Single Shot Damage Mechanism of Mo/si Multilayer Optics under Intense Pulsed Xuv- Exposure References and Links

We investigated single shot damage of Mo/Si multilayer coatings exposed to the intense fs XUV radiation at the Free-electron LASer facility in Hamburg-FLASH. The interaction process was studied in situ by XUV reflectometry, time resolved optical microscopy, and " post-mortem " by interference-polarizing optical microscopy (with Nomarski contrast), atomic force microscopy, and scanning transmission electron microcopy. An ultrafast molybdenum silicide formation due to enhanced atomic diffusion in melted silicon has been determined to be the key process in the damage mechanism. The influence of the energy diffusion on the damage process was estimated. The results are of significance for the design of multilayer optics for a new generation of pulsed (from atto-to nanosecond) XUV sources. Operation of a free-electron laser from the extreme ultraviolet to the water window, " Nat. " Multi-millijoule, highly coherent X-ray laser at 21 nm operating in deep saturation through double-pass amplification, " Phys. Rev. Demonstration of a desk-top size high repetition rate soft x-ray laser, " Opt. Evolution of optical properties of surfaces under influence of ultra short pulses of intense EUV radiation, " Enhanced reflectance of interface engineered Mo/Si multilayers produced by thermal particle deposition, " SPIE 6517 (2007). High-temperature stability multilayers for extreme-ultraviolet condenser optics, " Appl. Sub-nanometer scale measurements of the interaction of ultrafast soft x-ray free-electron-laser pulses with matter, " Phys. Soft-x-ray free-electron-laser interaction with materials, " Phys. Damage threshold of inorganic solids under free-electron-laser irradiation at 32.5 nm wavelength, " Appl. Characteristics of focused soft X-ray free-electron laser beam determined by ablation of organic molecular solids, " Opt. Non-thermal desorption/ablation of molecular solids induced by ultra-short soft x-ray pulses, " Opt. " Wavelength dependence of the damage threshold of inorganic materials under extreme-ultraviolet free-electron-laser irradiation, " Appl. Damage of amorphous carbon induced by soft x-ray femtosecond pulses above and below the critical angle, " Appl. Phys. Thermal stability of soft x-ray Mo–Si and MoSi2-Si multilayer mirrors, " Appl. Interfacial reactions and thermal stability of ultrahigh vacuum deposited multilayered Mo/Si structures, " J. Effect of heating rate on kinetics of high-temperature reactions: Mo-Si system, " AIChE J. Angular and energy dependence of ion bombardment of Mo/Si multilayers, " J. Enhancement of reflectivity of multilayer mirrors for soft-x-ray projection lithography by temperature optimization and ion-bombardment, " Microelectron. The soft x-ray free-electron laser FLASH at DESY: beamlines, diagnostics and end-stations, " N. Experimental station to study the interaction of intense femtosecond vacuum ultraviolet …


Introduction
The rapid development of a new generation of extreme ultraviolet (XUV) radiation sources providing ultrashort (from atto-to nanoseconds) pulses creates new challenges for optics.Instruments, like free-electron lasers (FELs) [1][2][3][4], higher harmonic generating sources (HHG) [5,6], high-energy coherent sources based on laser plasmas [7] and capillary discharge lasers [8] produce pulses of very high intensity which may induce radiation damage in optical coatings.This may be a limiting factor for many scientific and industrial applications.Therefore, for a proper design of optics for current and future XUV light sources, it is crucial to understand the physical mechanisms leading to radiation damage.It is especially important for multilayer coated mirrors where the absorbed energy density is the highest (at the resonant angle).
Multilayer coated optics are promising candidates for optical schemes at next generation XUV light sources.They were used in "front-line" experiments like XUV time resolved holography as a part of the imaging system [9], as diffraction limited XUV beam focusing optics for warm dense matter creation [10] and as a part of the delay line for one color pump and probe studies on XUV transmission of solids [11].Moreover, this kind of optics is nowadays a standard for control of XUV and soft X-ray radiation in many fields of science and technology [12][13][14].They can fulfill the extreme requirements in terms of figure errors and roughness, wavefront preservation, and stability in the XUV and soft x-ray regime.They have experienced a considerable technology boost due to the application in advanced photolithography.As a result, very stable, high reflectance coatings were developed [15].FOM Rijnhuizen achieved the world record of reflectivity of over 70% for 13.5 nm at normal incidence [16].Currently the know-how is used for the development of robust high reflectance multilayer optics that are stable even at enhanced temperatures and under high XUV flux irradiation [17,18].
The photon flux from new generation XUV light sources is extremely high.In the case of the Free-electron LASer in Hamburg, FLASH, operating in the EUV and XUV regime (primary wavelength range from 40 to 6.7 nm), the ~10-25 fs long pulses have an energy of up to 100 µJ [1].For a 4 mm beam spot diameter on the optics this corresponds to a radiation intensity of almost 10 11 W/cm 2 .This is at least 6 orders of magnitude higher than in a typical lithography application.Damage or even destruction of the optics can be expected.Moreover, for some applications the mirrors have to be placed in the focused beam [9,11] and the intensity on the optics can reach a value of 10 14 W/cm 2 .Under such conditions the optical properties of the reflecting elements could be changed already during the pulse and the mirror would fail to work [19,20].These two effects, permanent damage of the coatings and change of the optical properties of materials under high intensity XUV irradiation, can limit the performance of the multilayer optics.
Due to limited access to new sources the permanent damage mechanisms were only selectively studied until now.Basic inorganic and organic solids [21][22][23][24], single layer coatings [24,25] and Si/C multilayer systems [19] were examined.In a simple model the radiation is absorbed by the electron gas in the surface layer of the sample.The electron system thermalizes very quickly (<100 fs) at high temperatures, at which its optical properties may be changed compared to a cold material.At a picosecond time scale the electron gas cools down by heat transfer to the lattice and by energy diffusion.If the temperature of the lattice reaches the phase transition point, damage should occur.The depth of the damaged volume may depend on the thermal diffusion in the lattice, which occurs on a nanosecond time scale.In most cases the estimated energy density at the observed phase transition point corresponded to melting.In case of PMMA and amorphous carbon, damage thresholds below the melting point were observed, explained as non-thermal desorption [23] and graphitization [25], respectively.
On the other hand, sub-melting threshold damage was reported for Mo/Si multilayer systems during thermal annealing.Already above 325°C enhanced interlayer atomic diffusion and formation of molybdenum silicide occurs [26][27][28][29].The time constant for this process in annealing experiments is hours at the threshold temperature.With increasing temperature the atom mobility increases and the diffusion process speeds up (at ~600°C it takes less than 1 minute to almost completly intermix the Mo and Si atoms).Apart from the temperature, the duration of the damage process is strongly dependent on the heat rate and thickness of the layers [30].According to our best knowledge it has never been studied on the time scale shorter than milliseconds for temperatures above the melting point of amorphous silicon [30] and minutes at temperatures below the melting point of amorphous silicon [26][27][28][29].Thus no existing experimental results can help in predicting the damage threshold for multilayer optics at new generation XUV light sources.
The goal of the current paper is to define the mechanisms responsible for the radiation damage in Mo/Si multilayer systems exposed to an intense ultrashort pulse and to estimate the influence of the energy diffusion.The motivation for these studies is optics design for new generation of XUV light sources as well as fundamental understanding of the ultrafast processes that occur in the layers and at the interfaces at intense photon loads.

Experimental
We investigated a Mo/Si multilayer coating, deposited on superpolished Si substrate, a typical mirror as used for XUV lithography.The multilayer was deposited by e-beam evaporation in a UHV background of 1 × 10 −8 mbar, with post-deposition smoothing using low energy ion treatment [31][32][33][34][35].The sample was pre-characterized by means of x-ray and XUV reflectometry.The first technique provided information on the layered structure, including layer thicknesses, multilayer period, and roughness, and the latter technique determined the multilayer performance, i.e. angular resolved reflectivity of the multilayer for s-polarized light at 13.5 nm for low (non-destructive) irradiation intensities.From these measurements, the performance of the multilayer for any polarization and angle can then be predicted by means of simulations with the software package IMD [36].The multilayer consisted of 50 bilayers of Mo and Si, with a periodicity of 7.96 nm and Mo layer thickness of 40%, optimized for maximum reflectance.The resonant angle and maximum reflectance for p-polarized light were determined to be 29.0 degrees off-normal incidence and 45%, respectively.
The sample was irradiated at the FLASH facility in Hamburg, Germany [1,37].The radiation wavelength was 13.5 ± 0.1 nm and the XUV pulse duration was ~10 fs (FWHM).The experimental setup was similar to the one used in ref [38].at the first short wavelength free electron laser -TTF FEL.The sample was at resonant angle with respect to the incident photon beam which was p-polarized.The energy fluctuated from pulse to pulse in the range of 0.01 -1 µJ and was measured with a gas monitor detector [39].The radiation was focused with a grazing incidence carbon-coated ellipsoidal mirror to a spot size of 66 ± 3 µm 2 at the focal length of 2 m.To obtain a regular beam shape, a 3 mm diameter circular aperture in front of the focusing mirror was used.Most of the experiments were performed in "high intensity" mode, with the sample in the focus of the beam.For the given energy fluctuation, this mode corresponds to a beam fluence range of ~10 -1000 mJ/cm 2 .In addition, for the purpose of reflectance studies, lower intensity measurements were performed with the sample placed ~70 mm out of focus, corresponding to a ~15000 µm 2 spot area and a fluence range of 0.05 -5 mJ/cm 2 for the same energy range.The sample was irradiated with ~70 pulses in single shot mode, i.e., after each irradiation the sample was moved and was irradiated at an unperturbed position.The reflected radiation intensity was measured with a photodiode placed at ~140 mm distance from the sample.To avoid diode saturation, it was coated with 350 nm molybdenum and 500 nm silicon layers and in addition it was preceded by a 0.28 µm thick aluminum foil attenuator.To determine the absolute reflectance the filter/diode combination was characterized using the direct beam.
The irradiation spots were investigated "post-mortem" with different techniques: interference-polarizing optical microscopy (with Nomarski contrast) -sensitive to changes of morphology and/or material's optical properties, atomic force microscopy (AFM) -creating a 2D-map of the crater depths and scanning transmission electron microscopy (STEM) -to analyze the structural changes below the crater surface.
An additional experiment was performed to study the dynamics of the irradiated system.Time resolved microscopy was used in the XUV pump -optical probe mode.The experimental setup is similar to the one described in [40].The XUV pulse excited the surface of the multilayer coated sample.A time-delayed optical probe pulse of 800 nm wavelength and 100 fs duration, synchronized to the FEL with accuracy better than 2 ps, served as illumination for an optical microscope.This setup allows to measure the evolution of the optical pulse reflectivity of the XUV irradiated surfaces with temporal and spatial resolution.

Reflectivity
XUV reflectivity measurements of the Mo/Si multilayer were carried out using 13.5 nm radiation in three different intensity regimes.The reflectivity at low-intensity was measured at the Center for X-Ray Optics, Berkeley, USA (CXRO), using s-polarized radiation from the Advance Light Source (ALS), for angles ranging from 10°-50° from normal and transformed to p-polarized by means of IMD simulations.The reflectivity measurements at middle and high intensities were performed at FLASH at 28.2 ± 0.3° from normal.The reflectivity of ppolarized radiation at this angle is shown in the table below for all three intensity regimes.It is constant within the error-bars over the entire intensity-range investigated, from 100 W/cm 2 to approx.5 × 10 13 W/cm 2 corresponding to a fluence of 500 mJ/cm 2 .This is in agreement with theoretical models, where significant change of the reflectivity of femtosecond duration pulses is predicted only for fluences above 20 J/cm 2 [20].

Interference-polarizing microscopy
From each irradiated spot an image was made with an interference-polarizing microscope.
Initially the damage was defined as radiation induced surface changes observable in the image, corresponding to changes in surface morphology and/or material's optical properties.In Fig. 2 the damaged area is plotted against the logarithm of the pulse energy.A threshold behavior can be observed.The single shot damage threshold, determined [22,41] from the intersection of the line fitted to the experimental data points with positive damage area with the x-axis is 45 ± 7 mJ/cm 2 .

Atomic force microscopy
The morphology of the Mo/Si multilayer surface after irradiation was further investigated with atomic force microscopy.Two types of damage are observed for fluences between 45 and 125 mJ/cm 2 , further named as stage 1 and stage 2 of the damage (Fig. 3).In the first stage, a smooth crater is formed and its area matches the area of the damage observed with the interference-polarizing optical microscope.The crater depth ranges from a few nanometers for fluences just above damage threshold to more than 30 nm at 65 mJ/cm 2 .At fluences above 65 mJ/cm 2 a hill is formed in the middle of the crater (stage 2).The depth of the crater increases for fluences up to ~125 mJ/cm 2 , when the maximum crater depth of 68 nm is obtained (the influence of the hill formation on the crater profile is considered).

Scanning transmission electron microscopy
Scanning transmission electron microscopy (STEM) was used to analyze the structural changes below the crater surface.A 60 nm thin slab along the green line marked in the AFM map (Fig. 3) was cut from the multilayer by means of a focused ion beam and subsequent argon beam polishing.STEM images at different positions with respect to the crater borders were created with variable magnifications.The results are shown in Fig. 4(a-e).The analysis of the STEM together with its extension, EDX mass spectroscopy, shows that, similar to the AFM analysis, three regions can be distinguished: undamaged multilayer (region 1 in Fig. 4(a)), a fully polycrystalline region where the Mo layers are considerably thinner than the initial ones (region 2), and a region where Mo and Si atoms have fully interdiffused (below the crater-center, the right end of Fig. 4(a)).In Fig. 4(b) and 4(d) the undamaged region is magnified.A clear layer structure can be seen with sharp interfaces between the polycrystalline Mo and amorphous Si layers.In Fig. 4(c) an apparent border, similar to the one observed in AFM and optical microscopy pictures, separating the undamaged (1) and the damaged region (2) is shown.The magnified image of the damaged region is presented in Fig. 4(e).The polycrystalline / amorphous layer-structure of region 1 is abruptly changed into the fully polycrystalline layered structure of region 2, with the thickness of Mo being just a fraction of its thickness in the undamaged region, clearly indicating large layer interdiffusion and subsequent (polycrystalline) silicide formation.For even higher fluences, below the hill in the crater center, a fully intermixed amorphous structure can be observed.But, since the main interest of authors is the damage mechanism at the lowest threshold, detailed analysis of this fluence range is beyond the scope of this paper.

Time resolved microscopy
Time resolved microscopy was performed to study the dynamics of the Mo/Si multilayer system excited just above the damage threshold.The optical pulse (probe) delay was fixed at 10 ps, appropriate to examine the initial lattice temperature after relaxation of most of the energy absorbed by the electron gas to the atoms.Increase of the visible light reflectance in the exited region was observed (see Fig. 5).The rise of reflectivity has sharp edges which overlap with the crater border measured a long time after the XUV pulse (after full development of the damage process) using the same microscope.It saturates in the crater center at the maximum value 35% ± 5% larger than the reference outside the irradiation spot.The threshold behavior of the reflectance indicates that its rise is caused by an abrupt change of the optical properties of at least one of the materials.Molybdenum has a much higher phase transition temperature than amorphous silicon and as a metal it is characterized by only small changes of the optical properties when heated.On the other hand, melting of amorphous silicon changes its conductivity from 1.5 W/m-K (insulating) to 62 W/m-K (metalic), and consequently the imaginary part of the refractive index, k, increases abruptly [42].IMD simulations of the probe beam reflectivity were performed and a their best fit to the experimental data at saturation in the center of the crater was obtained for k = 1.85 ± 0.2, which is a typical value for metals [43].This implies melting of the amorphous silicon layers at a time scale shorter than 10 ps.

Discussion
All the experimental data indicate that the leading damage mechanism for Mo/Si multilayer coating, irradiated with intense femtosecond XUV radiation, is molybdenum silicide formation at the interfaces.This process has been observed previously in dedicated thermal annealing experiments.In such experiments, if the sample is heated to 325°C, the timescale of the diffusion process leading to almost complete intermixing of the layers is typically several hours [26][27][28][29], while at ~600°C it is measured to be shorter than a minute.Now let us consider the timescale of diffusion in our femtosecond experiments.Silicide formation can only take place if molybdenum or silicon atoms diffuse through the interface.The atomic interdiffusivity through the interfaces of a Mo/Si multilayer (D) is (4 ± 2) × 10 −4 nm 2 /s at 530°C, and from Arrhenius's law, approximately 1.5 × 10 −3 nm 2 /s just below the melting temperature of silicon [44].One can estimate the effect of atomic diffusion in case the sample is heated up to a temperature slightly below the melting point of amorphous silicon for a very short time.Assuming that the heat conductance to the Si substrate cools the sample down to room temperature in a time shorter than 1 µs, the diffusion length can be calculated to be (4D × t) 1/2 = 5 × 10 −5 nm, which is significantly smaller than the size of atoms.Hence, atomic diffusion and therefore silicide-formation can be neglected below the melting temperature of amorphous silicon at this relatively short time scale.
However, the pump and probe data show that the surface of our sample is melted in a time shorter than 10 ps after the excitation with the XUV pulse, and at an intensity above the damage threshold.In liquid silicon, the atomic diffusion coefficient is in the order of 10 10 nm 2 /s [45] which is ~15 orders of magnitude higher than in the amorphous phase.In this case the molybdenum atoms can penetrate the entire Si layer from both sides on the time scale of sub nanoseconds (much shorter than silicon resolidification time) and form a molybdenum silicide.The dependency of silicide-formation on melting implies the threshold behavior of the damage which can be observed in all experimental data, apart from reflectivity measurements that are, obviously, not sensitive to processes occurring on a time scale longer than the pulse duration.
There are various known stoichiometries of molybdenum silicide.The density of all of them is larger than the averaged density of Mo and Si atoms, resulting in a compaction of the multilayer structure upon silicide formation.The AFM data together with the STEM profile show that in case of the FLASH irradiated sample the compaction was ~17% (68 nm maximum depth of a crater for 50 bilayers, 7.96 nm thick each).This corresponds to the expected compaction if all silicon atoms are consumed for the formation of a MoSi 2 compound [26], which is the most thermodynamically stable state of all molybdenum silicides [46].It has a formation enthalpy of −132 kJ/mol and has also been observed to be the final state of silicide-formation in the thermal annealing experiments for similar Mo/Si multilayers.
After the silicides are formed, energy is released due to the negative formation enthalpy of MoSi 2 : the heat of formation of MoSi 2 is high enough to increase the mean temperature in the reaction volume (Mo/Si bilayer) from 350°C to just above the melting temperature of amorphous silicon.It serves as an energy reservoir for melting deeper layers and consequently their transformation into silicides.The number of the melted amorphous silicon layers (and consequently the total compaction of the multilayer) is dependent on (a) the initial temperature profile, defined by electric field intensity distribution in the multilayer and the optical constants, and (b) the energy dissipation process, which is mainly defined by the materials thermodynamic properties.
The XUV absorption profile in the multilayer can be calculated with the use of the optical parameters of Mo and Si.These parameters can, in general, be temperature-dependent.However, as described before, the optical parameters don't change significantly during the pulse and room-temperature values [47] can be used.Subsequently, the temperature profile in the multilayer can be calculated from the heat capacities of Mo and amorphous silicon [48,49], the melting temperature (1250 K [49,50]) and the latent heat (33.7 kJ/mol [51,52]) of amorphous silicon in a thin film.
Because of the heat of formation, silicide-formation would be an almost self-sustained reaction already at the threshold fluence if one neglects heat dissipation (transport) to the substrate.But this assumption is not valid in the studied system.Using the heat-capacities of thin film molybdenum, amorphous and liquid silicon [53][54][55][56][57][58][59], one can calculate the ratio of the heat conductivities in two regions: conducting (where temperature is higher than the melting temperature of amorphous silicon) and insulating (solid silicon).The dissipated fraction of the energy is directly related to the heat conductivity ratio in both regions.No heat dissipation corresponds to a ratio of 0, while no heat confinement at all corresponds to a ratio of 1.In the studied case it is in the range of 0.05-0.15.Consequently, most but not all excess energy is confined in the conducting region and is therefore used primarily to melt adjacent silicon layers at the conducting-insulating interface.One can calculate how much energy is needed to create silicides in a given number of bilayers.For that purpose the energy balance was calculated taking into account the absorbed energy profile, the energy released due to silicides formation, the energy needed to heat the silicon and molybdenum to a-Si melting temperature (including the latent heat of a-Si) and the energy loss due to heat dissipation into the substrate.It was assumed that each melted silicon layer is fully transformed into silicides.Since the deposited energy is defined by the incident radiation fluence, and the absolute compaction by the volume of the silicides formed, the fluence dependent compaction of the irradiated multilayer can be calculated.In Fig. 6 results of the calculations for different fractions of dissipated energy (0%, 10%, 15% and 20%) are shown.The damage threshold obtained from the calculations for each of the dissipation percentages is the same and is close (within error bars) to the experimentally obtained value (lines in Fig. 6 cross the x axis in the same point).On the other hand the predicted crater depth for fluences above the damage threshold varies significantly for different energy losses and the experimental data coincide very well with a narrow range of dissipation percentage from 10% to 20%.To calculate more precisely the heat dissipation for this multilayer, one has to solve the heat and atomic diffusion equation set.Due to the many boundary conditions, and the time-dependent heat release due to silicides-formation, advanced computer simulations are required.This goes beyond the scope of this article and will be described in the future work.

Conclusions
We exposed standard Mo/Si multilayers to intense femtosecond pulses at the FLASH (XUV free-electron laser) facility in Hamburg, Germany.We investigated both the change of optical properties during the pulse and the single shot damage threshold of the multilayer.
Up to a fluence of 500 mJ/cm 2 no measurable effect on the multilayer reflectance is observed, indicating no significant change of the optical properties during the pulse.This is in agreement with theoretical predictions.
Permanent damage of the multilayer occurs on a much longer timescale than pulse duration and, consequently, reflection process.The single-shot damage threshold of the multilayer is determined to be 45 ± 7 mJ/cm 2 .Silicide-formation was found as the leading mechanism for irreversible structural changes for fluences at and just above the damage threshold.It shows great similarity with the damage mechanism during thermal annealing experiments where silicide formation is caused by atomic diffusion in solids.However, in case of energy deposition by an intense ultrashort XUV pulse, the multilayer is hot for just a short time (typically few ns).In this timescale, atomic diffusion in amorphous silicon or solid molybdenum is negligible.Atomic diffusion occurs only when silicon is melted, in which case the atomic diffusivity is enhanced by 15 orders of magnitude.Molybdenum atoms diffuse from both sides into the melted silicon layer and form the energetically stable MoSi 2 .Therefore, when irradiated with a femtosecond XUV pulse the critical temperature at which damage of the multilayer occurs is increased from 325°C in annealing experiments to 980°Cthe melting temperature of a thin amorphous silicon film.In parallel, the timescale of the damage process is decreased from hours (at the threshold temperature) to nanoseconds in the present study.Furthermore, the energy diffusion is not significant for the single shot damage threshold, although, its effect on the crater profile for fluences above the damage threshold is observable.
The results show that standard Mo/Si multilayer optics can be used at the femtosecond XUV light sources for fluences up to 45 ± 7 mJ/cm 2 under the condition that the repetition rate of the source allows the deposited heat to dissipate between subsequent pulses (approx.100 kHz or less).The nature of the damage mechanism (atomic diffusion in melted silicon) allows one to extrapolate the results for other 4th generation light sources with pulses longer than FLASH, up to at least a few hundred picoseconds which is the time scale of atomic diffusion in a single silicon layer.

Fig. 2 .
Fig. 2. Damaged area of the Mo/Si multilayer plotted against the pulse energy.The red dots are the experimental results, the solid line is the best fit of the experimental data points with positive damage area and the dashed lines represent the 2σ error of the fit.

Fig. 3 .
Fig. 3. Examples of the damage at stage 1 (top) and stage 2 (bottom).On the left an AFM depth map of the surface is shown and on the right, the depth-profiles along the green lines.

Fig. 4 .
Fig. 4. STEM images of different spots along the crater cross-section made with different magnifications.Half of the damaged cross section is shown in (a).The undamaged region (1) is magnified in (b) and (d), the damaged region (2) in (c) and (e).Images (a), (b), and (c) were taken in dark field mode (the darker the image, the lower the density) and images (d) and (e) in bright field mode.

Fig. 5 .
Fig. 5. 2-D map of the reflectance of the probe pulse (10 ps delay) after excitation with a femtosecond XUV pulse (pump) of maximum fluence just above the damage threshold.The reflectance of the probe pulse is normalized to the reflectance of the unexcited region.The intensity color scale of the normalized reflectance is shown on the right.

Fig. 6 .
Fig. 6.Compaction as function of fluence.The dots are experimental values obtained from AFM studies.The lines are obtained from thermal dynamic calculations by assuming different dissipation percentages of the excess energy from conducting to insulating region (see detailed description in text).