Method of direct coulomb explosion in laser ablation of semiconductor structures

Abstract

A new technique and Method of Direct Coulomb Explosion in Laser Ablation of Semiconductor Structures in semiconductor materials is disclosed. The Method of Direct Coulomb Explosion in Laser Ablation of Semiconductor Structures provides activation of the “Coulomb explosion” mechanism in a manner which does not invoke or require the conventional avalanche photoionization mechanism, but rather utilizes direct interband absorption to generate the Coulomb explosion threshold charge densities. This approach minimizes the laser intensity necessary for material removal and provides optimal machining quality. The technique generally comprises use of a femtosecond pulsed laser to rapidly evacuate electrons from a near surface region of a semiconductor or dielectric structure, and wherein the wavelength of the laser beam is chosen such that interband optical absorption dominates the carrier production throughout the laser pulse. The further application of a strong electric field to the semiconductor or dielectric structure provides enhancement of the absorption coefficient through a field induced redshift of the optical absorption. The use of this electric field controlled optical absorption is available in all semiconductor materials and allows precise control of the ablation rate. When used in conjunction with nanoscale semiconductor or dielectric structures, the application of a strong electric field provides for laser ablation on sub-micron lateral scales.

Description

DETAILED DESCRIPTION

The following discusses use of the new technique and Method of Direct Coulomb Explosion in Laser Ablation of Semiconductor Structures for laser ablation of silicon semiconductor structures. It is understood that the Method of Direct Coulomb Explosion in Laser Ablation of Semiconductor Structures of the present description may be used to perform material removal on any semiconductor structure, the discussion of silicon semiconductor structures considered to be exemplary only and in no way limiting in scope.

As discussed in the background, the activation of the Coulomb explosion mechanism in laser ablation is predicated on the efficient and rapid evacuation of electrons. In the prior art activation of Coulomb explosion in typical dielectrics, a seed carrier density is first created though multi-photon absorption in an intense laser field, followed by the onset of avalanche photoionization. The avalanche photoionization term is due to free carrier absorption and is therefore also operative in metals, although no seed stage is necessary. In the disclosure contained herein, the wavelength of the laser is selected to maximize the linear optical absorption such that the avalanche process becomes secondary or unnecessary. In order to understand this, consider the exemplary case of an approximately 400 nm wavelength femtosecond laser applied to the ablation of silicon. At this wavelength, well above the band edge of silicon, the linear absorption, coefficient is substantial and any multi-photon absorption may be neglected. Neglecting the carrier relaxation term, the equation which describes carrier production in a laser field becomes:

dN _e /dt=[α(F)+α_D(N_e)]×I,

where α(F) is the linear optical absorption coefficient, which depends on the electric field F, and α_D(N_e) is the Drude carrier absorption, which depends on the carrier density. Note from this expression the formal connection between the Drude absorption and the avalanche absorption coefficient may be identified. The semiconductor optical absorption will dominate the carrier generation process provided a(F)≧α_D(N_e). At 400 nm wavelength, the Drude absorption is well approximated by α_D(N_e)≈1/ncτ×N_ee²/ε_om*ω², where n is the index of refraction at the laser wavelength and τ is the plasma relaxation time. The condition α(F)≧α_D(N_e) implies N_e≦ncτm*ω²ε_oα(F)/e². Taking n≈5.6, τ≈200 fs, m*≈0.3 m_e, λ≈400 nm, and α(F)≈1×10⁶/cm (constant), the condition α(F)≧α_D(N_e) is satisfied for carrier densities N_e≦7×10²⁵/cm³. This carrier density exceeds, by several orders of magnitude, the threshold density at which material is expected to undergo ablation due to Coulomb explosion. Hence, femtosecond Coulomb explosion of Si with 400 nm wavelength does not invoke or require the avalanche photoionization mechanism. Equivalently stated, the short absorption depth of Si at 400 nm wavelength would require a plasma density ˜10²⁵/cm³ in order to attain comparable plasma skin depths. In practice, this never occurs.

Without the avalanche photoionization term, the solution to the differential equation at the end of the laser pulse becomes: N_e≈α(F)×I×τ_p, where τ_p is the laser pulse width. Assuming values of α(F)≈1×10⁶/cm, τ_p≈150 fs, and N_th≈1×10²³/cm³, where N_th is the approximate Coulomb explosion threshold, a threshold intensity of I_th≈3.3×10¹¹ W/cm² may be estimated. This is well below the ˜10¹³-10¹⁴ W/cm² thresholds commonly seen for avalanche photoionization. For pulse lengths up to the plasma relaxation time τ, a longer laser pulse requires proportionally less intensity, since it is the laser fluence which governs the final carrier density. The presence of a relaxation term will suppress the induced carrier density by a factor of ˜exp{−τ_p/τ}. For Si and the carrier densities under discussion herein, relaxation times are commonly estimated to be in the range of ˜20-200 fs, corresponding to Si mobilities μ≈10²-10³ cm²/V·s.

An instructive counterpoint to this example is obtained when the activation of Coulomb explosion in silicon through the conventional avalanche photoionization is considered. In an exemplary case, consider an approximately 800 nm wavelength laser applied to the conventional avalanche photoionization activation of Coulomb explosion in silicon. This wavelength is above the band edge of silicon, so multi-photon absorptions may again be neglected. The linear absorption must develop a seed plasma density of N_e≈10²¹/cm³ within approximately the first half of the pulse. Using N_e≈α×I×τ_p÷2, with α≈1×10³/cm and τ_p≈200 fs, the estimated intensity to seed the avalanche I≈2.5×10¹² W/cm², or greater. An analogous estimate of the intensity required to seed the avalanche, for the case of 400 nm radiation of silicon, results in I≈5×10⁹ W/cm². However, as discussed, this estimate is purely hypothetical since the linear optical absorption will continue to dominate the avalanche photoionization even well beyond the Coulomb explosion threshold density.

Another key advantage inherent to the Method of Direct Coulomb Explosion in Laser Ablation of Semiconductor Structures is the ability to use an externally applied electric field to enhance the linear optical absorption. Nearby to strong features in the optical absorption spectra of a semiconductor material, the field dependence of the optical absorption coefficient will be large. In particular, the optical absorption of semiconductors and dielectrics undergoes significant redshifting in strong electric fields. This effect is known as the Franz-Keldysh effect [Keldysh, 1958], and may be explained as follows. Since the strong electric field tilts the semiconductor bandstructure spatially, electrons may tunnel from the valence band to the conduction band. Thus, at photon energies just below strong absorption features, the redshift of the absorption is due to photon-stimulated tunneling [Yu & Cardona, 2001]. The dependence of the absorption coefficient on electric field F is given by:

α(F)=KF² exp{−C/F},

where K and C are constants which depend on the “zero field” absorption, the effective electronic mass, and the difference in laser wavelength from the strong absorption feature. The “zero field” absorption is the optical absorption of the material wherein no electric field is applied. The expression above describes the redshifting of an optical absorption edge in the presence of a strong electric field [Keldysh, 1958]. The 400 nanometer wavelength laser is nearby to such an absorption edge in silicon, which occurs at a wavelength of approximately 375 nanometers. As an externally applied field approaches 10⁷ V/cm, the silicon optical absorption coefficient increases about an order of magnitude from 10⁵/cm to 10⁶/cm. Thus, an externally applied electric field may be used to enhance and control the optical absorption coefficient.

It is therefore instructive to understand the ablation threshold for Coulomb explosion in the case of electric fields F ˜10⁶-10⁷ V/m. For the laser pulse lengths under consideration herein, the electrons will thermally equilibrate but will not have time to transfer their energy to the lattice via collisions or thermal diffusion. The kinetic energy the electron attains from the field is given by ΔK=m*v_S²/2, where v_S is the saturation velocity (ΔK is on the order ˜10 meV, so it does not add substantial energy to the electron) [Yu & Cardona, 2001,]. The equation for the average change in electron temperature T_e (or energy) due to laser absorption is given by:

c _e(T_e)N_e×∂T_e/∂t=−∂S/∂x; S=(1−R)I_o×exp{−2x/δ},

where c_e is the specific heat of conduction electrons, and S is the absorbed energy flux as a function of depth (R is the reflectivity and I_o is the incident intensity) [Chichkov, 1996]. Near the laser ablation threshold T_e≈E_F, and c_e≈3/2. The average change in electron energy then may be expressed: T_e≈4/3×(1−R)Iτ_p/δN_at×exp{−2x/δ}. The threshold fluence for ablation is conventionally determined by the requirement the electron energy T_e reach, within a surface layer x<<δ, a value equal to the sum of the atomic binding energy and the electron ionization energy, i.e. T_e≧E_b+I_p. This is the threshold condition for energetic electrons to escape the solid and produce a strong charge separation field which then results in the Coulomb explosion of the surface layers [Gamaly, 2002]. Solving the relation T_e≧E_b+I_p for the fluence I_thτ_p, yields the threshold dependence on the static field:

(1−R)I_thτ_p≈3/8×N_at/α(F)×(E_b+I_p).

For Si at 400 nm, the reflectivity is roughly 50%. The Si binding energy is E_b≈4.62 eV/atom, and the ionization potential is I_p≈1.12 eV. The predicted threshold fluence is then I_thτ_p≈20 mJ/cm². For a pulse length of approximately 200 fs, this corresponds to a pulse intensity of approximately 10¹¹ W/cm². This estimate agrees with the earlier estimate from use of the linear semiconductor absorption to generate threshold carrier densities. It is instructive to compare this to the expression for threshold derived for avalanche activated ablation. For a plasma skin layer, we have 1−R≈2 ωδ/c, which is justified at critical density. The threshold fluence then becomes I_thτ_p≈3/8×λN_at/2π×(E_b+I_p). From this, it is seen the ablation threshold in the Method of Direct Coulomb Explosion in Laser Ablation of Semiconductor Structures is reduced by a factor≈2π/λ·α(F) relative to the conventionally used avalanche ablation mechanism. For the exemplary case of ablation of silicon using 400 nm radiation herein, this results in a more than six (6) times reduction in the threshold intensity. Using the relation α=4πk/λ, where k is the imaginary part of the complex index of refraction, known as the extinction coefficient, it may be seen the ablation process will proceed through semiconductor linear optical absorption, and not the avalanche (Drude) absorption, provided k≧½. Also note in the Method of Direct Coulomb Explosion in Laser Ablation of Semiconductor Structures, k depends on the applied electric field and therefore field induced shifts of the optical absorption may be used to effect reductions in ablation threshold.

In order to estimate the ablation rates attained in the Method of Direct Coulomb Explosion in Laser Ablation of Semiconductor Structures, we note that due to the exponential decrease of the electron energy into the surface, the ablation depth is of the order of the absorption depth and exhibits a logarithmic dependence on fluence. The ablation depth may therefore be written L_ab˜δ/2×ln{I/I_th}. The number of particles ablated per unit area per unit time can be estimated as j˜L_abN_at/τ_p˜δ/2×N_at/τ_p×ln{I/I_th}. For 400 nm irradiation of silicon using a femtosecond laser pulse, the ablation rate is estimated ˜1.67×10²⁹/cm²·s×ln{I/I_th}. For strong fields ˜10⁷ V/m, we obtained an estimate of I_th˜5×10¹¹ W/cm². Assuming an operational intensity such that I/I_th≈2, we find j˜10²⁹/cm²·s. The number of ablated ions per laser pulse is L_ab×N_at×S, where S is the surface area available for ablation. In the exemplary planar configuration, S is the focal area≈π×10⁻⁸ cm² (S≈π ω², where ω ˜1 micron). Then the number of ablated atoms per laser pulse is ˜10⁸-10⁹. Similarly, in a typical field emission tip application, the ablation rate ramps from zero at threshold to j ˜10²⁹/cm²·s at twice threshold. However the tip surface area is S≈2πr², where r≈50 nm, such that S≈1.6×10⁻¹⁰ cm², which implies a reduction in the number of atoms ablated per pulse to approximately 10⁶. Such large efficiencies of atom yield near threshold are a well above the rates seen in conventional field ion microscopy.

Therefore, as disclosed herein, the Method of Direct Coulomb Explosion in Laser Ablation of Semiconductor Structures provides a new and remarkable capability to effect and control laser ablation, and in so doing, substantially departs from the conventional concepts and designs of the prior art.

As to a further discussion of the manner of usage and operation of the present disclosure, the same should be apparent from the above description. Accordingly, no further discussion relating to the manner of usage and operation will be provided.

With respect to the above description then, it is to be realized that the optimum dimensional relationships for the parts of the disclosure, to include variations in size, materials, shape, form, function and manner of operation, assembly and use, are deemed readily apparent and obvious to one skilled in the art, and all equivalent relationships to those described in the specification are intended to be encompassed by the present disclosure.

Therefore, the foregoing is considered as illustrative only of the principles of the disclosure. Further, since numerous modifications and changes will readily occur to those skilled in the art, it is not desired to limit the disclosure to the exact construction and operation described, and accordingly, all suitable modifications and equivalents may be resorted to, falling within the scope of the disclosure.

REFERENCES

• U.S. Patent Documents:

6,878,900	April 2005	Corkum	216/121.69
6,590,182	July 2003	Domae	216/121.69
6,534,743	March 2003	Swenson	216/121.69
6,046,429	April 2000	Datta	216/121.69
6,534,743	March 2003	Sun	216/121.68

• Other Publications:
• “Scaling laws of femtosecond laser pulse induced breakdown in oxide films,” M. Mero et al., Phys. Rev. B, vol. 71, 115109 (2005).
• “Comment on “Coulomb explosion in femtosecond laser ablation of Si(111),” [Appl. Phys. Lett. 82, 4190 (2003)],” R. Stoian et al., Appl. Phys. Lett. 85(4), 694-695 (2004).
• “Model description of surface charging during ultra-fast pulsed laser ablation of materials,” N. M. Bulgakova et al., Appl. Phys. A 79, 1153-1155 (2004).
• “Electronic transport and consequences for material removal in ultrafast pulsed laser ablation of materials,” N. M. Bulgakova et al., Phys. Rev. B 69, 054102 (2004).
• “Coulomb explosion in femtosecond laser ablation of Si(111),” W. G. Roeterdink et al., Appl. Phys. Lett. 82, 4190 (2003).
• “Surface charging and impulsive ion ejection during ultrashort pulsed laser ablation,” R. Stoian et al., Phys. Rev. Lett., vol. 88, paper 097603 (2002).
• “Laser-induced breakdown and damage in bulk transparent materials induced by tightly focused femtosecond laser pulses,” C. B. Schaffer, A. Brodeur and E. Mazur, Meas. Sci. Technol., vol. 12, pp. 1784-1794 (2001).
• “Ablation of solids by femtosecond lasers: ablation mechanism and ablation thresholds for metals and dielectrics,” E. G. Gamaly et al., Phys. of Plasma, vol. 9, pp. 949-957 (2002).
• “Fundamentals of Semiconductors: Physics and Materials Properties, Third Edition,” P.Yu and M. Cardona, Springer-Verlag, Berlin Heidelberg, 2001.
• “Coulomb explosion in ultrashort pulsed laser ablation of Al₂O₃,” R. Stoian et al., Phys. Rev. B, vol. 62, pp. 13167-13173 (2000).
• “Short-pulse laser damage in transparent materials as a function of pulse duration,” A. Tien et al., Phys. Rev. Lett., vol 82, pp. 3883-3886 (1999).
• “Ultrashort-pulse laser machining of dielectric materials,” M. D. Perry et al., J. Appl. Phys., vol. 85, pp. 6803-6810 (1999).
• “Ultrafast Electron Dynamics in Femtosecond Optical Breakdown of Dielectrics,” M. Li et al., Phys. Rev. Lett., vol. 82, pp. 2394-2397 (1999).
• “Avalanche ionization and dielectric breakdown in silicon with ultrafast laser pulses,” P. P. Pronko et al., Phys. Rev. B, vol. 58, pp. 2387-2390 (1998).
• “Femtosecond Optical Breakdown in Dielectrics,” M. Lenzner et al., Phys. Rev. Lett., vol. 80, 4076 (1998).
• “High power laser semiconductor interactions: a Monte Carlo study for silicon,” K. Yeom, H. Jiang, and J. Singh, J. Appl. Phys., vol. 81, pp. 1807-1812 (1997).
• “Nanoscale modification of silicon surfaces via Coulomb explosion,” H. P. Cheng and J. D. Gillespy, Phys. Rev. B, pp. 2628-2636 (1997).
• “Ablation of Si and Ge using UV femtosecond laser pulses”, G. Herbst et al., Mater. Res Soc. Symp. Proc., vol. 397, pp 69-74 (1996).
• “Femtosecond, picosecond and nanosecond laser ablation of solids,” B. N. Chichkov et al., Appl. Phys. A, vol. 63, pp. 109-115 (1996).
• “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” B. C. Stuart et al., Phys. Rev. B, vol. 53, pp. 1749 (1996).
• “Optical ablation by high-power short-pulse lasers,” B. C. Stuart et al., J. Opt. Soc. Amer. B, vol. 13, pp. 459 (1996).
• “Reduction in multi-photon ionization in dielectrics due to collisions,” D. Du, X. Liu, and G. Mourou, Appl. Phys. B, vol. 63, pp. 617-621 (1996).
• “Laser-Induced Damage in Dielectrics with Nanosecond to Subpicosecond Pulses,” B. C. Stuart et al., Phys. Rev. Letters, vol. 74, pp. 2248 (1995).
• “Thermophysical effects in laser processing of materials with picosecond and femtosecond pulses,” P. P. Pronko et al., J. Appl. Phys., vol. 78, pp. 6233-6240 (1995).
• “Threshold dependence of laser induced optical breakdown on pulse duration,” M. H. Niemz, Appl. Phys. Lett., vol. 66, pp. 1181-1183 (1995). “Laser-induced breakdown by impact ionization in SiO2 with pulse widths form 7 ns to 150 fs,” D. Du et al., Appl. Phys. Letters, vol. 64, pp. 3071 (1994).
• “Dynamical theory of the laser-induced lattice instability of silicon,” P. Stampfli and K. H. Bemmemann, Phys. Rev. B, vol. 46, pp. 10686-10692 (1992).
• “CONTEMPORARY NONLINEAR OPTICS,” Edited by Govind P. Agrawal and Robert W. Boyd, Academic Press, New York, 1992.
• “Laser induced electric breakdown in solids,” N. Bloembergen, IEEE J. Quantum Electron, vol. QE-10, pp. 375-386 (1974).
• “PHYSICAL KINETICS,” E. M. Lifshitz and L. P Pitaevskii, Pergamon, Oxford, 1981.
• “IONIZATION IN THE FIELD OF A STRONG ELECTROMAGNETIC WAVE,” L. V. Keldysh, Sov. Phys. JETP 20, 1307 (1965).
• “THE EFFECT OF A STRONG ELECTRIC FIELD ON THE OPTICAL PROPERTIES OF INSULATING CRYSTALS,” L. V. Keldysh, Sov. Phys. JETP 7 (34), 788 (1958).

Claims

1. A method for obtaining primarily non-thermal ablation of material from a semiconductor or dielectric structure, the method comprising the steps of: a) illuminating an area of a surface of the semiconductor or dielectric structure using a pulsed laser beam, wherein the laser pulse length is commensurate with, or less than, the time it takes for electrons in the semiconductor or dielectric structure to transfer their energy to the atomic lattice, known as the plasma relaxation time;b) illuminating an area of a surface of the semiconductor structure using a pulsed laser beam of step a), wherein the wavelength of the laser beam is selected such that the interband optical absorption provides a carrier production rate in excess of multi-photon or avalanche photoionization rates;c) illuminating an area of a surface of the semiconductor structure using a pulsed laser beam of steps a) and b), wherein the intensity of laser light is selected such that electronic charge is sufficiently evacuated to induce Coulomb explosion of near-surface layers.

2. The method as defined in claim 1, wherein the wavelength of the laser beam is selected such that the linear optical absorption rate may be controlled by an electric field induced redshift of the optical absorption, known as the Keldysh effect, and wherein the linear absorption rate is controlled by the application an external electric field to the semiconductor or dielectric structure.

3. The method as defined in claim 2, wherein nanometer scale semiconductor surface variations are used to provide nanometer scale variations in the externally applied electric field, thereby achieving selective material ablation on scales smaller than one micrometer.

4. The method as defined in claim 1, wherein the ablated ions and/or materials are detected using time of flight detection techniques, position sensitive detection techniques, mass spectrometry, any other detection technique, or any combinations thereof.

5. The method as defined in claim 1, wherein the semiconductor or dielectric structure comprises silicon, carbon, germanium, silicon carbide, silicon germanium, boron, nitrogen, phosphorus, arsenic, or any combination thereof, or gallium arsenide, aluminum arsenide, gallium nitride, aluminum nitride, indium nitride, gallium phosphide, indium phosphide, indium arsenide, or any combination thereof.

6. Apparatus for inducing primarily non-thermal ablation of material from a semiconductor or dielectric structure, the apparatus comprising: a semiconductor or dielectric structure with an exposed surface;a pulsed laser system, providing an pulsed laser beam with pulse width in the range of 10 picoseconds to 10 femtoseconds, and containing at least one wavelength wherein the imaginary part of the complex index of refraction of the semiconductor or dielectric structure, known as the extinction coefficient, has a numerical value greater than ½;an optical system effective to focus the pulsed laser beam onto a focal spot on an exposed surface of the semiconductor or dielectric structure, with maximum light intensity in the range of 1010 W/cm2 to 1013 W/cm2.

7. The apparatus of claim 6, wherein the pulsed laser system provides at least one wavelength nearby a strong interband transition of the semiconductor or dielectric structure, and wherein the apparatus additionally comprises a capacitive DC circuit effective to apply an external electric field to the semiconductor or dielectric structure, and effective to control the optical absorption rate of the semiconductor or dielectric structure.

8. The apparatus of claim 7, wherein the semiconductor or dielectric structure with an exposed surface comprises nanometer scale semiconductor surface variations effective to provide nanometer scale variations in the externally applied electric field, and effective to achieve selective material ablation on scales smaller than one micrometer.

9. The apparatus of claim 6, wherein the apparatus additionally comprises a time of flight detector, a position sensitive detector, a mass spectrometer, any other detection apparatus, or any combination thereof, effective to analyze velocities, positions, masses, chemical compositions, electronic characteristics, or any other information related to the ablated ions or materials.

10. The apparatus of 6, wherein the semiconductor or dielectric structure comprises silicon, carbon, germanium, silicon carbide, silicon germanium, boron, nitrogen, phosphorus, arsenic, or any combination thereof, or gallium arsenide, aluminum arsenide, gallium nitride, aluminum nitride, indium nitride, gallium phosphide, indium phosphide, indium arsenide, or any combination thereof.