IT-4-P-1829 Determination of the second critical energy of primary electrons in relation to dielectric thickness and angle of incidence

At the second crossover energy E_2C of incident electrons the equilibrium is maintained between the electron probe currents I₀, the second electron emission (SEE) currents I₀δ, the backscattered electron (BSE) currents I₀η, as well as the leakage currents I_L and the displacement currents I_d that are responsible for the accumulated charge Q. At the equilibrium state the equality I₀=I₀(δ+η)+I_L+I_d is fulfilled, while for the target remaining uncharged the condition δ+η=1, V_S=0 is valid, where δ and η are the emission coefficients of SE and BSE.

Experimental results for dielectrics, in the case when incident electrons impinge on the sample surface at the angle α, can be described by the following semi-empirical expression: E_2C=E_2C(0)exp[(ln(R_2C/2λ))(1-cosα)], (1)

where λ is the effective emission depth of SE, R_2C=76E₀^1,67 ρ is the depth of penetration of primary electrons with the energy E₀, ρ is the specific density of the dielectric material. As an example, fig.1(a) shows the experimental dependence and the dependence calculated by formula (1) of the second critical electron energy E₀=E_2C on the angle of incidence α, for the target potential V_S=0, i.e. when the target remains uncharged. Fig.1(b) shows the dependence of the energy E_2C on the angle of incidence α for ungrounded metals.

Consider the dependences of the V_S of PММА films with the thickness d on a silicon substrate at the electron energy E₀.

The experimental results are in qualitative agreement with the calculated results as shown in fig.2(a), presenting the dependences V_S(d) for MICA plates 2 to 30 μm thick and for PММА films 0.4, 1.4, 2.7, 4 μm thick on the Si-substrate.

At the radiation energies E₀ in the range of 0.5–1.0 keV the negative charging begins (note that according to previous views, positive charging was expected because E₀<E_2C). At this energy the sign polarity of V_S changes, i.e. at the point where V_S=0 V. For PММА this value lies in the range E₀=0.4–0.6 keV, with the thicknesses of the layers of positive and negative charges and the values of these charges are approximately equal (λ≈R₀, Q₊=Q_-), which is responsible for the total absence of charging. In the region of 1 keV <E₀<E_cr2 one can clearly observe negative charging, and the greater d, the higher the value of -V_S. This range corresponds to the condition λ<R₀<d. The value of -V_S at first increases and reaches the maximum, then as E₀ and R₀ grow, it starts decreasing slowly in the absolute value and reaches zero at the points of E_cr2, that are different for each film thickness d. These points can be used in high-voltage lithography, because it is at these values of R₀≥2d that the conduction current I_T is generated and it carries excessive negative charges (electrons) onto the substrate, hence V_S=0 V.