Free-Electron Screening Mechanism of the Shallow Impurity Breakdown in n-GaAs : Evidences from the Photoelectric Zeeman and Cyclotron Resonance Spectroscopies

A novel breakdown (BD) mechanism of shallow impurity (SI) under the electric field at low temperatures is suggested for n-GaAs samples with the donor concentrations 1014 cm−3 ≤ND ≤ 1016 cm−3 and the compensation degree 0.3≤K � NA/ND ≤ 0.8 with acceptors of concentration NA in the external magnetic fields up to H � 6.5T, oriented parallel or perpendicular to the external electric field. Diagnosis of the BD mechanism was performed by SI Zeeman (mainly from the ground state 1s to 2p+1 and other excitation states) and cyclotron resonance photoelectric spectroscopy (PES) methods in the wide interval of the electric field including the BD region too. /e obtained results reveal that the BD electric field εBD does not correlate with K and the carrier’s mobility μ of the samples, which contradict to the well-known impact ionization mechanism (IIM). A serious discrepancy with IIM is that εBD does not almost depend on the magnetic field up to H � 6.5T when ε‖H though the SI ionization energy increases two times. /e cyclotron resonance (CR) measurements show that the line width does not depend on the electric field for ε< εBD, indicating the lack of free-carrier (FC) heating in contradiction with IIM. A considerable decrease of the free carriers’ capture cross section (CCS) area by ionized SI centers with a subsequent increase in the FC concentration n is observed by means of PES investigation of the 1s⟶ 2p+1 and CR lines in the electric fields ε≤ εBD and at different magnetic fields, applied along (H‖ε) the electric field or perpendicular (H⊥ ε) to the electric field. /e slope of the 1s⟶ 2p+1 line intensity on the electric field for ε‖H does not depend on the magnetic field, which is valid for εBD too. Various effects determined in the PES measurements at ε � εBD, such as a drastic narrowing of the 1s⟶ 2p+1 and CR lines, a shift of the CR line to higher magnetic fields, and disappearing of the lines to higher excited SI states, were clarified to be a result of screening of the SI Coulomb potential by free carriers. /e FC screening at the BD reduces the potential fluctuation and its influence to the PES line shape of 1s⟶ 2p+1 and other excited states. It is shown that an increase in the FC concentration reduces the CCS, which can be assumed as the main factor along with the increase in the ionization coefficient for the SI breakdown in the electric field. /e screening length rs of the SI Coulomb potential decreases with the increasing FC concentration, reducing the CCS; the latter seems to vanish completely at rs � aB (a ∗ B is the effective Bohr radius), when high screening results in vanishing of all the bound states of the Coulomb potential. Note that this limit is similar to the Mott transition. Many experimental facts and our calculation of the CCS support the suggested mechanism for the SI breakdown./e well-known IIM is valid for samples with SI concentrations N≪ 1013 cm−3 and takes place at very high electric fields.

N D = 0.3 ÷ 0.8 with acceptors of concentration N A in the external magnetic fields up to H = 6.5 T , oriented toward parallel or perpendicular to the external electric field. Diagnosis of the BD mechanism was performed by SI Zeeman (mainly from the ground state 1s to the 2p +1 and other excitation states) and cyclotron resonance photoelectric spectroscopy (PES) methods in the wide interval of the electric field including the BD region too.
The obtained results reveal that the BD electric field E BD does not correlate with K and the carriers mobility µ of the samples, which contradict to the well-known impact ionization mechanism (IIM).
A serious discrepancy with IIM is that, E BD does not almost depend on the magnetic field up to H = 6.5 T when E H, though the SI ionization energy increases two times. The cyclotron resonance (CR) measurements show that the line width does not depend on the electric field for E < E BD indicating the lack of free carriers (FC) heating in contradiction with IIM. A considerable decrease of the free carriers' capture cross section (CCS) by ionized SI centers with a subsequent increase in the FC concentration n is observed by means of PES investigation of the 1s → 2p +1 and CR lines in the electric fields E ≤ E BD and at different magnetic fields, applied along H E or perpendicular H ⊥ E to the electric field. The slope of the 1s → 2p +1 line intensity on the electric field for E H does not depend on magnetic field, which is valid for E BD too. Various effects determined in the PES measurements at E = E BD , such as a drastic narrowing the 1s → 2p +1 and CR lines, a shift of the CR line to higher magnetic fields and disappearing of the lines to higher excited SI states, were clarified to be a result of screening of SI Coulomb potential by free carriers. The FC screening at the BD reduces the potential fluctuation and its influence to the PES line-shape of 1s → 2p +1 and other excited states. It is shown that an increase in the FC concentration reduces the CCS, which can be assumed as the main factor along with the increase in the ionization coefficient for the SI breakdown in the electric field. The screening length r s of the SI Coulomb potential decreases with increasing the FC concentration, reducing the CCS; the latter seems to vanish completely at r s = a * B (a * B is the effective Bohr radius), when high screening results in vanishing of all the bound states of the Coulomb potential. Note that this limit is similar to the Mott transition. Many experimental facts and our calculation of the CCS support the suggested mechanism for the SI breakdown. The well-known IIM is valid for samples with SI concentrations N ≪ 10 13 cm −3 , and takes place at very high electric fields.

I. INTRODUCTION
The gallium arsenide is one of the most utilized semiconductor in the modern electronics technology. n − GaAs epitaxial layers are the widely used hetero-junctions for the investigation of the comprehensive class of 2D modern electronic and spintronic phenomena and for fabrication of different devices on their basis such as Gann diodes, photodetectors operating in the wide range of frequency, high frequency field transistors etc. In order to improve the electro-physical characteristics of these devices, fabricated by using high-purity semiconductors, it is necessary to know the chemical nature and the relative concentration of residual impurities. Many of these devices operate at low temperatures and sufficiently high electric fields when shallow impurities (SI) breakdown (BD) takes place (see, for review, e.g. [1,2]).
Therefore more careful investigation of SIBD mechanism in n − GaAs is essential.
The low temperature sub-millimeter wave photoelectric spectroscopy (PES) of SI is the most sensitive method for identification of the SI contents in semiconductors [3]. A significant information on SI can be obtained from the photoconductivity spectra line-width and the line broadening mechanism. The line-width of the SI PES was shown [4,5] to be determined by the concentrations of the major and compensated impurities as well as their distribution.
The difference of ground state energies E(1s) for different SI atoms, which is called a chemical shift (CS) or central cell correction, is a result of deviations (∆V ) of SI Coulomb potential for the inhomogeneous broadening of the charged impurities. Note, that such a small value of CS, which is the same order as the impurity photoexcitation line width is inherent to the most of A 3 B 5 semiconductors (InSb, GaAs, InP ). However the difference of SI ionization energies for different impurities in Ge and Si are in the order of Ry * . That is why the CS in these materials does not affect to the line width.
For the n − GaAs samples with the SI concentrations higher than 10 14 ÷ 10 15 cm −3 the picture is significantly different [6]. First of all, our experiments have determined that the line width for these samples does not correlate with the SI concentration, so that for a sample with smaller concentration the line width may be larger than that of more doped samples (see , Table I). Our investigations show that the line width of these samples is determined not only with the SI concentration but with the potential fluctuation due to the inhomogeneous SI donors and acceptors distribution too. Such an inhomogeneous SI distribution creates a potential fluctuation, which gives an additional contribution to the line width. At lower temperatures, close to zero, the electrons are captured by impurities, providing a correlated distribution of electrons, which is realized by minimizing the total Coulomb energy of the system of the charged donors, acceptors and electrons [7]. At higher temperatures, when T ≫ T c = e 2 ǫ 0 rmk B with r m = (4π/3N I ) 1/3 being the mean distance between charged impurities, the electrons are activated, and their distribution becomes random. The 1s → 2p +1 transition line width in this case depends on the charged impurity concentration N I = 2N A , and does not depend on the compensation K = N A /N D . Instead, the line width in the real experiments, which are realized at lower temperatures, the electrons distribution is correlated, since the acceptors are charged, taking an electron from nearest donor [5], and the former strongly depends on K. A transformation from the correlated to the random distribution can be reached not only by increasing temperature but also applying an external electric field.
The impurities in a strongly inhomogeneous sample gather into cluster with higher impurity concentration. Hall measurement yields only mean value of the impurity concentration.
Since these clusters are optically active, they are responsible for the radiation absorption.
The impurity orbitals of the neighboring donors in the cluster are overlapped. Therefore, the 1s → 2p +1 transition is allowed not only to the excited 2p +1 state of the owner atom but to neighboring impurity 2p +1 states too. Note that just such kinds of transitions cause potential fluctuations broadening of 1s → 2p +1 transition line-width. The line-width for these transitions depends on the radiation intensity also [8,9]. The transition between different impurity states may provide an additional inhomogeneous broadening mechanism for inhomogeneous impurity distribution at higher concentrations. Therefore, identification of the lines becomes difficult due to inhomogeneous line broadening, which increases significantly at the SI concentrations higher than 10 14 ÷ 10 15 cm −3 .
It is clear that the width of the impurity PEL has to be reduced in order to increase the resolution of the PES, which needs an investigation of the inhomogeneous broadening mechanisms of PES of SI. An additional inter-band illumination of samples causes the some narrowing of SI PES line width [10] due to decreasing of charged impurities concentration.
Nevertheless, our experiments showed that a narrowing of the 1s → 2p +1 line in PES by interband illumination is effective only in samples with high compensations K = N A /N D > 0.5.
We found that the SI PES line widths are considerably narrowed at the SI breakdown electric field.
The aim of this work is to investigate a mechanism of the electric field breakdown and of the broadening of the photoelectric excitation spectra lines of shallow impurities and the According to the existence theories [1,2,[11][12][13][14], the SI breakdown occurs by means of the impact ionization of the neutral impurities by hot electrons, heated in the electrical field to energies more than 2E i . The idiom of 'impact ionization' was introduced in physics firstly by Townsend [15] in order to explain the effects of an electrical discharging in gas. Further, Ioffe was argued [16] that the impact ionization may be a reason of the electric breakdown in solid insulators. The electron multiplication effect in Ge and Ga p − n junctions [17] as well as in n − Ge and p − Ge [18,19] was attributed to the impact ionization of impurities by free charge carriers. We present in this work a new mechanism of the SI PES line broadening and of the electric field breakdown mechanism of SI in a n − GaAs sample, consisting of the charged impurities screening with free electrons, which is an alternative one to the impact ionization. This SI BD mechanism takes place at higher concentrations of the SI when N D > 10 13 cm 3 A brief description of this mechanism was mentioned firstly in Ref. [20]. The non-homogeneity degree of the impurity distribution in samples with similar concentrations of the major and the compensated impurities was shown to be determined by the width of 1s → 2p +1 SI PES in the linear part of the current-voltage characteristics (CVC) and by the electric field dependence of the width in the pre-breakdown electric field.
The main scattering mechanism of electrons in the samples under our experimental condition is scattering on the ionized impurities. However, the investigation of the CR line width at the pre-breakdown electric fields shows no correlation with ionized impurity concentration as it must be ω c ∼ Hµ. A reason of the CR line width broadening and different values of the cyclotron mass under the same experimental conditions is established to be a potential fluctuation due to non-homogeneous distribution of the impurities. Drastic increase of the free electron concentration at BD results in two kind of CR line shift; the first shift is connected with influence of the plasma oscillation as a result of enhancement of the free electron, and it increases with decreasing the magnetic field. The second shift, which takes place at higher magnetic fields, increases with magnetic field due to decrease of influence of fluctuation potential on CR line-shape as a result of free carriers screening. Note that ∆H < 0 at the plasma shift, while ∆H > 0 at the screening shift of the CR line. It is worthy to note that a comparison of the CR line-shapes between breakdown and pre-breakdown electric fields allows us to characterize a degree of the non-homogeneous distribution of the impurities.
The dependence of the CR line width on the electrical field around the breakdown E ≈ E BD is experimentally observed to be non-homogeneous: the CR line is considerably narrowed at the beginning part of the breakdown, whereas the line width increases and exceeds several times its own pre-breakdown value. The analysis of the experimental data establishes that the breakdown takes place by means of the current filament formation in the sample. At the beginning stage of the breakdown, the released free electrons in the current filament screen the charged impurities and reduce their influence on the cyclotron motion of the electrons.
The further increase in the electron concentration with the current, the electron-electron correlations dominate over the electron-impurity interactions, which lead to the broadening of the CR line width. The reason of the increase in the CR intensity with the electric field is established to be an increase in the free electron concentration in the first Landau level and in the life-time of the photoexcited electrons in the first Landau level due to reduction of the capture coefficient at the impurity centers.
The novelties can be summarized as follows: 1. The PES of the Zeeman lines of n − CaAs samples with SI donors concentrations smaller than that corresponding to Mott transition N D ≈ 10 14 ÷ 10 16 cm −3 and with the intermediate compensations K = N A /N D = 0.3 ÷ 0.8 at the breakdown electric field undergoes to drastic narrowing of the PES lines 1s → 2p +1 and 1s → 3p +1 ; 2. All PES lines, corresponding to transitions from the ground state of the donors to the quasi-discrete excited states higher than 3p +1 , disappear at pre-breakdown region of CVC; 3. Drastic narrowing of the CR line-width in PES occurs at break-down region of CVC of samples; 4. All these experimental facts can be explained by screening of the charged impurity potential by free electrons released in the breakdown process. Calculations of the 1s → 2p +1 transition line-shape for the two main line broadening mechanisms, namely the quadratic Stark and the quadrupole-gradient effects, by replacing the surrounding the neutral impurity charged impurities Coulomb potential with the screened Coulomb potential, (e/ǫ 0 r) exp (−r/r s ), explain the narrowing of the FES line. The calculations yield that the 1s → 2p +1 line is narrowed several times for the value of the screening length r s = (4πe 2 n −1 ǫ −1 0 ) 1/2 corresponding to free electron concentration n smaller than the neutral impurity concentration; 5. Two different kinds of shifts of the CR line at the break-down takes place, both of them are connected with abrupt increase of free carrier concentration n at breakdown.
The first shift (∆H CR < 0), which increases with decreasing of CR magnetic field value H CR is due to free carriers plasma influence on CR line-shape. The second shift (∆H CR > 0), which increases with H CR is due to the screening of charged impurities potential fluctuations with free carriers. 6. Two kinds of the CR are observed at small electric fields corresponding to the linear region of CVC in PES. The first is the free carriers CR line, at slightly smaller magnetic field with very low intensity in comparison with that of broader line of the pseudofree carriers CR of electrons localized on fluctuation of potential CR (FPCR). With increasing the electric field, activation of carriers from the potential fluctuation to the zeroth Landau level causes strong increase in the free carrier CR in comparison to FPCR broad line. Such kind of CR electric field dependence is typical for samples with inhomogeneous distribution of impurities. So this fact can be used in characterization of impurity distribution in samples of n − GaAs with nearly equal N D and K.
7. The intensity ∆σ/σ of photoelectric excitation spectra 1s → 2p +1 and CR lines was shown to increase with the pre-breakdown electric field due to the decrease in the capture cross-section α(E) and increase in the coefficient of thermal ionization from excited states β(E). So the concentration of free electrons was shown increases exponentially at pre-breakdown electric fields. Cross-modulation method was used in registration of photoconductivity with modulation of radiation intensity at frequency 750 Hz. Alternating signal of photoconductivity was measured from load resistor R L series-connected with sample with resistivity of R S by using of the lock-on method. Voltage drops from R L and R S were used in CV C registration respectively. Line-shapes of CR and SIPES were studied at different regions of samples' CVC. At electric fields smaller than the breakdown one E < E BD , the measurements were done in constant voltage regime, when R L ≪ R S for different values of the electric field.
In this case the photosignal is proportional to ∆σ under the radiation. At pre-breakdown and at "candle"-like region E ≈ E BD , the measurements are performed in constant current regime, when R L is much greater than sample resistivity R S , R L ≫ R S . In constant voltage regime PC signal is proportional to the change of conductivity ∆U ∼ ∆σ under the radiation and as a result PC line shape corresponds to real line-shape at E < E BD . However, it is not suitable at E ≈ E BD due to the instability of electric parameters of sample. Constant current condition gives the possibility to detect line shapes at candle-like region of CVC at different free carrier concentration. In this case PC of sample ∆U ∼ ∆ρ = 1 where σ dark is a dark conductivity. At small dark conductivity σ dark ≪ e∆nµ (which correspond to small electric field) PC signal would have a saturation with increasing of ∆n, as a result PC spectra do not correspond to true line-shape. In opposite case, which corresponds to the breakdown region (σ dark > e∆nµ), photo-signal is proportional to the number of resonance transition ∆n, and it corresponds to the true line-shape. The analysis of PC signals ∆U at breakdown region shows that the saturation of ∆U on the radiation intensity takes place at sufficiently high ∆n comparable with impurity concentration. This means that the line widths of CR and 1s → 2p +1 transitions obtained at the breakdown in the current regime are only broader than the true line shapes. This is important for us because our conclusions partially are based on strong decreasing of these line-shapes at SI breakdown. It is obvious that at constant voltage only and constant current conditions it is possibility to observe N-and S-like regions of CVC of samples respectively.
Nevertheless, CVC of samples obtained at constant current regime should not show a S-like region as illustrated in CVC at different magnetic fields in Fig.1. Note that in the case of CVC recording in constant voltage regime at E ≈ E BD , the voltage drop switches from sample to load resistor at the beginning of the breakdown, and this causes decreasing of E on sample; and as a result of this, an external voltage drop returns back to sample after time τ cap , when the excited free carriers are captured back to impurity sites again. This corresponds to the first cycle of the oscillation, which is known as low frequency current oscillations (LFCO) on sample at impurity breakdown and other switching effects. The amplitude of these oscillations decreases with increasing the load resistance, and it disappears at strong constant current regime. The points on CVC line, obtained at strong constant current condition correspond to load resistance value nearly 10 times greater than the resistivity of sample at the beginning of the breakdown. As it is seen from Fig. 1, fluctuations of voltage in the sample decrease at strong current regime.   impurities. It is worthy that E BD increases linearly with magnetic field at E ⊥ H, whereas it does not depend practically on H at E H, as it is shown in Fig. 2.

TOELECTRIC SPECTROSCOPY
According to the conventional explanation [3][4][5]7], the main mechanism of the SI photoexcitation line broadening in magnetic field is the quadratic Stark effect and the electric field gradient of the quadrupole interactions of charged impurities. Our experiments show that there exists an additional line broadening mechanism in the samples with high impurity concentrations, which is caused by the potential fluctuations. As it is seen from Table I, there is no correlation of the PES line width neither with SI concentration nor with the degree of the compensation for N D ≈ 10 14 to 10 15 cm −3 and K ≈ 0.3 to 0.8. This evidence can be understood, providing that an inhomogeneous SI distribution plays an essential role in the line broadening. At high impurity concentrations, the impurity states are broadened forming an impurity band. In this case, a transition takes place not only from the 1s ground state of a given neutral donor to the 2p +1 excited state to the same atom but to the nearestneighboring charged donors too. Since high SI concentration makes it possible a partially wave function overlapping of the excited states. The distribution function of the charged SI, randomly distributed in the sample, was proposed to be [22] in the Gaussian form where δ is half-width of Gaussian distribution, and δ = 0.29e 2 N 1/3 characterizes the theoretically predicted value of the line width E 0 ; δ increases with the impurity concentration and the compensation degree. This line broadening mechanism dominates at N D > 10 14 cm −3 in n − GaAs, [6]. The values of δ for the samples under investigation with ǫ 0 = 12.5 are given in Table I. Although the magnitudes of δ are of the same order as ∆E, they are 1.5 and 3 times greater than the experimental values of the 1s → 2p +1 line widths for VPE and LPE samples, correspondingly.
A discrepancy between the theoretical and experimental values of the PES line width seems to be explained by screening of charged impurity potential by electron gas. The screening of δ can be qualitatively described as where r m = 4π is the mean distance between the charged impurities N I ≈ 2N A and r m ≈ 13.5 a B , and r s ≈ 10 a B at Helium temperature, provided that ∼ 10% of the acceptors is ionized. These values reduce the value of δ to δ * ≈ 0.27δ, which is in consistence with the experimentally measured value.
The requirement that δ and the experimentally measured half-line width ∆E take the same values imposes a condition that the intra-impurity transitions have to be neglected at all, and inter-impurity transitions not only between the nearest-neighboring donors but between any two impurities have to be realized with equal probability. δ takes larger values yielding wider line width where a local donor concentration is higher in the inhomogeneous impurity distribution even for a sample with smaller N D . Therefore, the value ∆E/δ as well as (∆E − δ) can serve as a measure of SI inhomogeneous distribution degree in samples with nearly equal values of N D and K. One concludes that if a sample with higher SI concentration has smaller line width then it has more homogeneous distribution of the donors. The value of δ/∆E is a suitable parameter for comparison of a sample quality, so that the higher δ/∆E the better is the quality of a sample in comparison with other ones with less homogeneous SI distribution. This parameter is shown in Table I for H ≈ 61 kOe only, since neither δ nor ∆E depends on magnetic field.
The energy distance or gap between the 1s ground state and 2p +1 excited state of electron in the impurity increases with magnetic field, and the resonance 1s → 2p +1 transition occurs when the gap becomes equal to the radiation energy. At H > 20kOe, which corresponds to the intermediate magnetic fields γ = ωc 2Ry * = 0 ÷ 1 with ω c = eH/m * c being the cyclotron frequency (γ = 1 in n − GaAs corresponds to H ≈ 65 kOe), the 2p +1 level of shallow impurities in n − GaAs lies higher than the zeroth Landau level ensuring a transition for the photoexcited electrons to the conduction band (see, Fig. 3). Therefore, there is not a necessity to argue other mechanism, like field induced tunneling or impact ionization from excited 2p +1 state to explain a generation of the PES signal.
It is worthy to note that the line shape of high purity samples in the PES is asymmetric ( Fig. 3 in [6]). The line width at lower energy or higher magnetic field side of the 1s → 2p +1 transition is considerably wider in accordance with the quadratic Stark effect broadening mechanism. Instead, all other samples have symmetric line shape. The line width for the 1s → 2p +1 transition of the purest sample is 1.5 times narrowed when the magnetic field increases from H ≈ 36 kOe to ∼ 61 kOe, which confirms also a validity of the quadratic Stark broadening mechanism [4]. The above specified features of the PES at the breakdown electric field can be explained by assuming that the free electrons, released at the breakdown, screen the Coulomb potential of charged impurities. Note that a screening influences to excited states of neutral donors much more, resulting in their disappearance. The estimations show that the line broadening due to the excitation finite life-time is negligibly small, ∼ 10 µeV [24], in comparison to the experimentally observed data even in a ultra-pure n − GaAs samples. Therefore, the homogeneous broadening mechanism can be neglected for the samples under investigation.
The non-homogeneous PES broadening is determined as a shift between the transition energy of the impurity states in crystal and that of an isolated hydrogen-like impurity atom.
In this case the PES line-shape is determined by statistical distribution of the optical transitions from the ground state to the excited ones for all impurity atoms. The nonhomogeneous broadening of the PES line can be caused by [4,5,25]  by the randomly distributed charged impurities on neutral impurities. Note that the linear Stark effect is absent in magnetic field [4].
Interactions between the neutral donors have a dipole-dipole interaction origin, which broaden the line width symmetrically in comparison with a unperturbed transition energy.
The dipole-dipole interactions mediated half-width of the line in the absence of the magnetic field is given [3]   We show that the distribution functions of quadratic electric field P 1 (E 2 ) and of the electric field gradient P 2 ∂Ez ∂z , which determine the quadratic Stark effect and the gradient broadening of PES line correspondingly, are squeezed due to the screening of the Coulomb potential of surrounding charged impurities by free electrons. Calculations of the distribution functions of E 2 and ∂Ez ∂z on the neutral donors are performed according to the method developed by Shklovskii and Efros [26]. In order to realize the ground state of a doped compensated semiconductor, the coordinates of N donors and KN acceptors are generated where n i = 1 if a donor is neutral and between the mth donor and all other impurities. The dimensionless radius-vectors R i , the square of the electric field E 2 and its derivative ∂Ez ∂z are expressed in units N and eN D ǫ 0 , correspondingly. The directions of the Cartesian coordinate system are chosen to be along the cube axes. E 2 and ∂Ez ∂z are calculated according to Eqs. (3) and (4)  It is necessary to take into account screening of the Coulomb potential of charged impurities by the free electrons at the breakdown. At enough high concentration n of the free electrons, when the Debye radius r D = (ǫ 0 k B T /4πe 2 n) 1/2 is smaller than the mean distance R i between the neutral donors and the charged impurities, r D ≤ R I , the distribution probabilities E 2 and ∂Ez ∂z can be calculated by replacing in Eqs. (3) and (4) the Coulomb potential e/ǫ 0 r by the screened potential e ǫ 0 r exp − r r D . This replacement yield, The where ∆Q is a difference of the quadrupole moments of the ground state and an excited state. Note that, a dependence of quadrupole moments of several states on the magnetic field for an isolated hydrogen-like atom is presented in Ref. [4]. Estimation of ∆ for a sample with N D ≈ 4 × 10 14 cm −3 and K = 0.5 in the magnetic field when γ ∼ 0.5 yields 1 µmeV and 0.7 µmeV correspondingly for non-correlated and correlated electron distributions.
In Fig. 8 we show the dependence of the half-width ∆E, caused by the quadratic Stark effect, on the screening radius, calculated for the 1s → 2p +1 line according to the formula, All these calculations show that the distribution probabilities E 2 and ∂Ez ∂z are squeezed and their long tails disappear gradually with decreasing of the screening radius or increasing of the free electron concentration. In order to narrow the 1s → 2p +1 line, e.g. 4 times the Debye radius has to be r D ∼ 10a * B (see, Fig. 8) which corresponds to n ∼ 2 × 10 13 cm −3 for the free electron concentration or 10% of the total neutral donor concentration. Possible ionization of a such high concentration of neutral donors at E = E BD seems to be doubtful.
Nevertheless, we have to note that (i) although the 1s → 2p +1 line-shape was calculated for zero magnetic field, the experiments were done at strong magnetic fields when γ = ωc 2Ry * ∼ 1, and (ii) the most line narrowing occurs in the "candle"-like region of the sample CVC. It is known that a current filament with high carrier concentration, much more than the average bulk concentration, is formed in this region. We think that the main contribution to the current comes from the filaments, which determines the PES line shape at the breakdown. Coulomb e/(ǫ 0 r), has the finite number of the discrete states. Investigation of the screened Coulomb potential spectrum [29] in the absence of a magnetic field yields that all discrete states higher than N ≥ 4 disappear for the screening radius r s = 10a * B , and the states N ≥ 3 disappear for r s = 9a * B . The quasi-discrete states of the Coulomb potential in a magnetic field are higher excited states with large radii; so they are more sensitive to the screening of The narrowing of 1s → 2p +1 PES line at the breakdown electric field reveals a finestructure of the line due to the spin-splitting of particular donor's states especially for donor with higher concentrations. Similar splitting of the shallow impurities 1s → 2p +1 lines in GaAs was observed in [30,31]. The splitting in the samples with the parameters similar to those in our samples was reported [31] at 119µm wavelength due to the narrowing the 1s → 2p +1 line by means of an additional illumination of the sample with a fundamental absorption edge. The authors of Ref. [30] argue that the spin-splitting of 1s and 2p +1 states differ each other in magnetic field with a small difference in the 1s → 2p +1 transition energies, e.g. different g-factor for 1s and 2p +1 states, whereas a reason of the splitting is assumed in Ref. [31] to be an exchange interaction between neutral donors. We have IIIa. Dependence of 1s → 2p +1 line intensity on pre-breakdown electric field As mentioned above, PES signal at pre-breakdown electric field must be detected in constant voltage regime. PES signal is determined by ∆U = AU ∆σ, where A is a circuit factor, and it is not changed when the line intensity varies with voltage U in all possible acceptable interval. Therefore, a dependence of the intensity on the electric field can be learned by analyzing a dependence of ∆σ(U ) ∼ ∆U/U on applied voltage. A mechanism of the SI PES line intensity enhancement with electric field for a 1s → 2p +1 transition close to breakdown would shed a light on the breakdown mechanism too.
An increase in the PES line intensity with the electric field has been observed and analyzed in various works [35][36][37], where this effect was interpreted either as increase of the hopping conductivity from the excited states [35] or with impact ionization [36] by free carriers from the excited states 2p +1 , 2p −1 . In Ref. [37], an increase in PES was explained by electric field ionization (tunneling) of electrons from optically excited states of SI atom to the conduction band. In [35][36][37] SI final states are far from the conduction band minimum, so E c − E SI (2p 1 ) is much higher than k B T . We consider the case when optically excited states 2p +1 and 3p +1 of SI are higher than N = 0 conduction sub-band minimum. In in conduction band at 1s → 2p +1 photoexcitation of SI, µ c is N = 0 conduction subband mobility of electrons. It is important to note that heating of electrons takes place at electric fields mach higher than brake-down field value. The criterion for heating of the electrons is that the CR line width should be asymmetric broadened due to a transition from (N = 0, k z ) → (N = 1, k z ), with k z = 0 , which takes place, as will be shown in the next Section, at fields mach stronger than the breakdown field.
As it was shown in Ref. [38], heating of electrons in n − GaAs samples at almost the same SI concentrations and similar to our experimental conditions takes place at electric fields much higher than those in our experiments. Concentration of nonequilibrium electrons ∆n(U ) at 1s → 2p +1 photoexcitation from SI to the conduction band can be expressed as a multiplication of the rate G 1s→N =0 of such excitation and the time τ (H, U ) necessary for an photoexcited electron to spend in conduction band, before it would be captured back Generation rate of electrons from the ground state 1s into the conduction band N = 0 through the 2p +1 state can be written as a product of the neutral donor concentration N 0 D , radiation intensity P , and the probabilities W 1s→2p +1 and W 2p +1 →N =0 for the 1s → 2p +1 transition and the isoenergetic transition from the 2p +1 state to the N = 0 Landau zone, correspondingly, It is obvious that all above mentioned quantities do not depend on the external electric field. The only parameter which does depend under our experimental conditions on the external electric field according to [39,40] Let us consider the relation (11) in two limiting cases, τ kz→0 ≫ τ c (H, 0) and τ kz→0 ≪ τ c (H, 0).
In the first case ∆σ(E)/∆σ(0) ≈ 1, and there would be no electric field dependence of the 1s → 2p +1 line intensity. In the second case which means that the reason of 1s → 2p +1 PES line intensity enhancement is an increase of the capture time in electric field. The experimental results of 1s → 2p +1 line intensity dependence on the electric field are shown in Fig. 9. As it is seen from Fig. 9, the power-like increase in the intensity with electric field is considerably slowed down with increasing the magnetic field for a case when the electric field and magnetic field directions are orthogonal each other; whereas the intensity increase with the electric field in the case of parallel electric and magnetic fields is much sharper than that of the case of orthogonal electric and magnetic fields, and furthermore δσ(U )/∆σ(0) increase with U does not depend in this case on the magnetic field strength. In the first glance it seems that all results can be easily explained with carriers' heating mechanism, which is more effective in the case of E H k z than that in the case of E ⊥ H. However, in order to understand the SI electric field breakdown mechanism it is important to know that the common reason of the 1s → 2p +1 line intensity increase as well as super linear increase of the current and increase of cyclotron resonance intensity at pre-breakdown electric fields in CVC is the capture time increase (or the capture cross section decrease) with the electric field. One can conclude that, although the carriers' heating is extremely important to explain the impact ionization, this mechanism is negligible for a moderately doped n − GaAs as our samples even if it takes place at all. There are two reasons, which increase the capture time in the electric field. The first one is a destruction of all discrete states of the SI Coulomb center up to the value ǫ E ≈ 2(e 3 E/ǫ 0 ) 1/2 [41] and, as a consequence a reduction of the capture efficiency of the excited carriers by traps.
In difference from the E = 0 case, electron cannot be captured when, by wandering in excited states of impurity, it appears in distance k B T below the conduction band. At E = 0 it would have a probability to tunneling back by field ionization. So, the tunnel ionization in electric field will prevent diffusive descent of excited carriers to 1s ground state. The influence of this mechanism on capture time is more effective at highly excited states of carriers [25]. It is clear that impurity levels at which the carriers are practically captured, would be shifted down in energetical scale with increasing the electric field. We must explain why does the relative intensity decrease with increasing H in the case of E ⊥ H, while it becomes unchanged for E H. Note, that this is in consistent with another experimental fact that the breakdown E-field much weakly depends on H for E H as it is shown in Fig. 9.   The wave functions of the SI localized states are compressed in a plane normal to the magnetic field within the cyclotron radius l c = (c/eH) 1/2 , nevertheless they are almost unchanged along the direction of H. Therefore, it is natural to expect that depth of the SI energy states' spreading, as well as tunnel ionization in the case of E H would be much more than those in the case of E ⊥ H. So, the relative intensity increase ∆σ(U )/∆σ(0) in the electric field for the 1s → 2p +1 transition is due to decrease of capture cross section of photoexcited carriers.

IVa. Influence of shallow impurities on the electronic effective mass in n − GaAs
The CR measurements were performed in n − GaAs in a large interval of the electric field including the post-breakdown electric field, which allow us to understand deeper many features of the CR line-shape. The CR is well-known method to determine the carrier's effective mass m * c = eH cr /cω in semiconductor at the H cr resonance magnetic field for a given ω radiation frequency. Usually a measured effective mass differs from this definition, e. g. in n − GaAs, due to particularly non-parabolic zone structure and plasma oscillation of the free electrons. The cyclotron frequency ω c is shifted from its resonance value ω due to the plasma oscillation [42] with frequency ω p = (4πne 2 m * −1 Then, the plasma shift of the CR line in the magnetic field at fixed value of ω is which means that the plasma oscillation shifts the CR line to lower values of the magnetic field, which is indicated by the minus sign in the front of the last term. A correction to the cyclotron mass (∼ ∆H), caused by the plasma shift, is significant at small magnetic fields and decreases as ∼ H −1 with increasing the magnetic field. Estimation of the free electron concentration from expression (14), which determine the plasma shift of the CR line, provides Then, the correction to the cyclotron mass can be estimated according to the above considerations to be not more than 0.03% at H ≈ 21 kOe and for n ≈ 10 12 cm −3 . A negligible correction to the effective mass from the plasma oscillation confirms the experimental fact that at pre-breakdown electric field no shift in the CR lines is observed while the free electron concentration increases.
Nevertheless, at the electric fields, higher than the breakdown value E > E BD , and H ≈ 21 kOe a correction to the effective mass due to the plasma shift becomes essential [28]. A considerable shift in the CR line to the small magnetic field (Fig. 10) and a reduction of the cyclotron mass (Fig. 11)   from the filament. A considerable asymmetric line shape of the CR to smaller values of the magnetic fields in Fig. 10 at post-breakdown fields is a result of the free electron distribution inside the filament.
Correction to the cyclotron mass m * c due to a non-parabolic conduction band results in increase of the effective mass with increasing of the CR magnetic field [40] according to As it is seen from Table II,  imentally observed difference of the effective masses is due to the non-paraboliticity, then the difference would be 0.874 %, which is much smaller than the experimental observation. It is worthy to note that the effective cyclotron mass of electrons differs each other more that 0.5% at pre-breakdown electric field even in the samples with close physical properties, which is much more than the experimental error and it increases with the impurity concentrations.
It is necessary to stress out an existence a contribution to the effective mass due to the polaronic effects. Indeed, an electron mass is renormalized by means of the polaron constant α as [46,47], with ω LO being a LO phonon energy, ω LO ≈ 36 meV .
The effective dielectric constant ǫ * , existing in the polaron theory, is defined as where, ǫ ∞ and ǫ 0 are high-frequency-and static-dielectric constants, respectively. According to the percolation theory of Efros and Shklovskii [48], the static dielectric constant in a system with randomly distributed metallic and dielectric regions diverges with approaching to a critical percolation threshold value of the metallic region's volume fraction, where a insulator-metal phase transition takes place. In the insulator phase ǫ 0 takes small values, comparable with ǫ ∞ , yielding relatively high value for the effective dielectric constant ǫ * .
In this case, the polaron constant α takes small values, which does not change the effective mass. The static-dielectric constant ǫ 0 diverges [48] in the breakdown regime, which can be considered as a insulator-metal phase transition too. As a result, the polaron constant α increases due to decrease in ǫ * , yielding a considerable enhancement of the effective mass.
Estimation of α for GaAs far from the breakdown regime yields α ≈ 0.06 by taking ǫ 0 ≈ 12.5 and ǫ ∞ ≈ 10.9. The effective mass of an electron takes the value m pol = m * 1 + 0.006 6 ≈ 0.06767, which is in consistence with our experimental results (see , Table II Shape of the CR line at the radiation wavelength λ ≈ 119 µm for different values of the electric field, including the breakdown field, is depicted in Fig. 12. It is clearly seen from this picture that the CR lines shift to higher values of the magnetic field (∆H > 0) at E ≈ E BD . Although similar shift observed in e.g. n − InSb [49], CdHgT e [50] and n − GaAs [38] crystals, has been explained as a result of electrons heating in the electric field when a resonance absorption in the non-parabolic band occurs at higher magnetic field, our investigations of the CR lines and CVC at different magnetic fields such as 21 kOe (λ ≈ 337 µm), 43 kOe (λ ≈ 172 µm) and 61 kOe (λ ≈ 119 µm) contradict to the electrons heating mechanism for the CR line shift [51].
The dependence of the effective mass m * on the electric field E is depicted in Fig. 13.
The CVC for this sample is shown by dashed curve at the magnetic field H ≈ 61kOe, The free electrons of a semiconductor, placed in the magnetic field, lie at zeroth Landau level at low temperatures, k B T ≪ ω c , and the peak in the CR (solid curve in Fig. 14) corresponds to a transition from a state with the maximal density of states (DOS) ρ 0 (E) in this level to the state in the first Landau level. Fluctuations of the charged impurities' density result in a randomly distributed potential of impurities, which smears the electronic states in the crystal. Therefore, the maximum of the DOS in the magnetic field shifts; the values of the shift ǫ 0 0 and ǫ 1 0 from the DOS maxima ω c /2 and 3 ω c /2 for a crystal depend on the impurity distribution and on the degree of non-homogeneity of this distribution. This fact allows us to determine a degree of the non-homogeneity in the impurity distribution [52].
The shift decreases with increasing the number N of the Landau level due to the increase in the cyclotron radius r N cr = [c (2N + 1)/He] 1/2 , i.e. the value of the DOS peak shift for zero Landau level is higher than that for the first one. Thus, the CR line peak shifts to the higher values of the energy; the value of the CR line intensity shifts for semiconductors with  Table II). This method allows us to determine a degree of non-homogeneity in a given sample. Note that a difference between the CR masses for different samples considerably decreases at the breakdown, which supports our model.

IVb. PES Intensity Dependence of the CR Line on pre-breakdown Electric Field
and influence of potential fluctuations on the CR line shape PES for SI 1s → 2p +1 transition must be nonzero at arbitrary small electric field because of the final state 2p +1 in our experiments is higher than N = 0 Landau level. As a result, an electron photoexcited to 2p +1 appears in the N = 0 conduction band after its first relaxation step. However, for CR to be detected, the existence of sufficient free carrier concentration is obligatory condition. We must consider the dependence of the CR intensity on E-field up to its pre-breakdown value E < E BD . In the linear region of CVC, where the electric field induced enhancement of the free electrons is negligibly small, the free electron concentration n(T ) in magnetic field H can be expressed (n(T ) ≪ N D ) [45] as where N c = 2(m * k B T /2π 2 ) 3/2 is the electronic density of sates in the bottom of the con- electric fields was investigated in constant voltage regime, so PES signal ∆U = AU ∆σ, where ∆σ = n 0 (µ 1 − µ 0 )J( ω c ), n 0 is the free carrier concentration, ∆µ = µ 1 − µ 0 is the difference of the mobilities in the first and zeroth Landau levels (LL), correspondingly, and J( ω c ) is the radiation intensity at the CR magnetic field. The CR line intensity is determined as a product of ∆U/U and CR line width, the latter of which does not depend on electric field up to the breakdown field. In order to detect the CR in PES experiment it is necessary to determine the mobilities difference at two adjacent LL. At low temperatures, the dominant mechanism of free electron scattering is a scattering on ionized impurities (µ ∝ ǫ 3/2 ). So, the mobilities' difference at CR in the absence of the external electric field (k z = 0) or in the absence of free carriers' heating at pre-breakdown field is given by This means that CR induced conductivity change is due to not free carrier concentration redistribution between LLs only, but also on mobility difference two adjacent Landau bands.
The mobility difference in electric fields leading to heating of electrons (k z = 0) reads as where the selection rules for the CR (∆N = 1, ∆k z = 0) are taken into account [53].
Supposing that the heating takes place at pre-breakdown electric fields for H = 61 kOe, when the heating causes an increase in the energy 2 k 2 z /2m * = 30K ≈ 2.5 meV . Then ∆µ is calculated from the relations (20) and (21), which would differ each other only about 10%.
Therefore, an increase in the line intensity is provided not by an increase in the mobility but by an increase in the free electron concentration. The above described heating of the free carriers has to increase the CR line-width asymmetrically to higher magnetic field side from the CR line maximum, which is not the case at pre-breakdown electric fields and takes place only at E > (3 ÷ 4)E bd . This is confirmed by two facts. The first, the experimental observations, that at the breakdown electric field E = E bd a strong narrowing takes place not only in 1s → 2p +1 line but as well in CR line-shape, refuse the heating of free carries in external electric field as a breakdown mechanism. Indeed, this fact contradicts to IIM, where heating of free carriers in pre-breakdown electric field is the necessary condition. Second, increase of CR intensity at pre-breakdown electric field is not due to increase of mobility difference ∆µ = µ 1 − µ 0 of free electrons at CR transition, but with increasing of carrier concentration no at zero N = 0 LL.
Provided that the ionization energy decreases in external electric field according to Pool-Frankel effect, the free electron concentration increase ∆n would differ from formula (19) by a factor β(E) [41], which takes into account the cascade ionization of donor from 1s state to the excited states of SI where E E = 2(e 3 E/ǫ 0 ) 1/2 is an ionization energy reduction of the SI Coulomb potential in the electric field E. Its value at breakdown electric field E E ≈ 0.1 meV for n − GaAs is much smaller than SI ionization energy E i in CR magnetic field. Two times increase of the electric field E from 1 to 2 V · cm −1 results in increase of CR intensity, determined by the electron concentration (19) 1) and (2)) with the characteristic value [54][55][56]. For the samples used in our experiments, with the parameters N D and K given in Table I  Finally, we would like to discuss the low-temperature breakdown mechanism of SI by an electric field. The free carrier concentration n increases in the electric field E not only due to an increase in the ionization coefficient β(E) but also a decrease in the capture coefficient α(E). The value of n can be estimated from the condition of balance between the capture and the thermal ionization as [20] n(E)αN where N + D = N A + n and N 0 D are the concentrations of charged and neutral donors. β increases with electric field and diverges at E = E BD , instead α decreases with increasing E and vanishes at E = E BD , resulting in sharp enhancement of the electron concentration The concentration n reaches a critical value by approaching the breakdown electric field, when the charged donors become strongly screened as e ǫ 0 r e −r/rs . Further increase in n provide a realization of a specific potential V (r), so-called a fluctuation potential. This random potential is assumed to distribute according to Gauss law, [54,55] where γ is the mean-square fluctuation potential, which characterizes a non-homogeneous The similar picture is realized in the process of the illumination, which increases again the band electrons due to band-to-band excitation of electrons by illumination.
One can conclude that a non-homogeneous distribution of the impurities in the sample and its fluctuation potential results in the alternative resonance lines near the CR line.

IVc. Effects of the electric field on the CR line width
Dependence of the CR lines on the magnetic and electric fields, temperature, the concentrations of neutral and ionized impurities yields an essential signature on the broadening mechanism of the lines. If the CR line broadening is determined by scattering of the current carriers in a semiconductor, then the momentum relaxation time τ CR is expressed through the resonance magnetic field H p , the half-width ∆H 1/2 and the radiation frequency ω as [57] τ CR = 2H p ∆H 1/2 ω .
Although τ CR is determined by all scattering mechanisms, the main scattering mechanisms in n − GaAs at T = 4.2 K are scattering on acoustic phonons as well as on neutral and ionized impurities. Since the number of the ionized impurities is much more than that of the neutral impurities, one can neglect scattering on the neutral impurities. Two experimental facts demonstrate that the scattering on the ionized impurities dominates over scattering on the acoustic phonons. First, the electron mobility ∆µ = µ 1 − µ 0 > 0 is changed in the cyclotron absorption, which is testified by equal polarities of the CR photo-signal and of the photoexcited impurities. The energy dependencies of the mobility for ion µ ion ∼ E 3/2 [47] and acoustic phonon µ ph ∼ E −1/2 [58] scattering mechanisms differ each other. Since the electron energy increases amount of ω c in the CR, which coincides with the ion-scattering mechanism when ∆µ > 0 and contradicts to the phonon scattering mechanism when ∆µ < 0.
Second, according to the perturbation theory, the CR line should be narrowed with increasing the magnetic field either ∼ H −1/4 [59] or ∼ H −1 [60,61] for the dominant ion-scattering mechanism, and it should broaden as ∼ H [58,62] for the dominant phonon-scattering mechanism. The CR line measurements in n−GaAs [24,63] with the impurity concentration one order smaller than that in our samples were reported to show the line narrowing in the magnetic fields from 21 kOe to 61 kOe, confirming that a scattering on the ionized impurities is a dominant mechanism at T = 4.2 K even at low impurity concentrations. Note that the charged impurities either scatter the electrons or their potential shifts the cyclotron frequency of the electrons. The relaxation time for the non-adiabatic electron scattering on the charged impurities, when the cyclotron radius l c is smaller that the radius a of an impurity potential, l c < a, was calculated [60] to be On the other hand, a broadening of the CR line [59], due to the cyclotron frequency shift ∆ω c = (V xx + V yy )/2m * ω c with V xx and V yy being the second derivative of the impurity potential at the cyclotron orbit center, is given as, The relaxation time, determining from the CR line width according to Eq. (26), seems to be one order higher than that determining from Eqs. (27) and (28). One of the peculiarity of the CR measurements in n − GaAs is that there is not a monotonically dependence of the line width on the ionized impurities concentration. The CR lines in Fig. 20 given for two samples with similar physical parameters show an increase in the line width with decreasing the impurity concentrations. As it is seen from these curves, the CR line of sample 5 is wider than that of sample 6, though the concentration of the ionized impurities in sample 5 is less than that in sample 6.
The considerable fact is an existence of a correlation between the width and the value of shift of the CR lines at the pre-breakdown electric fields. A broadening of Landau levels due to the impurity potential fluctuations results in an additional broadening of the CR lines and shifting of their peak positions. Therefore, the CR line widths of two samples with the same concentrations of the ionized impurities can differ each other, so that the higher is the non-homogeneity of the impurity distribution the wider is the CR line.
The CR line width is defined in the energetic unit as ∆E = ∂E ∂H ∆H, where the change rate of the cyclotron energy with a magnetic field ∂E ∂H can be estimated to be for the first two Landau levels 0.17 meV /kOe. This value is comparable with fluctuation potential of the charged impurities, the correct expression of which is given for a small compensation as [22], This expression takes a value of 0.1 ÷ 0.2 meV for the samples under investigation.
Broadening of the Landau levels due to the potential fluctuations results in a broadening of the CR line in addition to the broadening due to the scattering of electrons on the ionized impurities. Therefore, the wider is the CR line for the samples with equal concentration of the charged impurities the higher the non-homogeneous distribution of impurities is.
Influence of the distribution non-homogeneity on the width and the peak position of the CR line is essential only for higher magnetic fields when the cyclotron radius of the zero-th Landau level l 0 c is smaller than the potential size a * B of an impurity, l 0 c < a * B . At smaller H a cyclotron orbit with larger radius contains several charged impurities with opposite signs, the effects of which cancel each other in the averaging.
Th free electron concentration increases several order at the breakdown electric field, corresponding to a sharp enhancement of the current at E = E BD in the CVC, which changes strongly the CR line shapes. The CR line narrows approximately two times in the close vicinity of the pre-breakdown electric field (see, Figs. 12 and 13), which is observed at the radiation wave length λ ≈ 119µm as well as at λ ≈ 337µm with increasing the electric field. Recalling that the CR line broadening is caused by the ionized impurity potential, the narrowing the line width at the breakdown field can be understood as a reduction of the potential fluctuations due to the screening of the ionized atoms by free electrons released at the breakdown. The photoelectric spectrum of the CR lines, presented in Fig. 21, is measured in the steady current regime with its different values and at λ ≈ 337µm , which shows instead a broadening approximately three times with increasing the value of the current. The similar measurement at λ ≈ 119 µm (H ≈ 61 kOe) at the breakdown field E ≈ E BD = 15 V · cm −1 yields the similar results. Since the broadening occurs at a steady current, it rules out the impact ionization mechanism by means of the electron heating.
The theories of the CR line broadening, suggesting either ∆H 1/2 ∼< ωτ >∼ N −1/2 I [59] or ∆H 1/2 ∼< ωτ >∼ N −1 I [60,61] on the base of the impurity ionization mechanism, can not explain the measured broadening, the value of which needs several times increase in the The corresponding values of the current is shown in the inset of the CVC curve. The value of the current corresponding to the curve 5 is the same as in the curve 4, but the radiation intensity is 7 times lower.
concentration. The observed broadening of the CR line seems to be caused by electronelectron correlations, which act similar to the scattering on the ionized impurities. Indeed, an increase in the free electron concentration with the current J of cross-section area S can be estimated according to The free electrons of a small concentration at the beginning step of the breakdown screen the charged impurities potential, weakening their effect on the CR line broadening. Further increase in the free electrons concentration changes the scattering mechanism from the electron-impurity to the electron-electron mechanism. The free electrons concentration in the current filament reaches the ionized impurity concentration which is several order higher than that of the average bulk concentration of the impurities.
One of the experimental evidence is that the CR line width in the broadening regime depends also on the radiation intensity. The radiation intensity for the CR line, shown by the curve 5 in Fig. 21, is 7 times higher than that of the curve 4, which results in strongly reduction in the line width. In this case, the free electron concentration considerably decreases due to an increase in the current filament cross-section resulting in a narrowing of the line width. Note that an asymmetry in the line width broadening is observed at higher breakdown fields. The asymmetry at E ≈ 2E BD reaches 20% around the line maximum ( Fig.   12), which seems to occur due to an electron heating by high electric field. The electron heating enhances the electron concentration with k z = 0. Thus, the resonance condition ν = E(1, k z ) − E(0, k z ) for a non-parabolic zone is satisfied at higher magnetic fields, yielding an asymmetric broadening.

V. CONCLUSIONS
In this paper we suggest a new mechanism of SI breakdown in n − GaAs samples particularly for an intermediate donor concentration 10 14 cm −3 < N D < 10 16 cm −3 and for the compensation degree 0.3 < K = N A N D < 0.8 when the electric field is varied in wide interval from the linear part of CVC up to 3-4 times higher than the SI BD field. All the obtained results contradict the impact ionization mechanism of the breakdown. The main contradiction with the IIM is the absence of carrier heating at pre-BD and BD electric fields. In difference from the N -like CVC dependence, which is observed in constant voltage regime [64], S-like CVC dependence should be observed in the heating mechanism due to strongly increase of carriers' mobility µ(E) ∝ E 3/2 in the scattering process of electrons from charged impurities. CVC characteristics of our samples have shown no S-like dependence in the constant current regime measurements. The other fact, which contradicts to the IIM, is that the BD electric field practically does not depend on the magnetic field in the case of parallel electric and magnetic fields E H although the impurity ionization energy increases two times at the magnetic field γ = ωc 2Ry * ≈ 1. We showed that the PES line-width of 1s → 2p +1 transition is determined not only by the SI concentration and the compensation degree but also by the potential fluctuation, which is provided by non-homogeneous distribution of the charged impurities. The potential fluctuation disappears at the breakdown electric field E = E BD , when the released electrons screen the charged impurities, which may be caused also with quadratic-Stark effect and gradient-broadening mechanism of PES. Disappearance of Zeeman spectra, corresponding to the transitions from the ground state to highly excited Boyle-Howard's states up to 1s → 3p +1 at the BD, also confirms the screening mechanism of the ionized impurities by free carriers at RD. The PES line-width is strongly narrowed at E = E BD .
For small concentration of impurities N D < 10 12 cm −3 the above described mechanism is not valid, since the free electron concentration is insufficient for screening of the charged impurities. Nevertheless, the conventional impact ionization mechanism may work and the breakdown occurs at much higher (several order higher than that of for our samples) electric fields.
At higher concentrations of the SI, when N D > 10 16 cm −3 , the mean distance between the donors becomes comparable with the Bohr radius. In this case, all donors become ionized, and therefore a Mott's regime is realized. Therefore, further ionization of the impurities is not expected. The CVC in this case should not display a 'candle'-like jump, and the current will increase super-linearly with the electric field.
A breakdown of the SI in n−GaAs under electric field was investigated in the work in two different configurations of the magnetic field, when the latter is parallel-and perpendicular (H E and H ⊥ E) to the electric field. For H ⊥ E, the breakdown field E BD strongly depends on the magnetic field at H = 61 kOe, corresponding to γ = ωc 2Ry * ≈ 1, as a result of two-times increases of the ionization energy of SI. Instead, CVC investigation for the case of H E showed practically no dependence of E BD on the magnetic field. Indeed, magnetic field does not change the wave function shape along the electric field when it is parallel to the electric field. A weak dependence on the higher magnetic field is a result of localization of the electronic wave in the perpendicular to the electric field plane, which reduces a transition of an electron to the excited states of the neighboring impurities.
Investigations of PES of 1s → 2p +1 transition as well as CR line-shape at pre-breakdown electric fields have shown no correlation between the physical characteristics and the compensation K.
Our CR investigation of n − GaAs samples yields an effective electron mass value, which varies in a wide interval. Moreover our measurements reveal that an effective mass of a sample even smaller SI concentration has higher than that of more dirty samples. Moreover, at the breakdown the effective masses of all samples become comparable each other, which means that the potential fluctuation plays an essential role. Therefore, in order to provide more correct data for an electron effective mass, it is necessary to measure the latter at the breakdown region.