Microwave Absorption in Ge After Bombardment of Helium Ions Beam

In this work, the effect of Ge sample bombardment by energy Ei = 1.2 MeV mono‐energetic He+ ions within the fluence range of 1013–1.2 × 1015 cm−2 on the microwave reflection/transmission modification in the frequency range of 26–38 GHz is investigated. It is shown for the first time that such Ge treatment allows achieving a drastic increase in its interaction with microwaves. After the 1 µm thick undersurface area of Ge, accounting for less than 10−3 of its bulk, underwent the fluence of 1.2 × 1015 cm−2, the increase of the microwave absorption coefficient from 0.06 to 0.78 and decrease of the microwave reflection coefficient from 0.7 to 0.18 are observed. This is caused by the occurrence of dangling atomic bonds in nanoscale cavities inside the material. Most probable energy loss mechanisms of microwaves in modified Ge are suggested. Modified semiconductor structures can be used as microwave‐absorbing coverings, devices employing a periodic structure of materials or a gradient of its properties.


Introduction
[6][7] In the latest research, [8][9] were shown the newest possibilities of CoFe 2 O 4 and Fe 3 O 4 for electromagnetic wave DOI: 10.1002/apxr.202300090absorption in the form of lightweight foam controlled by 3D structure.This proved the high efficiency of the use of ultra-thin films and their combinations for such applications.At the same time, a requirement of the multi-stage process for successive covering with layers of different properties is among the drawbacks which more or less inherent in the above technologies.Therefore, the search for new methods of creating absorbing coatings, methods of their application, as well as the development of new devices based on it, continues intensively.This is facilitated and the presence of an extremely large and diverse field of application of adsorbing microwave coatings.
Alternatively, modification by monoenergetic high-energy beams of light ions (He + or H + ) can be considered a promising technology.The demand characteristics of the formed structure can be exactly specified by a selection of size, arrangement, electric conductivity, and other parameters of the modified areas.It is possible to modify a material at an exactly assigned depth while the upper and lower layers of the bulk remain unchanged.The lattice defects are the main factors of semiconductor properties modification by light ions.Normally, the defect formation is accompanied by the appearance of energy levels in the semiconductor band gap.Those levels could be electrically active donors or acceptors and also centers of recombination.Under poor irradiation doses, local defects are formed (Freckle's pairs), coalesce at sufficiently high doses, and form nanoscale pores inside a matrix. [10]At the same time, local levels are transformed into zones. [11]n the case of monocrystalline Ge, irradiation by a monoenergetic beam of light ions enables its fundamental modification: formation of p-type electric-conductive areas inside the material (hidden channels, plates, and wires) that is easy to observe experimentally and then compare with the data of other studies. [11,12]To form such layers, one can apply ionic beams similar to those used in the "Smart Cut" technology. [10,13]with necessary energy and fluence.The proposed modification of Ge or other materials by light ion beams can be promising for the creation of microwave-absorbing coverings or devices with periodic layered structures of successive conductive layers with different refractive indices as well as simply defected slices. [2]The technology of modification with high-energy ion beams enables the formation of 1-, 2-, or 3D photonic crystals as well as other passive and active structures in Ge.The main advantage is that those structures can be fabricated in a single technological cycle.The depth of high-conductive (defective) formations occurrence is regulated by the ion beam energy, whereas their electric properties are defined by the irradiation fluence.

Experimental Section
The samples for microwave measurements were made of monocrystalline germanium of high purity.After the cutting operation, the faces of the specimen were polished to achieve its accurate size.Such sample is shown on inset in Figure 1; it had a rectangular parallelepiped shape where the largest facet coincided with (111) lattice plane.The sample side dimensions corresponded to the microwave waveguide cross-section with the small gaps between the sample facets and the walls of the waveguide (Figure 2).
The implantation of ions with energy E i = 1.2 MeV was carried out through the (111) surface.Figure 1 shows the concentration N distribution of the ions He + implanted through the (111) Ge face, as calculated by the Stopping and Range of Ions in Matter program. [14]As shown in Figure 1, the implanted layer lied on the depth d i ≈ 4 μm and its thickness on one-half height of distribution is  i ≈ 0.25 μm.The greatest energy loss and the formation of stable electrically active defects occured at the end of the particle stopping distance.Thus, the implanted subsurface layer of  i thickness was created by the implantation of ions at a distance d 1 from the surface.Note, that the thickness of the modified region in Ge was less than 10 −3 of the sample thickness L = 3 mm (Figure 1) and was shaped in the subsurface layer of one certain facet of the sample.The implantation covered the entire sample surface (111) by lateral movement.The diameter of the unfocused beam was 5 mm.As a result of implantation irradiated layer was created (shaded strip in Figure 1).A detailed description of the irradiation technique using Kyiv ion microprobe is available in ref. [15].The study of the electrodynamic properties (microwave transmission and reflection coefficients) of the irradiated Ge samples was performed in the frequency range of 26-38 GHz.In this wide enough frequency range, high-precision measurements can be performed using one set of rectangular waveguides with no need to change the size or reshape the samples.The standard rectangular hollow waveguide 7.2 × 3.4 mm 2 was used.The tested samples were interposed into the waveguide to close the crosssection completely.Measurements of microwave transmission and reflection coefficients were carried out according to standard technique.Measuring setup block diagrams are presented in Figure 2.
It is known that the attenuation of microwaves depends on the dielectric and magnetic properties of the sample.Also, both the electric and the magnetic components of the microwave have an associated effect on the other when propagated and absorbed by the sample.Therefore, the separation of the contributions of the dielectric and magnetic losses is possible if one can extract only the electric or magnetic component of the microwave energy separately in the experiment. [2]In our case, we measured the general dielectric and magnetic losses coupling.
The technology of Ge samples preparation (Figure 3) for implantation and the further study of transport phenomena included: i) cutting the chunk of Ge for (10 × 10 × 2) mm sizes; ii) burning Indium contacts to (112) facets; iii) cleaving the sample across (111) facets to achieve the smooth surfaces.Good Ohm contacts to the modified regions on a different implantation depth d i were obtained due to the passing of cleavage crack over (112) facets covered by In.
The irradiation of Ge samples for further transport phenomena study was realized much as for the samples intended for microwave measurements.They were closely located with one another and were irradiated simultaneously in a single cycle Figure 3a.However, the ion beam was additionally focused to produce samples shown in Figure 3b.Emerging p-type conductive regions were shaped under the irradiated areas at the depth d i (shaded areas on the inset in Figure 1) [11,12] ; their sizes and arrangement are illustrated in Figure 3.
Indium contacts on the side (112) facets are black-labeled in bold in Figure 3.Those contacts were reliable Ohm contacts with implanted p-type layers and enabled the measurements of the conductivity  i as well as the concentration Γ i and mobility  i of free charge carriers (holes).Transport parameters measurements were done by DC.This study is based on two versions of the Hall method: Hall current method and Hall Electromotive Force (EMF) technique.Measurements were fulfilled at 77 K temperature which allows neglecting the conductivity of the bulk of the samples or it is surely electrically insulated by the p-n junction in n-type Ge.Hereinafter,  i , Γ i , and  i are exclusive characteristics of the subsurface conductive layer resulting from the irradiation.

Interaction of Microwaves with Ge Samples Implanted by Helium Ions
We can estimate the degree of interaction between microwaves using coefficients of absorption K A , transmission K T , and reflection K R These can be calculated from S-parameters S 11 and S 21 of the scattering matrix of an object.After the implantation of He + has been carried out, measurement of the frequency dependencies of microwave scattering parameters S 11 and S 21 of the Ge sample were measured in the range of 26-38 GHz.The obtained dependences are shown in Figures 4 and 5, respectively.They correspond to irradiation with He + ions of fluence between 10 14 and 1.2 × 10 15 cm −2 .Changes of S 11 = f() and S 21 = f() were noticeable under He + ionic fluencies of F i ≥ 10 14 cm −2 .If F i ≤ 10 14 cm −2 then the changes in S 11 = f() and S 21 = f() were insignificant and comparable to the accuracy of the measurements.
As one can see in Figure 4, changes in S 11 are minor in all the investigated frequency ranges for each irradiation dose.Two weak maxima were observed at frequencies  1 ≈ 26.5 GHz and  2 ≈ 35 GHz.These frequencies correspond to two wavelengths inside the waveguide filled with Ge; i)  1 ≈ 3 mm, coinciding with the sample's length width L = 3 mm; іі)  2 ≈ 2 mm corresponding with L = 3 mm = ( 2 /2) × 3.Because of this, S 11 maxima can be considered as connected with interference resonances due to internal multi-reflection between the inlet and outlet facets of the sample.At the resonant frequencies, the length of the sample equals to integer of halves of the wavelength.A similar situation is observed also in Figure 5 where the frequency dependencies of S 21 () are shown.Curves 1-5 in Figure 5   curves (≈3.5 db) are much more significant compared with analogous extrema of S 11 ().This is caused by the known effect of reduction of introduced attenuation inside the reentrant cavity at resonant frequencies. [16]he nature of the minor irregularities on curves S 11 () and S 21 () of Figures 4 and 5 can be attributed to the inhomogeneity of the waveguide (in particular, its flange connections).This is also confirmed by peculiarities of S 11 () after several doses of irradiation.On curves 2-5 of Figure 4, small peaks and depressions are observed which are obviously reproduced on these curves at i ≥ 10 14 cm −2 .A similar picture is observed in Figure 5 as well.
The scattering matrix parameters S 11 and S 21 were measured experimentally, thus allowing the calculations of the power reflection coefficient K R and the transmission coefficient K T by formulas K R = antlg(S 11 × 10 −1 ) and K T = antlg(S 21 × 10 −1 ), respectively.With knowing K R and K T values, the absorption coefficient K A can be easily calculated using the formula Dependencies of these coefficients at frequency 37 GHz on He + fluence are presented in Figure 6.
As seen from the data of Figure 6, irradiation with He + ions under F i ≤ 10 14 cm −2 introduces negligible influence on the values of K A (F i ) (curve 1), K T (F i ) (curve 2), and K R (F i ) (curve 3), and their variations lie within the error of the experiment.If F i ≥ 10 14 cm −2 then the degree of the material modification achieves a certain critical value after which the absorption coefficient K A shows fast augmentation, whereas the coefficients of reflection K R and transmission K T decrease.

Transport Characteristics of the Implanted Layers
To comprehend the causes of the behavior of the obtained dependencies of coefficients K A (F i ), K T (F i ), and K R (F i ) (see Figure 6), electric conductivity  i , concentration Γ i , and mobility  i of free holes inside the hidden conductive channels were investigated as a function of implantation fluence F i of bombarding ions.Experimental points of  i (F i ) curve 1, concentration Γ i (F i ) curve 2, and mobility  i (F i ) curve 3 dependencies are shown in Figure 7.The investigated sample contains the stable hidden conductive layer (channel).The  i , Γ i , and  i values of the channels were practically unchanged after a long stay in laboratory conditions or multiple short-time (≈10 min) heating up to 150 °C.
The electric conductivity value is  i = e × Γ i ×  i .When comparing data of curve 1 and curves 2 and 3 of Figure 7 it is seen that increase  i with augmentation of F i is explained by increase of Γ i within the interval of Γ i = 6 × 10 11 -10 14 cm −2 .Inside this interval, Γ i value increases by ≈100 times, whereas the mobility  i wanes by ≈10 times as a result of an increase in the holes scattering on charged centers.If F i ≥ 10 14 cm −2 then the reduction mobility  i compensates the Γ i augmentation thus eliminating the dependence of  i on Γ i (horizontal section near the maximum  imax ≈ 3 × 10 −3 Ohm −1 curve 1, Figure 7).
Supplying free holes electric-active centers are intrinsic and not associated with admixtures.Conductivity-responsible centers are caused by dangling atomic bonds resulting from Ge crystal lattice rupture. [11,12]Upon small fluence values generated by light ions, simple defects (knocked-on atoms and lattice vacancies) are formed.Implanted ions are located in internodal intervals.[19] They coalesce in pressed gas-filled cavities of rising dimensions.The formation of defects starting with F i ≥ 10 12 cm −2 is the reason for conductivity  i (F i ) occurrence (Figure 7).
At the same time rather high fluence values of F i ≥ 10 14 cm −2 provide the effect of defect formation on the microwave absorption coefficient K A .K A starts to rise steeply (curve 1) while both the transmission coefficient K T (curve 2) and reflection coefficient K R (curve 3) diminish (Figure 6).[19] and data of Figure 6, the threshold value F i ≥ 10 14 cm −2 can be associated with the start of defects coalescence into nanopores and further micropores.The presence of micropores is a possible physical reason for changes in the process of interaction of microwaves with matter.This process is associated with gas availability in caverns with permittivity and permeability values equal to 1. That's why the average values are reducing in the subsurface Ge region.This means the reduction of the microwave impedance discontinuity at the air/Ge interface and the decrease of the reflection coefficient K R .Concurrently, at F i ≥ 10 14 cm −2 the conductivity in the modified region approaches the maximum value of  imax ≈ 3 × 10 −3 Ohm −1 (Figure 7) which provides the microwave energy loss rise.In this case, the magnetic part of the microwaves induces an eddy electrical current.At that, the concentration of free holes Γ i (F i ) keeps rising (Figure 7) which shows the increase in the concentration of unpaired dangling atomic bonds. [11]They can generate magnetic moments from their spin orientation.Such defects are paramagnetic centers and give rise to the magnetic loss of microwaves.In cavities with closely spaced unpaired electrons, magnetic ordering can evolve from the exchange interaction which causes magnetodynamic effects, and magnetic loss can further increase.The effect of microscopic magnetic resonance is effectively accompanied by energy loss mechanisms. [1,20]Thus, the conductivity  i (F i ) concurrently with paramagnetic centers occurrence results in the rise of microwave energy loss, i.e., the increase of the absorption coefficient K A .Such a shift in the energy balance K R + K T + K A = 1 means the decrease of the reflection coefficient K R at the insignificant observed change in the transmission coefficient K T (Figure 6).

Conclusion
The modification effect of monochromatic high-energy light ion beams on the reflection and transmission of microwaves by the Ge sample in the frequency range of 26-38 GHz is studied.
Such modification results in structural defects in the thin subsurface layer of single-crystal germanium; unpaired dangling atomic bonds and He 2 -filled micropores in the subsurface region appear.The main results of the study are as follows: Under the fluence of F i = 10 12 -10 14 cm −2 by He + ions, predominantly simple defects (vacancies, interstitial atoms) are formed, and unpaired dangling bonds occurrence results in the p-type conductivity in the subsurface modified Ge layer with the concurrent change in its magnetic properties.
Further increase in the fluence to F i ≥ 10 14 cm −2 provides the formation of more complicated defects (micropores) with regions, which may overlap with each other.Such He 2 -filled micropores result in a considerable decrease in the average permittivity and permeability of the subsurface layer and, accordingly, in a severe decrease of the microwave reflection coefficient K R from 0.7 to 0.18.Despite eddy current due to conductive layers in Ge, unpaired dangling bonds as the reason for the exchange interaction of electrons can contribute to the drastic increase of microwave energy loss.Electric and magnetic loss concurrent increase can explain the sharp rise in the microwave absorption coefficient K A from 0.06 to 0.78.
Fundamental change in the absorption coefficient K A and reflection coefficient K R occurs at the modification of ≈0.001 bulk fraction of Ge by high-energy light ion beams.Such Ge modification can be a basis of new techniques for the fabrication of gra-dient structures, electromagnetic-absorbing materials and coatings, and the formation of photonic crystals.

Figure 1 .
Figure 1.Distribution of the concentration N of implanted ions He + along the coordinate x perpendicular to the (111) lattice plane of Ge sample.Inset shows the sample with an implanted layer inside it (shaded strips are in (110) and (112) lattice planes).

Figure 2 .
Figure 2. Block diagram of the experimental setup to measure transmission (a) and reflection (b).

Figure 3 .
Figure 3. Location of irradiated areas on (111) sample faces (shaded strips) to measure transport phenomena.a) Hall current, b) Hall EMF.Indium contacts on the side (112) facets are black-labeled in bold.

Figure 6 .
Figure 6.Dependencies of coefficients of absorption K A (F i ) (curve 1), transmission K T (F i ) (curve 2), and reflection K R (F i ) (curve 3) after He + fluence.The curves correspond to data from Figures 4 and 5 at frequency  ≈ 37 GHz.

Figure 7 .
Figure 7. Dependencies of electric conductivity  i (F i ) -curve 1 crosses (+), concentration Γ i (F i ) -curve 2 open circles (o) and mobility  i (F i )curve 3 solid circles (•) of free holes of the conductive layer.The sample irradiated by He + ions.