Comparison between optical and electrical data on hole concentration in zinc-doped p-GaAs

The optical and electrical properties of zinc-doped Cz p-GaAs have been studied. Reflection spectra of ten p-GaAs specimens have been taken in the mid-IR region. Van der Pau galvanomagnetic, electrical resistivity and Hall coefficient measurements have been carried out for the same specimens (all the measurements were carried out at room temperature). The reflection spectra have been processed using the Kramers–Kronig relations, spectral dependences of the real and imaginary parts of the complex dielectric permeability have been calculated and loss function curves have been plotted. The loss function maximum position has been used to calculate the characteristic wavenumber corresponding to the high-frequency plasmon-phonon mode frequency. Theoretical calculations have been conducted and a calibration curve has been built up for determining heavy hole concentration in p-GaAs at T = 295 K based on known characteristic wavenumber. Further matching of the optical and Hall data has been used for determining the light to heavy hole mobility ratio. This ratio proves to be in the 1.9–2.8 range which is far lower as compared with theoretical predictions in the assumption of the same scattering mechanism for light and heavy holes (at optical phonons). It has been hypothesized that the scattering mechanisms for light and heavy holes differ

Сравнение результатов оптических и электрофизических измерений концентрации дырок в образцах p-GaAs, легированных цинком

Optical and electrophysical properties of Cz-grown zinc doped p-GaAs samples have been investigated. Middle-infrared reflection spectra of ten p-GaAs samples have been obtained. Galvanomagnetic Van der Pau measurements have been made on these samples also, and the values of resistivity and Hall coefficient have been calculated. All experiments have been carried out at room temperature.Reflection spectra have been processed by Kramers–Kronig relations. The spectral dependences of real and imaginary parts of complex dielectric permittivity have been obtained and loss function has been calculated. The value of characteristic wave number corresponding to high-frequency plasmon-phonon mode has been determined by loss function maximum position.The theoretical calculations have been made, and the dependence has been obtained which gave the possibility to determine heavy hole concentration value at T = 295K by the value of characteristic wave number. Then by comparison of optical and Hall data the values of light hole mobility to heavy hole mobility ratio have been determined. This mobility ratio has been shown to be equal to (1.9–2.8) which is considerably less, than predicted theoretical value based on assumption that both light and heavy holes are scattered by optical phonons. It has been suggested that scattering mechanisms of light and heavy holes might be quite different.Исследованы оптические и электрофизические свойства образцов p-GaAs, выращенных методом Чохральского и легированных цинком. Измерены спектры отражения десяти образцов p-GaAs в средней ИК-области. На этих же образцах проведены гальваномагнитные измерения по методу Ван-дер-Пау и определены значения удельного электрического сопротивления и коэффициента Холла (все измерения проведены при комнатной температуре). Спектры отражения обработаны с использованием соотношений Крамерса—Кронига; вычислены спектральные зависимости действительной и мнимой частей комплексной диэлектрической проницаемости и построены функции потерь. По положению максимума функции потерь определено значение характеристического волнового числа, отвечающего частоте высокочастотной плазмон-фононной моды. Проведены теоретические расчеты и построена градуировочная зависимость, позволяющая по известному значению характеристического волнового числа определить концентрацию тяжелых дырок в p-GaAs при Т = 295 К. Далее путем сопоставления оптических и холловских данных определены значения отношения подвижностей легких и тяжелых дырок. Показано, что оно лежит в пределах 1,9—2,8, что значительно меньше значений, предсказываемых теорией в предположении, что и легкие, и тяжелые дырки рассеиваются одинаково (на оптических фононах). Высказано предположение, что механизмы рассеяния легких и тяжелых дырок различны

Сравнение результатов оптических и электрофизических измерений концентрации свободных электронов в образцах n-GaAs, легированных теллуром

A theoretical model has been developed that allows one to determine free electron density in n-GaAs from the characteristic points on far-infrared reflection spectra. It was shown that, in this case, it is necessary to take into account the plasmon-phonon coupling (otherwise, the electron density is overestimated). The calculated dependence of electron density, Nopt, on the characteristic wave number, ν+, which is described by a second degree polynomial, has been obtained.Twenty-five tellurium-doped gallium arsenide samples were used to measure the electron density in two ways: according to traditional four-contact Hall method (Van der Pauw method) and using the optical method we developed (measurements were carried out at room temperature). Based on the experimental results, the dependence was constructed of the electron density values obtained from the Hall data, NHall, on the electron density obtained by the optical method, Nopt. It is shown that this dependence is described by linear function. It is established that the data of optical and electrophysical measurements coincide if the electron density is Neq = 1.07 ⋅ 1018 cm-3, for lower values of the Hall density NHall < Nopt, and for large values NHall > Nopt. A qualitative model is proposed to explain the results. It has been suggested that tellurium atoms bind to vacancies of arsenic into complexes, as a result of which the electron density decreases. On the surface of the crystal, the concentration of arsenic vacancies is lower and, therefore, the condition Nopt > NHall should be satisfied. As the doping level increases, more and more tellurium atoms remain electrically active, so electron density in the volume begins to prevail over the surface one. However, with a further increase in the doping level, the ratio NHall/Nopt again decreases, tending to unity. This, probably, is due to the fact that the rate of decomposition of the complexes “tellurium atom + arsenic vacancy” decreases with increasing doping level.Разработана теоретическая модель, позволяющая определять концентрацию свободных электронов в n-GaAs по характеристическим точкам на спектрах отражения в дальней инфракрасной области. Показано что при этом необходимо учитывать плазмон-фононное взаимодействие (в противном случае значение концентрации электронов оказывается завышенным). Получена расчетная зависимость концентрации электронов Nопт от характеристического волнового числа ν+, которая описывается полиномом второй степени.На двадцати пяти образцах арсенида галлия, легированных теллуром, проведены измерения концентрации электронов двумя способами: по традиционной четырехконтактной методике (метод Ван дер Пау) и с помощью разработанного авторами оптического метода (измерения проводились при комнатной температуре). По результатам экспериментов построена зависимость значений концентрации электронов, полученных из холловских данных, Nхолл от значений концентрации электронов, полученных оптическим методом, Nопт. Показано, что эта зависимость описывается линейной функцией. Установлено, что данные оптических и электрофизических измерений совпадают, если концентрация электронов равна Nравн = 1,07 ⋅ 1018 см-3. При меньших значениях холловской концентрации Nхолл < Nопт, а при больших — Nхолл > Nопт. Предложена качественная модель, объясняющая полученные результаты. Высказано предположение, что атомы теллура связываются с вакансиями мышьяка в комплексы, вследствие чего концентрация электронов уменьшается. На поверхности кристалла концентрация вакансий мышьяка меньше и, следовательно, должно выполняться условие Nопт > Nхолл. По мере увеличения уровня легирования все больше атомов теллура остается электрически активными, поэтому концентрация электронов в объеме начинает превалировать над поверхностной концентрацией. Однако при дальнейшем увеличении уровня легирования отношение Nхолл/Nопт опять убывает, стремясь к единице. Это, по-видимому, связано с тем, что интенсивность распада комплексов «атом теллура + вакансия мышьяка» при увеличении уровня легирования уменьшается

Calculation of current-voltage characteristics of a single-electron transistor with discrete spectrum of energies in the island

The paper contains the results of calculation of current-voltage characteristics (CVC) of a single-electron transistor with discrete spectrum of energies based on the extended orthodox theory. The calculation of curves is carried out with the aid of the Monte-Carlo procedure. The transistor model describes the transport of electrons and holes in the device. The numerical results show that the fine structure of the CVC depends strongly on the density of states and on distance between the levels of carriers’ energies in the island

Calculation of current-voltage characteristics of a single-electron transistor with continuous spectrum of energies in the island

The paper contains the results of calculation of current-voltage characteristics of a single-electron transistor with continuous spectrum of energies based on the orthodox theory. The calculation of curves is carried out with the aid of the Monte-Carlo procedure

Comparison between optical and electrophysical data on free electron concentration in tellurium doped n-GaAs

A theoretical model has been developed for determining free electron concentration in n-GaAs from characteristic points in the far infrared region of reflection spectra. We show that when determining free electron concentration one should take into account the pasmon–phonon coupling, otherwise free electron concentration will be overestimated. We have calculated electron concentration Nopt as a function of characteristic wave number ν+ which is described by a second order polynomial. Twenty-five tellurium doped gallium arsenide specimens have been tested for electron concentration using two methods, i.e., the conventional four-probe method (Van der Pau) and the optical method developed by us (the measurements have been carried out at room temperature). We have used the experimental results to plot the dependence of electron concentration based on the Hall data (NHall) on electron concentration based on the optical data (Nopt). This dependence is described by a linear function. We show that the data of optical and electrophysical measurements agree if the electron concentration is Neq = 1.07 · 1018 cm-3. At lower Hall electron concentrations, NHall Nopt. We have suggested a qualitative model describing these results. We assume that tellurium atoms associate into complexes with arsenic vacancies thus reducing the concentration of electrons. The concentration of arsenic vacancies is lower on the crystal surface, hence the Nopt > NHall condition should be met. With an increase in doping level, more and more tellurium atoms remain electrically active, so the bulk concentration of electrons starts to prevail over the surface one. However with further increase in doping level the NHall/Nopt ratio starts to decrease again and tends to unity. This seems to originate from the fact that the decomposition intensity of the tellurium atom + arsenic vacancy complexes decreases with an increase in doping level

Comparison between results of optical and electrical measurements of free electron concentration in n-InAs specimens

A theoretical model has been developed for determining the free electron concentration in n-InAs specimens from characteristic points in far IR reflection spectra. We show that this determination requires plasmon-phonon coupling be taken into account, otherwise the measured electron concentration proves to be overestimated. A correlation between the electron concentration Nopt and the characteristic wavenumber ν+ has been calculated and proves to be well fit by a third order polynomial. The test specimens have been obtained by tin or sulfur doping of indium arsenide. The electron concentration in the specimens has been measured at room temperature using two methods: the optical method developed by the Authors (Nopt) and the conventional four-probe Hall method (the Van der Pau method, NHall). The reflecting surfaces of the specimens have been chemically polished or fine abrasive ground. The condition Nopt > NHall has been shown to hold for all the test specimens. The difference between the optical and the Hall electron concentrations is greater for specimens having polished reflecting surfaces. The experimental data have been compared with earlier data for n-GaAs. A qualitative model explaining the experimental data has been suggested