Heating effect of an electron beam impinging on a solid surface, allowing for penetration

Vine, J.; Einstein, P.A.

doi:10.1049/piee.1964.0147

Cited by 23 publications

(9 citation statements)

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“…When one compares these dimensions to the lateral extension of the window (typically some millimeters), it is no longer possible to assume a constant temperature on the top surface (window-environment interface, see Fig. 1) as it has often been proposed in other models [9][10][11][12]. Our model takes this geometry constraint into account to accurately simulate the field temperature in the system.…”

Section: Modeling Steady-state Temperature Of Edge-cooled Windowmentioning

confidence: 99%

“…For those energies and considering heavy metals as required for our application, the depth of complete diffusion is small compared to the range of electrons. So the absorption volume can be considered hemispherical [10,11,[15][16][17]. The range of the electrons is obviously energy-dependent and it directly determines the radius of the heat source.…”

Section: Heat Source Modelingmentioning

confidence: 99%

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Nanofocus diamond X-ray windows: Thermal modeling of nano-sized heat source systems

Delfaure

Mazellier

Tranchant

et al. 2015

Diamond and Related Materials

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a b s t r a c tAn analytical thermal model is proposed to study heat transfers occurring at high power density in X-ray tubes with micron to submicron sized source. The use of a simple analytical approach instead of a complex numerical simulation allows readily modeling of more and more challenging systems such as multi-source X-ray tubes. By significantly reducing the computing time, it enables a wider parameter range evaluation for engineering phase. We focused our work on tubes integrating a transmission window that is mainly edge-cooled. Our approach can be generally used in cylindrical lateral heat spreaders with distributed small sized source systems. The model enables an efficient estimation of temperature distributions for a large range of parameters and source designs and is, for instance, wellsuited to described nanosized heat source systems. It is developed from an electrostatic analogy with the point charge particle model and uses of a series of virtual sources. A multiscale resolution of the heat equation is proposed, hence providing the temperature distribution at any point within the whole system. Moreover, the non-linearity of equations caused by temperature-dependent thermal conductivities is solved by using Kirchhoff's transformation, giving a more realistic approach of heat conduction in diamond X-ray windows, where temperature in excess of 1000°C can be encountered. The influence of convective and radiative transfers has been discussed and the physical accuracy of the predicted temperature is controlled by adjusting the number of virtual sources of the model.

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Section: Modeling Steady-state Temperature Of Edge-cooled Windowmentioning

confidence: 99%

Section: Heat Source Modelingmentioning

confidence: 99%

Nanofocus diamond X-ray windows: Thermal modeling of nano-sized heat source systems

Delfaure

Mazellier

Tranchant

et al. 2015

Diamond and Related Materials

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show abstract

“…The electron beam-induced sample heating has been estimated by Myhajlenko et al (1983) on the basis of the Vine-Einstein model (Vine and Einstein, 1964), predicting a maximum temperature rise under steadystate conditions from The electron beam-induced sample heating has been estimated by Myhajlenko et al (1983) on the basis of the Vine-Einstein model (Vine and Einstein, 1964), predicting a maximum temperature rise under steadystate conditions from…”

Section: Emission Efficiency Energy Peak Position and Line Shapementioning

confidence: 99%

Assessment of Semiconductors by Scanning Electron Microscopy Techniques

Salviati

Lazzarini

Sekiguch³

et al. 2011

Comprehensive Semiconductor Science and Technology

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“…Objective lens to workpiece spacing, / 3 The working distance / 3 has a strong effect on the spherical aberration. The focal length / of the lens is approximately equal to / 3 , for small values of / 3 , and the spherical aberration coefficient C s is proportional to / (eqn.…”

Section: Electron Optical Configurationmentioning

confidence: 99%

“…diameter of polepiece at the air-gap D" maximum diameter of polepiece d diameter of aberrated spot (cm) / focal length k Boltzmann's constant = 8-6xl(T 5 eV/degK /j electron gun to condenser lens distance l 2 condenser lens to objective lens distance / 3 objective lens to workpiece distance M electron optical magnification M x , M y , n registers NJ lens excitation in ampere turns …”

mentioning

confidence: 99%