Eijiro Haga

Free-Carrier Infrared Absorption and Determination of Deformation-Potential Constant in n-type InSb

A quantum mechanical theory of the infrared absorption by conduction electrons in InSb is developed according to the second-order perturbation formula in degenerate cases. The absorption coefficient due to acoustical phonons is calculated by means of the deformation-potential method. The deformation-potential constant E 1 is only contained as an unknown parameter and the values of the other quantities are obtainable from measurements. The magnitude of E 1 can be easily determined from the comparison between the theory and experiments, and thus an information about the scattering mechanism is obtainable. When | E 1 | is taken as 30 eV, the present theory is in excellent agreement with the experiment of Kessler and Sutter for various carrier concentrations and wave lengths and also with that of Spitzer and Fan for a more wide range of wavelength. It is also shown that the theoretical value of the optical cross section for free electrons in pure materials is quite consistent with the value found by Kurnick a...

Free-Carrier Infrared Absorption in III-V Semiconductors III. GaAs, InP, GaP and GaSb

The free carrier absorption data for n -GaAs, -InP, -GaP and -GaSb are analysed in order to investigate the scattering mechanism of electrons. The magnitudes of the deformation potential constant E 1 are found to be ∼6 eV for GaAs, ∼0 eV for InP, ∼55 eV for GaP and ∼60 eV for GaSb. It is found from this that, among acoustic and optical phonon scatterings, the former is predominant in GaP and GaSb, and the latter predominant in GaAs and InP. The impurity concentration is found to be very large compared with the electron concentration, for the samples of GaAs and InP with low carrier concentrations. This suggests the presence of some additional scatterers different from the ordinary ones, that is, lattice vibrations and ionized impurities. From the present analysis, it is inferred that the absorption coefficient due to additional scatterers have a wavelength dependence very similar to the one due to ionized impurities.

Free-Carrier Infrared Absorption in III-V Semiconductors IV. Inter-Conduction Band Transitions

The infrared absorption bands observed in 1∼5 µ are theoretically investigated under the assumption that the absorption is due to the transition of electrons between two conduction bands which have the minima being located at different points in the zone. With use of the second order perturbation in the presence of photons and crystal imperfections, the theoretical curves give different shapes according as the possible intermediate states are the D - or I -type. The first has a sharp peak in the absorption band, while the latter forms a broad band. For AlSb and GaSb, the observed shapes of the absorption bands agree reasonably with the calculated ones for the D - type . The carrier concentration dependence of the absorption coefficient in AlSb can also be explained fairly well. For GaAs, the absorption band calculated for the I - type agrees well with the experimental one at the points of the shape, the carrier concentration dependence and the temperature dependence. Also, the gap energy between two minim...

Free-Carrier Infrared Absorption in III-V Semiconductors II. InAs

An analysis for the infrared absorption by free carriers in n -type InAs is carried out on the basis of the previous theory developed for n -type InSb, in order to investigate the scattering mechanism. The magnitude of the deformation potential constant E 1 is found to be 10 eV , and it is found that the contribution from acoustical phonons is not important for all samples of Dixon. The impurity concentration is found to be N imp =11 N e for the sample A of the smallest carrier concentration: N e =2.8×10 16 cm -3 , and to be N imp = N e for the other samples. Optical phonons make the most important contribution for samples of relatively low carrier concentrations except the sample A , in which the contribution from impurities is comparable to the one from optical phonons. The presence of an unknown scatterer in the sample A is suggested and a discussion for this is given. A discussion on the screened Coulomb potential used in the calculation of the impurity scattering also is given.

Infrared Absorption of Semiconductor at Low Temperatures

The infrared absorption observed at low temperatures, where the wavelength dependence of absorption is like the free carrier absorption and also the magnitude is even larger than at room temperature, is explained on the basis of the direct transition of electrons from a shallow donor level to the lowest conduction band. It is shown that the absorption coefficient resulting from this mechanism is in good agreement with experiments for n -type AlSb, GaP and Si when a reasonable value is taken for the concentration of donor electrons. For the excess absorption observed in the above materials, the indirect transition from a shallow donor level to the conduction bands of subsidiary minima is investigated as a possible mechanism. The calculated absorption curve is shown to be very similar to that due to the interconduction band transition investigated previously.

Nuclear Quadrupole Interaction in Simple Metals

The spin lattice relaxation time due to the interaction between nuclear quadrupole moments and conduction electrons is calculated by taking into account the interaction between conduction electrons. It is shown that, for Au 197 , it contributes to the measured value. The sudden change of the exchange enhancement factor as one goes from Ag 0.05 Au 0.95 to pure Au, which is found without taking into account the quadrupolar interaction for pure Au, is explained by this mechanism. Interactions between nuclei due to the direct and indirect quadrupolar interactions are also calculated and compared with the dipolar interaction.

Nuclear Spin-Lattice Relaxation Time Due to the Orbital Interaction

In the free electron model the spin-lattice relaxation time T 1 (orb) due to the interaction with the orbital motion of conduction electrons diverges if the nuclear Zeeman energy is neglected. Without neglecting it, T 1 (orb) with the field dependence of a form log ( H ext ) is derived for high magnetic fields. The divergence which arises for H ext =0 is removed by taking into account the dipole interaction between nuclear spins. The effect of the electron correlation at high fields is examined by use of the RPA approximation. The Hubbard approximation for the exchange interaction has no effect. Therefore, by use of a reasonable approximation, the result that ( T 1 (orb) ) -1 increases in the presence of the exchange interaction is found. It is seen that the enhancement is small compared with the one for the spin paramagnetism.

Optical Properties due to Donor Electrons in Semiconductors

The free carrier-like absorptions observed at low temperatures have been interpreted, in the previous theory, as due to excitations of donor electrons into the lowest conduction band. This theory is modified by making use of the hydrogen-like wave function for the continuous spectrum of a donor electron. According to the present theory, the maximal value of the absorption coefficient appears at the photon energy of about 2.2 times the donor activation energy. And the qualitative behavior is similar to that by the previous theory. The theory is compared with experiments for n-type GaP and Si, and gives a better agreement with experiments for GaP with respect to the wavelength dependence. The Faraday rotation due to donor electrons is calculated considering the presences of the excited donor states and the lowest conduction band. The result is found to be similar to that due to free carriers with respect to the magnitude and the wavelength dependence, for the photon energy larger than about three times the ...

Spin-Lattice Relaxation Time Due to the Quadrupole Moment of Au197 in Gold Metal

By use of the single-OPW, the expression for the spin-lattice relaxation time T 1 ( Q ) due to the quadrupole interaction is derived taking into account the electron interaction. The matrix element of the quadrupole interaction is calculated by use of the representation of the rotation group, and it is found that the effect of the core enhancement is represented by a function, α( q ), depending on the magnitude of the scattering wave vector q of an electron and α(2 k F ) agrees with the core enhancement factor by Kohn and Vosko. The numerical calculation leads to T 1 ( Q ) T =32 sec K which is considerably large in comparison with the value, 13 sec K, estimated from the deviation from the Korringa relation due to the electron interaction. When the value of α(2 k F ), for silver, estimated by Fukai by use of the single-pseudo-wave function is taken into account, a reasonable value is obtained.

Theory of Thermoelectric Power of Ionic Crystals, III

When temperature gradient is given in a specimen of AgCl doped with CuCl, its thermoelectric power changes with time owing to the thermal diffusion of copper ions, and then reaches its steady value. If the temperature gradient is removed after such a steady state is attained, the electronmotive force continues to exist for a while, but it decreases with time according as the copper ions diffuse again to the previous homogeneous distribution. The expressions for such processes are derived under proper assumptions. The time constant for them is estimated with use of the conductivity data of Ebert and Teltow. The information on the heat of transport of Cu + will be obtained if experiments on such processes are carried out.