Lowest Conduction Band Minimum Research Articles

Nanometer-scale investigation of metal-SiC interfaces using ballistic electron emission microscopy

We report ballistic-electron emission microscopy (BEEM) investigation of Pd, Pt Schottky contacts on 6H-, 4H-SiC, and Pd/15R-SiC. Measured Schottky barrier heights of 6H- and 4H-SiC samples appear spatially uniform up to the fitting error due to noise (0.03–0.04 eV and 0.1–0.2 eV for 6H- and 4H-SiC, respectively). In 4H-SiC, we observed an additional conduction band minimum (CBM) ∼0.14 eV above the lowest CBM, which provide direct experimental verification of band theoretical calculation results. Additionally, we sometimes observed enhancement in ballistic transmittance over regions intentionally stressed by hot electron injection using BEEM. We also report recent results on Pd/15R-SiC sample indicating a higher CBM ∼0.5 eV above the lowest CBM. In Pd/15R-SiC, interesting large variations in BEEM spectra at different locations were observed, possibly suggesting an inhomogeneous metal/semiconductor interface.

Direct observation of conduction-band structure of4H- and6H−SiCusing ballistic electron emission microscopy

We performed ballistic electron emission microscopy (BEEM) measurements on Pt and $\mathrm{Pd}/4H$- and $6H\ensuremath{-}\mathrm{SiC}$ Schottky contacts, obtained Schottky barrier heights, and observed qualitatively different behavior of the BEEM spectra for $4H$- and $6H\ensuremath{-}\mathrm{SiC}.$ In particular, in $4H\ensuremath{-}\mathrm{SiC}$ we observed an additional minimum $\ensuremath{\sim}0.14\mathrm{eV}$ above the lowest conduction-band minimum. We calculated the electronic band structure for both polytypes and found it in good quantitative agreement with our BEEM observations as well as good qualitative agreement with previous SiC band-structure calculations.

Nanometer-Scale Investigation of Schottky Contacts and Conduction Band Structure on 4H-, 6H- and 15R-SiC Using Ballistic Electron Emission Microscopy

We have performed ballistic-electron emission microscopy (BEEM) of Pd and Pt Schottky contacts on 6Hand 4H-SiC and Pd Schottky contacts on 15R-SiC. Measured Schottky barrier heights (SBH’s) appear spatially uniform up to the fitting error due to noise (~0.03 and ~0.1 eV for 6Hand 4H-SiC, respectively). In 4H-SiC, we observed an additional conduction band minimum (CBM) ~0.14 eV above the lowest CBM, which is in good agreement with our band theoretical calculation. Preliminary results on Pd/15R-SiC indicate a higher CBM ~0.5 eV above the lowest CBM, and possibly another higher CBM ~0.3 eV above the lowest CBM. Also, in Pd/15RSiC, large variations in BEEM spectra at different locations were observed, suggesting an inhomogeneous interface. Additionally, we sometimes observed enhancement in ballistic transmittance over regions intentionally stressed by hot electron injection. We report ballistic-electron emission microscopy (BEEM) measurements of Pd and Pt Schottky contacts on 6Hand 4H-SiC, and Pd contacts on 15R-SiC. The BEEM technique is an extension of scanning tunneling microscopy (STM) and can be used to probe local electronic properties of buried metal/semiconductor interfaces with nanometer-scale spatial resolution and high energy resolution [1,2]. Figure 1 shows the schematic experimental setup with corresponding energy-level diagrams for BEEM. The STM tip is used to inject hot electrons into a thin metal film, with the hot-electron peak energy controlled by the applied tip bias VT . Provided the metal film is thin enough compared with the electron mean free path, a small fraction of these electrons can cross the metal film elastically and can enter the semiconductor conduction band if injected with sufficient energy. Hence, the local Schottky barrier height (SBH) [3] qVB can be directly determined by measuring BEEM Ic-VT curves (also called BEEM spectra) and evaluating the threshold voltage Vth for Fig. 1: (a) Physical setup of the BEEM experiment on SiC and (b) the corresponding energy level diagram (only the lowest CBM is shown). By measuring the dependence of Ic (flux of ballistic electrons from the STM tip into the SiC) on tunnel voltage VT (at constant tunnel current IT) we can probe the local Schottky barrier height and SiC band structure. A

Relativistic band structure calculation of cubic and hexagonal SiC polytypes

A full-potential band structure calculation, within the local density approximation to the density functional theory, has been performed for the polytypes 3C, 2H, 4H, and 6H of SiC. The calculated effective electron masses are found to be in very good agreement with experimental values. The electron-optical phonon coupling has been estimated and the polaron masses are calculated to be 3%–13% larger than the corresponding bare masses. The effective electron masses of the second lowest conduction band minima are also presented and the calculated energy difference between the two lowest minima in 4H–SiC is only 0.12 eV. The lowest conduction band in 6H–SiC is found to be very flat and to have a double-well-like minimum along the ML line. The top of the valence bands has been parametrized according to the k⋅p approximation, whereupon the effective hole masses have been determined. The spin-orbit interaction was found to have a strong influence on the value of the effective hole masses. Furthermore, total and partial densities of states are presented.

Ab initio calculations of structural and electronic properties of 15R SiC

We report on ab initio calculations of structural and electronic properties for rhombohedral 15R SiC within the density-functional theory in the local density approximation. Besides the structural parameters we present the electronic band dispersion along high-symmetry lines of the irreducible part of the Brillouin zone and compare the position of the lowest conduction-band minimum with those of cubic and hexagonal polytypes. Furthermore we derive from the conduction-band dispersion the components of the effective-mass tensor and compare these with experimental data.

Intervalley scattering potentials of Ge from direct exciton absorption under pressure.

We have measured the dependence on pressure of the low-temperature (10 K) direct exciton optical absorption of Ge up to 12.3 GPa. The sharp exciton peak at the direct energy gap (${\mathit{E}}_{0}$) of Ge is found to broaden significantly with increasing pressure. This effect, which is attributed to intervalley scattering via electron-phonon interaction, is most pronounced for pressures above \ensuremath{\sim}0.6 GPa, where the X valley becomes the lowest conduction-band minimum. From the pressure-induced exciton broadening we determine the \ensuremath{\Gamma} to X point intervalley deformation-potential constant ${\mathit{D}}_{\mathrm{\ensuremath{\Gamma}}\mathit{X}}$=2.2(3) eV/\AA{} and an upper bound of ${\mathit{D}}_{\mathrm{\ensuremath{\Gamma}}\mathit{L}}$=4.5 eV/\AA{} for scattering from \ensuremath{\Gamma} to the L valleys. The deformation potential ${\mathit{D}}_{\mathrm{\ensuremath{\Gamma}}\mathit{X}}$ of Ge is about 50% smaller compared to isoelectronic GaAs. This difference is attributed to the fact that interatomic matrix elements between s and d states of the \ensuremath{\Gamma} and X conduction-band minima as well as the d character of the X minimum are larger in GaAs.

The location of the lowest conduction band minima in gallium phosphide from bound exciton luminescence

Two weak satellite series with acceptor-independent displacement energies of 4.2 3 meV and 7.8 3 meV have been observed in the luminescence of excitons bound to neutral acceptors in GaP. These satellites contain broad background luminescence. Rather well defined superimposed peaks show relative strength which increases dramatically with decrease in exciton binding energy. The most plausible mechanism for these satellites involves bound exciton recombination with emission of one phonon to conserve momentum in the indirect transition and one or two further phonons to conserve momentum in g-type inter-valley scattering processes. This model is consistent with all known properties of the satellites and is strongly supported by a quantum-mechanical line width calculation. The narrow components arise from a diffuse tail on the bound exciton wave-function which is enhanced by the electron—hole correlation. The existence of this g-scattering process shows that the conduction band minima in GaP lie at 0.953 K (100) max , not exactly at K (100) max as believed hitherto. This revision has important consequences for several properties of n-type GaP.

Phonon dispersion in AgBr and exchange of the transverse mode Eigenvectors at L

Using inelastic neutron scattering, phonon dispersion curves for AgBr at 85 K are measured along the 〈100〉, 〈110〉 and 〈111〉 directions in reciprocal lattice. Special attention is payed to the anomalous behaviour of the TA and TO branches at the L-point (0.5; 0.5; 0.5). With high resolution ( Δv = 0.24 THz) their frequencies are determined to be 1.54 and 1.93 THz, respectively. The ratio of their integrated intensities is found to be 2.15 ± 0.4. This value is in good agreement with the ratio of 2.38 calculated under the assumption that at L the heavier (Ag +) ions is vibrating with the higher and the lighter (Br -) ion with the lower frequency, as suggested by recent lattice dynamical calculations. Comparison of our phonon frequencies with corresponding optical data prove that the momentum-conserving phonons associated with the lowest indirect exciton transition belong to the TO and LA phonon branches at L. Since the lowest conduction band minimum at Γ is well established experimentally, our results in turn imply that the uppermost valence band maximum is right at the L-point.

Hydrostatic pressure resistivity variation in n-type ZnSiP2, CdSiP2and CdGeAs2

Hydrostatic pressure resistivity measurements up to 15 kbar at 300K have been made on n-type single crystals of ZnSiP2 and CdSiP2. Results are consistent with recent theoretical conduction band structures. In both cases the pressure characteristics can be analysed in terms of the lowest conduction band minima not having direct Gamma 1C properties. For CdSiP2 results indicate that more than one conduction band minimum is close in energy at atmospheric pressure. An increase in resistivity with pressure is observed for CdGdAs2 implying that the Gamma 1C minimum is lowest in energy.

Shubnikov-de Haas effects in Bi 2Se 3 with high carrier concentrations

Shubnikov-de Haas frequencies were measured in highly degenerate n-type Bi 2Se 3 having a higher carrier density (∼9 × 10 25m -3) than previously reported. The Fermi surface was found to be elongated along the trigonal axis, fitting a spheroidal model with an axial ratio of 5.0 for angles up to θ = 45°. Comparison of the number of carriers obtained from Hall measurements with that obtained from the Shubnikov-de Haas measurement supports the contention that the lowest conduction band minimum is a single surface located in the center of the Brillouin zone. The higher effective mass (0.25 m 0) found for these carrier concentrations indicates that the band is non-parabolic.

The Lowest Conduction Band Minima of A2B4C‐Type Semiconductors

AbstractStudies of the influence of hydrostatic pressure up to 6500 kp/cm2 on the fundamental absorption edge of eleven A2B4C‐type compounds of chalcopyrite structure were carried out at room temperature. The large values of dEg/dP ≈ (7.3 to 10.0) × 10−6 eV kp−1 cm2 were obtained for CdGeAs2, ZnSnAs2, ZnGeAs2, CdSnP2, CdSiAs2, ZnSnP2, CdGeP2 (first group of crystals) and much smaller values ≈(—0.7 to + 1.6) × 10−6 eV kp−1 cm2 for ZnSiAs2, ZnGeP2, ZnSiP2, and CdSiP2 (second group of crystals). The comparison of these pressure coefficients with those of Γ15‐Γ1 and Γ15‐Γ1 energy gaps in A3B5 compounds leads to the conclusion that the lowest conduction band minima in the first and second groups of A2B4C crystals are Γ1 and Γ3 (or T1 + T2), respectively. This conclusion is in a good agreement with the calculated band structure of the investigated compounds and is confirmed by the studies of the slope of the fundamental absorption edge. The absorption edge of the first group of crystals is sharp due to the optical transitions Γ4 → Γ1 (derived from Γ15 → Γ1 in zincblende) and that of the second group of crystals is smooth and is caused by the transitions Γ4 → Γ3 or Γ4 → Γ1 + T2 (both correspond to indirect transitions Γ15 → X1 in zincblende).

Longitudinal Piezoresistance of AlxGa1−xAs

Samples of n-type AlxGa1−xAs were prepared by liquid phase epitaxy on a GaAs substrate. When x≳0.4 the material has the indirect band structure characteristic of AlAs. Longitudinal piezoresistance measurements were performed on this material with stress along the 〈100〉 and 〈111〉 crystallographic directions. The results indicate that the lowest conduction-band minima in the alloy, and by inference in pure AlAs, lie along the 〈100〉 directions in k space as in silicon.

The gunn effect and conduction band structure in Ga xIn 1− xSb alloys

The observation of the Gunn effect in Ga x In 1− x Sb alloys is reported and shown to be consistent with a conduction band structure having a next higher set of minima along the <111> directions in k space above the lowest conduction band minimum at the center of the Brillouin zone for all values of x.

Band structure of gray tin under uniaxial stress

Gray tin, a perfect semimetal, becomes a semiconductor under uniaxial stress. The lowest conduction band minimum at k = 0 becomes strongly anisotropic. The valence band of the compressed material has highest maxima away from k = 0 ; toroidal constant energy surfaces are obtained for [111] and for [100] compression.

Intervalley-Scattering Selection Rules in III-V Semiconductors

Selection rules are presented for intervalley scattering between the lowest conduction-band minima at $\ensuremath{\Gamma}$, $X$, and $L$ in the Brillouin zone of a III-V semiconductor. These selection rules are required for theories of the Gunn effect. The two most important crystals experimentally are GaAs, where longitudinal optic phonons cause the intervalley scattering, and InP, where longitudinal acoustic phonons produce the scattering.

Electroluminescence and Lasing Action in GaAsxP1−x

The electroluminescence of Zn diffused diodes was studied in forward and reverse bias. Emission spectra obtained for forward biasing showed a near-edge as well as a low-energy line. In the composition range x&amp;gt;0.55, where the lowest conduction band minimum is at k=0, most photons are emitted in the near-edge line. Lasing action could be observed in this range, and the shortest wavelength where stimulated emission was obtained at 77°K was 6380 Å. For x&amp;lt;0.55, where the lowest conduction band minimum is the (100) minimum, the low-energy emission becomes dominant. The energy separation between near-edge and low-energy line varies between 0.4 and 0.47 eV at 77°K depending on composition. This suggests that the same defect is responsible for the low-energy emission in all these diodes (including GaAs and GaP). In reverse bias, near-edge emission and emission at higher energies than bandgap could be observed for x&amp;lt;0.55. The cutoff energy of the emission on the high-energy side was measured as a function of composition. It was found to vary in a manner similar to the variation of the energy of the (000) conduction band minimum. The external quantum efficiency of the forward bias emission drops sharply by two orders of magnitude at the composition x=0.55 when x is decreased. The efficiency of the reverse bias emission is independent of composition.

Intrinsic edge absorption in diamond

The optical transmission spectra of several diamonds have been studied over the range 5·0 to 6·0 eV (2450 to 2000 Å) and at many temperatures between 90 and 600 °K. The reflexion spectrum was also recorded between 5 and 14 eV (2450 to 900 Å) at 295 °K and between 5 and 8 eV (2450 to 1550 Å) at 133 °K. The intrinsic features of the absorption edge spectrum are discussed in terms of allowed indirect electronic transitions into exciton and free carrier states of the crystal. A weak absorption component, exhibited only by a p -type semiconducting specimen (type II b ), is tentatively identified with an exciton state bound to the acceptor centre. Analysis of the absorption data yields six phonon energies. Three of these are greater than the Raman energy ( hω ) R and appear to represent combinations of two or more phonons having the following energies: (1) ( kω ) Raman = 0·167 ± 0·010 eV, (2) ( kω ) transverse optical = 0·143 ± 0·002 eV, (3) ( kω ) longitudinal optical, acoustical =0·132 + 0·002 eV, (4) ( kω ) transverse acoustical = 0·083 ± 0·003 eV. The classification of the phonons (2) to (4) given above is discussed in the light of the current knowledge of the lattice vibrational spectrum of diamond. The present results suggest that the lowest minima of the conduction band are near to the boundaries of the reduced zone in the &lt;;100&gt; direction (symmetry point X 1 ), if the maximum of the valence bands lies at the zone centre. The binding energy of the indirect exciton, measured from the absorption spectra, is 0·070 ± 0·004 eV. The density of states effective mass of electrons at the lowest conduction-band minima, estimated from this result, is ca. 0·2 m 0 , where m 0 is the mass of a free electron. The indirect energy gap at 295 °K and its rate of change of temperature between 135 and 295 °K, obtained from the absorption data, are E g = 5·470 ± 0·005 eV ; d E g /d T = -5·4 ± 0·5 x 10 -5 eV /degK The corresponding values for th e direct energy gap, obtained from th e reflexion d ata, are E g = 7·02 ± 0·02 eV ; d E g /d T = -6·3 ± 1·8 x 10 -4 eV /degK Finally, a broad peak has been observed in the reflexion spectrum at the energy predicted for the direct transition at &lt;111&gt; zone boundaries in diamond (9·2 ±0·1 eV).