4.3.1 Illuminator Design Result
After resolving the obstructions, the resultant paraxial results can be converted to actual mirror surface geometries (i.e. radius of curvatures) through the relationship
Rn= −2 · EFLn. (121)
During the conversion, deviation from paraxial calculations is inevitable, due to the pres-ence of optical aberrations. Figure71shows the illuminator design resulting from a direct conversion from the paraxial parameters, and as can be clearly seen in the lower mag-nified portion of the ray trace diagram, at the mask, the illuminated field from different array elements do not overlap as was predicted by the paraxial system.
Figure 72: The aberration corrected illuminator.
the mirror surface of the field lens is changed to a more complex conic profile. A quick optimization sun by setting the chief ray deviation on the mask as the error function yields the corrected result, shown in Figure72. The required compensation parameters are given in Table11.
Table 11: Obstruction resolved illuminator parameters.
Radius Conic Constant
Pupil Array -1012.7
-Field Array -867.1
-Field Lens 1 -2548.7 -19.314
Field Lens 2 -2648.2 13.124
FA Tilt Adjust Array Element Angle Uppermost 0.045◦
Middle 0.013◦
Lowermost 0.035◦
Figure 73: The eight mirror projector design from which the illuminator specifications are derived from.
4.4 Illuminator Projector Integration
At the final step, the illuminated mask is imaged by the projector. Shown in Figure73 is the lens layout of the projection tool for which the specifications of the illuminator are derived from. The result of the illuminator-projector integration is shown in Figure74, and Figure75is the illumination profile at the mask side and the wafer end respectively.
As can be seen in Figure 74, the illuminator matches well with the projector. In this demonstration of the illuminator design, for the explicit purpose of integration with an existing projector design, the lens data of a projector design in a previous work by the authors [5] (Figure 73) is used. As such, important optical properties of the projector (i.e. entrance pupil location and size, and designed mask height) can be known exactly, to ensure that the resultant illuminator designed matches with the projector.
Between projector layout (Figure73) and the combined layout (Figure74), one might notice a difference in the color of the rays shown, which is the result of the color code used by the optics software. In the projector layout, different ray colors represents light originating from different points on the mask. In the combined layout, the different ray colors now represent light originating from the light reflecting off different array elements
Illuminator
Projector
Figure 74: The combined system of the illuminator and the projector.
X-Field (mm)
Figure 75: Upper: The resultant ringfield illumination profile at the mask side. Lower:
The illumination profile at the wafer end.
on the pupil array and field array, which is distributed uniformly onto the mask as can be seen in the illuminator layout (Figure72), and therefore also uniformly onto the wafer as imaged by the projector.
5 Conclusion
A systematic design method for both the EUVL projector and the illuminator has been described. For the projector, an eight mirror design with 0.4 NA has been demonstrated to verify the capability of this design method. This novel application of GGC on EUVL tool design is beneficial in that the relationship between optical properties and requirements can be derived through GGC and implemented into existing optical design software to assist the design process. With GGC, complex optical systems can be analyzed in greater depth, and in relative ease to conventional ABCD matrix.
For the illuminator, using GGC, the optical properties of various parts of the illumi-nator can be derived, and can be combined to form a general governing equation that, if followed, guarantees the desired optical properties. For simple optical system of few elements, the application of GGC analysis may be overly cumbersome and redundant, however for complex optical systems such as the EUVL illuminator and projector tool, GGC greatly eases the analysis and design difficulty.
Using the obtained governing equations as the kernel, an unobstructed illuminator de-sign can be obtained through application of the Monte Carlo random walk algorithm, and can be implemented into existing optical design software to assist in the optical system optimization.
As a design example, the illuminator specifications are derived from the optical prop-erties of an existing projection tool design (author’s previous work [5]). The result of the illuminator design matches well to the projector specs and properties, and is demonstrated to perform well in providing the necessary illumination as required for the projection tool.
6 References References
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7 Appendices
7.1 GGC Implementation into MATLAB
The following is an implementation of the Gaussian bracket in the MATLAB environ-ment, which can be used to assistance with simple analysis of an optical system.
Basic Definition
temp2 = temp; temp2(:,[1 2])=[];
stopflag = 0;
while stopflag == 0;
c1_ = gb_base(temp1(:,1:2)).*c1 + temp2(:,1).*c2;
c2_ = temp1(:,1).*c1 + c2;
out = c1.*gb_base(temp1) + c2.*gb_base(temp2);
end
7.2 GGC Implementation into Code V
The codes demonstrated in this section is an implementation of the Gaussian bracket and GGC into the commercial optics design software CodeV. This can be used to enhance and finetune its already powerful optical design and analysis capability, allowing for more precise and minute control of a complex optical system, where the optical properties of individual subsystem within the entire system is of importance.
Basic Definition
FCT @gb_base(NUM ^gb_base_in(100), NUM ^gb_base_ind) IF ^gb_base_ind = 4;
^gb_base_out ==
^gb_base_in(1)*^gb_base_in(2)*^gb_base_in(3)*^gb_base_in(4) + ^gb_base_in(1)*^gb_base_in(4) + ^gb_base_in(3)*^gb_base_in(4) + ^gb_base_in(1)*^gb_base_in(2) + 1;
ELS IF ^gb_base_ind = 3;
^gb_base_out == ^gb_base_in(1) + ^gb_base_in(3) + ^gb_base_in(1)*^gb_base_in(2)*^gb_base_in(3);
ELS IF ^gb_base_ind = 2;
^gb_base_out == ^gb_base_in(1)*^gb_base_in(2) + 1;
ELS IF ^gb_base_ind = 1;
^gb_base_out == ^gb_base_in(1);
ELS IF ^gb_base_ind = 0;
^gb_base_out == 1;
END IF
END FCT ^gb_base_out
Gaussian Bracket
! =============================================== Begin Code FCT @gbrac(NUM ^gb_in(100), NUM ^gb_ind)
^gb_c1 == ^gb_in(1);
^gb_c2_ == ^gb_in(2*^gb_n)*^gb_c1 + ^gb_c2;
^gb_c1 == ^gb_c1_;
^gb_c2 == ^gb_c2_;
^gb_n == ^gb_n+1;
^c_v(^k*2-1) == ((IND S^k)-(IND S^k-1))/(RDY S^k);
^c_v(^k*2) == -(THI S^k)/(IND S^k);
END FOR
^c_v(^j*2-1) == ((IND S^j)-(IND S^j-1))/(RDY S^j);
^c_out == @gbrac(^c_v, (^j-^i+1)*2-1);
END FCT ^c_out
FCT @a(NUM ^i, NUM ^j) ! --- GGC (A) FOR ^k ^i (^j-1) 1
^a_v(^k*2-1) == ((IND S^k)-(IND S^k-1))/(RDY S^k);
^a_v(^k*2) == -(THI S^k)/(IND S^k);
END FOR
^b_v(^k*2-1) == -(THI S^k)/(IND S^k);
END FOR
^b_out == @gbrac(^b_v, (^j-^i+1)*2-3);
END FCT ^b_out
FCT @d(NUM ^i, NUM ^j) ! --- GGC (D)
^d_v(1) == -(THI S^i)/(IND S^i);
FOR ^k (^i+1) (^j-1) 1
^d_v(^k*2-2) == ((IND S^k)-(IND S^k-1))/(RDY S^k);
^d_v(^k*2-1) == -(THI S^k)/(IND S^k);
END FOR
^d_v(^j*2-2) == ((IND S^j)-(IND S^j-1))/(RDY S^j);
^d_out == @gbrac(^d_v, (^j-^i+1)*2-2);
END FCT ^d_out
!! ============================================== End Code
7.3 GGC Implementation into Zemax
The codes detailed in this section implements the ability to evaluate the GGC of the cur-rent optical system, and any arbitrary subsystems within, as a merit function operand in ZEMAX.
##========================================================##
## Integration of GGC into ZEMAX
##========================================================##
gb_in(ind1) == ( INDX(k)-INDX(k-1) ) * CURV(k) gb_in(ind2) = -THIC(k) / INDX(k)
NEXT
FOR k, s1+1, s2-1, 1 ind1 = 2*(k-s1) ind2 = 2*(k-s1)+1
gb_in(ind1) = ( INDX(k)-INDX(k-1) ) * CURV(k) gb_in(ind2) = -THIC(k) / INDX(k)
NEXT
gb_in(ind1) = ( INDX(k)-INDX(k-1) ) * CURV(k) gb_in(ind2) = -THIC(k) / INDX(k)
NEXT
ind3 = 2*(s2-s1)+1
gb_in(ind3) = ( INDX(s2)-INDX(s2-1) ) * CURV(s2) gb_ind = 2*(s2-s1)+1
gb_in(ind1) = -THIC(k-1) / INDX(k-1)
gb_in(ind2) = ( INDX(k)-INDX(k-1) ) * CURV(k) NEXT
temp = gb_base_out
gb_c1_temp = temp*gb_c1 + gb_in(2*gb_n+1)*gb_c2;
gb_c2_temp = gb_in(2*gb_n)*gb_c1 + gb_c2;
gb_c1 = gb_c1_temp;
gb_out = gb_c1*temp1 + gb_c2*temp2 ENDIF
gb_out = gb_c1*temp1 + gb_c2*temp2 ENDIF
SUB GB_Base
IF gb_base_ind == 0 gb_base_out = 1 ENDIF
IF gb_base_ind == 1
gb_base_out = gb_base_in(1) ENDIF
IF gb_base_ind == 2
gb_base_out = gb_base_in(1)*gb_base_in(2) + 1 ENDIF
IF gb_base_ind == 3
gb_base_out = gb_base_in(1) + gb_base_in(3) +
gb_base_in(1)*gb_base_in(2)*gb_base_in(3) ENDIF
IF gb_base_ind == 4 gb_base_out =
gb_base_in(1)*gb_base_in(2)*gb_base_in(3)*gb_base_in(4) + gb_base_in(1)*gb_base_in(4) + gb_base_in(3)*gb_base_in(4) + gb_base_in(1)*gb_base_in(2) + 1;
ENDIF RETURN