## Etching of photosensitive chalcogenide glasses:experiments and simulations

Optics Express, Vol. 15, Issue 19, pp. 12539-12547 (2007)

http://dx.doi.org/10.1364/OE.15.012539

Acrobat PDF (272 KB)

### Abstract

We have developed a three-dimensional simulation algorithm based on fast marching method that mimics the etching behavior of chalcogenide photoresists, especially for maskless interference lithography. This lithography exposure is characterized by continuous variation of the exposure intensity inside the photoresist, without step like variation. Furthermore, the chalcogenide photoresist has a “gray-scale” behavior, without definite threshold. The resulting etching process is very sensitive to exposure dose and etching time. The optimal relations between these parameters are determined both theoretically and experimentally. A very good agreement between calculation and experimental results is shown, opening the door to complex nanostructures engineering.

© 2007 Optical Society of America

## 1. Introduction

1. K. Shimakawa, A. Kolobov, and S. R. Elliott, “Photoinduced effects and metastability in amorphous semiconductors and insulators,” Adv. Phys. **44**, 475 (1995). [CrossRef]

4. G. Rosenblum, B. G. Sfez, Z. Kotler, V. Lyubin, and M. Klebanov, “Nonlinear optical effects in chalcogenide photoresists,” Appl. Phys. Lett. **75**, 3249 (1999). [CrossRef]

6. A. Arsh, M. Klebanov, V. Lyubin, L. Shapiro, A. Feigel, M. Veinger, and B. Sfez, “Glassy *m*As_{2}S_{3}·nAs_{2}Se_{3} photoresist films for interference laser lithography,” Opt. Mater. **26**, 301–304 (2004). [CrossRef]

7. M. Vlcek, P. J. S. Ewen, and T. Wagner, “High efficiency diffraction gratings in As-S layers,” J. Non-Cryst. Solids **227**–**230**, 743 (1998). [CrossRef]

8. A. V. Stronski, M. Vlcek, A. Sklenar, P. E. Shepeljavi, S. A. Kostyukevich, and T. Wagner, “Application of As40S60-xSex layers for high-efficiency grating production,” J. Non-Cryst. Solids **266**–**269**, 973 (2000). [CrossRef]

9. S. Wong, M. Deubel, F. Pérez-Willard, S. John, G. A. Ozin, M. Wegener, and G. von Freymann, “Direct Laser Writing of Three- Dimensional Photonic Crystals with a Complete Photonic Bandgap in Chalcogenide Glasses,” Adv. Mater. **18**, 265–269 (2006). [CrossRef]

10. A. Feigel, M. Veinger, B. Sfez, A. Arsh, M. Klebanov, and V. Lyubin, “Two dimensional photonic band gap pattering in thin chalcogenide glassy films,” Thin Solid Films **488**, 185–188 (2005). [CrossRef]

12. A. Feigel, M. Veinger, B. Sfez, A. Arsh, M. Klebanov, and V. Lyubin, “Three-dimensional simple cubic woodpile photonic crystals made from chalcogenide glasses,” Appl. Phys. Lett. **83**, 4480 (2003). [CrossRef]

17. J. A. Sethian and D. Adalsteinsson, “Overview of level set methods for etching, deposition, and lithography development,” IEEE Transactions on Semiconductor Devices **10**, 167–184 (1997). [CrossRef]

13. R. C. Rumpf and E. G. Johnson, “Fully three-dimensional modeling of the fabrication and behavior of photonic crystals formed by holographic lithography,” J. Opt. Soc. Am. A **21**, 1703–1713 (2004). [CrossRef]

## 2. Developing of the etching model

### 2.1 Light interference pattern

### 2.2 Formulation of Etching Model

14. J. A. Sethian, “A fast marching level set method for monotonically advancing fronts,” Proc. Nat. Acad. Sci. **93**, 1591–1595 (1996). [CrossRef] [PubMed]

19. D. Adalsteinsson and J. A. Sethian, “A level set approach to a unified model for etching, deposition, and lithography II: three-dimensional simulations [integrated circuits],” J. Comp. Phys. **122**, 348–366 (1995). [CrossRef]

20. R. C. Rumpf, P. Srinivasan, and E. G. Johnson, “Modeling the fabrication of nano-optical structures,” Proc. SPIE **6110**, 611004 (2006). [CrossRef]

21. R. C. Rumpf and E. G. Johnson, “Comprehensive modeling of near-field nano-patterning,” Opt. Express **13**, 7198 (2005). [CrossRef] [PubMed]

*t*is a parameter without units which determines the relative etching time (the etching time of the illuminated area divided by the etching time of the non-illuminated area) and

_{0}·γ(x,y,z). γ*t*is the etching time of a unit length non-illuminated sample. Applying γ on the illumination pattern

_{0}*I*provides the relative local etching time

_{(x,y,z)}*γ*. The arrival time (

_{(x,y,z)}*T*) is then governed by the Eikonal equation:

*t*is measured experimentally. The numerical scheme appropriate for the solution of this equation must be able to treat the possible cases when a sharp corner develops in the front, the front separates into a few pieces or different parts of the front merge. We use both the first-order and the second-order schemes. The first-order one is defined by the following finite-difference equation:

_{0}*D*

^{±y}_{ijk}*T*and

*D*

^{±z}_{ijk}*T*are similarly defined for

*j*and

*k*indices respectively. The key point here is the correct choice of the right and the left derivatives. The second-order scheme is built on the same principles.

*T*assuming that the neighboring grid values are given. An examination of the equation shows that

_{ijk}*T*depends only on the neighboring values which are smaller than it. This means that the numerical information flows only in the direction of the time growth. The points with smallest T are the initial points where

_{ijk}*T*=0. In the beginning the photoresist forms a homogeneous slab while the solvent is on top of it. The method then starts from the boundary, builds a narrow zone of trial points in its vicinity and propagates it in the direction of growing T. The first step of the algorithm is to label the boundary points as

*known*. The second step is to compute the values in the points neighboring to the

*known*ones. The values in these points are considered as

*trial*because they still can change in the following steps. The next step is to find the trial point with the smallest T. This point may be then frozen (considered

*known*) because its value can not change due to the updates in the neighboring points. Next if necessary, the algorithm updates the narrow zone of

*trial*points around the new

*known*point. It is important to notice that at this stage the values in all trial points surrounding the new

*known*one must be computed or re-computed since the new path may be faster. From now on the algorithm proceeds with the same scenario until all the grid points become

*known*. As soon as the arrival time T(x,y,z) is computed, the position of the front at any given moment of time is easily found through the isosurfaces of T(x,y,z).

^{3}

## 3. Experimental setup and photosensitivity measurement

### 3.1 Samples preparation and photosensitivity measurement

_{2}S

_{3}):1(As

_{2}Se

_{3}) in a high-vacuum evaporation chamber at a pressure of 5×10

^{-6}mbar, and with a rate, measured with a quartz microbalance, of approximately 2–3 nms

^{-1}. The absorption coefficient and index of refraction were measured using an Ellipsometer (V.A.S.E Series of J. A. Wollam Co.). At the writing wavelength 532 nm the index of refraction of 5(As

_{2}S

_{3}):1(As

_{2}Se

_{3}) composition is 2.79 and the absorption is approximately 10,000cm

^{-1}.

4. G. Rosenblum, B. G. Sfez, Z. Kotler, V. Lyubin, and M. Klebanov, “Nonlinear optical effects in chalcogenide photoresists,” Appl. Phys. Lett. **75**, 3249 (1999). [CrossRef]

^{2}range. The etching time was measured for all the samples. Then, the ratio between the etching time of illuminated and non-illuminated samples was calculated. In Fig. 2 an experimental curve of γ values versus exposure dose is shown. This curve is slightly non-linear at low intensity and saturates at high intensity. In the simulation we use an analytic function that fits the experimental results. The best fit is given by

*a=0.416, b=0.00716, n=1.92*. The exposure dose units are

*J/cm*.

^{2}### 3.2 Writing setup

*λ*(2·sin(

*θ*2)), where λ=0.532 µm is the laser wavelength and

*θ*is the angle between the arms. Each beam is spatially filtered and then collimated to a diameter of 20 mm (FWHM). The sample size is 8×8 mm

^{2}, smaller than the beam size, exposed only to the central flat part of the beam. The laser output power is limited to 900 mWatt (450 mWatt per beam) to prevent damage to the irises of the spatial filters.

_{2}S

_{3}):1(As

_{2}Se

_{3}) chalcogenide material in order to enable effective photo-structural process as well as deep penetration of the laser light into the photoresist film. For example, 1 µm thick layer absorbs 60% of the light.

## 4. Experimental results and comparison with the simulation

### 4.1 Shape and etching time comparison

^{2}to 22 J/cm

^{2}the mismatch in the upper surface wall thickness was less then 10%. Comparing the lower surface walls thickness yields the same agreement.

## 5. Discussion

_{B}- t

_{E}is positive and characterizes the structure stability: larger dwell time meaning better tolerance to parameter fluctuations. It can be seen that at about 30 J/cm

^{2}, the dwell time is maximal. In order to be less sensitive to parameters fluctuations, the etching time should be chosen in the vicinity of (t

_{E}+t

_{B})/2.

## 6. Conclusion

## Acknowledgment

## References and links

1. | K. Shimakawa, A. Kolobov, and S. R. Elliott, “Photoinduced effects and metastability in amorphous semiconductors and insulators,” Adv. Phys. |

2. | K. TanakaA.V. Kolobov, ed., |

3. | A. Ozols and K. Shvarts, “Photosensitivity of amorphous semiconductor As-S and As-Se films under CW, nanosecond and picosecond laser irradiation,” Cryst. Latt. Def. and Amorph. Mat. |

4. | G. Rosenblum, B. G. Sfez, Z. Kotler, V. Lyubin, and M. Klebanov, “Nonlinear optical effects in chalcogenide photoresists,” Appl. Phys. Lett. |

5. | V. M. Lyubin, A. M. Sedikh, N. N. Smirnova, and V. P. Shilo, Microelectronica18, 523 (1989). |

6. | A. Arsh, M. Klebanov, V. Lyubin, L. Shapiro, A. Feigel, M. Veinger, and B. Sfez, “Glassy |

7. | M. Vlcek, P. J. S. Ewen, and T. Wagner, “High efficiency diffraction gratings in As-S layers,” J. Non-Cryst. Solids |

8. | A. V. Stronski, M. Vlcek, A. Sklenar, P. E. Shepeljavi, S. A. Kostyukevich, and T. Wagner, “Application of As40S60-xSex layers for high-efficiency grating production,” J. Non-Cryst. Solids |

9. | S. Wong, M. Deubel, F. Pérez-Willard, S. John, G. A. Ozin, M. Wegener, and G. von Freymann, “Direct Laser Writing of Three- Dimensional Photonic Crystals with a Complete Photonic Bandgap in Chalcogenide Glasses,” Adv. Mater. |

10. | A. Feigel, M. Veinger, B. Sfez, A. Arsh, M. Klebanov, and V. Lyubin, “Two dimensional photonic band gap pattering in thin chalcogenide glassy films,” Thin Solid Films |

11. | A. Feigel, Z. Kotler, B. Sfez, A. Arsh, M. Klebanov, and V. Lyubin, “Chalcogenide glass-based three-dimensional photonic crystals,” Appl. Phys. Lett. |

12. | A. Feigel, M. Veinger, B. Sfez, A. Arsh, M. Klebanov, and V. Lyubin, “Three-dimensional simple cubic woodpile photonic crystals made from chalcogenide glasses,” Appl. Phys. Lett. |

13. | R. C. Rumpf and E. G. Johnson, “Fully three-dimensional modeling of the fabrication and behavior of photonic crystals formed by holographic lithography,” J. Opt. Soc. Am. A |

14. | J. A. Sethian, “A fast marching level set method for monotonically advancing fronts,” Proc. Nat. Acad. Sci. |

15. | J. A. Sethian, |

16. | S. Osher and R. Fedkiw, |

17. | J. A. Sethian and D. Adalsteinsson, “Overview of level set methods for etching, deposition, and lithography development,” IEEE Transactions on Semiconductor Devices |

18. | D. Adalsteinsson and J. A. Sethian, “A level set approach to a unified model for etching, deposition, and lithography. I. Algorithms and two-dimensional simulations,” J. Comp. Phys. |

19. | D. Adalsteinsson and J. A. Sethian, “A level set approach to a unified model for etching, deposition, and lithography II: three-dimensional simulations [integrated circuits],” J. Comp. Phys. |

20. | R. C. Rumpf, P. Srinivasan, and E. G. Johnson, “Modeling the fabrication of nano-optical structures,” Proc. SPIE |

21. | R. C. Rumpf and E. G. Johnson, “Comprehensive modeling of near-field nano-patterning,” Opt. Express |

**OCIS Codes**

(050.7330) Diffraction and gratings : Volume gratings

(160.2900) Materials : Optical storage materials

**ToC Category:**

Materials

**History**

Original Manuscript: July 17, 2007

Revised Manuscript: August 9, 2007

Manuscript Accepted: August 13, 2007

Published: September 14, 2007

**Citation**

Raphi Dror, B. Sfez, Sh. Y. Goldin, and A. Cashingad, "Etching of photosensitive chalcogenide glasses:experiments and simulations," Opt. Express **15**, 12539-12547 (2007)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-19-12539

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### References

- K. Shimakawa, A. Kolobov, S. R. Elliott, "Photoinduced effects and metastability in amorphous semiconductors and insulators," Adv. Phys. 44, 475 (1995). [CrossRef]
- K. Tanaka, "Sub-Gap Photo-Induced Phenomena in Chalcogenide Glasses," in Photo-Induced Metastability in Amorphous Semiconductors, A.V. Kolobov, ed., (Wiley, Weinheim, 2003) pp 69. [CrossRef]
- A. Ozols and K. Shvarts, "Photosensitivity of amorphous semiconductor As-S and As-Se films under CW, nanosecond and picosecond laser irradiation," Cryst. Latt. Def. and Amorph. Mat. 17, 235-239 (1987).Q1
- G. Rosenblum, B. G. Sfez, Z. Kotler, V. Lyubin, and M. Klebanov, "Nonlinear optical effects in chalcogenide photoresists," Appl. Phys. Lett. 75, 3249 (1999). [CrossRef]
- V. M. Lyubin, A. M. Sedikh, N. N. Smirnova and V. P. Shilo, Microelectronica 18, 523 (1989).Q2
- A. Arsh, M. Klebanov, V. Lyubin, L. Shapiro, A. Feigel, M. Veinger, B. Sfez, "Glassy mAs2S3·nAs2Se3 photoresist films for interference laser lithography," Opt. Mater. 26,301-304 (2004). [CrossRef]
- M. Vlcek, P. J. S. Ewen and T. Wagner, "High efficiency diffraction gratings in As-S layers," J. Non-Cryst. Solids 227-230, 743 (1998). [CrossRef]
- A. V. Stronski, M. Vlcek, A. Sklenar, P. E. Shepeljavi, S. A. Kostyukevich, and T. Wagner, "Application of As40S60-xSex layers for high-efficiency grating production," J. Non-Cryst. Solids 266-269, 973 (2000). [CrossRef]
- S. Wong, M. Deubel, F. Pérez-Willard, S. John, G. A. Ozin, M. Wegener, and G. von Freymann, "Direct Laser Writing of Three- Dimensional Photonic Crystals with a Complete Photonic Bandgap in Chalcogenide Glasses," Adv. Mater. 18, 265-269 (2006). [CrossRef]
- A. Feigel, M. Veinger, B. Sfez, A. Arsh, M. Klebanov, V. Lyubin, "Two dimensional photonic band gap pattering in thin chalcogenide glassy films," Thin Solid Films 488,185-188 (2005). [CrossRef]
- A. Feigel, Z. Kotler, B. Sfez, A. Arsh, M. Klebanov and V. Lyubin, "Chalcogenide glass-based three-dimensional photonic crystals," Appl. Phys. Lett. 77, 3221 (2000). [CrossRef]
- A. Feigel, M. Veinger, B. Sfez, A. Arsh, M. Klebanov and V. Lyubin, "Three-dimensional simple cubic woodpile photonic crystals made from chalcogenide glasses," Appl. Phys. Lett. 83, 4480 (2003). [CrossRef]
- R. C. Rumpf and E. G. Johnson, "Fully three-dimensional modeling of the fabrication and behavior of photonic crystals formed by holographic lithography," J. Opt. Soc. Am. A 21, 1703-1713 (2004). [CrossRef]
- J. A. Sethian, "A fast marching level set method for monotonically advancing fronts," Proc. Nat. Acad. Sci. 93, 1591-1595 (1996). [CrossRef] [PubMed]
- J. A. Sethian, Level Set Methods and Fast Marching Methods, (Cambridge Univ. Press, 2nd ed., 1999).
- S. Osher and R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces (Springer, 2003).
- J. A. Sethian and D. Adalsteinsson, "Overview of level set methods for etching, deposition, and lithography development," IEEE Transactions on Semiconductor Devices 10, 167-184 (1997).Q3 [CrossRef]
- D. Adalsteinsson and J. A. Sethian, "A level set approach to a unified model for etching, deposition, and lithography. I. Algorithms and two-dimensional simulations," J. Comp. Phys. 120, 128-144 (1995).Q4 [CrossRef]
- D. Adalsteinsson and J. A. Sethian, "A level set approach to a unified model for etching, deposition, and lithography II: three-dimensional simulations [integrated circuits]," J. Comp. Phys. 122, 348-366 (1995).Q5 [CrossRef]
- R. C. Rumpf, P. Srinivasan, and E. G. Johnson, "Modeling the fabrication of nano-optical structures," Proc. SPIE 6110, 611004 (2006). [CrossRef]
- R. C. Rumpf and E. G. Johnson, "Comprehensive modeling of near-field nano-patterning," Opt. Express 13, 7198 (2005). [CrossRef] [PubMed]

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