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The energy distributions of major ions in the cathode zone of a strongly abnormal nitrogen DC glow discharge
Vacuum/volume
Pergamon
All rights
49/number 2/pages 97 to loo/1998 0 1998 Elsevier Science Ltd reserved.
PII: 80042-207x(97300138-3
Printed in Great Britain 0042-207X/98 $19.00+.00
The energy distributions of major ions in the cathode zone of a strongly abnormal nitrogen DC glow discharge Z Wronski and H Murlak-Stachura, accepted in revised form I I September
Institute
of Physics, M. Curie-Sklodowska
University,
20-031 Lublin, Poland
1997
Energy distributions of N+ and N$ ions bombarding the aluminium cathode of a glow discharge at high current densities (few mA cm-*) have been calculated and compared with experimentally determined values. The results show a high proportion of N+ compared to fN;+N;) which are characteristic of a nitrogen discharge and arise from the small value of the cross-section for the process N;+N,-+ N,+N;. Energy distributions calculated with the analytical model based on the Boltzmann equation are close to the experimental distributions measured by mass spectrometry in the higher range of ion energy fnormalised to anode cathode voltage). This agreement is closer at higher pressures 6 0.1 mbar) when the condition of plane geometry of a discharge is more closely satisfied than at lower pressures (few 0.01 mbar). 0 1998 Elsevier Science Ltd. All rights reserved
Introduction
N:+N;+N;+N;,
Ions created in a DC glow discharge are often used to modify solid (cathode) surfaces. Because of the high flux density of ions arriving at such surfaces, these discharges are particularly effective for plasma etching. From a practical and theoretical point of view, for example in modelling of plasma surface interactions,’ a knowledge of the energy spectrum of the bombarding particles is essential. Here we present results of measurements and calculations of the energy spectrum of nitrogen ions bombarding the aluminium cathode of an abnormal DC glow discharge. The experiments were conducted in a cell where extremely high intensities (few mAcm_ ‘) of ion flux were obtained.
and electron ionisation: ,for both species
Calculation (i) Wronski et al.’ have published a model of the energy distribution of discharge ions in a gas mixture. The model may be used to calculate the energy spectra of molecular N: and atomic NT ions of an ‘assumed’ mixture (N,,N). For this particular model we should choose experimentally determined values of the cross-sections of ionic processes, see Eqs (6) and (7) of Wronski, Sullivan and Pearce.’ If we assume NT, NT ions to be quantities A and B of the (N:, NT) mixture, then considering the important charge transfer processes occurring within the gas: the symmetric charge transfer process
N:+N;+N;+N:, asymmetric
charge transfer,
(1)
(2)
e+N,+2e+N:
(3)
e+Nz-+2e+N:+N”
(4)
these may be represented quantitatively by appropriate crossionisation may be sections La, ~,4.~ z,,, 241. Ionmolecular represented by respective cross-sections [PA,*, Pa.4, 1. Typical values of the above normalised cross-section are: t,,, = few tens of cm-‘, TR,A= few cm-‘, CI~,= - 3*r, = few cm-‘. Cross-section of ion ionisation [fia,a, b,,,, ] are assumed to be one order smaller than those of electron ionisation. Values of all crosssections are taken from McDaniel3 and Mark.4 The rest of the cross-sections appearing in Eqs (6) and (7) of Wronski, Sullivan and Pearce* were assumed to be equal to zero. The energy spectra of the both ion components NL and NT calculated from this model may be expressed as; F(t,)
= COtlSti ‘jd. exp (-
cp, * 6J/Sqrt(En)
(5)
where t, is the normalised ion energy relating the real ion energy (t) to the anode cathode voltage (U,,). ,jd is a discharge current density. cp, is a parameter representing the energetic state of ions i. This parameter depends on the macroscopic parameters of the discharge [cross-sections, species and pressure of the gas, r/,,, j,, cathode fall length L,r] and was calculated by solution of Eq. (3 1) of Ref. 2. (ii) We have assumed a plane geometry discharge described in 97
Z Wronski and H Mur/ak-Stachura:The
energy distributions
the experimental section (Section 3) in the model energy spectra of ions produced in this source.
of major ions in the cathode zone
to describe
b
3. Experimental 5.0 1 Ions were created in the cathode zone of the special ion source, see Figure la. Screen S having a local floating potential focused the discharge on a small surface around the extraction hole made in the membrane M of the cathode C. The focusing effect allowed us to obtain high densities of discharge currents, i.e. high flux intensities of ions passing the extraction hole. Ions leaving the extraction hole were accelerated and focused by the electrostatic lens set. The velocity and momentum of ions were analysed with the Wien filter and with the magnetic mass spectrometer respectively. A more exact description of the experimental apparatus and measuring equipment is given elsewhere.5~6 The formulae taking into account ion parameters, geometric and electric parameters of the Wien filter and those of the mass spectrometer were used to convert measured ion current peaks to values of the energy distribution function. We have assumed for this formulae that ions coming in the Wien filter have a velocity perpendicular to the intensities of both magnetic and electric fields of the velocity filter. Figure 2 shows a typical measured spectrum of nitrogen ions arriving at the cathode of this source. Ion current peaks measured with the mass spectrometer collector were not very stable and a record of several peaks was necessary to obtain one point of an energy spectrum as displayed above. This procedure allowed us to reduce experimental errors and obtain the repeatability of measured spectra. The spectrum of Figure 2 was recorded at very low pressure when the assumption of the plane geometry was not fulfilled. The discharge took place in a narrow channel and radial gradients of plasma parameters were high. In this spectrum may be observed a characteristic pool of low energy ions. This feature is characteristic of the mass spectrometry of a glow discharge, see Bondarenko.’ This is due to: l
l
the defocusing effect of the plasma-extraction orifice on low energy ions, the charge transfer process outside the discharge chamber.
N2+ \
-T d g 9
4.5 ?
4.0 i
3.5 + 0.0
7
0.2
-”
-7(1--T
0.4
0.6
0.8
1.0
Ncxmalizedenergy [Vuac] Figure 2. The example of spectrum [log(F(t,)) = f(t/U,,)] of fundamental ions arriving at the cathode of abnormal DC glow discharge in nitrogen measured by authors: p = O.O532mbar, j, = 4mAcmm2, (Iac = 3500V. L,,-3.1 cm.
Low energy ions are spread to a greater extent than high energy ions by the electrostatic lens (plasma-orifice) see Figure 1b. Unfortunately the focusing system of the spectrometer is not reliable enough to reduce the defocusing effect totally. The defocusing effect can be reduced by the use of the suppressor grids method to measure ion energy distribution, see Wronski,’ but this method does not allow us to distinguish between ions NT, NT and this represents an experimental limitation of this system. Moreover low energy ions are more likely than high energy ions to be lost due to the charge transfer process with residual gas atoms outside the orifice because of a particular dependence of the transfer cross-section on ion energy.’
a. plasma
Figure 1. a. Scheme of principal part of ion source. Dashed lines are electric field lines. b. Scheme of the defocusing lens on accelerated ions. Dashed lines are equipotential surfaces. 1, trajectory of some low energy ion; 2, trajectory 98
effect of the plasma-extraction of some high energy ion.
hole
Z Wonski
and H Murlak-Stachura:
The energy
distributions
of major ions in the cathode
4. Results and discussion
Figure 3 shows calculated (lines) and the measured (symbols) energy distributions of N: and NT ions arriving at the cathode surface of DC glow discharge at a pressure p = 0.0665 mbar for various discharge current densities. For every diagram we have given: discharge current density jd, anode cathode voltage U,, and cathode fall length L,,. This set of parameters characterises the fundamental properties a glow discharge. High fractions (NT + NC *)/(N: + N; + + N:) of atomic ions are characteristic of the nitrogen glow discharge arising from the low value of the cross-section of the asymmetric charge transfer, see eqn (2). The spectra consist of the majority ions (N:) and minority ions (N:, N:+). Mark“ has published results of measurements of cross-sections of electron ionisation for nitrogen, which suggest that the efficiency of production of N:ions is one order higher than that of NC+ ions in the energy range appropriate to our experiments, that is, cth
N: +). should be pointed out that in the case of the oxygen DC discharge fractions of atomic ions 0: were much lower that characteristic of nitrogen.’
zone
Figure 4 shows calculated (line) and measured (symbols) energy distributions of NT and NT ions arriving at the cathode surface of a DC glow discharge at the same discharge current Jd = 0.5 mA, but for various gas pressures. It may be seen that the measured and calculated energy distributions of both ion species are similar in the higher part of the energy range. However, the slope of measured spectra is higher than that of calculated spectra particularly at low pressures. There are several reasons for this disagreement, e.g. the model does not take into account the exact dependence of the crosssections on the energy of interacting particles. Moreover, the buffer gas is heated in the discharge canal and the gas concentration is probably different from that assumed to calculate the macroscopic cross-sections of charge transfer. The agreement becomes better as gas pressure increases, i.e. when the assumption of the plane geometry and the assumption of gas concentration more closely satisfied.
5. Conclusion
Energy spectra of fundamental ions produced in the cathode zone of a DC glow discharge can be properly described by an
1\ 5
b.
\
7 d
! 4
0.0 0.0
0.5 E4Jac
1.0
4
i 0.0
010
I
0.5
wuac
1.0
0.0
0.5
tzxac
1.0
Figure 3. Measured and calculated energy spectra of nitrogen ions created in the nitrogen discharge at constant pressure p = 0.0665 mbar and various discharge currents. a).& = 0.71 mAcm-*, U,, = 1006V, L,,-2.2 cm. b). j, = 1.06mAcmm2, U,, = 122OV, L,,-2cm. c.) j,, = 1,4mAcm-‘, u,, = 134ov, L,,- 1.6cm.
Lcp 1.8cm.
d.)
j,, = 1.76mAcmm2,
U,, = 16OOV,
Figure in the various U,, = U,, = U,, = CJai,,=
, 015 E/kc
110
00
0.5 E/&x
I
1.0
4. Measured and calculated energy spectra of nitrogen ions created nitrogen discharge for same discharge current Jd = 0.5mA and gas pressure. a.) p = O.O532mbar, j,, = 2.54mAcm..*, 173OV, L,,-2.1 cm. b.) p = O.O665mbar, j, = 1.76mAcm-*, c.) p = 0.0798mbar. jd = 1.82mAcm~*, 1600 V, L,,- 1.6cm. 1070 V, L,,- 1.3cm. d.) p = 0.1 mbar, jd = 1.5mAcmmZ, 1070V,L,,-l.lcm. 99
Z Wronski
and H Murlak-Stachura:The
energy
distributions
of major ions in the cathode
model based on a solution of Boltzmann equation for a mixture of N:, NT ions. The model applies to a discharge which fulfils the condition of the plane geometry of cathode zones. High values of the ratio (NT/N:) ions is characteristic of a nitrogen discharge and this is due to the low value of crosssections of asymmetric charge transfer between NT ions and Nz molecules. The spectrum of both ion species exhibit exponential variations. Results of measurements of this spectrum show agreement with this analytical model in the high energy interval of this spectrum and at higher pressures. analytical
100
zone
References 1, Sullivan, J.L., Wronski, Z., Saied, S.O. and Sielanko, J., Vacuum, 1995,46, 1333. 2. Wronski, Z.. Sullivan, J.L. and Pearce, C.G., J. Ph~~s. D:, ilppl. Phj,s., 3, 1994, 27, 553. McDaniel, E.W.. Collision Phenomena in Ionized Gasex J. Wiley and Sons, New York, 1964. 4. Mark, T.D., J. Chem. Phys., 1975. 63. 3731. 5. Wronski, Z., Vacuum, 1995,35. 271. f: Wronski, Z.. Vacuum. 1986.36, 329. Bondarenko, A.W.. Zh Tekn Fiz, 1973, XLIII, 821 and 1975, XLV, 308. 8, Wronski, Z., Vacuum, 1988.38, 533. 9. Wronski, Z.. Vacuum, 1989,39.941.
Pergamon
All rights
49/number 2/pages 97 to loo/1998 0 1998 Elsevier Science Ltd reserved.
PII: 80042-207x(97300138-3
Printed in Great Britain 0042-207X/98 $19.00+.00
The energy distributions of major ions in the cathode zone of a strongly abnormal nitrogen DC glow discharge Z Wronski and H Murlak-Stachura, accepted in revised form I I September
Institute
of Physics, M. Curie-Sklodowska
University,
20-031 Lublin, Poland
1997
Energy distributions of N+ and N$ ions bombarding the aluminium cathode of a glow discharge at high current densities (few mA cm-*) have been calculated and compared with experimentally determined values. The results show a high proportion of N+ compared to fN;+N;) which are characteristic of a nitrogen discharge and arise from the small value of the cross-section for the process N;+N,-+ N,+N;. Energy distributions calculated with the analytical model based on the Boltzmann equation are close to the experimental distributions measured by mass spectrometry in the higher range of ion energy fnormalised to anode cathode voltage). This agreement is closer at higher pressures 6 0.1 mbar) when the condition of plane geometry of a discharge is more closely satisfied than at lower pressures (few 0.01 mbar). 0 1998 Elsevier Science Ltd. All rights reserved
Introduction
N:+N;+N;+N;,
Ions created in a DC glow discharge are often used to modify solid (cathode) surfaces. Because of the high flux density of ions arriving at such surfaces, these discharges are particularly effective for plasma etching. From a practical and theoretical point of view, for example in modelling of plasma surface interactions,’ a knowledge of the energy spectrum of the bombarding particles is essential. Here we present results of measurements and calculations of the energy spectrum of nitrogen ions bombarding the aluminium cathode of an abnormal DC glow discharge. The experiments were conducted in a cell where extremely high intensities (few mAcm_ ‘) of ion flux were obtained.
and electron ionisation: ,for both species
Calculation (i) Wronski et al.’ have published a model of the energy distribution of discharge ions in a gas mixture. The model may be used to calculate the energy spectra of molecular N: and atomic NT ions of an ‘assumed’ mixture (N,,N). For this particular model we should choose experimentally determined values of the cross-sections of ionic processes, see Eqs (6) and (7) of Wronski, Sullivan and Pearce.’ If we assume NT, NT ions to be quantities A and B of the (N:, NT) mixture, then considering the important charge transfer processes occurring within the gas: the symmetric charge transfer process
N:+N;+N;+N:, asymmetric
charge transfer,
(1)
(2)
e+N,+2e+N:
(3)
e+Nz-+2e+N:+N”
(4)
these may be represented quantitatively by appropriate crossionisation may be sections La, ~,4.~ z,,, 241. Ionmolecular represented by respective cross-sections [PA,*, Pa.4, 1. Typical values of the above normalised cross-section are: t,,, = few tens of cm-‘, TR,A= few cm-‘, CI~,= - 3*r, = few cm-‘. Cross-section of ion ionisation [fia,a, b,,,, ] are assumed to be one order smaller than those of electron ionisation. Values of all crosssections are taken from McDaniel3 and Mark.4 The rest of the cross-sections appearing in Eqs (6) and (7) of Wronski, Sullivan and Pearce* were assumed to be equal to zero. The energy spectra of the both ion components NL and NT calculated from this model may be expressed as; F(t,)
= COtlSti ‘jd. exp (-
cp, * 6J/Sqrt(En)
(5)
where t, is the normalised ion energy relating the real ion energy (t) to the anode cathode voltage (U,,). ,jd is a discharge current density. cp, is a parameter representing the energetic state of ions i. This parameter depends on the macroscopic parameters of the discharge [cross-sections, species and pressure of the gas, r/,,, j,, cathode fall length L,r] and was calculated by solution of Eq. (3 1) of Ref. 2. (ii) We have assumed a plane geometry discharge described in 97
Z Wronski and H Mur/ak-Stachura:The
energy distributions
the experimental section (Section 3) in the model energy spectra of ions produced in this source.
of major ions in the cathode zone
to describe
b
3. Experimental 5.0 1 Ions were created in the cathode zone of the special ion source, see Figure la. Screen S having a local floating potential focused the discharge on a small surface around the extraction hole made in the membrane M of the cathode C. The focusing effect allowed us to obtain high densities of discharge currents, i.e. high flux intensities of ions passing the extraction hole. Ions leaving the extraction hole were accelerated and focused by the electrostatic lens set. The velocity and momentum of ions were analysed with the Wien filter and with the magnetic mass spectrometer respectively. A more exact description of the experimental apparatus and measuring equipment is given elsewhere.5~6 The formulae taking into account ion parameters, geometric and electric parameters of the Wien filter and those of the mass spectrometer were used to convert measured ion current peaks to values of the energy distribution function. We have assumed for this formulae that ions coming in the Wien filter have a velocity perpendicular to the intensities of both magnetic and electric fields of the velocity filter. Figure 2 shows a typical measured spectrum of nitrogen ions arriving at the cathode of this source. Ion current peaks measured with the mass spectrometer collector were not very stable and a record of several peaks was necessary to obtain one point of an energy spectrum as displayed above. This procedure allowed us to reduce experimental errors and obtain the repeatability of measured spectra. The spectrum of Figure 2 was recorded at very low pressure when the assumption of the plane geometry was not fulfilled. The discharge took place in a narrow channel and radial gradients of plasma parameters were high. In this spectrum may be observed a characteristic pool of low energy ions. This feature is characteristic of the mass spectrometry of a glow discharge, see Bondarenko.’ This is due to: l
l
the defocusing effect of the plasma-extraction orifice on low energy ions, the charge transfer process outside the discharge chamber.
N2+ \
-T d g 9
4.5 ?
4.0 i
3.5 + 0.0
7
0.2
-”
-7(1--T
0.4
0.6
0.8
1.0
Ncxmalizedenergy [Vuac] Figure 2. The example of spectrum [log(F(t,)) = f(t/U,,)] of fundamental ions arriving at the cathode of abnormal DC glow discharge in nitrogen measured by authors: p = O.O532mbar, j, = 4mAcmm2, (Iac = 3500V. L,,-3.1 cm.
Low energy ions are spread to a greater extent than high energy ions by the electrostatic lens (plasma-orifice) see Figure 1b. Unfortunately the focusing system of the spectrometer is not reliable enough to reduce the defocusing effect totally. The defocusing effect can be reduced by the use of the suppressor grids method to measure ion energy distribution, see Wronski,’ but this method does not allow us to distinguish between ions NT, NT and this represents an experimental limitation of this system. Moreover low energy ions are more likely than high energy ions to be lost due to the charge transfer process with residual gas atoms outside the orifice because of a particular dependence of the transfer cross-section on ion energy.’
a. plasma
Figure 1. a. Scheme of principal part of ion source. Dashed lines are electric field lines. b. Scheme of the defocusing lens on accelerated ions. Dashed lines are equipotential surfaces. 1, trajectory of some low energy ion; 2, trajectory 98
effect of the plasma-extraction of some high energy ion.
hole
Z Wonski
and H Murlak-Stachura:
The energy
distributions
of major ions in the cathode
4. Results and discussion
Figure 3 shows calculated (lines) and the measured (symbols) energy distributions of N: and NT ions arriving at the cathode surface of DC glow discharge at a pressure p = 0.0665 mbar for various discharge current densities. For every diagram we have given: discharge current density jd, anode cathode voltage U,, and cathode fall length L,,. This set of parameters characterises the fundamental properties a glow discharge. High fractions (NT + NC *)/(N: + N; + + N:) of atomic ions are characteristic of the nitrogen glow discharge arising from the low value of the cross-section of the asymmetric charge transfer, see eqn (2). The spectra consist of the majority ions (N:) and minority ions (N:, N:+). Mark“ has published results of measurements of cross-sections of electron ionisation for nitrogen, which suggest that the efficiency of production of N:ions is one order higher than that of NC+ ions in the energy range appropriate to our experiments, that is, cth
N: +). should be pointed out that in the case of the oxygen DC discharge fractions of atomic ions 0: were much lower that characteristic of nitrogen.’
zone
Figure 4 shows calculated (line) and measured (symbols) energy distributions of NT and NT ions arriving at the cathode surface of a DC glow discharge at the same discharge current Jd = 0.5 mA, but for various gas pressures. It may be seen that the measured and calculated energy distributions of both ion species are similar in the higher part of the energy range. However, the slope of measured spectra is higher than that of calculated spectra particularly at low pressures. There are several reasons for this disagreement, e.g. the model does not take into account the exact dependence of the crosssections on the energy of interacting particles. Moreover, the buffer gas is heated in the discharge canal and the gas concentration is probably different from that assumed to calculate the macroscopic cross-sections of charge transfer. The agreement becomes better as gas pressure increases, i.e. when the assumption of the plane geometry and the assumption of gas concentration more closely satisfied.
5. Conclusion
Energy spectra of fundamental ions produced in the cathode zone of a DC glow discharge can be properly described by an
1\ 5
b.
\
7 d
! 4
0.0 0.0
0.5 E4Jac
1.0
4
i 0.0
010
I
0.5
wuac
1.0
0.0
0.5
tzxac
1.0
Figure 3. Measured and calculated energy spectra of nitrogen ions created in the nitrogen discharge at constant pressure p = 0.0665 mbar and various discharge currents. a).& = 0.71 mAcm-*, U,, = 1006V, L,,-2.2 cm. b). j, = 1.06mAcmm2, U,, = 122OV, L,,-2cm. c.) j,, = 1,4mAcm-‘, u,, = 134ov, L,,- 1.6cm.
Lcp 1.8cm.
d.)
j,, = 1.76mAcmm2,
U,, = 16OOV,
Figure in the various U,, = U,, = U,, = CJai,,=
, 015 E/kc
110
00
0.5 E/&x
I
1.0
4. Measured and calculated energy spectra of nitrogen ions created nitrogen discharge for same discharge current Jd = 0.5mA and gas pressure. a.) p = O.O532mbar, j,, = 2.54mAcm..*, 173OV, L,,-2.1 cm. b.) p = O.O665mbar, j, = 1.76mAcm-*, c.) p = 0.0798mbar. jd = 1.82mAcm~*, 1600 V, L,,- 1.6cm. 1070 V, L,,- 1.3cm. d.) p = 0.1 mbar, jd = 1.5mAcmmZ, 1070V,L,,-l.lcm. 99
Z Wronski
and H Murlak-Stachura:The
energy
distributions
of major ions in the cathode
model based on a solution of Boltzmann equation for a mixture of N:, NT ions. The model applies to a discharge which fulfils the condition of the plane geometry of cathode zones. High values of the ratio (NT/N:) ions is characteristic of a nitrogen discharge and this is due to the low value of crosssections of asymmetric charge transfer between NT ions and Nz molecules. The spectrum of both ion species exhibit exponential variations. Results of measurements of this spectrum show agreement with this analytical model in the high energy interval of this spectrum and at higher pressures. analytical
100
zone
References 1, Sullivan, J.L., Wronski, Z., Saied, S.O. and Sielanko, J., Vacuum, 1995,46, 1333. 2. Wronski, Z.. Sullivan, J.L. and Pearce, C.G., J. Ph~~s. D:, ilppl. Phj,s., 3, 1994, 27, 553. McDaniel, E.W.. Collision Phenomena in Ionized Gasex J. Wiley and Sons, New York, 1964. 4. Mark, T.D., J. Chem. Phys., 1975. 63. 3731. 5. Wronski, Z., Vacuum, 1995,35. 271. f: Wronski, Z.. Vacuum. 1986.36, 329. Bondarenko, A.W.. Zh Tekn Fiz, 1973, XLIII, 821 and 1975, XLV, 308. 8, Wronski, Z., Vacuum, 1988.38, 533. 9. Wronski, Z.. Vacuum, 1989,39.941.