Keisuke Mitsumoto

Quadrupole Effects of Vacancy Orbital in Boron-Doped Silicon

We have investigated low-temperature properties at a longitudinal elastic constant C L[111] of a boron-doped silicon crystal grown by a floating zone (FZ) method. The softening of C L[111] depending on magnetic fields indicates that a magnetic charge state V + of a vacancy orbital accommodating three electrons is stable. Appreciable anisotropy in the softening of C L[111] at magnetic fields along the [111] and [1\bar10] axes up to 10 T is described in terms of a quadrupole susceptibility for the vacancy orbital consisting of a Γ 8 quartet ground state and Γ 6 doublet excited state due to the spin–orbit interaction.

Elastic Softening of Surface Acoustic Wave Caused by Vacancy Orbital in Silicon Wafer

We have performed surface acoustic wave (SAW) measurements to examine vacancies in a surface layer of a boron-doped silicon wafer currently used in semiconductor industry. A SAW with a frequency of fs = 517 MHz was optimally generated by an interdigital transducer with a comb gap of \(w=2.5\) µm on a piezoelectric ZnO film deposited on the (001) silicon surface. The SAW propagating along the [100] axis with a velocity of \(v_{\text{s}}=4.967\) km/s is in agreement with the Rayleigh wave, which shows an ellipsoidal trajectory motion in the displacement components ux and uz within a penetration depth of λp = 3.5 µm. The elastic constant Cs of the SAW revealed the softening of ΔCs/Cs = 1.9 × 10−4 below 2 K down to 23 mK. Applied magnetic fields of up to 2 T completely suppress the softening. The quadrupole susceptibilities based on the coupling between the electric quadrupoles Ou, Ov, and Ozx of the vacancy orbital consisting of Γ8–Γ7 states and the symmetry strains eu, ev, and ezx associated with the SAW ac...

Dissipation in Non-Kramers Doublet of PrMg3

The low-temperature ultrasonic dispersion in the transverse ( C 11 - C 12 )/2 mode of PrMg 3 with the non-Kramers-doublet ground state has been investigated in temperatures down to 20 mK. The dispersion is caused by a thermally activated motions characterized by an Arrhenius-type relaxation time of τ=τ 0 exp ( E / k B T ) with low activation energy, E = 500 mK, and slow attempt time, τ 0 =8.5×10 -10 s. The coupling of the electric quadrupoles of the non-Kramers-doublet ground state to transverse lattice vibrations leads to a vibronic ground state with dissipation. The vibronic state in PrMg 3 releases the entropy of k B ln 2 with lowering temperature across the activation energy. A Kondo-like singlet state due to the binding of the non-Kramers doublet to the lattice vibrations appears at low temperatures far below the activation energy.

Quadrupole Ordering and Rattling Motion of Clathrate Compound Pr3Pd20Ge6

We have investigated the quadrupole ordering of 4f-electrons and the rattling motion of guest rare-earth ions in the clathrate compound Pr 3 Pd 20 Ge 6 using ultrasonic measurements. The elastic constants ( C 11 - C 12 )/2 and C 44 exhibit considerable softening at low temperatures. A minimum of ( C 11 - C 12 )/2 at T Q1 = 0.25 K indicates antiferroquadrupole ordering associated with a Γ 3 doublet of a crystal-field ground state at the 8c site, while a minimum of C 44 at T Q2 = 60 mK indicates the ferroquadrupole ordering of a Γ 5 triplet of a crystal-field ground state at the 4a site. The antiferroquadrupole phase depending on magnetic field direction shows a highly anisotropic behavior. The field-induced ordered phase due to the level crossing of the CEF ground state at the 8c site in magnetic fields along the [001] direction has been found. Furthermore, for the elastic constant C 44 and the attenuation coefficient α 44 we found a frequency dependence at two different temperatures of 15 and 25 K, which ...

Ultrasonic study of vacancy in single crystal silicon at low temperatures

We have performed ultrasonic measurements at low temperatures in order to investigate vacancy in single crystal silicon. The longitudinal elastic constants of non-doped and boron-doped silicon grown by a floating zone method exhibit appreciable softening with decreasing temperature down to 20 mK. The softening of boron-doped silicon is easily suppressed in applied magnetic field up to 2 T, while the softening of non-doped silicon is robust in fields even up to 16 T. The softening of elastic constants in high-purity crystalline silicon is certainly caused by the coupling of elastic strains of the ultrasonic waves to electric quadrupoles of the vacancy orbital.

Surface acoustic wave diagnosis of vacancy orbital with electric quadrupoles in silicon

We demonstrate ultrasonic diagnosis of vacancies in boron-doped silicon wafers currently used in device manufacturing. The low-temperature softening of elastic constants measured by surface acoustic waves (SAW) as well as bulk ultrasonic waves is caused by a coupling of elastic strains to electric quadrupoles of the vacancy orbital in silicon wafers. Using interdigital transducers with a comb gap of 2.5 μm on a piezoelectric ZnO film deposited on the (001) surface of the wafer, we observed the softening of 1.9×10−4 in relative amount of the elastic constant Cs below 2 K down to 23 mK. Taking account of the strong quadrupole-strain interaction, we deduced a small vacancy concentration 3.1×1012 cm−3 in the surface layer of the wafer within a penetration depth 3.5 μm of the SAW.

Quadrupole Ordering and Rattling in Clathrate Compound Pr3Pd20Ge6

We have studied quadrupole ordering and rattling in clathrate compound Pr3Pd20Ge6 using ultrasonic measurements. The softening were observed in temperature dependence of elastic constants C11, (C11 - C12)/2 and C44. The C11 and (C11 - C12)/2 show minimums at 250 mK indicating a transition point to an antiferroquadrupole ordered phase due to a Γ3 doublet ground state at 8c site. Furthermore, the C11, (C11 - C12)/2 and C44 exhibit discontinuitive anomalies at 60 mK revealing a ferroquadrupole ordering due to a Γ5 triplet ground state at 4a site. Two distinctive ultrasonic dispersions caused by thermally activated Γ5-type rattling were observed in C44 around 15 K and 25 K.

Low-Temperature Elastic Properties of Non-Kramers Doublet Compound PrMg3

We have investigated low-temperature elastic properties of PrMg3 with a non-Kramers Γ3 doublet ground state by using ultrasonic measurements under high field up to 18 T down to 20 mK. A softening of the elastic constant (C11–C12)/2 has been observed below 8 K due to the non-magnetic Γ3 doublet possessing electric quadrupole Ou and Ov with Γ3 symmetry and magnetic octupole Txyz with Γ2. This result appreciably is deviated from a theoretical fitting of the quadrupole susceptibility based on the crystal-electric-field levels below 800 mK. Furthermore, the (C11–C12)/2 shows strange magnetic dependence up to 18 T below 1.7 K, which are inconsistent with the theoretical results.

Quadrupole order in clathrate compound Pr3Pd20Si6

In order to investigate ordered phases revealed at low temperatures in clathrate compound Pr3Pd20Si6, we have performed ultrasonic measurements using a single crystal in magnetic fields at low temperatures. Temperature dependence of elastic constant C11 and CL[10] = (C11 + C12 + 2C44)/2 shows the anomalies at about 150 mK in zero field. Magnetic phase diagrams are determined by measuring C11 in H || [001] and CL[l0] in H || [111]. The magnetic phase diagrams along the three principal axes indicate a closed loop and a strong magnetic anisotropy. This result suggests that antiferroquadrupole ordering appears at low temperatures in Pr3Pd20Si6.