{Te}}_{3}$ has been clarified. The Hall mobility parallel to the cleavage planes varies as ${T}^{\ensuremath{-}1.5}$ for holes and ${T}^{\ensuremath{-}2.7}$ for electrons. Room temperature values are ${\ensuremath{\mu}}_{p}=420$ ${\mathrm{cm}}^{2}$ ${\mathrm{v}}^{\ensuremath{-}1}$ ${\mathrm{sec}}^{\ensuremath{-}1}$ and ${\ensuremath{\mu}}_{n}=270$ ${\mathrm{cm}}^{2}$ ${\mathrm{v}}^{\ensuremath{-}1}$ ${\mathrm{sec}}^{\ensuremath{-}1}$. The energy gap is ${E}_{g}=0.20$ electron volts. From thermal conductivity measurements over the temperature range from 77\ifmmode^\circ\else\textdegree\fi{}K to 380\ifmmode^\circ\else\textdegree\fi{}K the lattice conductivity was found to be ${\ensuremath{\kappa}}_{L}=5.10\ifmmode\times\else\texttimes\fi{}\frac{{10}^{\ensuremath{-}2}}{T}$ watt-${\mathrm{deg}}^{\ensuremath{-}1}$ ${\mathrm{cm}}^{\ensuremath{-}1}$. The sharp rise in the thermal conductivity in the vicinity of room temperature was attributed to transport of energy by ambipolar diffusion of electrons and holes.

Effect of Zone‐Refining Variables on the Segregation of Impurities in Indium‐Antimonide

Upon zone‐refining indium‐antimonide, ultimate concentrations of two slowly segregating impurities are approached. The most slowly segregating impurity, identified as tellurium, was found to be n‐type which lowers the melting point of indium‐antimonide. The second most slowly segregating impurity, identified as zinc, was shown to be p‐type which raises the melting point of indium‐antimonide. Both impurities originated in the indium. Electrorefining is an effective technique for removal of zinc from indium. Zone‐refining is an effective technique for removal of tellurium from indium. There are no indications that deviations from stoichiometry prevent the attainment of extrinsic carrier concentrations below 1014/cm3 in indium‐antimonide.

Electrical Properties of Silicon Containing Arsenic and Boron

Electrical conductivity and Hall effect have been measured from 10\ifmmode^\circ\else\textdegree\fi{} to 1100\ifmmode^\circ\else\textdegree\fi{} Kelvin on single-crystal silicon containing arsenic and boron. Extrinsic carrier concentration is computed from Hall coefficient. Analysis of extrinsic carrier concentration indicates the ionization energy of arsenic donor levels to be 0.049 ev and of boron acceptor levels to be 0.045 ev for low impurity concentrations. Fermi degeneracy is found to occur in the range ${10}^{18}$ to ${10}^{19}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ impurity concentration. Extrinsic Hall mobility is computed from Hall coefficient and conductivity. Curves of Hall mobility against resistivity at 300\ifmmode^\circ\else\textdegree\fi{}K are computed from theory and compared with experiment. The temperature dependence of lattice-scattering mobility is found from conductivity to be ${T}^{\ensuremath{-}2.6}$ for electrons and ${T}^{\ensuremath{-}2.3}$ for holes. From conductivity mobility and intrinsic conductivity, it is found that carrier concentration at any temperature below 700\ifmmode^\circ\else\textdegree\fi{}K is given by the expression: $np=1.5\ifmmode\times\else\texttimes\fi{}{10}^{33}{T}^{3}\mathrm{exp}(\ensuremath{-}\frac{1.21}{\mathrm{kT}})$. The temperature dependence of the ratio Hall mobility/conductivity mobility is determined for holes and electrons.

Optical Studies of Injected Carriers. I. Infrared Absorption in Germanium

The infrared absorption of injected carriers in germanium has been observed by a modulation technique. For injection into low-resistivity material, the data indicate a linear relationship between injected carrier density and injection current. For injection into high-resistivity material, departure from a linear relationship is indicated. The absorption spectrum of injected carriers resembles that of extrinsic carriers.

Further studies on the electron theory of solids: Sir J. J. Thomson. ( Phil. Mag., October, 1922)

There is a number of materials where bipolarons (BP) are probably the main extrinsic carriers. We discuss a dense system of BP produced by the equilibrium charge injection at the surface of Schottki or MIS junctions. Possible super-conductivity of this system due to the Bose-condensation of BP is studied.