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УДК 519.6
Measuring Thickness of Thin Metallic Films with the Use of Laser Probing Technique
V. A. Komotskii, M. V. Kuznetsov, S. M. Okoth
Radiophysics Department, The Peoples Friendship University of the Russia, 6, Miklukho-Maklaya sir., Moscow, 117198, Russia
Proposed and practically carried out non-contact method of measuring thickness of thin metallic films. The recommended range of the thickness measured is from 100A to 1500A. The method is based on probing by a laser beam periodic rectangular patterns, formed on a small portion of the film being studied and coated with a secondary metallic layer.
Methods of measuring thickness of thin metallic films are described in details in [1-3], where the results of the numerous research works carried out at different times are systematized. Among the non-contact methods, the most accurate ones are the interferometers, their accuracy reaching some few angstroms. In order to achieve such accuracy, unique equipment and high-quality polishing of substrates are necessary before depositing the film.
The method being presented in this article for measuring thickness of thin metallic films is related to the class of non-contact methods. It is based on measuring the intensities of the diffraction orders formed as a result of the interaction of laser beam with the periodic patterns formed on the film sample being studied. The measurement result of the thickness of the film being studied is expressed in terms of the wavelength of the probing beam and the intensities of the zero and the first diffraction orders. The method does not require any information on the characteristics of the film sample being studied and is so simple in carrying out.
The essence of the presented method of measuring thickness of thin metallic films is as follows. On a small portion of the sample being studied is formed a rectangular periodic pattern of non-metallic and metallic strips of the film being measured. Thus, the optimum result is a pattern of metallic and non-metallic strips of equal widths, i.e. periodic rectangular patterns. Photolithographic method was applied to produce such a pattern in our experiments. The stages for the formation of periodic rectangular patterns are shown in figures 1 (a-f).
After formation of the periodic rectangular patterns from metallic and non-metallic strips (fig. le) an additional film from a well reflecting metal, which is opaque to the probing laser beam is then deposited on the surface. As a result of this, a periodic pattern with a depth equal to the thickness of the metallic film is obtained (fig. If). Alongside the described technique for formation of the periodic rectangular patterns it is also possible to apply the so-called reverse photolithographic technique (liftoff), whereby periodic rectangular patterns from a photoresist are first formed on the substrate, then on its surface a metallic film being studied is deposited, and finally the photoresist with the metallic layer deposited on its top are removed with the help of a solvent. After that on the obtained periodic pattern (such as le) is also necessary to deposit an additional film from a well reflecting metal. This technique for the formation of metallic strips could be replaced with depositing metal through a removable mask similar to the mask from a photoresist, however in this case the removable mask should be very tightly adjoined to the substrate.
Further, the obtained periodic rectangular pattern (such as If) is probed on reflection by the laser beam of a diameter size of about 4 to 5 or more periods of the periodic rectangular patterns. Probing is done under a small incident angle 7 = 5°
Рис. 1. Stages for the formation of periodic rectangular patterns: a) coating.the sample on study with thin metallic film; b) applying photoresist on the film; c) forming periodic patterns on the photoresist; d) etching the metallic film; e) removing photoresist; f) coating a second layer of metallic film.
to 10° in order to separate the incident and the reflected beams in the space. The plane of incidence and reflection coincides with the direction of the strips of the illuminated periodic pattern. With the help of the spatial filter, zero and first diffraction orders are selected from the obtained diffraction pattern as a result of the reflection of the laser beam and then their intensities measured with the help of the photodiode connected to the circuit in the reverse-biased mode. In practice, we measure the corresponding currents Jo and Ij of the reverse-biased photodiode by successively placing it in the zero and first orders, thus in this state with a high degree of accuracy it is taken that the current of the photo diode is directly proportional to power of the detected beam. From the measurement results obtained the thickness of the metallic film is then calculated using formula (1), earlier obtained in [4], and used for measuring the depth of the periodic rectangular patterns on glass
Л arctan
27rcos7
Here h — thickness of the metallic film being measured, A — wavelength of the probing optical beam, Iq and /] — the measured photodiode currents proportional to the powers Po and Pi of the diffracted beams of the zero and first orders respectively, 7 — incident angle of the probing beam.
Formula (1) is justified only where the form of the periodic rectangular pattern formed as a result of the application of the earlier mentioned techniques represents
ЛЛ --
фм
Lyp
z
Рис. 2. Phase front of an optical wave for different form patterns of the stationary reference grating (SRG). Continuous line — front in case of unequal widths of the rectangular pattern, dashed line — front of an ideal periodic rectangular pattern.
an idea! periodic rectangular pattern. In this case the power of the diffracted beams of zero (Po) and first (Pi) orders are related to the incident power Pinc by a simple expression [4]:
2
Po = y Pine (cos<J>m)2 . and P\ = rPinc((2/tt)sin3>m) ,
where <J>m = (2-k/X)hcos7 — amplitude of the spatial phase modulation of the wave front after reflection from an ideal periodic rectangular pattern, r — coefficient of reflection of the metallic film.
In case of deviation in the form of the periodic patterns from the ideal periodic rectangular patterns, the dependence of power of the diffraction orders on the amplitude of the spatial phase modulation of the wave front takes a more complicated nature. For example, in a special case, when the width of the bottoms (Lvs) is not equal to the width of the tops (Lvp) (fig. 2), the powers of the lower diffraction orders will be expressed by the following formulas [4]:
Po - ?-Pnafl(cos2 $m + sill2 $mj , (2)
(3)
Owing to the deviation in the form of the periodic rectangular patterns from the ideal form, second diffraction orders will be observed in the diffraction patterns, the value being related to the deviation AL is as follows:
(4)
In practice, the absence of the second diffraction order is a sufficient criterion for using formula (1) in calculating the thickness of the films being measured.
A detailed analysis of the errors in determining the depth of the periodic rectangular patterns using the measurement results of the intensities of zero and first diffraction orders was carried out in [4]. The basic components of the measurement errors are as follows:
— an error due to the random changes in the laser power between the measurement intervals of the zero and the first order intensities. A decrease in the error to a level less than 1% is achieved by stabilizing the power, or by measuring the dissipated power of the laser and then moderating on this value the results of the measured powers of the diffraction orders.
— an error due to the power (photocurrents) measuring instrument in the zero and first orders. At h = 100 A and a probing power of 1 mWt, the detected power in the first order is approximately 4 • 10~6 Wt, while the measured currents in units of microamperes. It is also necessary to note, that the level of the diffused radiation incident within the diaphragm's boundaries should be much less than the level of the detected radiation corresponding to the diffraction orders (in our experiments it is in the order of 1 ■ 10-7 Wt to 2 • 10~7 Wt. The highest measurement errors are observed in the region h < 100 A, where the power of the first order tends to zero, and also in the region h — (Л/4) = 1507 A, where the power of the zero order tends to zero on the condition of a small incident beam angle 7, (cos 7 % 1). Remember, however, that at a depth of the periodic rectangular patterns close to Л/4, it is possible to avoid a sharp increase in the measurement errors if essentially increase the incident angle of the probing beam to within an angle range of 7 и 30° to 45°. Thus the depth of spatial phase modulation decreases in accordance with the expression Фт — (27r/A)/icos7, and so the measurements are moved away from the unfavourable zone, where the intensity of the diffraction zero order tends to zero. Some expressions for estimating the measurement errors are given in the appendix.
— a specific error can arise due to deviations in the form of the periodic patterns from the ideal periodic rectangular patterns. Controlling this component of measurement error is based on the absence or the presence of the second diffraction order in the diffraction patterns. As it follows from formula (4), the absence of the second order is a guarantee of the absence of deviations in the pattern form from the ideal periodic rectangular patterns, i.e. (ДЛ/Л — 0). On deviating from the ideal periodic rectangular patterns there appears a second order and the power of the first and zero orders therefore varies. Thus it is possible to carry out some recalculations of the thickness value h using the method of successive approximation and obtain an accurately measured depth. This does not complicate the measurement procedure very much. Let's estimate here the role of the small deviations ДЛ/Л. Let ДЛ/Л = 0.01 then P2/Pinc = 4 - 10"4sin2 фт. On measuring thickness close to a minimal value (h — ЮОА), Фт « 0.1°, the value (Pi/Ptnc) = 4 • 10^3 while the value Р2/РгПс = 4 • 10~6.
1. Experimental results of a trial method
For carrying out experimental trials, periodic rectangular patterns with periods of L — 100fim and L — 200fim were made. Such a range of the pattern periods was chosen based on the following reasons: on one hand, reducing the pattern period increases the effects of the photolithographic errors; while on the other hand, its increase requires the use of a beam with a large cross-sectional area, which somehow complicates the experimental set-up.
A special experiment was set up with the purpose of checking the reliability of the values measured. Three samples used were obtained as follows. On two closely placed substrates № 1 and № 2 in a vacuum chamber was deposited a film of copper metal of thickness hi. Substrate № 1 was then removed from the chamber and replaced with a new substrate № 3. After that metal of thickness h2 was again deposited on substrates № 2 and № 3.
Thus, three samples for study were obtained: substrate № 1 with a film of thickness hi, substrate № 2 with a film of thickness h\ + h2, and substrate № 3 with a film of thickness h2.
With the application of the photolithographic method and subsequent etching on each of the filmed substrate, filmed periodic rectangular patterns with forms close to ideal periodic rectangular patterns were obtained. Further on each of the periodic rectangular patterns was deposited an opaque reflecting metallic film. Then with the help of the laser probing technique described above, the depths of the periodic
Sample № 1 № 3 № 2
^measured 338 A 472 A 818Â
Таблица 1
rectangular patterns and, hence, the thickness of the primary deposited layers was determined. The measured results are given in table 1.
From the table given it can be seen that the sum of the thickness of the metallic films on substrates № 1 and № 3 (i.e. 338 + 472 = 810 A) is very close to the total thickness of the film on substrate № 2 (818 A), which confirms the reliability of the measurement results.
After carrying out the measurements, an additional check on the effects of the secondary deposit was carried out. On the surface of the periodic rectangular patterns was deposited a solid metallic film of thickness equal to the thickness of the additional film after carrying out the optical measurements. After that, the optical measurements were again repeated. The measurement results gave the same values, as those of the depth measurements of the periodic rectangular patterns showing that additional uniform film deposits do not affect the depth of the periodic rectangular patterns.
2. Conclusion
In this work is presented a new method of measuring thickness of thin metallic films with an accuracy that is comparable to the accuracy of the interferometers. Practical realization of the method does not require complicated experimental equipment. The range of the measured thickness values by the optical probing method is in the order from of 100A to 1500A. On measuring thickness of films of more than 1507 a there appears non-synonymous measurements, nevertheless such measurements are not impossible. In article [4] is described a sequence of activities done which synonymously determine the depth of periodic rectangular patterns and, hence, film thickness in the range of 1500 a to 3000 a.
The required sizes of the probed periodic rectangular patterns are in the range of 10mm2 to 20mm2. The method is related to the class of non-contact, and consequently is suitable for measuring thickness of films from materials that are not all that hard.
3. Appendix
The following are ratios for estimating the measurement errors of the thickness taking into account the inaccurate power measurements in the diffraction orders (when
r = 1):
Ah id h \ _ Att 1 APi
1 ~ \dFj 1 ~ 8 cos7 (1 + tan2 $m) sin 2$m P„ ' (5)
1ПС
Ah0 = (§-W = 4 A n t f ^. (6)
VOP0 ) 4?r cos 7 ( 1 + tan $m) cos3 $m Pinc
Here — amplitude of spatial phasor modulation; A hi and A h0 — components of measurement errors of the thickness taking into account the inaccurate power measurements in the first and in the zero diffraction orders. The total error Ah is determined as:
(Ah)2 = (Ahi)2 + (Ah0)2 .
In a field of small film thickness an error of Ah\ appears. For example, if Л —
100 a, Л = 0,6328 a, then Фт a 0.1, and at APi = 10~7 Wt, Pinc = ИГ3 Wt, then
calculating Ah using formula (5) gives Ah ~ 4.7 A.
Литература
1. Технология тонких пленок. Справочник. Под ред. Майссела, Глэнга Р. — М.: Сов. радио, 1947. - Т. 1. - Гл. 1. - С. 140-159. (Handbook of Thin Film Technology edited by Leon I. Maissel and Reinhard Glang, McGraw Hill Company, 1970).
2. Берндт К. Г. В сб. под ред. Г. Хасса и Р. Э. Туна. Физика тонких пленок (современное состояние исследований и технические применение). — М.: Мир, 1968. — Т. 3. — С. 7-57. (Physics of Thin Films, Advances in Research and Development edited by Georg Hass, Night Vision Laboratory U.S. Army Electronics Command, Fort Belvoir, Virginia and Rudolf E. Thun, International Business Machines Corporation Owego, New York, Volume III, 1960, Academic Press, New York and London).
3. Беннет X. E., Беннет Дж. M. В сб. Физика тонких пленок под ред. Г. Хасса и Р. Э. Туна. - М.: Мир, 1970. - Т. IV. - С. 7-122. (Physics of Thin Films, Advances in Research and Development edited by Georg Hass, Night Vision Laboratory U.S. Army Electronics Command, Fort Belvoir, Virginia and Rudolf E. Thun, Raytheon Company Missile Systems Division Bedford, Massachusetts, Volume IV, 1967, Academic Press, New York and London).
4. Кащенко H. M., Комоцкий В. A. II Вестник Российского университета дружбы народов. Серия «Физика». — 1999. — № 7, Вып. 1. — С. 55-65.
5. Комоцкий В. А. Способ измерения толщины металлической пленки. Патент на изобретение. 24.12.2001. Решение о выдаче № 2001134569 (037162).
иОС 519.6
Измерение толщины тонких металлических пленок с помощью
лазерного зондирования
В. А. Комоцкий, М. В. Кузнецов, С. М. Окот
Кафедра радиофизики, Российский университет дружбы народов, Россия, 117198, Москва, ул. Миклухо-Маклая, 6
Предложен и реализован на практике бесконтактный метод измерения толщины тонких металлических пленок. Рекомендуемый диапазон измеряемых толщин 100-1500 А. Метод основан на зондировании лазерным пучком периодической рельефной структуры прямоугольного профиля, которая сформирована на небольшом участке исследуемой пленки и покрыта вторичным металлическим слоем.
