Equivalent circuit extraction

An equivalent circuit model shown in Fig. 5-6 was used to extract the circuit components.

The resistance Rm represents the mirror loss, while the Ra accounts for the active region resistance. Ca represents a combination of the capacitance of the active area and oxide layer.

A shunt resistance Rp is also included to account for pad loss, and the pad capacitance is represented by Cp. This equivalent circuit can also be applied to examine the extrinsic limitations on the modulation speed and to determine the influence of parasitic capacitance

and mirror resistance on the modulation bandwidth. The values of the circuit components were extracted using ADS (Advanced Design System, Agilent) by fitting both the magnitude and phase of S11 over the measured frequency range. Based on a co-optimization at several bias conditions, Rm was around 42 ohm and Ra was found to be bias dependent, varying from 80 to 37 ohm in 1~6 mA. The major difference between oxide-only and oxide-implanted devices was the capacitance Ca and Cp. Moreover, the Ca and Cp of oxide-only devices were 1.8 and 0.4 pF, respectively, while the Ca and Cp of oxide-implanted devices were 0.5 and 0.28 pF, respectively. Therefore, proton-implantation is shown to effectively reduce both bond pad capacitance and oxide capacitance.

References

[1] Ian Aeby, Doug Collins, Brian Gibson, Christopher J. Helms, Hong Q. Hou, Wenlin Luo, David J. Bossert, Charlie X. Wang, Photonic West, San Jose, CA, pp. 152-161, Vol. 4994, 2003.

[2] Noriyuki Yokouchi, Norihiro Iwai, Akihiko Kasukawa, Photonic West, San Jose, CA, pp.

189-196, Vol. 4994, 2003.

[3] R.C. Strijbos , G. Verschaffelt , M. Creusen, W.C. Vleuten, F. Karouta, T.G. Roer, M. Buda, J. Danckaert, B. Ryvkin, I. Veretennicoff, and H. Thienpont, Photonics West, San Jose, CA, Tech. Rep. OE 3946–14, pp. 69-77, 2000.

[4] F. Mederer, M Grabherr, F. Eberhard, I. Ecker, R. Jager, J. Joos, C. Jung, M. Kicherer, R.

King, P. Schnitzer, H. Unold, D. Wiedenmann, K.J. Ebeling, Electronic Components and Technology Conference, Proceedings. 50th , pp. 1242 –1251, 2000

[5] H.C. Yu, S.J. Chang, Y.K. Su, C.P. Sung, Y.W. Lin, H.P. Yang, C.Y. Huang, J.M. Wang, CLEO PR 2003, Conference Digest, pp. 159, 2004

[6] H.C. Yu, S.J. Chang, Y.K. Su, C.P. Sung, Y.W. Lin, H.P. Yang, C.Y. Huang, J.M. Wang, Mater. Sci. Engi. : B., to be published.

[7] K.D. Choquette , A.J. Fischer, K.M. Geib , G.R.Hadley, A.A. Allerman, J.J. Hindi, Semiconductor Laser Conference, Conference Digest, pp.59 –60, 2000.

Fig. 5-1 L-I-V curves of three oxide-implanted VCSELs (solid lines) and three oxide-only VCSELs

(a)

0 2 4 6 8 10 12 14 16 18

-30 -25 -20 -15 -10 -5 0

Bias current 3mA 4mA 5mA 6mA 8mA 9mA 10mA

Modulation response (dB)

Frequency (GHz)

0 2 4 6 8 10 12 14 16 18

-30 -25 -20 -15 -10 -5 0 5 10

Bias current 3mA 4mA 5mA 6mA 7mA 8mA 9mA 10mA

Modulation response (dB)

Frequency (GHz)

(b)

FIG. 5-2 Small signal modulation response of (a) oxide-only VCSEL (b) oxide-implanted VCSEL

2 3 4 5 6 7 8 9 10 11 2

3 4 5 6 7 8 9 10 11

fr f3dB fr f3dB

Frequency (GHz)

Bias current (mA)

FIG. 5-3. Resonant frequency and 3 dB frequency for oxide-only VCSELs (square symbol) and oxide-implanted VCSELs (circle symbol)

(a)

(b)

FIG. 5-4. Eye diagram of (a) oxide-only VCSEL (b) oxide-implanted VCSEL

Fig. 5-5 Reflection coefficient (S11) for oxide-only device (dashed line) and oxide-implanted device (solid line) at 3 mA

FIG. 5-6 Equivalent circuit used for the oxide-confined VCSEL impedance

CHAPTER 6 High Speed (>13GHz) Modulation of 850nm VCSELs with Tapered Oxide Confined Layer

For optical communication applications, high modulation bandwidth is desirable.

Principal factors affecting laser diode modulation bandwidth are the relaxation oscillation frequency, optical nonlinearities, and parasitic circuit effects. Spatial hole burning (SHB) was known as one of the limitations on the bandwidth of VCSELs by inhibiting high resonance frequencies [2-3]. Due to the nonuniform optical intensity, carriers at different locations in the quantum well have different stimulated recombination rates, and therefore exhibit different dynamic responses to small signal modulation. This nonuniformity causes an overdamping of the relaxation oscillation, and makes the intrinsic maximum bandwidth of oxide VCSELs much smaller than predicted by the conventional rate equation model which assumes uniform optical intensity.

6.1 Review of tapered oxide layer

Tapered oxide layer were first introduced to reduce scattering loss for small aperture VCSELs [4]. Recently, tapered oxide was theoretically investigated to reduce the nonlinear damping effect by making the electrical aperture smaller than the optical aperture, and thereby improves the modulation bandwidth [5]. Additionally, the tapered aperture also has lower parasitic capacitance. When devices are under modulation, the parasitic capacitance across a thin oxide layer (~ 30 nm) will limit the high speed performance [6]. A thicker oxide layer would help on reduction the capacitance. Unfortunately, thick oxide layer incur excess scattering losses. The tapered oxide can be thick at the boundary of mesa to provide a lower capacitance without the expense of excess scattering losses.

We previously demonstrated a simple planar approach for high-speed oxide-implanted VCSELs with good static operation characteristics and reliability [7-8]. In this chapter, we discuss the improved VCSELs utilizing a tapered oxide layer. The VCSELs exhibited similar static performance comparing with the previous devices, but superior high speed performance.

The improvement was attributed to the reduced damping rate in the tapered oxide VCSEL.

The extrinsic bandwidth limitation of the tapered oxide VCSELs was determined based on the equivalent circuit model.

6.2 Sample structure and fabrication process

The VCSEL epi-wafers were grown by Aixtron 2400 G3 metal-organic chemical vapor-phase deposition (MOCVD) on n⁺-GaAs substrate, the structure of which consists of three GaAs/Al0.3Ga0.7As (80Å/80Å) quantum well, sandwiched by fully doped n- and p-DBR mirrors. Both n- and p-DBR are composed of interlaced 1/4λ-thick Al0.15Ga0.85As and Al0.9Ga0.1As layers, with the periods of 39.5 and 22, respectively. The gain peak position = 835 nm was determined by photoluminescence while the FP-dip resonant wavelength = 845 nm was determined by reflection measurement. For blunt oxide VCSELs, a 30-nm-thick Al0.98Ga0.02As layer was placed in node position. For tapered oxide VCSEL, the tapered oxide layer was formed of a 10-nm-thick Al0.99Ga0.01 layer adjacent to a 200-nm-thick Al0.98Ga0.02As layer, which is similar to Ref. [4]. The oxide-confined VCSEL process procedure has been described elsewhere [7-8]. Moreover, the mesa diameter of the fabricated device was 30 µm with a 5.5 µm oxide aperture. The diameter of oxide aperture was determined by dark-field microscopy and the size of spontaneous emission pattern. The device surface was quasi-planar so that the annular p-contact metal and the bond pad were on the same level. The p-contact was created by directly depositing Ti/Pt/Au on the upper heavily doped p⁺ GaAs contact layer, and Au/Ge/Ni/Au was deposited on the bottom backside of the substrate following thinning down. Multiple proton implantations with a dose in the range of 10¹³ ~ 10¹⁵ cm^-2 and four different proton energy ranges between 200 to 420 keV were adapted according to simulation results of the stopping and range of ions in matter (SRIM). The implantation region was kept away from the mesa to prevent damage to the active region and consequent voiding of triggering reliability issues.

6.3 LIV performance and small signal response

The DC characteristics of completed VCSELs were measured with a probe station, an Agilent 4145A semiconductor parameter analyzer and an NIST traceable integration sphere with a photodiode. Fig. 6-1 plots curves of light output and voltage versus current (LIV) of typical VCSELs for both tapered oxide VCSELs and blunt oxide VCSELs with 5.5 µm aperture. The threshold current is ~ 1 mA (0.9 mA) for tapered (blunt) type VCSELs with the same slope efficiency of ~ 0.35 mW/mA. The similar static performance is not surprising since 1. the oxide apertures here have the same size of 5~6µm and 2. the blunt oxide don’t incur excess scattering except at very small oxide size (< 3µm ). The maximal output power

exceeds 3 mW at room temperature and output power rollover occurs as the current increases above 12 mA.

The small signal response of VCSELs was measured using a calibrated vector network analyzer (Agilent 8720ES) with wafer probing and a 9 µm optical fiber connected to a New Focus 40 GHz photodetector. The emission of VCSEL was collimated and then focused to a diffraction-limited spot by a 10×/20× objective pair (NA=0.25/0.4). The overall coupling efficiency is around 20% ~ 30%. Fig. 6-2(a) and 6-2(b) show the modulation response of the VCSELs with the bias current for both tapered oxide VCSELs and blunt oxide VCSELs. At low bias currents, the bandwidth increased in proportion to the square root of the current above threshold, as expected from the rate equation analysis. For blunt oxide VCSEL, low frequency rollover was observed and the modulation response became gradually overdamped as the bias current increasing. In contrast, no rollover was observed in low frequency for tapered oxide VCSELs and the 3-dB bandwidth reached a maximum value of 13 GHz before fully overdamped. The observations coincide with the simulation results for blunt oxide VCSEL in which a significant overdamping was reported in the relaxation oscillation due to the nonuniformity of the transverse mode and significantly reduced the modulation bandwidth.

[2, 5]

In Fig. 6-3, the 3-dB bandwidth is plotted with the root square of the bias current above threshold. The bandwidth are similar at low bias current for both tapered oxide VCSELs and blunt oxide VCSELs and saturated at the bias current higher than 8 mA. The maximal bandwidth for the blunt oxide VCSELs was 9.5 GHz and was enhanced to 13.2 GHz for the tapered oxide VCSELs. The modulation current efficiency factor was ~6.5 GHz/(mA)^1/2. As the Fig. 6-2 shows, the peak height of modulation response was higher in the tapered oxide VCSEL than that of blunt oxide VCSEL. The higher modulation amplitude in tapered oxide VCSELs implies the lower damping rate which was known to approximately proportion to the ratio between resonant frequency and peak modulation amplitude [9]. In depth, the damping rate, resonant frequency, and parasitic roll-off frequency can be obtained by fitting the experimental data to a three-pole approximation of the modulation response equation [9]. The K factor can be found out from the slope of damping rate with the square of resonant frequency, as plotted in Fig. 6-4. It was shown the damping rate indeed about two times higher than that in the blunt oxide VCSELs and the K factors were 0.15 ns and 0.4 ns, respectively. The comparison of the damping rate is also coincident with the theoretical prediction [2, 5]. If parasitic and other heating effects are ignored, the theoretical damping limited 3-dB bandwidth may be over 59 GHz for tapered oxide VCSEL and 22 GHz for blunt

oxide VCSEL, from the ration of 2　(2)^1/2/K. [9]

As previously shown in Fig. 6-2(a), the 3-dB bandwidth reached a maximum value of

~13 GHz before fully overdamped. We therefore investigate the extrinsic bandwidth limitation on the tapered oxide VCSELs in the next. An equivalent circuit for the VCSEL impedance is useful for analysis of electrical bandwidth limitations. Inset of Fig. 6-5 shows the equivalent circuit model used to extract the circuit components. The resistance Rm represents the mirror loss while the Ra accounts for active region resistance. Ca represents a combination of capacitance of active area and oxide layer. A shunt resistance Rp is also included to account for pad loss and the pad capacitance is represented by Cp. Using this equivalent circuit, we can also investigate the extrinsic limitations on the modulation speed and determine the influence of the parasitic capacitance and the mirror resistance on the modulation bandwidth. To extract the capacitance of VCSELs, the measured amplitude and the phase of S11 data were fitted from 100 MHz to 20 GHz. Fig. 6-5 illustrates measured and fitted S11 results of the tapered oxide VCSEL at 6mA. Convergence of the fitting values to physically reasonable values was obtained using the following procedure. First, the Cp, Rp, Rm, Ca were extracted using zero bias S11 data (where Ra is very large and can be neglected).

Second, the Ra and Ca values were extracted by fitting the S11 data for different bias currents.

Finally, all the circuit parameters were allowed to vary about these values in order to minimize the squared error. The resulting Cp, Rp, and Rm were 160 fF, 5Ω and 51Ω respectively and the extracted Ra and Ca values for different bias currents were listed in Table 6-Ⅰ. Based on these extracted values, the electrical bandwidth can be determined from -3dB of the S21 of the equivalent circuit shown in inset of Fig. 6-5. In consequence, electrical bandwidth of ~ 12.5 GHz was obtained and showed weak dependence on bias current. The calculated electrical bandwidth is coincident with the maximal measured modulation bandwidth and confirms the parasitic effects as the main limitation on the tapered oxide VCSELs.

6.4 Eye diagram of tapered oxide VCSEL

Finally, the eye diagram of the tapered oxide VCSELs was demonstrated. Microwave and light wave probes were used in conjunction with a 10 Gb/s pattern generator (MP1763 Anritsu) with a pseudorandom bit sequence of 2³¹-1 and a 12.5 GHz photoreceiver. Eye diagrams were obtained for back-to-back (BTB) transmission on VCSELs via a multimode

fiber. Fig. 6-6 shows the room temperature eye diagram of the tapered oxide VCSEL with compliance OC-192 mask. The eye diagram was measured at 6mA with an extinction ratio of 6dB. The clear open eye pattern indicates good performance of these VCSELs with the rising time (Tr) of 26 ps, the falling time (Tf) of 40 ps, and jitter(p-p) < 20 ps.

In conclusion, planarized oxide-implanted VCSELs were fabricated utilizing tapered oxide layer. The VCSELs exhibited similar static performance, but superior modulation bandwidth up to 13 GHz, compared with the VCSELs utilizing conventional blunt oxide layer.

A very clean eye was demonstrated with rising time of 26 ps, falling time of 40 ps and jitter of less than 20 ps operating at 10Gb/s with 6mA bias and 6dB extinction ratio. The devices are fabricated using a simple, reliable planarized process and can be suitable for mass production.

The high bandwidth and good eye characteristics make these devices very promising in future 10 Gb/s or even higher modulation applications.

Reference

[1] Ian Aeby, Doug Collins, Brian Gibson, Christopher J. Helms, Hong Q. Hou, Wenlin Luo, David J. Bossert, Charlie X. Wang, Photonic West, San Jose, CA, pp. 152-161, 4994, (2003).

[2] A. Valle, J. Sarma, and K. A. Shore, “Spatial hole burning effects on the dynamics of vertical cavity surface-emitting laser diodes,” IEEE J.Quantum Electron., 31, pp.

1423–1431, 1995.

[3] Y. Liu, W.-C. Ng, F. Oyafuso, Klein and K. Hess, “Simulating the modulation response of VCSELs: the effects of diffusion capacitance and spatialhole-burning,” IEE Proc.-Optorlectron., 149, 182-188, 2002

[4] E. R. Hegblom, B. J. Thibeault, R. L. Naone, and L. A. Coldren, “Vertical cavity lasers with tapered oxide apertures for low scattering loss,” Electron. Lett., 33, pp. 869–879, 1997.

[5] Y. Liu, W.-C. Ng, B. Klein, and K. Hess, IEEE J. QUANTUM ELECTRONICS, 39, 99-108 (2003)

[6] C. H. Chang, L. Chrostowski, and Constance J. Chang-Hasnain, “Parasitics and Design Considerations onOxide-Implant VCSELs”, Photon. Technol. Lett. 13, 1274, 2001

[7] H. C. Yu, S. J. Chang, Y. K. Su, C. P. Sung, Y. W. Lin, H. P. Yang, C. Y. Huang, J. M.

Wang, Mater. Sci. Eni. B., 106 (2004) 101-104.

[8] Y. H. Chang, Fang-I Lai, C. Y. Lu, H. C. Kuo, H. C. Yu, C. P. Sung, H. P. Yang and S. C.

Wang, Semicond. Sci. Technol. 19 (2004) L74–L77

[9] G. P. Agrawal and N. K. Dutta, “Semiconductor Lasers,” 2^nd 276-280, Van Nostrand Reinhold published.

0 2 4 6 8 10 12 14 0.0

0.5 1.0 1.5 2.0 2.5 3.0 3.5

tapered oxide blunt oxide

Current (mA)

Power (mW)

0 1 2 3 4 5 6

Vol ta g e (V)

0 2 4 6 8 10 12 14

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

tapered oxide blunt oxide

Current (mA)

Power (mW)

0 1 2 3 4 5 6

Vol ta g e (V)

FIG. 6-1. L-I-V curves of the tapered oxide VCSELs (solid lines) and the blunt oxide VCSELs (dashed lines). Inset is top view image of the VCSEL.

2 4 6 8 10 12 14

FIG. 6-2. Small signal modulation response of (a) the tapered oxide VCSEL and (b) the blunt oxide VCSEL.

0.0 0.5 1.0 1.5 2.0 2.5 3.0 0

2 4 6 8 10 12 14 16 18

tapered blunt

f

3dB

(G Hz)

(I - I

_th

)

^1/2

FIG. 6-3 3-dB frequency of the oxide-implanted VCSELs as a function of root square of bias current above threshold. (Filled square: tapered oxide VCSELs, Opened square: blunt oxide VCSELs)

0 10 20 30 40 50 60 70 80 90 100 0

5 10 15 20 25 30 35 40 45 50 55

tapered blunt

K= 0.40 ns

Da mpi n g r a te ( 1 0

9

s

-1

)

Resonant frequeny

²

( GHz

²

)

K= 0.15 ns

FIG. 6-4 Damping rate as a function of resonance frequency squared for VCSELs. (Filled square: tapered oxide VCSELs, Opened square: blunt oxide VCSELs)

-2 0 2 4 6 8 10 12 14 16 18 20 22

FIG. 6-5 Real and Imaginary part of S11 parameter versus frequency from model and measured data. Inset is the equivalent circuit model of VCSELs.

20%

80%

FIG. 6-6 Eye diagram of the tapered oxide VCSELs at PRBS of 2³¹-1 and 6dB extinction ratio, biased at 6 mA. (the time scale is 15.6 ps/div)

Bias (mA)

0 1 2.5 4 6 8 10

R

_a

( Ω ) ∞ 200 162 136 113 96 87 C

_a

(fF) 185 191 197 202 210 221 240

Table 6-Ⅰ Extracted circuit values at different bias current for the tapered oxide VCSELs.

CHAPTER 7 Summary

In summary, we have studied the high speed performance of vertical-cavity surface-emitting laser. The high speed performance was improved through modifying the gain region, proton-implantation process, and tapered oxide layer.

In chapter 4, we present the fabrication and characteristics of high performance 850 nm InGaAsP/InGaP strain-compensated MQWs vertical-cavity surface-emitting lasers. The InGaAsP/InGaP MQWs composition was optimized through theoretical calculations and the growth condition was optimized using photoluminescence. These VCSELs exhibited superior performance with characteristics threshold currents ~0.4 mA, and the slope efficiencies ~ 0.6 mW/mA. The threshold current change with temperature is less than 0.2 mA and the slope efficiency drops less than ~30% when the substrate temperature is raised from room temperature to 85^oC. High modulation bandwidth of 14.5 GHz and modulation current efficiency factor of 11.6 GHz/(mA)^1/2 are demonstrated. We have also accumulated life test data up to 1000 hours at 70^oC/8mA. Although the BCB planaried process has very low capacitance, the cost was relatively high due the lower yield. We adapted a simple, reliable process by proton implantation to cut down the device capacitance. In chapter 5, we reported the high speed performance of 850nm oxide-confined vertical cavity surface emitting lasers (VCSELs) with planar process and reduced parasitic capacitance. The parasitic capacitance of VCSELs was reduced using additional proton implantation. The small signal modulation bandwidth which was restricted by electrical parasitic capacitance expanded from 2.3 GHz to 9 GHz after proton implantation. To investigate the extrinsic bandwidth limitation of the oxide VCSELs, an equivalent circuit for the VCSEL impedance was introduced. The reflection coefficient showed that the electric parasitic pole exceeded 20 GHz. The eye diagram of VCSEL with reduced parasitic capacitance operating at 10Gbps with 6mA bias and 6dB extinction ratio showed a very clean eye with a jitter of less than 20 ps. This simple method can be applied to mass production with low cost.

In the last part, we present the improved oxide-implanted VCSELs utilizing the tapered oxide layer. The VCSELs exhibited similar static performance, but superior modulation bandwidth up to 13.2 GHz, compared with conventional blunt oxide VCSELs. The damping rate was reduced two times in the tapered oxide VCSEL and therefore enhanced the maximal modulation bandwidth. A very clean eye was demonstrated from improved VCSEL with rising time of 26 ps, falling time of 40 ps and jitter of less than 20 ps, operating at 10Gb/s

with 6mA bias and 6dB extinction ratio. A comprehensive small signal measurement and analysis was conducted. Based on the equivalent circuit model, the extrinsic bandwidth limitation of the tapered oxide VCSELs was determined.

Curriculum Vita

Name: Mr. Ya-Hsien Chang Place of Birth: Taipei, Taiwan Date of Birth: Jan 12, 1976

Electronic Mail: orson.eo90g@nctu.edu.tw Education:

Ph.D. Electro-Optical Engineering, National Chiao Tung University, Taiwan M.S. Electronics, National Tsing-Hua University, Taiwan

B.S. Electronic Engineering, National Tsing-Hua University, Taiwan

Areas of Special Interest:

High speed Vertical-Cavity Surface-Emitting Laser Optical / RF photonics measurement

Optical microscopy and micro-photoluminescence

Title of Ph.D. Thesis:

High speed characteristics of Vertical-Cavity Surface-Emitting Laser

RECENT PUBLICATIONS ( 2003.10-2005.6 ) Ya Hsien Chang (張亞銜) I. JOURNAL PAPERS:

2005

1. Ya-Hsien Chang, Hao-Chung Kuo^*, Yi-An Chang, Jung-Tang Chu, Min-Ying Tsai and Shing-Chung Wang, “10 Gbps InGaAs:Sb-GaAs-GaAsP Quantum Well Vertical Cavity Surface Emitting Lasers with 1.27 µm Emission Wavelengths”, J. J.

Appl. Phys. 44(4B), 2556-2559 (2005)

2. Y. H. Chang, T. H. Hsueh, F. I. Lai, C. W. Chang, C. C. Yu, H. W. Huang, C. F.

Lin, H. C. Kuo and S. C. Wang,” Fabrication and micro-photoluminescence investigation of Mg-doped gallium nitride Nanorods “ J. J. Appl. Phys. J. J. Appl.

Phys. 44(4B), 2657-2660, (2005)

3. Y. H. Chang, H. C. Kuo, Fang-I Lai, K. F. Tzeng, H. C. Yu, C. P. Sung, H. P. Yang and S. C. Wang, “High Speed (>13GHz) Modulation of 850nm Vertical Cavity Surface Emitting Lasers (VCSELs) with Tapered Oxide Confined Layer”, IEE Proc.-Optoelectron., Vol. 152(3), pp. 170-173, 2005

4. Hao-Chung Kuo, Ya-Hsien Chang, Yi-An Chang, Jung-Tang Chu, Min-Ying Tsai, and Shing-Chung Wang,” Single mode 1.27-µm InGaAs:Sb-GaAs-GaAsP Quantum Well Vertical Cavity Surface Emitting Lasers” IEEE J. Selected Topic of Quantum Electronics, 11(1) p.p 121-126 (2005)

5. H. C. Kuo, Y. H. Chang, H. H. Yao, Y. A. Chang, M. Y. Tsai, and S. C. Wang,”

High-Speed modulation of InGaAs:Sb-GaAs-GaAsP Quantum Well Vertical Cavity Surface Emitting Lasers with 1.27 µm Emission Wavelength” Photonics Technology Letter, 17(3) p.p 528-530 (2005).

High-Speed modulation of InGaAs:Sb-GaAs-GaAsP Quantum Well Vertical Cavity Surface Emitting Lasers with 1.27 µm Emission Wavelength” Photonics Technology Letter, 17(3) p.p 528-530 (2005).

在文檔中 面射型雷射高頻特性之研究 (頁 71-0)