Vol. 20, No. 7 (1964)
1964, 111 (7): 579-595. doi: 10.7498/aps.20.579
Using the theory developed in , certain questions of transport process in strong magnetic field are discussed. In the first place, we show that for this type of transport process one must consider the boundary condition explicitly. For transverse conductivity, it is not necessary to solve the kinetic equation of the Boltzmann type when the boundary condition is treated correctly, and Titeica's picture is shown to be correct in general order of perturbation expansion. Secondly, the solution of the case of external electric field's ω≠0 and its transition to the classical case are discussed. We show that under the same condition ωHτ>1, E0τ? 1, the quantum solution is different from that of the classical case. Finally, in an appendix, the question of eliminated divergence produced by the integral of state density is discussed. We indicate that in the realizable case a term of magnitude (εc/kT)° is as important as that of -ln (εc/kT). This correction makes the theoretical value of ρT/ρL consistent with the experimental data.
ASYMPTOTIC BEHAVIOUR OF π-π SCATTERING AMPLITUDE AND SINGULARITIES IN COMPLEX L-PLANE IN STRIP APPROXIMATION
1964, 111 (7): 596-606. doi: 10.7498/aps.20.596
The contribution of inelastic intermediate states to the singularities in complex l-planc and to the asymptotic behaviour of crossed channel are investigated in the strip approximation. The procedure is to solve the simultaneous equations suggested by Chew, Frautschi and Mandelstam by means of iteration method. The general iteration expressions for the s channel high energy amplitude f(s,t) and the t channel partial wave amplitude fl(t) are derived. It is shown that the divergence difficulty mentioned by Chew, Frautschi and Mandelstam is not present in the iteration results of the above f(s,t). The main results of first iteration are as follows: i) The total cross section falls slowly for not very high energies, but at the end tends to a constant.ii) The diffraction angular distribution will have a long tail. As the energy increases, this long tail extends towards the small angle region.iii) In the t channel a cut will appear along the real axis in complex l-plane; the right ending point of the cut is at l=1 when t=0, and moves to the left as t decreases, with a speed nearly half that of the vacuum pole.Higher order iterations are also investigated; the results are qualitatively analogous to those of first order.
1964, 111 (7): 607-623. doi: 10.7498/aps.20.607
The surface impedance of a ferromagnetic metal in a parallel magnetic field has been calculated. Both exchange interaction and the anomalous character of skin-effect havebeen taken into account. Calculation has been carried out for both the "exchange" boun-dary condition (?m)/(?n)=0 and the "pinning" condition m = 0 for the magnetic moment.The influence of the boundary scattering character of conduction electrons has been also considered. Furthermore, by making use of the Aзбелъ-KaHep method in the theory of cyclotron resonance the surface impedance has been evaluated with the gyrotropy of the electrical conductivity taken into account.
1964, 111 (7): 624-635. doi: 10.7498/aps.20.624
The Green's function method is applied to the study of isotropic antiferromagnetism for the case S≥1/2. Expressions are obtained for the energy of the ground state, the sublattice spontaneous magnetization, and the parallel susceptibility. These results are compared with those of the spin wave theory for low temperatures. For high temperatures they are found in agreement with the well known results of other theories. Thus, the present theory gives a unified result which is approximately valid in the whole temperature range.
MEASUREMENT OF THE IMPURITY DISTRIBUTION OF DIFFUSED LAYERS IN SILICON BY THE FOUR-POINT PROBE AND THE ANODIC OXIDATION TECHNIQUE
1964, 111 (7): 643-653. doi: 10.7498/aps.20.643
Discussed in this paper are (1) the technique of removing thin layers of silicon by the anodic oxidation method; (2) the measurement of the sheet conductance of diffused layers in silicon by the four-point probe method; and (3) the measurement of impurity distribution of diffused layers in silicon by the four-point probe and the anodic oxidation technique.Emphasis has been given to the practical aspects of the experimental techniques including the precautions to be taken to achieve uniform and thin (300-1500?) layer removals from the silicon surface by the anodic oxidation method; the methods to control and to check the thickness of the layer removal; the errors introduced in the sheet conductivity and in the impurity distribution measurements respectively; and the steps to be taken for error reduction.For illustration, a typical example is given for the measurement of the impurity distribution of phosphorus diffusion into silicon. The diffusion depth is 4.9 /μm. Spacings between measurement points range from 400? to 1600?. The error for sheet conductivity measurement is estimated to be less than 3%, that for impurity distribution is estimated to be less than 20%. Problems that remain to be solved are briefly mentioned.
1964, 111 (7): 654-661. doi: 10.7498/aps.20.654
In the research work of silicon devices, it is often needed to measure and control accurately the thicknesses of SiO2 thin films. Although it is well known that SiO2 thin films exhibit vivid colours under sunlight due to interference effects, yet there is no simple relationship between the thickness of the thin film and the wave length of the light corresponding to the observed colour. Described in this paper is a method for the measurement of the thicknesses of thermally grown SiO2 thin films. From the measured data, we have calculated the index of reflection of the SiO2 thin film as well as the phase shift difference between the SiO2-Si interface and the Si-air interface.By measuring the thicknesses of a set of SiO2 thin films of different colours, a chart is obtained which lists the thicknesses and the corresponding colours of the thermally grown SiO2 thin films. The results are found to be in fairly good agreement with that calculated from Roller's table. Our results include the thickness range of 3300-4200? which was not covered in Rollet's table.
1964, 111 (7): 662-669. doi: 10.7498/aps.20.662
Detailed distributions of diffusion of phosphorus into silicon have been measured by the four-point probe method. During the measurement, each successive layer is removed by the anodic oxidation technique. These impurity distributions are found to deviate from the error function complement even with the surface concentration kept constant during diffusion. If it is assumed that this is due to a concentration denpendence of the diffusion coefficient, the experimental results would indicate that the diffusion coefficient rises very rapidly when the concentration exceeds 1019/cm3.Detailed distributions of diffusion of phosphorus into silicon through silicon dioxide films of different thicknesses grown by thermal oxidation have also been measured by the method described above. The experimental data indicate that the silicon dioxide films remain effective for masking at a diffusion temperature as high as Td = 1300℃. With diffusion time close to masking failure time, the surface concentration is found to be close to l017/cm3 and the diffusion depth is found to be very small (～1 μ). However, for sufficiently long diffusion times, the surface concentrations apparently reach an ultimate value not influenced by the thickness of the oxide film, it remains a constant as long as the vapour pressure of diffusont source is kept constant. Detailed distributions of diffusion of phosphorus through a silicon dioxide film are also found to be strongly dependent on the nature and the condition of the diffusing source. An increase of the thickness of the oxide film during diffusion has been observed; it might affect the impurity distribution especially in the region near the surface.