Micron 67 (2014) 74–80

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Analysis of microscopic parameters of surface charging in polymer caused by defocused electron beam irradiation Jing Liu ∗ , Hai-Bo Zhang Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Department of Electronic Science and Technology, Xi’an Jiaotong University, Xi’an 710049, People’s Republic of China

a r t i c l e

i n f o

Article history: Received 22 April 2014 Received in revised form 26 June 2014 Accepted 26 June 2014 Available online 5 July 2014 Keywords: Polymer Defocused electron beam Irradiation Surface charging Numerical simulation PACS: 61.80.Fe 73.61.Ph 02.60.Cb

a b s t r a c t The relationship between microscopic parameters and polymer charging caused by defocused electron beam irradiation is investigated using a dynamic scattering-transport model. The dynamic charging process of an irradiated polymer using a defocused 30 keV electron beam is conducted. In this study, the space charge distribution with a 30 keV non-penetrating e-beam is negative and supported by some existing experimental data. The internal potential is negative, but relatively high near the surface, and it decreases to a maximum negative value at z = 6 ␮m and finally tend to 0 at the bottom of film. The leakage current and the surface potential behave similarly, and the secondary electron and leakage currents follow the charging equilibrium condition. The surface potential decreases with increasing beam current density, trap concentration, capture cross section, film thickness and electron–hole recombination rate, but with decreasing electron mobility and electron energy. The total charge density increases with increasing beam current density, trap concentration, capture cross section, film thickness and electron–hole recombination rate, but with decreasing electron mobility and electron energy. This study shows a comprehensive analysis of microscopic factors of surface charging characteristics in an electron-based surface microscopy and analysis. © 2014 Elsevier Ltd. All rights reserved.

1. Introduction Charging characteristics and space charge of various polymer microscopic factors caused by defocused electron beam irradiation have always been an interesting aspect in scanning electron microscopy (SEM) (Cazaux, 2012; Cazaux et al., 2013; Maekawa et al., 2007; Pawley, 1992; Reimer, 1993; Touzin et al., 2006; Ura, 2001), electron beam microanalysis, lithography (Bai et al., 2003; Bolorizadeh and Joy, 2007; Ciappa et al., 2010; Ko and Joy, 2001), and space application since 1960s (Oatley et al., 1966). Various microscopic parameters may influence the surface charging characteristics and distort the accuracy of the electron beam microanalysis. Moreover, polymer charging may cause the breakdown of the polymer of microelectronic devices, but it may also lead to undesirable image effects induced by emitted electrons from the polymer surface (Joy and Joy, 1996; Li and Zhang, 2010; Ura, 1998). Therefore, more efforts are needed to understand the relationship between various microscopic parameters and surface charging characteristics for predicting and diminishing the charging effect.

∗ Corresponding author. Tel.: +86 29 82664963. E-mail address: [email protected] (J. Liu). http://dx.doi.org/10.1016/j.micron.2014.06.011 0968-4328/© 2014 Elsevier Ltd. All rights reserved.

Polymers are widely used to protect, resist, and assist materials in various fields, and the related microscopic parameters of their surface charging characteristics have already been preliminarily investigated (Belkorissat et al., 2005; Cazaux, 2005; Fakhfakh et al., 2012; Jbara et al., 2008). Based on low electron mobility (Sessler et al., 2004) and resistivity (Vila et al., 2005), the charging characteristics and charging equilibrium are jointly influenced by the primary electron current, secondary electron current, leakage current, and physical parameters of the electron mobility, electron energy, film thickness, trap concentration, capture cross section and recombination rate. Several approaches that address the issue have been developed and proposed in a number of theoretical analyses. The radiation-induced conductivity model (Berraissoul et al., 1986; Cornet et al., 2008; Tyutnev et al., 2007; Yang and Sessler, 1992; Yasuda et al., 2008) is an empirical model that predicts experimental results. The generation-recombination model (Sessler et al., 2004) considers the generation of a carrier pair by incident electrons and the microscopic transport mechanisms of both electrons and holes, respectively. More recently, SEM-based analysis of the charging characteristics and surface charging of various parameters has attracted much attention (Dapor et al., 2010; Fakhfakh et al., 2012; Jbara et al., 2008; Kechaou et al., 2008; Mahapatra et al., 2006). However, only a few studies have

J. Liu, H.-B. Zhang / Micron 67 (2014) 74–80

been conducted to determine the influence of complex microscopic parameters on surface charging because of the difficulty in measurement. Moreover, insufficient microanalysis had been conducted on the surface potential of the charge transport condition corresponding to a defocused electron beam. We have recently proposed a comprehensive model for defocused electron beam charging of grounded polymer films, and simulated transients of negative charging by considering electron scattering, transport, and trapping (Cao et al., 2012; Feng et al., 2013; Li and Zhang, 2010). Thus, this study was designed to reveal the microscopic parameters of surface potential characteristics of polymers using a defocused electron beam using our newly developed model for self-consistent simulation of surface charging characteristics. The trapping process of an electron and hole is considered by the Poole–Frenkel effect and accordingly clarified the negative charging effect of polymer (Cornet et al., 2008; Touzin et al., 2006). In this paper, we report the relationship between complex microscopic factors with space charge, space potential and total charge densities as well as surface potential. These results regarding polymer characteristics are considered as examples in our simulation, but the general results are applicable to other polymers. 2. Numerical model 2.1. Electron scattering The scattering of atoms and electrons entering the film is simulated using the Monte Carlo method (Czyzewski et al., 1990; Joy, 1995) and the elastic scattering is computed using the Rutherford scattering cross-section (>10 keV electrons) (Cao et al., 2012; Feng et al., 2013).  = 5.21 × 10−21

z2 4 E 2 ˛(1 + ˛)

 E + 511 2 E + 1022

,

(1)

where , E, z, ˛ denote the Rutherford scattering cross section, the incident electron energy, the mean atomic number, the shielding factor, respectively. The average rate of energy loss during inelastic scattering is calculated using the modified Bethe equation (Joy, 1995). The fast secondary model is used in our simulation to deal with the secondary electrons (SEs) (Joy, 1995). SE is generated for each inelastic scattering event after gaining the lost energy of the scattered primary electrons (PEs). The inelastic scattering process is described as follows: din e4 = 2 d˝ E



1 1 + + ˝2 (1 − ˝)2

  2 +1

−

2 + 1



( + 1)2 ˝ 1 − ˝





, (2)

where  in , E, , e,  denote the inelastic scattering cross section, the incident electron energy, the energy transfer E normalized with E, the basic charge, the electron kinetic energy normalized by the rest mass energy of an electron, respectively. Furthermore, the inelastic mean free path can be written as: in =

A , Na zin

(3)

where A, , z, Na , and  in are the atomic weight, the density of polymer, the mean atomic number, the Avogadro constant, and inelastic scattering cross section, respectively. The electrons, including primary electrons (PEs), secondary electrons (SEs), and holes, eventually deposited on the polymer sample are either transported (drift and diffuse) because of the internal electric field and charge density gradient or trapped. The

75

charge transport and trapping are neglected during electron scattering because the whole scattering process is extremely fast, that is, the scattering process is 10−5 s for the incident electron with an energy of 30 keV.

2.2. Charge transport and trapping The electron density n(z, t), trapped electron density ntrap (z, t), hole density h(z, t), trapped hole density htrap (z, t), electron current density Jn (z, t), hole current density Jh (z, t), and internal potential distribution V(z, t) satisfy the continuity, transport and Poisson equations:



∂ n (z, t) + ntrap (z, t)



∂t



∂ h (z, t) + htrap (z, t) ∂t

=

 =

∇ · J n (z, t) e

− Rn(z, t)h (z, t) ,

−∇ · J h (z, t) − Rn(z, t)h (z, t) , e

(4)

(5)

J n (z, t) = −e e n(z, t)∇ V (z, t) + eDe ∇ n(z, t),

(6)

J h (z, t) = −e h h(z, t)∇ V (z, t) − eDh ∇ h(z, t),

(7)

where e denotes the absolute value of electron charge; R is the electron–hole recombination rate, which is set to 10−15 cm3 s−1 (Le Roy et al., 2012); V(z, t) is the internal potential; e and h are the electron and hole mobilities, respectively; De and Dh are the electron and hole diffusion coefficients, respectively. The mobility and the diffusion coefficient satisfy the Nernst–Einstein equation. Considering that the hole mobility is much less than the electron mobility in polymers, we use hole mobility h 10−12 cm2 V−1 s−1 (Sessler et al., 2004). Electrons and holes that eventually deposit on the polymer will either drift or diffuse because of the internal electric field and charge density gradient or be trapped. Some charges may be trapped by trapping centers while being transported through the polymer. At the same time, electron–hole recombination will occur. In principle, the trapped charges may also be released again via detrapping based from several experiment data (Sessler et al., 2004). However, several experimental studies have shown that the charges in some polymers could persist for significant period of time (Sessler et al., 2004), which indicates that detrapping effect is often very weak and therefore negligible. The charge-trapping process in polymer is complex (Sessler et al., 2004; Touzin et al., 2006). Thus, space charges may either be free or trapped. In this paper, we describe the trapping process and neglect the detrapping process to reduce the computation time as follows:



∂ ntrap (z, t)



∂t



∂ htrap (z, t) ∂t











= n (z, t) e E (z, t) Se Ne − ntrap (z, t) ,

= h (z, t) h E (z, t) Sh Nh − htrap (z, t) .

(8)

(9)

Here, htrap (z, t) and ntrap (z, t) are densities of trapped holes and electrons, respectively. Ne and Nh are the electron trap and hole trap concentrations respectively, and Se and Sh are the electron capture and hole capture cross sections, respectively. Trap rate (Ne × Se ) is the product item of the trap concentration Ne and capture cross section Se in a polymer position, which is subordinated to the Poole–Frenkel trapping/detrapping mechanisms (Sessler et al., 2004; Touzin et al., 2006). In addition, the internal electric field distribution E(z, t) satisfies the charge continuity and transport equations.

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2.3. Total charge density and charging equilibrium The internal potential V(z, t) is determined using the Poisson equation:

∇ 2 V (z, t) =

−[h(z, t) + htrap (z, t) − n(z, t) − ntrap (z, t)]e , ε0 εr



H

e[n(z, t) − h(z, t) + ntrap (z, t) − htrap (z, t)]dz.

z =0 Scattering

(10)

where ε0 and εr are the dielectric constant in the vacuum and relative dielectric constant, respectively (εr = 3.45ε0 ). The simultaneous Eqs. (4)–(10) are solved via the finite difference method with zero initial or boundary conditions, such that the space charge density and internal potential can be obtained. The image charge method should be used to satisfy the boundary condition at the polymer film and vacuum interface for the computation of the internal potential V(z, t). In addition, the total charge density per unit area in absolute value, QT , accumulated over the thickness (H) of the polymer during a charging process, can be readily calculated as follows: QT =

JSE

JPE

z

Transporting Kapton

Sample substrate

Jn+Jh

H

+

Trapping

Js = JE+JD

Fig. 1. Illustration of sample configuration in our simulation. JPE and JSE are the incident electron current and secondary electron current density, respectively. Jn and Jh are the electron current and hole current density, respectively. Sample current density JS consists of leakage JE and displacement JD current densities. Thickness of Kapton film is H, and z denotes electron irradiation direction.

(11)

0

According to our previous simulation (Feng et al., 2013; Li and Zhang, 2010), in a polymer film that is negatively charged by a nonpenetrating e-beam, many electrons can flow downwards because of the transport and arrive at the grounded substrate, forming a leakage current. When the leakage current is increased with irradiation and eventually saturated, the transient charging process will stop, and the accumulated space charge and the resulting surface potential will reach their equilibrium values. In the next section, we present the simulated space charges, internal potential, surface potentials and total charge densities in the equilibrium state.

is similar to our previous study (Feng et al., 2013). In the present simulation, the e-beam and film parameters have typical values without further notation. The primary electron current density JPE and beam energy EP are 2 nA cm−2 and 30 keV, respectively. The film thickness is 25 ␮m, and the electron mobility e and trap concentration NT are 10−11 cm2 V−1 s−1 (Cornet et al., 2008; Ferreira and de Figueiredo, 2003; Sessler et al., 2004;) and 1021 cm−3 (Touzin et al., 2006), respectively. The capture cross section CS and recombination rate R are 10−13 cm2 (Cornet et al., 2008; Touzin et al., 2006) and 10−15 cm3 s−1 (Le Roy et al., 2012), respectively. 3.2. Space charges

2.4. Procedure of numerical simulation Above the numerical model, we solved the Eqs. (1)–(11) and developed a computer program to calculate the scattering electron, scattering hole, electron, hole and space charge density of polymer irradiated by defocused electron beam. The scattering electron nscatter (z, t) and scattering hole density hscatter (z, t) of calculation is defined by Eqs. (1)–(3). Then, we corrected incident electron energy by a surface potential. Setting the initial value of electron density n(z, t) = n(z, t) + ntrap (z, t) + nscatter (z, t) and hole density h(z, t) = h(z, t) + htrap (z, t) + hscatter (z, t) for the calculation of transporting process. We solved the Eqs. (4)–(11) and calculated the transporting process, getting the new charge density, surface potential. Finally, we repeated the above simulation until the appearance of charging equilibrium state. 3. Results and discussion 3.1. Simulation parameters Fig. 1 displays the model for simulating the surface charging in polymer caused by defocused electron beam irradiation. We used a defocused electron beam of 1000 ␮m2 leading to a primary electron current density of JPE = 2 nA cm−2 (Cornet et al., 2008; Touzin et al., 2006). We restrited our simulation to a broad primary electron beam, so this study can be described by a one-dimensional model (Renoud et al., 2005). The value of initial PE energy and current JPE are the same with those in an experiment (Sessler et al., 2004). The SE current JSE has included the internal effect of negative charging on secondary electrons emissions, according to the correction of PE landing energy by the surface potential. The SE influence on charging is then simplified by using the net PE current of JPE − JSE for the scattering simulation. Note that displacement current JD included is induced by variation in the electric field (Jbara et al., 2008), which

Fig. 2 (a) shows the experimental and simulated space charge profiles in Kapton charged with 40 nC cm−2 at the irradiation time of 20 s. The optimized transport parameters are obtained from experimental data (Sessler et al., 2004). Other parameters, such as the electron mobility (4.5 × 10−11 cm2 V−1 s−1 ), the hole mobility (4.5 × 10−12 cm2 V−1 s−1 ), and trap density (1020 cm−3 ) have been adopted with the help of the sensitivity analysis. They have been chosen to better fit the experimental profile (Sessler et al., 2004). Compared with other models, the present model can reproduce the majority of the characteristics highlighted in the experiment. Good agreement is found between the space charge peak maximum of the GR (generation-recombination) model (Sessler et al., 2004) data, RIC (radiation-induced conductivity) model (Sessler et al., 2004) data and this work data at irradiation time 20 s in Fig. 2 (a). The general shape of the experimental charge density profiles is similar to the shape of the simulated curves. However, the main difference consists in the higher calculated space charge density of the amplitude, probably because of difference between simulation and experimental parameters or the accumulated effects of the charges during the experiment. On the hand, the electron exiting from the electrode leads to a certain positive charge distribution near the surface of polymer film in the experimental data (Sessler et al., 2004; Cazaux, 2005), which does not appear in our simulation probably because of contribution of more negative charges though located far from the surface as well as the downward diffusion of positive charges (Cazaux, 2005). The negative space charge density is distributed along the depth incident (z) direction. Fig. 2(b) shows the simulated profile of the space charge density in Kapton within the film along the beam incident (z) direction at different e-beam irradiation times t1 (20 s), t2 (127 s), and t3 (500 s). The effective range of the electron scattering in the beam incident direction is shown in Fig. 2(b). In the initial irradiation stage at t1

This work(20 s)

0 −0.02 −0.04 −0.06

GR model RIC model Experiment data

−0.08 0

5

10

z (µm)

15

−3

(a)

Space charge density (mC cm )

−3

Space charge density (mC cm )

J. Liu, H.-B. Zhang / Micron 67 (2014) 74–80

77

0.1 0

20 s

−0.1 −0.2

(b)

Electron scattering region

127 s

500 s

−0.3 0

10

20

z (µm)

−2

Leakage current JE (nA cm )

Internal potential VZ (V)

−2

Secondary electron current JSE (nA cm )

Fig. 2. (a) Comparison of space charge density between simulation results and experimental data (Sessler et al., 2004) at sample thickness (25 ␮m) and electron mobility

e = 4.5 × 10−11 cm2 V−1 s−1 . The simulated results are in good agreement with that in the experiment data (Sessler et al., 2004). (b) Depth profiles of space charge densities simulated at different irradiation time t1 (20 s), t2 (127 s), and t3 (500 s).

0

20 s −1000

127 s 500 s

−2000

z =6µm 0

10

20

z (µm )

0.20

1.9

1.85

0.15

JE

1.8 15

JSE 20

25

EP (keV) Fig. 3. Simulated internal potentials in the depth incident (z) direction at different irradiation time t1 (20 s), t2 (127 s) and t3 (500 s).

(20 s), electrons and holes generated by electron scattering have high density in the e-beam irradiated area. At this point, the departure of the electrons from the region will produce and intensify the internal electric field, facilitating the outward movement of more electrons along the axial direction, and more holes move inwards. The increased electric field along the beam incident (z) direction caused by the space charge may then force more electrons to move outwards. Evidently, negative space charges are distributed along the beam incident (z) direction. The electron injection depth is at 11.8 ␮m (Yasuda et al., 2008), and that of the electrode is at 25 ␮m. The distribution of the space charge density is available from experimental data (Yasuda et al., 2008).

30

0.10

Fig. 4. Steady-state characteristics of secondary electron current density JSE and leakage current density JE .

ground with the electron irradiation time. In addition, some holes can still move outwards through both drift and diffusion along the radial direction during the transient charging process, in spite of the lower mobility of the polymer. Fig. 3 shows that a positive electric field should be generated near the surface in the beam incident direction. This local electric field can make fewer emitted secondary electrons (SEs) return to the surface, which causes secondary electrons (SEs) redistribution even under positive charging, which is measured in the experiment (Perrin et al., 2008; Liu et al., 1995).

3.3. Internal potential

3.4. Influence of microscopic parameters on surface potential

Fig. 3 presents the simulated internal potential in the beam incident direction in the equilibrium state. The internal potential is negative within the region of 0 ␮m < z < 25 ␮m. The profile characteristic of the space charges results mainly from the outward electron diffusion along the axial direction during the transient charging process. The internal potential is negative, but relatively high around the surface of the polymer, and it decreases to a maximum negative value at z = 6 ␮m. Although some other electrons may drift inwards through the internal electric field, more electrons can leave the region because of the stronger diffusion, and then will be trapped, given that the electron density is much higher within the region than outside. Moreover, hole mobility is much lower than the electron mobility (Sessler et al., 2004). Hence, excess holes are left behind within the region, and the peak location of negative space charges is distributed along the axial direction and shift to the

Fig. 4 illustrates the steady-state current characteristics from our numerical simulation. In the simulation, the sample thickness is 25 ␮m, and the electron mobility takes a reasonable value (10−11 cm2 V−1 s−1 ) from the literature (Sessler et al., 2004). In this study, along with the first increase in JSE resulting from the decreasing landing energy of PEs caused by the negative surface potential and the subsequent appearance of leakage current JE , the charging process proceeds to its equilibrium state after 500 s with the steady-state JSE and JE . Similar transient pattern of JSE can also be observed in other experiments (Fakhfakh et al., 2012). The measurement of JE cannot completely avoid the influence of the displacement current, and therefore, the measured JE is not null at the beginning of irradiation time in previous work (Feng et al., 2013). In addition, current conservation is satisfied as JSE + JS = JPE = 2 nA/cm2 , in which JS = JE in steady state of charging.

26

24

VS 20

25

EP (keV )

30

−4000 40

QT 15

−2

−1500 −11

10

−10 2

10

0

−9

−1 −1

20

Fig. 7. Simulated surface potential VS and total charge density QT in the equilibrium state at different electron mobilities e . The surface potential is shown to decrease rapidly with decreasing e . The total charge density increases with increasing e .

−2

60

10

Total charge density QT (mC cm )

Surface potential VS (V)

VS

5

10

QT

Electron mobility µe(cm V s )

80

−6000

−1000

10

Fig. 5. Simulated surface potential VS and total charge density QT in the equilibrium state at different electron beam energies EP .

−2000

20

−500

20

−2

15

VS

−1700

28

VS −1800

26 −1900 24 −2000

QT

−2

Beam current density JPE(nA cm ) Fig. 6. Simulated surface potential VS and total charge density QT in the equilibrium state at different electron beam current densities JPE . Evidently, the surface potential decreases with increasing JPE and the total charge density increases with increasing JPE .

The electron beam energy EP is an important factor for charging in microscopic parameters because it directly determines the SEs yield and the electron range. Fig. 5 shows the simulated surface potential VS . If the beam energy is further increased, the electron range will be close to or even larger than the film thickness. Therefore, some scattered electrons can readily arrive at the substrate. In this case, the charging reaches its equilibrium state faster, and fewer space charges are accumulated in the film, such that the surface potential increases and the total charge density decreases. Consequently, in this study, the surface potential in the equilibrium state has the maximum negative value in the energy range of the non-penetrating e-beam. The total charge density in the equilibrium state should have the maximum value when the electron energy is 15 keV. The effect of the beam current density JPE on the surface potential is illustrated in Fig. 6, in which the surface potential decreases with increasing JPE . The total charge density increases with increasing JPE . This result indicates that for the polymer irradiated by the non-penetrating e-beam, the negative charging can be suppressed by reducing JPE . Thus, the transient charging process takes less time to reach its equilibrium state with the decrease in JPE because the leakage current density JE is reduced in the equilibrium state. This phenomenon should result in the lesser accumulation of excess negative space charges and total charge density in the polymer. In addition, the total charge density will remain constant after the appearance of charging equilibrium state. Electron mobility e may accordingly affect the process of charge transport with the surface potential and the total charge density in the equilibrium state. Fig. 7 shows that the surface potential decreases with a decrease in e (Li

Total charge density QT (mC cm )

−2500

Surface potential VS (V)

−2

QT −2000

0

Surface potential VS (V)

Surface potential VS (V)

28

Total charge density QT (mC cm )

J. Liu, H.-B. Zhang / Micron 67 (2014) 74–80

Total charge density QT (mC cm )

78

16

10

18

10

20

10

22

22

10

−3

Trap concentration NT (cm ) Fig. 8. Simulated surface potential VS and total charge density QT in the equilibrium state at different trap concentration NT . It can be seen that the surface potential decreases with increasing NT , especially in the condition of NT > 1021 cm−3 .

and Zhang, 2010). The transient charging process reaches its equilibrium state more slowly as e decreases. Therefore, more negative space charges can be accumulated on the film, thus decreasing the surface potential and increasing the total charge density. The effects of the trap concentration and capture cross section are also observed. The influence of the trap concentration NT on the surface potential and total charge density is shown in Fig. 8. The surface potential decreases with an increase in NT , especially when NT > 1021 cm−3 . The increase in NT facilitates the accumulation of more electrons and holes in the space charge region. Thus, more electrons will be transported and trapped in the film. That is, the amount of negative space charges in the polymer will increase. When NT is low ( 1021 cm−3 , the number of trapped electrons increases more, and therefore, the surface potential clearly decreases, and the total charge density increases with an increase in NT . Fig. 9 shows the simulated surface potential and the total charge density with the capture cross section CS (Cornet et al., 2008; Touzin et al., 2006). The surface potential decreases with an increase in the capture cross section. When the capture cross section is low (CS < 10−13 cm2 ), the surface potential decreases only slightly with an increase in capture cross section CS because the increased trapped electrons are not sufficient to significantly affect the surface potential. However, when the capture cross section is CS > 10−13 cm2 , the number of trapped electrons increases, and therefore, the surface potential and total charge density clearly

28

−1800 26

−1900

24

−2000

QT −15

−14

10

−13

10

−12 2

10

−1200 −1400

22 −1600 −1800

−2

Total charge density QT (mC cm )

25

−1000 20 −1500

QT

15

−2000 15

20

25

Film thickness H (µm)

30

20

−17

10

−16

10

−15

10

−14

10

−13

10

−2

3 −1

Recombination rate R (cm s )

Fig. 9. Simulated surface potential VS and total charge density QT in the equilibrium state at different capture cross section CS . It can be seen that the surface potential decreases and the total charge density increases with increasing capture cross section CS , especially in the condition of capture cross section CS > 10−13 cm2 .

VS

QT

−2000

Capture cross section CS(cm )

−500

VS

Total charge density QT (mC cm )

24

Surface potential VS (V)

VS

10

Surface potential VS (V)

79

−2

−1700

Surface potential VS (V)

Total charge density QT (mC cm )

J. Liu, H.-B. Zhang / Micron 67 (2014) 74–80

Fig. 10. Simulated surface potential VS and total charge density QT in the equilibrium state at different sample thicknesses H. Here, the surface potential decreases and the total charge density increase with increasing H.

decreases and increases, respectively, with an increase in the capture cross section CS . Note that more diverse trap parameters of trap concentration and capture cross section selection and optimization will be done when more direct comparison with experimental data. Fig. 10 shows the simulated surface potential and total charge density with varying film thickness H. The surface potential clearly decreases with increasing H (Li and Zhang, 2010; Liu et al., 1995). Increasing H will extend the transient charging process, resulting in an increase in the amount of negative space charges in the film. Additionally, the measured surface potential and total charge density decreases and increases, respectively, with increasing H. Fig. 11 shows the simulated surface potential and total charge density with varying electron–hole recombination rate R. The surface potential clearly decreases with increasing electron–hole recombination rate R. Increasing the recombination rate will extend the transient charging process, resulting in an increase in the amount of negative space charges in the film. Therefore, the surface potential and total charge density decreases and increases, respectively, with an increase in the electron–hole recombination rate R. 3.5. Discussion We consider the influences of the trap concentration and capture cross section to achieve a comprehensive charge-trapping process to improve the accuracy and efficiency of the present simulation. In this study, the detrapping effect is not considered important in the reduction of the computational time in our simulation. Numerous ranges of physical parameters influence the

Fig. 11. Simulated surface potential VS and total charge density QT in the equilibrium state at different electron–hole recombination rates R. Here, the surface potential decreases with increasing recombination rate R and the total charge density increase with increasing recombination rate R.

dynamic charging process of polymer. The in-depth relationship between the polymer properties and the surface charging characteristics is investigated by analyzing the comprehensive factors of the charging characteristics using different electron beam energies, beam current densities, sample thicknesses, electron mobility, trap concentration, capture cross section, and electron–hole recombination rate. Therefore, evaluating the charging characteristics that are sensitive to sample parameters is important. However, another interesting feature is observed near the surface. A positive charge peak appears within the first minutes of irradiation. This observation provides an evidence of the existence of the positive carriers in the charge distribution. Positive charging occurs during irradiation upon secondary electronic emission following the impact ionization of the macromolecules by high energetic electrons in the electron beam. The defocused model of electron beam charging used in this study can be considered as a reasonable approximation of the negative charging effect in the charging mode of the e-beam as seen in SEM, including the fast transient charging process of e-beam irradiation. However, although more complex, we will further simulate the negative charging effect caused by the multi-energy electron in the charging mode in various fields, such as SEM images and space application. Finally, further study is still needed to deeply investigate the effects of temperature (Cornet et al., 2008; Touzin et al., 2006) and the model when incident electrons inside the polymer have an energy less than 1 keV. In this study, the irradiation mode is based on the defocused electron beam, and the dynamic electron beam is analyzed by SEM. Therefore, studying the dynamic charging characteristics of different irradiation modes such as dynamic scanning model based on SEM may be an interesting topic in our future research. 4. Conclusions Based on our comprehensive model with simultaneous consideration of electron scattering charge transporting for simulating charging process for a polymer irradiated by a defocused electron beam, we have addressed the surface charging characteristics of negatively charged polymer. The surface potential in the equilibrium state is determined using the accumulated space charges during the dynamic charging process related to the microscopic parameters. Affected jointly by electron scattering, charge transport, complex charge trapping, and potential spread over a wider area along the electron beam irradiation direction, while holding relatively high values around the center. These parameters

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J. Liu, H.-B. Zhang / Micron 67 (2014) 74–80

then decrease to maximum negative values and eventually recover to zero. The surface potential increases with increasing electron beam energy and decreases with increasing beam current, film thickness, and electron–hole recombination rate. The decrease in the electron mobility and increase in the trap concentration and capture cross section can reduce the surface potential significantly at e < 10−10 cm2 V−1 s−1 , NT > 1021 cm−3 and capture cross section CS > 10−13 cm2 . Moreover, the increase in the trap concentration and capture cross section can enhance the trap rate, which increases the total charge density and decreases the surface potential. Hence, a good fit of the simulated and measured one validate the simulation model and related results. The results will be helpful for predicting and suppressing the surface charging of a polymer irradiated by a defocused electron beam.

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