RU2538073C2 - Research method of nonlinear spin resonance in semiconductors and device for its implementation - Google Patents

Abstract

FIELD: nanotechnology.

SUBSTANCE: use: for research of nonlinear spin resonance in bulk, thin film and two-dimensional semiconductor nanostructures. The essence of the invention consists in the fact that for research of nonlinear spin resonance the sample is cooled, affected with changing constant and weak alternating magnetic field that changes with sound frequency Ω, the sample is affected with two coherent radiations: the powerful pump radiation and weak test radiation, having the right circular polarization, the signal is registered, which is proportional to the second derivative of the power of the test radiation at a frequency of 2Ω, the resonant magnetic field is determined, the shape of curve of the nonlinear spin resonance is studied, the aligned coherent radiations are directed parallel to the constant magnetic field, the g-factor of the semiconductor under study is determined.

EFFECT: ensuring the possibility of determining the parameters of the energy zones in thin-film and two-dimensional semiconductor nanostructures.

2 cl, 1 dwg

Description

The invention relates to the field of opto-, micro- and nanoelectronics and can be used to study nonlinear spin resonance in bulk, thin-film and two-dimensional semiconductor nanostructures, to determine the parameters of the energy bands of semiconductors and the frequencies of the spectrum of laser radiation.

, и слабым переменным магнитным полем, изменяющимся со звуковой частотой, имеющим амплитуду, во много меньшую $$\overrightarrow{B}$$

, и вектор индукции $$\overrightarrow{B}$$

, направленный параллельно вектору $$\overrightarrow{B}$$

, воздействуют на образец полупроводника двумя когерентными излучениями, имеющими взаимно перпендикулярные плоскости поляризации, направленными перпендикулярно вектору $$\overrightarrow{B}$$

либо перпендикулярно друг другу, исследуют нелинейный спиновый резонанс в объемных образцах полупроводника.A known method of studying nonlinear spin resonance in semiconductors [1], which consists in the fact that the semiconductor sample is cooled to helium temperatures by placing it in liquid helium, they are exposed to it by a constant magnetic field, the induction vector of which $$\overrightarrow{B}$$

, and a weak alternating magnetic field, changing with a sound frequency having an amplitude much smaller $$\overrightarrow{B}$$

, and the induction vector $$\overrightarrow{B}$$

directed parallel to the vector $$\overrightarrow{B}$$

act on a semiconductor sample by two coherent radiation having mutually perpendicular planes of polarization directed perpendicular to the vector $$\overrightarrow{B}$$

or perpendicular to each other, examine nonlinear spin resonance in bulk semiconductor samples.

вдоль активного слоя образца полупроводника из-за рассеяния свободных носителей заряда на границах раздела исследуемого полупроводника.The disadvantage of this method and device is the impossibility of measurements on thin-film and two-dimensional semiconductor nanostructures due to strong scattering and absorption of coherent radiation in the case of directing them along the active layer of the investigated semiconductor sample, and in the case of the direction of the magnetic field $$\overrightarrow{B}$$

along the active layer of the semiconductor sample due to scattering of free charge carriers at the interfaces of the investigated semiconductor.

и слабым переменным магнитным полем, изменяющимся со звуковой частотой Ω, имеющим амплитуду во много меньшую $$\overrightarrow{B}$$

и вектор индукции

, направленный параллельно вектору $$\overrightarrow{B}$$

, воздействуют на образец полупроводника двумя совмещенными когерентными излучениями: мощным излучением накачки частотой ω_р и слабым тестовым излучением ω_t, имеющими взаимно перпендикулярные плоскости поляризации, направленными перпендикулярно вектору $$\overrightarrow{B}$$

и поверхности исследуемого образца полупроводника, регистрируют сигнал, пропорциональный второй производной мощности тестового излучения на удвоенной частоте 2Ω, определяют резонансное магнитное поле $${\overrightarrow{B}}_r$$

по минимуму регистрируемого сигнала, исследуют форму кривой нелинейного спинового резонанса в объемных полупроводниках.Closest to the proposed method and device for studying non-linear spin resonance in semiconductors is the prototype method and device for its implementation [2], which consists in the fact that the semiconductor sample is cooled to helium temperatures by placing it in liquid helium, it is exposed to it constant magnetic field whose induction vector $$\overrightarrow{B}$$

and a weak alternating magnetic field, changing with a sound frequency Ω, having an amplitude much smaller $$\overrightarrow{B}$$

and induction vector

directed parallel to the vector $$\overrightarrow{B}$$

act on a semiconductor sample by two combined coherent radiation: a powerful pump radiation with a frequency of ω _p and a weak test radiation of ω _t having mutually perpendicular planes of polarization directed perpendicular to the vector $$\overrightarrow{B}$$

and the surface of the investigated semiconductor sample, register a signal proportional to the second derivative of the test radiation power at a double frequency of 2Ω, determine the resonant magnetic field $${\overrightarrow{B}}_r$$

at the minimum of the recorded signal, investigate the shape of the curve of nonlinear spin resonance in bulk semiconductors.

The disadvantages of this method and device

и поверхности исследуемого образца полупроводника. Это не позволяет проводить измерения на тонкопленочных и двумерных полупроводниковых наноструктурах, поскольку невозможно эффективно осуществлять квантование вырожденного газа носителей заряда исследуемых тонкопленочных и двумерных образцов полупроводника по уровням Ландау и осуществить вынужденное комбинационное рассеяние излучения накачки. Вторым недостатком способа и устройства является низкая чувствительность для исследования объемных полупроводников, тонкопленочных и двумерных полупроводниковых наноструктур, поскольку происходит сильное рассеяние и поглощение когерентных излучений в газообразном и жидком гелии, а также на границах раздела исследуемого активного слоя полупроводника, а в случае направления магнитного поля $$\overrightarrow{B}$$

вдоль активного слоя образца полупроводника из-за рассеяния свободных носителей заряда на границах раздела исследуемого слоя полупроводника.In the device, the combined coherent radiation is directed perpendicular to the magnetic field $$\overrightarrow{B}$$

and the surface of the investigated semiconductor sample. This does not allow measurements on thin-film and two-dimensional semiconductor nanostructures, since it is impossible to quantize degenerate carrier gas of the studied thin-film and two-dimensional semiconductor samples from Landau levels and to perform stimulated Raman scattering of pump radiation. The second disadvantage of the method and device is the low sensitivity for the study of bulk semiconductors, thin-film and two-dimensional semiconductor nanostructures, since there is strong scattering and absorption of coherent radiation in gaseous and liquid helium, as well as at the interfaces of the investigated active layer of the semiconductor, and in the case of the direction of the magnetic field $$\overrightarrow{B}$$

along the active layer of the semiconductor sample due to scattering of free charge carriers at the interfaces of the investigated semiconductor layer.

, и слабым переменным магнитным полем, изменяющимся со звуковой частотой Ω, имеющим амплитуду, во много меньшую $$\overrightarrow{B}$$

, и вектор индукции

, направленный параллельно вектору $$\overrightarrow{B}$$

, воздействуют на образец полупроводника двумя совмещенными когерентными излучениями: мощным излучением накачки частотой ω_р и слабым тестовым излучением частотой ω_t регистрируют сигнал, пропорциональный второй производной мощности тестового излучения на удвоенной частоте 2Ω, определяют резонансное магнитное поле B_r по минимуму регистрируемого сигнала, исследуют форму кривой нелинейного спинового резонанса, согласно изобретению совмещенные когерентные излучения, имеющие правую круговую поляризацию, направляют параллельно магнитному полю $$\overrightarrow{B}$$

, образец полупроводника помещают в вакуумную ячейку криостата на конец хладопровода, вводят в устройство два отражающих зеркала, закрепляют их с обеих сторон образца полупроводника под углом 45° к исследуемому активному слою образца полупроводника, направляют совмещенные когерентные излучения на одно из зеркал, после отражения от которого, параллельно вектору $$\overrightarrow{B}$$

и перпендикулярно активному слою образца полупроводника, после отражения совмещенных излучений от второго зеркала регистрируют сигнал и исследуют форму кривой нелинейного спинового резонанса в объемных, тонкопленочных и двумерных полупроводниках, определяют резонансное магнитное поле $${\overrightarrow{B}}_r$$

, g-фактор исследуемого полупроводника и неизвестную частоту исследуемого спектра ω_х по формулам:This result is achieved by the fact that by the method of studying nonlinear spin resonance and a device for its implementation, namely, that a semiconductor sample is cooled to helium temperatures, exposed to it by a changing constant magnetic field, the induction of which $$\overrightarrow{B}$$

, and a weak alternating magnetic field, changing with a sound frequency Ω, having an amplitude much smaller $$\overrightarrow{B}$$

, and the induction vector

directed parallel to the vector $$\overrightarrow{B}$$

act on the semiconductor sample with two combined coherent radiation: a powerful pump radiation with a frequency of ω _r and a weak test radiation with a frequency of ω _t register a signal proportional to the second derivative of the power of the test radiation at a double frequency of 2 Ω, determine the resonant magnetic field B _r from the minimum of the detected signal, examine the shape the nonlinear spin resonance curve, according to the invention, the combined coherent radiation having a right circular polarization is directed parallel to the magnetic th field $$\overrightarrow{B}$$

, the semiconductor sample is placed in the vacuum cell of the cryostat at the end of the refrigerant conduit, two reflective mirrors are introduced into the device, they are fixed on both sides of the semiconductor sample at an angle of 45 ° to the active layer of the semiconductor sample under investigation, the combined coherent radiation is directed to one of the mirrors, after reflection from which parallel to the vector $$\overrightarrow{B}$$

and perpendicular to the active layer of the semiconductor sample, after reflection of the combined radiation from the second mirror, a signal is recorded and the shape of the curve of nonlinear spin resonance in bulk, thin-film and two-dimensional semiconductors is examined, and the resonant magnetic field is determined $${\overrightarrow{B}}_r$$

, the g-factor of the investigated semiconductor and the unknown frequency of the studied spectrum ω _x according to the formulas:

;

;

where μ _B is the Bohr magneton, ħ is the Planck constant, and B _x is the magnitude of the resonant magnetic field measured when testing radiation of an unknown frequency ω _x .

A comparative analysis with the prototype shows that the claimed method and device for its implementation allow to measure and study non-linear spin resonance in thin-film and two-dimensional semiconductor nanostructures, which distinguishes them from the prototype.

The claimed method and device meet the criterion of "novelty", since the proposed method and device for its implementation are not found in known sources.

Therefore, the proposed technical solution has significant differences, and the sequence of operations when registering a useful signal characterizing nonlinear spin resonance in thin-film and two-dimensional semiconductor nanostructures differs from existing ones.

This method and device for its implementation are proposed for use by scientific laboratories, enterprises and organizations involved in research in the field of opto-, micro- and nanoelectronics. The invention and possible implementations of the proposed method and device are illustrated by the following graphic material presented Fig. one.

The device (Fig. 1) contains prisms 1 for tuning the frequency of laser radiation sources, translucent mirrors 2, lasers 3, rods 4, resonator flanges 5, radiation focusing lenses 6, sample 7, a plate for combining laser beams 8, reflecting mirrors for direction laser radiation along a magnetic field 9, a source of a constant magnetic field 10, a magnetometer 11, a power source for a smooth sweep magnetic field 12, a current source of an electromagnet 13, a selective amplifier with a synchronous detector 14, photodetectors 15, a monochromat OP 16, computer 17, interferometer 18, helium cryostat 19, modulation coil 20, sound generator 21, frequency doubler 22, magnetometer power supply 23, quarter wavelength plate 24.

Prisms 1 can, for example, be trihedral prisms of barium fluoride, translucent mirrors 2 can, for example, be made of barium fluoride plates, lasers 3 can, for example, be carbon monoxide lasers, or carbon dioxide lasers, rods 4 may, for example, be Invar rods, the flanges of the resonator 5 may, for example, be Invar flanges, lenses for focusing laser radiation 6 may, for example, be serial lenses for infrared radiation, sample 7 may, for example, be a bulk, thin-film, or two-dimensional sample of a narrow-gap degenerate semiconductor, plate 8 may be, for example, a germanium plate, reflecting mirrors 9 may, for example, be duralumin blind mirrors, a constant magnetic field source 10 may, for example constitute a serial electromagnet with the diameter of the pole pieces, for example, 200 mm, the magnetometer 11 may, for example, be a Hall sensor based on a gallium arsenide film, a power source the coil 12 may, for example, be a serial DC generator, the current source of the electromagnet 13 may be, for example, a serial DC source to create a magnetic field, for example, 1.8 T, a selective amplifier with a synchronous detector 14 may, for example, be made based on a universal device such as Unipan-232B, photodetectors 15 can, for example, be serial FSG-22 photodetectors, monochromator 16 can, for example, be a serial device SPM-2, computer 17 can be, for example, serial m computer, interferometer 18 may be, for example, a Fabry-Perot interferometer, helium cryostat 19 may, for example, be of the Janis CCS 400 / 204N brand, modulation coil 20 may, for example, have an internal diameter of 10 mm and contains 960 turns of PEL wire 0, 2 mm. As the sound generator 21 can be used, for example, a device of type G3-33. As the doubler 22 can be used, for example, a serial frequency multiplier. As the power source of the magnetometer 23, for example, a serial dc device can be used. As a quarter-wavelength plate 24, a plate made of barium fluoride is used.

The test sample 7 is placed in a cryostat vacuum cell at the end of the helium cryostat 19 cold conduit together with reflecting mirrors 9 and a modulation coil 20 and is located in the magnetic field of the electromagnet 10. The high-power CO1 laser pump radiation is polarized in the plane of FIG. 1. The weak test radiation of a CO2 laser is polarized in a plane perpendicular to the plane of FIG. 1. The combined laser radiation is directed to the plate 24, focused by the first lens 6, sent to the first reflecting mirror 9, passed through the sample 7, reflected from the second mirror 9, focused by the second lens 6. The high-power pump radiation is cut off by a monochromator 16, the weak test radiation is detected by a photodetector 15. The signal from the photo detector 15 is fed to the first input of a selective amplifier with a synchronous detector 14. The modulation coil 20 is connected to the first input of the sound generator 21, the second output of which one with the input doubler 22, a second output of which is connected to the reference input of the detector-amplifier 14, which is the reference input of the synchronous detector having an information input coupled to an output of the selective amplifier. The output of the amplifier-detector 14, which is the output of the synchronous detector, is connected to the input Y of the computer 17, the input X of which is connected to the output of the magnetometer 11 located in the working volume of the constant magnetic field source 10. The Fabry-Perot interferometer 18 with the photodetector 15 together with the monochromator 16 serve to determine the frequency of laser radiation. Invar rods 4 have a low coefficient of thermal expansion equal to 5 · 10 ^-8 deg ^-1 . This eliminates the instability of the frequency of the lasers 3. The germanium plate 8 is installed at a Brewster angle equal to 7 ° to the incident test radiation.

New in relation to the prototype in the proposed method and device is the introduction of a plate at a quarter wavelength, two mirrors reflecting laser radiation, the direction of the combined laser radiation parallel to the magnetic field and the placement of a semiconductor sample in the vacuum cell of the cryostat at the end of the cold pipe. This eliminates the scattering of laser radiation both outside and in the active layer of the semiconductor sample and allows measurements on bulk semiconductors, thin-film and two-dimensional semiconductor nanostructures at various temperatures.

The sensitivity of the method increases, since the sample is turned by the active layer to the front of the incident wave and the magnetic field is directed parallel to the combined radiation and perpendicular to the active layer of the sample. In a quantizing magnetic field, the motion of free charge carriers of a degenerate semiconductor occurs in orbits whose areas are parallel to the active layer of the semiconductor. Then the scattering of free charge carriers at the interfaces of the active layer of the semiconductor decreases. When the direction of propagation of laser radiation is parallel to the direction of the magnetic field and the sample is turned by the active layer to the front of the incident polarized wave, the sensitivity of the method increases due to the conversion of plane-polarized radiation into a wave with right circular polarization.

Powerful coherent pump radiation ω _p = ω ₁ non-linearly polarizes the medium, experiencing inelastic stimulated Raman scattering (SRS). Weak test radiation ω _t = ω ₂ combined with a pump beam can be amplified under certain conditions.

In this case, the energy of the pump radiation quanta decreases by the energy interval between the spin Landau sublevels. This occurs at the Stokes frequency when, with a smooth change in the magnetic field, the resonance condition pω _p -ħω _t = gµ _B B _{r is} achieved, where g is the spin-orbit interaction factor, characterized by the magnitude of the spin-orbit interaction energy and the effective mass of the charge carrier, and weakly depending on the concentration of charge carriers and magnetic field B.

представим в видеConsider the process of amplifying a test wave. Components of the nonlinear component of the medium polarization vector $$R_i^{nl}$$

imagine in the form

where χ _ijkl is the dielectric susceptibility tensor.

From the Maxwell equations follows a nonlinear wave equation for the total electric field E of the wave directed along the z axis:

Where

cs are complex conjugate terms.

The last term in (2) is responsible for the generation of waves with different combinations of frequencies by the medium. In the third order of interaction, the nonlinear susceptibility χ _ijkl has a resonance and waves with combinations of frequencies are possible

If the semiconductor sample has a spectrum of electronic states with a transition energy between the levels ħω ₀ (in our case, between spin Landau sublevels), then when the resonance condition

there is an increase in the inelastic interaction between the incident waves and the semiconductor with the amplification of the test radiation ω _t during stimulated Raman scattering of the pump wave at the Stokes frequency ω ₄ , = ω _p -ω ₀ = ω _t . Stimulated emission scattering ω _p occurs at electron coherently phased throughout the sample volume spin transitions from the lower sublevel to the upper Landau sublevel. As a result, the intensity of the stimulated component of the scattered radiation detected by the Raman amplification method increases by several orders of magnitude compared with the intensity of spontaneous Raman scattering.

To implement the SRS amplification method, we used the tuning of the energy spectrum of the medium ħω ₀ to the resonance condition (5) by changing the energy intervals between the Landau spin sublevels with a smooth change in the magnetic field:

The resonance condition (5) was achieved in two stages: by discrete tuning the lasers to the selected frequency range, and then by smoothly scanning the magnetic field. The shape of the resonance curve was recorded on an amplified test wave with a frequency equal to the Stokes wave during stimulated Raman scattering of the pump wave.

The recorded signal is proportional to the intensity of the test wave emerging from the sample I (ω _t ) associated with the intensity I ₀ (ω _t ) entering the sample and the characteristics of the sample by the ratio

where I (ω _p ) is the intensity of the pump radiation incident on the sample;

l is the length of the investigated medium (sample) in which amplification occurs;

β is the coefficient of conversion of the optical signal into electric;

G is the gain of the investigated medium:

G is the half-width at half maximum of the resonant Raman gain line.

In case of small amplifications

For I (ω _t ) << I (ω _p ), in the absence of pump depletion and saturation of the spin transition, the resonance curve has a bell-shaped shape and the shape of a line of spontaneous Raman scattering. In this case, the gain loop has a Lorentzian shape.

To achieve the ultimate accuracy in measuring the positions of the line peaks and determining the g-factor, it is required to work at the minimum intensities of lasers with signals at the noise level. The application of the modulation technique of double differentiation with synchronous detection of the measured signal provides high sensitivity from 10 nV to 1 μV, the ultimate accuracy of 0.05% and the reproducibility of experimental results of 0.02% on one sample. The magnetic field is stabilized with an error of ~ 2 G. From (5) and (6) the dependence of the g factor on the magnetic field follows

where K = 2.141946 Tm

и $$\raisebox{1ex}{${\omega }_t$}\!\left/ \!\raisebox{-1ex}{$2\pi c$}\right.=1842,8210с{м}^{-1}$$

. Оба лазера изготовлены в одной арматуре из инваровых стержней, поэтому их температурное расширение одинаково изменяло частоты, разность которых оставалась постоянной. Нестабильность работы лазеров составляет ~30 мГц или 5·10^-3%. Источник тока магнита имеет два контура стабилизации: долговременный дрейф и быстрые изменения. Дрейф по магнитному полю не превышает 0,01% за 1 ч.The laser wavelengths were determined up to the eighth sign of accuracy. For example, to study the anisotropy of the g-factor, frequencies are used $$\raisebox{1ex}{${\omega }_p$}\!\left/ \!\raisebox{-1ex}{$2\pi c$}\right.=1842,8210\mathrm{from}{m}^{-\mathrm{one}}$$

and $$\raisebox{1ex}{${\omega }_t$}\!\left/ \!\raisebox{-1ex}{$2\pi c$}\right.=1842,8210\mathrm{from}{m}^{-\mathrm{one}}$$

. Both lasers are made in one armature of Invar rods, so their thermal expansion equally changed the frequencies, the difference of which remained constant. The instability of the laser is ~ 30 MHz or 5 · 10 ^-3 %. The magnet current source has two stabilization loops: long-term drift and rapid changes. The magnetic field drift does not exceed 0.01% per 1 hour.

In order to significantly increase the signal-to-noise ratio in comparison with direct methods for modulating the laser intensities, the proposed method widely used the modulation of the magnetic field. When applying an alternating field B = h ₀ sinΩt to a constant magnetic field B _{0, the} signal U (B) in the chart of the recorder changes nonlinearly. Expanding U (B) in a Taylor series and restricting ourselves to second-order terms, we obtain

The amplitude of the first harmonic signal is proportional to h ₀ , and the amplitude of the second harmonic signal:

In the case when the modulation amplitude h ₀ is comparable with the line width, the signal

A study of the shape of the curve of nonlinear spin resonance determines the resonant magnetic field B _r . This allows us to determine the g factor with high accuracy, depending only on the measurement of one parameter B _r . Knowing the g-factor, one can study the spectrum of unknown radiation, since resonance is also observed in the absence of test radiation. Then, instead of ω _t , an unknown frequency is determined:

,

,

where B _x is the corresponding resonant magnetic field at the resonance of the investigated radiation ω _{x of} some laser.

The technical and economic result consists in increasing the reliability of determining the parameters of bulk, thin-film and two-dimensional semiconductor micro- and nanostructures, in the development of new methods for diagnosing materials and structures of electronic equipment.

Literature

[1] Brueck S.R.J., Moordian A., Spontaneous Spin-flip Raman linear and nonlinear processes in InSb.// Opt. Communs. 1973. V / 8. Number 3. P. 263.

[2] Vdovin A.B., Kornilovich A.A., Skok E.M., Uvarov E.I. Non-contact methods for studying nonlinear spin resonance and the Shubnikov-deGaaz effect in bulk semiconductors. // Autometry. 2001. No4. S. 62-75.

Claims (2)

1. A method for studying nonlinear spin resonance in semiconductors and a device for its implementation, including cooling the semiconductor to helium temperatures, exposure to it with a changing constant magnetic field, the induction vector of which $$\overrightarrow{B}$$

, and a weak alternating magnetic field, changing with a sound frequency Ω, having an amplitude much smaller $$\overrightarrow{B}$$

and induction vector

directed parallel to the vector $$\overrightarrow{B}$$

, exposure of a semiconductor sample to two combined coherent radiation: powerful pump radiation with a frequency of ω _r and weak test radiation with a lower frequency of ω _t , recording a signal proportional to the second derivative of the power of the test radiation at a double frequency of 2 Ω, determining the resonant magnetic field B _r from the minimum of the detected signal , the study of the shape of the curve of nonlinear spin resonance, characterized in that the combined coherent radiation having a right circular polarization directs the pair allele to the magnetic field $$\overrightarrow{B}$$

, the semiconductor sample is placed in a vacuum cell of the cryostat, at the end of the cold conductor, determine the resonant magnetic field $${\overrightarrow{B}}_r$$

, the g-factor of the investigated semiconductor and the unknown frequency of the studied spectrum ω _x according to the formulas:

;

,
where μ _B is the Bohr magneton, ħ is the Planck constant, and B _x is the magnitude of the resonant magnetic field measured when testing radiation of an unknown frequency ω _x . 2. A device for studying nonlinear spin resonance in semiconductors, containing coherent radiation sources, characterized in that a quarter-wavelength plate, two reflecting mirrors are inserted into the device, and they are fixed on both sides of the semiconductor sample at an angle of 45 ° to the active layer of the semiconductor sample under study , direct the combined coherent radiation to one of the mirrors, after reflection from which, parallel to the vector $$\overrightarrow{B}$$

and perpendicular to the active layer of the semiconductor sample, after reflection of the combined radiation from the second mirror, a signal is recorded and the shape of the curve of nonlinear spin resonance in bulk, thin-film and two-dimensional semiconductors is studied.