A gap capacitance method for slider flying
height measurement in near-field
optical disk drives
J.W. Chen, T.S. Liu
*Department of Mechanical Engineering, National Chiao Tung University, Hsinchu 30010, Taiwan, ROC Received 5 November 2003; accepted 28 June 2004
Abstract
In order to overcome the diffraction limit of conventional optical disk drives, and substan-tially increase data storage capacity and density, near-field optical disk drives remain to be realized. The slider of a flying pickup head in a near-field optical disk drive has to fly at a sta-ble spacing above the disk surface. To sense the slider flying height, a gap capacitance method is developed in this study to measure capacitance variation between the pickup head and disk surface. The capacitance varying with the flying height is modulated by a Colpitts oscillator. Subsequent demodulation accounts for height variation of the flying pickup head. Measure-ment results of this method are verified by using a laser Doppler interferometer.
Ó 2004 Elsevier Ltd. All rights reserved.
Keywords: Flying pickup head; Near-field optical disk drive; Flying height; Gap capacitance
1. Introduction
Conventional optical disk drives have a diffraction limit in optics, since its oper-ation situoper-ation is in far-field i.e. d k; where d is the distance between a sample and a source and k is the free space wavelength of a light source. In view of this,
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*
Corresponding author. Fax: +886 35720634. E-mail address:[email protected](T.S. Liu).
cal disk drives that apply near-field optics [1] employ a flying pickup head with a solid immersion lens [2], thereby substantially increasing data storage capacity and density. Near-field optical disk drives employs a flying pickup head that flies in a manner similar to that in hard disk drives as shown in Fig. 1. The laser spot size can be reduced according to near-field optics theory so as to substantially in-crease data storage capacity, since achievable bit density is determined by the laser spot size, i.e., k/NA, where k is the free space wavelength and NA the numerical aperture of an objective lens. The use of a solid immersion lens increases the effec-tive numerical aperture.
However, a critical requirement in increasing areal density is the low flying head height i.e. the spacing between the flying pickup head and disk surface must be very small. The flying pickup head has to maintain a stable near-field height for focusing. In this study, to measure height variation of the flying head; i.e., head–disk gap, a gap capacitance method is developed. Experimental results are presented to demon-strate the effectiveness of the proposed method.
It has been attempted to achieve stable and small spacing between a flying pickup head and a disk surface by using passive air-bearing sliders to implement near-field recording[2,3]. It is common to use laser Doppler vibrometers for sensing optical disk flutter and flying height variation[4,5]. Although laser Doppler vibrometers are accu-rate in measurement, this study aims to develop an alternative approach––a gap capacitance method––that is more economical than other approaches.
2. Gap capacitance method
This study develops a gap capacitance method to measure the flying height of a pickup head. To use the gap capacitance sensor has to make the pickup head exces-sively close to the near-field optical disk. The proposed method can measure the var-ying spacing between the flvar-ying pickup head and the disk without regard to varvar-ying disk rotation speed.
The piezoelectric (PZT) elements have been widely applied to be a micro-actuator in the high data storage density disk drive development, and its response perform-ance is qualified to deal with fast and precise movement. PZT actuators can generate rapid and fine motion for the flying pickup head, where a controller with high pre-cision is required. Among PZT actuators, PZT benders are popular in many small structure applications, such as individual blade control of rotorcraft, vibration dampening, and positional control. In the presence of disk surface vibration, a flying head with a PZT bender is attached to a suspension arm to maintain the near-field flying height.
This study pastes a copper electrode to the bottom surface of a PZT bender, as illustrated inFig. 2. The metal thin layer coated on an optical disk becomes another electrode, whose electric charge density is constant. Hence, the metal electrode on the PZT bender and the metal thin layer constitute a capacitor, whose capacitance varies with the head–disk gap distance. The gap capacitance is generally written as
[6–8]
Cgap¼ e A
X ð1Þ
where e is a permittivity, A is the effective area of the electrode, and X is the gap be-tween the electrode and the disk surface.
The block diagram of the GCS system is depicted inFig. 3. The capacitance signal enters a Colpitts oscillator circuit and converts into an approximate sinusoidal sig-nal, for which one can tune a suitable frequency. As shown inFig. 4, a Colpitts oscil-lator circuit is employed in this study to convert capacitance variation into a
sinusoidal carrier signal of frequency f by capacitance C1, C2, and inductance L1. The carrier frequency f is expressed by[9]
f ¼ 1 2p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi L1 CC1C2 1þC2 r ð2Þ
When the Colpitts oscillator circuit is parallel with a gap capacitance Cgap, its mod-ulation frequency fibecomes, based on Eq. (2),
fi¼ 1 2p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi L1 CgapþCC11þCC22 r ð3Þ
Eq. (3) can be used to calculate the capacitance value Cgap, which depends on the flying height X according to Eq. (1). However, the frequency modulation fi can not be measured directly in time domain. After frequency modulation (FM) by the Colpitts oscillator, an FM demodulation meter converts the modulated signal, thereby obtaining a demodulation voltage signal whose magnitude can be translated into the flying height variation.
Fig. 3. Block diagram of gap capacitance sensor.
3. Measurement An FM signal s(t) defined by sðtÞ ¼ Accos hiðtÞ ¼ Accos 2pfctþ 2pkf Z t 0 mðtÞdt ð4Þ is a nonlinear function of a modulating signal m(t), which makes frequency modula-tion a nonlinear process, where fcdenotes a carrier frequency and kfa constant. Con-sider the disk surface displacement in vibration as a sinusoidal modulating signal defined by
mðtÞ ¼ Amcosð2pfmtÞ ð5Þ
The instantaneous frequency of the resulting FM signal is written as
fiðtÞ ¼ fcþ kfAmcosð2pfmtÞ ¼ fcþ Df cosð2pfmtÞ ð6Þ where Df = kfAmdenotes a frequency deviation, representing the maximum depar-ture of the instantaneous frequency of an FM signal from the carrier frequency fc. A fundamental characteristic of FM signals is that the frequency deviation Df is pro-portional to the amplitude Amof the modulating signal and is independent of the modulating frequency. Since the instantaneous frequency of the FM signal is fi, the FM phase can be written as
hiðtÞ ¼ 2p Z t
0 fiðtÞdt
Using Eq.(6), the phase hiof the FM signals is obtained as hiðtÞ ¼ 2pfctþ
Df fm
sinð2pfmtÞ ð7Þ
The ratio of the frequency deviation Df to the modulation frequency fmis commonly called the modulation index of the FM signal, denoted by b; i.e.
b¼Df fm
ð8Þ and Eq.(7) becomes
hiðtÞ ¼ 2pfctþ b sinð2pfmtÞ ð9Þ
Accordingly, the parameter b in radians represents the phase deviation of the FM signal, i.e. the maximum departure of the phase hi(t) from the phase 2pfct that is the unmodulated carrier. Using Eq.(9), the FM signal in Eq.(4)can be rewritten as
sðtÞ ¼ Accos½2pfctþ b sinð2pfmtÞ ð10Þ
At first, the disk vibration signal enters a Colpitts oscillator circuit. The disk vibra-tion signal 90 Hz is modulated on the carrier signal.Fig. 5depicts a resulting carrier signal shown on the oscilloscope, where the oscillation frequency is at 4.42 MHz. In Eq. (3), L1= 33 lH and C1= C2= 78 pF, hence f = 4.436 MHz. If Cgap= 10 pF,
f = 3.958 MHz. After modulation, the carrier frequency signal reduces from 4.42 to 3.958 MHz which is an FM signal. The frequency response of disk modulation signal on the oscilloscope is shown inFig. 6, where the resonance at f = 3.958 MHz comes from carrier signals in the Colpitts oscillator and the frequency deviation about 0.46 MHz is caused by Cgap that varies with disk rotating at 90 Hz.
This study investigates gap capacitance dealing with three disks. The first disk tested has a polycarbonate substrate and has been aluminum-coated beforehand to enhance measurement signal. When the disk does not rotate, the demodulation signal remains zero, as shown inFig. 7. During disk rotation, the demodulation sig-nal is shown in Fig. 8, where jerks arise from scratches on the tested disk surface.
The second disk is chromium-coated with a polycarbonate substrate and its demodulation signal is shown inFig. 9. The third is essentially a glass-substrate disk, whose resulting demodulation signal is shown inFig. 10.Fig. 11compares frequency spectrums between idle and rotating disks. It is observed that the fundamental fre-quency of idle and rotating signals are 60 and 90 Hz, respectively. The idle signals of 60 Hz and its multiple frequencies are caused by a power source. ComparingFigs.
Fig. 5. Measured signal of Colpitts oscillator.
9–11shows that the disk substrate material dominates vibration behavior of disks. A stiffer disk yields smoother signals.
Finally, disk vibration and the capacitance gap between the electrode and disk are measured by a laser Doppler vibrometer (LDV) whose resolution is 0.2 nm, finer than a GCS. The single-beam LDV measures vibration of the chromium-coating
Fig. 7. Demodulation signal of aluminum-coated disk at 0 rpm.
Fig. 8. Demodulation signal of aluminum-coated disk at 5400 rpm.
disk rotating at 5400 rpm is shown inFig. 12, where the dominant frequency of the disk vibration is 88.97 Hz synchronous with the spindle motor speed and the peak-to-peak amplitude is 44.34 lm. By contrast, the measurement result for a glass-sub-strate optical disk is shown in Fig. 13, where the dominant frequency of the disk vibration is 89.75 Hz synchronous with the spindle motor and the peak-to-peak amplitude is 37.87 lm. Accordingly, the glass-substrate disk generates smaller defor-mation due to its larger hardness. Furthermore, using a dual-beam LDV, the meas-urement result of the gap between the electrode and the chromium-coated disk is shown in Fig. 14, where the resonant frequency is 89.84 Hz and the peak-to-peak amplitude is 92.32 lm. In addition, the dual-beam LDV is also employed to measure the gap between the electrode on a PZT bender and a glass-substrate optical disk as shown inFig. 15, where the vibration frequency is 89.96 Hz and the magnitude of peak-to-peak is 38.82 lm. Comparing Figs. 9 and 14yield a relationship between
Fig. 10. Demodulation signal of glass-substrate disk at 5400 rpm.
the demodulated voltage and capacitance gap as 1.0 V = 57.7 lm for the chromium coating disk. By contrast,Fig. 16yields the relationship between voltage and capac-itance gap as 1.0 V = 12.4 lm for the glass-substrate disk. The curves for flying
Fig. 12. Measured result by single beam LDV for optical disk with chromium coating.
Fig. 13. Measured result by single beam LDV for glass-substrate optical disk.
height and demodulated voltage are out of phase, since according to Eq.(1) flying higher correspond to smaller capacitance and hence smaller demodulated voltage.
Fig. 16(a) resulting from LDV measurement validates the proposed gap capacitance
method that yieldsFig. 16(b).
4. Electrode and gap capacitance
Fig. 17 shows capacitance values vs. air gap in measurement, where dots are
obtained by capacitance meter measurement in static state. The regression curve in
Fig. 17can be expressed by
Fig. 15. Flying height variation measured by dual-beam LDV for glass-substrate optical disk.
0 5 10 15 20 25 -40 -30 -20 -10 0 10 Time (ms) (a) Displacement (µ m) 0 5 10 15 20 25 -2 -1 0 1 2 Time (ms) (b) Voltage (V)
C¼ 24534:82
X þ 1363:79 ð11Þ
where X is the distance in lm between the disk and pickup head. Eq.(11)is similar to Eq.(1)other than the appearance of a constant term in the denominator. Denoting Cgapand Cpas measured gap capacitance and parasitic capacitance, respectively, the equivalent capacitance of two capacitors in series is written as
C¼ 1 1 Cgap þ 1 Cp ð12Þ
Substituting Eq.(1)into(12)yields
C¼ 1 1 eA X þ 1 Cp ¼ eA XþeA Cp ð13Þ
Comparing Eq. (11) with(13) leads to eA = 24534.82 and Cp= 18 pF. Hence, the present experimental data consists with the general model, i.e. Eq. (1).
Eq.(12)can also be rewritten as C¼ CgapCp
Cgapþ Cp
ð14Þ Accordingly, if Cgapis much larger than Cp, then C ;
CgapCp
Cgap ¼ Cpsuch that the gap
capacitance effect is not apparent. If Cgap* Cp, then Eq. (14) yields C ; C2
gap
2Cgap¼
Cgap=2. By contrast, if Cgapis much smaller than Cp, then C ; CgapCp
Cp ¼ Cgap.
There-fore, a too large gap capacitance is not amenable to gap capacitance measurement. Moreover, a smaller Cgap i.e. smaller size electrode is essential. A smaller size elec-trode can produce more uniform capacitance distribution on a measured surface.
0 10 20 30 40 50 60 70 80 90 100 110 16.6 16.8 17 17.2 17.4 17.6 17.8 18 Gap ( m) Capacitance (pF)
5. Simulation results
This study carries out control simulation with an identified model of a PZT bender and uses measured vibration data of an optical disk to demonstrate the effec-tiveness of the gap capacitance sensing method. By using system identification, a PZT bender transfer function that relates control voltage U (volt) to bender vertical displacement Y (lm) is written as PZTðsÞ ¼YðsÞ UðsÞ ¼ 1:735 10 8s2þ 2:094 1010sþ 1:844 1015 s4þ 1231s3þ 1:03 108s2þ 2:547 1010sþ 4:142 1014 ð15Þ To suppress variation of the head/disk spacing, the optical pickup head is demanded to track disk deformation in the focusing direction.Fig. 18illustrates the block dia-gram for the present control system, in which D(s) minus PZT(s) output becomes the flying height error to be minimized. Considering a PZT model without disturbance and system uncertainty, this study designs a controller expressed by
CðsÞ ¼130sþ ð2p90Þ 2
s2þ ð2p90Þ2 ð16Þ
which aims to deal with 90 Hz vibratory deformation of a disk surface. As depicted
in Fig. 18, the error can be written as
Gap Capacitance Sensing
C(s) PZT(s) 4 . 12 1 + – Disk deformation D(s) Error E(s)
EðsÞ ¼ 12:4
12:4þ PZTðsÞCðsÞDðsÞ ð17Þ
where 12.4 is the gain of a gap capacitance sensor from displacement to voltage and D(s) denotes disk surface deformation. Eq. (15)multiplied by (16)yields the Bode diagram of the open loop gain as shown inFig. 19, which shows remarkably high
Frequency (rad/sec) Phase (deg) Magnitude (dB) -100 0 100 200 300 400 102 103 104 105 0 45 90 135 180 225 270
Fig. 19. Bode diagram of open loop system.
0 0.05 0.1 0.15 0.2 0.25 -40 -20 0 20 40 Time (s) (a) Displacement ( µ m) 0 0.05 0.1 0.15 0.2 0.25 -20 -10 0 10 20 Time (s) (b) Error ( µ m) PZT Output Disk Vibration
in practice, discharge arc between electrodes may occur, which is to be avoided. To this end, the circuit inFig. 4has to be modified.
6. Conclusion
Gap capacitance sensor accuracy has been verified by the measurement result of a dual-beam LDV. Hence, the proposed sensing method is validated. For the flying pickup head in near-field optical disks, this study develops a gap capacitance method for position sensing. In experiments, the gap capacitance sensor has been used to measure head flying heights above polycarbonate-substrate and glass-substrate disks, respectively. In the present gap capacitance sensing method, the varying spac-ing between flyspac-ing pickup head and disk surface can be detected by frequency mod-ulation and demodmod-ulation. Experimental results yield gains 1.0 V = 57.7 lm for a polycarbonate-substrate optical disk and 1.0 V = 12.44 lm for a glass-substrate opti-cal disk. Therefore, polycarbonate-substrate optiopti-cal disks indeed deform more severe than glass-substrate optical disks. The flying height and demodulated voltage are out of phase. It is seen that measurements results obtained by both gap capacitance sen-sor and LDV are consistent. Although GCS is much cheaper than LDV, its draw-backs include high output noise and uneven capacitance distribution, which can be improved by designing a high performance oscillator circuit and a smaller electrode.
Acknowledgments
This work was supported by Department of Education in Taiwan, Republic of China under Grant No. 89E-FA06-1-4.
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