A Treatise on Side Lobes
Moitreyee Mukherjee-Roy and Navab Singh, Institute of Microelectronics, Singapore -- Semiconductor International, 9/1/2002
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Although reticle enhancement techniques have made significant progress in subwavelength patterning, attenuated phase shift masks (attPSMs) have retained their popularity in the industry. This is because of the relative ease of design and fabrication of attPSMs compared with tri-tone and hard PSMs.
As the name indicates, an attPSM has partially transmitting regions that have opposite phase, replacing the fully opaque chrome of chrome-on-glass masks. Because of their partially transmitting nature, sometimes attPSMs are referred to as leaky chrome — on darkfield attPSMs, the background is leaky, while the features are leaky on brightfield versions. With attPSMs, phase reversal at the edge of the features causes destructive interference, enhancing image contrast and normalized image log slope (NILS),1
and resulting in enhanced process latitudes.
Ideally, the partially transmitting regions do not print. However, the main drawback of attPSMs is unwanted resist erosion caused by side lobes, which are formed as a result of the partial transmission. Higher transmission tends to increase the process latitudes but also increases the intensities of side lobes, which makes their printing inevitable. This article discusses the basic theory of side lobes and the main factors affecting them.
Side-lobe formationThere are basically two main factors governing the formation of side lobes. The first factor is the result of Gibb's phenomenon,2,3 which creates electric field overshoot and undershoot at the transition between bright and dark areas. This is a result of the non-uniform convergence of the Fourier series for discontinuous functions. The non-uniform convergence results in 9% overshoot and undershoot near a discontinuous interval from fully transmitting to partially transmitting region. The second factor is the background field. The superposition of the first factor with the second produces the regions of higher intensity that are known as side lobes.
As stated earlier, the intensity of a side lobe increases with higher transmission. The equation governing the intensity of the side lobe for coherent light can be given by:
Iside-lobe = |Emin|2
= E2 * (1.09 ÖT + 0.09)2
where T is the transmission of the partially transmitting region. Hence, for an attPSM with 8% transmission, the Iside-lobe can be calculated as 0.159E2, while a binary mask with no background transmission will have a side-lobe intensity of 0.0081E2, a significant difference. Although Gibb's phenomenon occurs with a binary mask, the resulting intensity is too small to cause resist erosion. Resist erosion is inevitable, however, when using a PSM with higher transmissions.
The side-lobe intensity given by the Equation is the intensity when there is no interaction with neighboring features. The worst case would be when the side lobes of diagonally located features interfere constructively. In this case, the intensity of the side lobe could be as high as 16× that calculated by the Equation.
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| 1. This graph shows the intensity profile at the transition edge with a binary mask and an attPSM with 24% transmission. |
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| 2. In experimental SEMs,
side lobes are seen inside a line (left) and outside a trench
(right). |
Feature size affects the placement and intensity of secondary maxima causing side lobes. For small contact holes — those equal to or less than the width of point spread function (PSF) (0.66 l/NA) — the location of secondary maxima is governed by PSF (~0.8 l/NA from the center of the hole). Similarly, the line spread function (LSF) governs for spaces (~0.7 l/NA from the center of the feature).4,5 With an increase in the feature size beyond PSF or LSF, the secondary maxima shift out nearly equal to the shift of the feature edge.
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| 3. A PROLITH simulated
graph shows the location and relative intensity vs. the distance from
feature center. The features considered are holes ranging 160-500 nm in
size (s
=0.31, NA=0.68, l=248 nm). |
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| 4. Feature size dependency of side lobes at a coherency of 0.55.
Design size and duty ratios are labeled. |
Pitch is an important parameter and decides the various possible interactions of the secondary maxima. The constructive interference among the secondary maxima of nearest neighbors increases the intensity of side lobes. The worst situation is when the secondary maxima of four neighboring contact holes interact at their diagonal interaction and produce maximum intensity regions. It occurs for the pitches having diagonal distance equal to double the distance of secondary maxima from the feature center. The other but relatively less severe situation is when the secondary maxima of two neighboring contact holes interact at their common center. This occurs for pitches equal to double the distance of secondary maxima from the feature center.
The third and least severe possibility is the case of no interaction of secondary maxima when the pitch is larger than or equal to double the distance of second secondary minima from the feature center. The dense patterns (e.g., 1:1) generally do not have side lobes because the first-order maximum from each hole overlaps into an adjacent hole. However, when the overlap occurs outside the actual pattern, the extra pattern is printed. Experimental verification of the above stated facts can be observed in Figure 5.
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| 5. Top-view SEMs show the effects of pitch on a 180 nm via. The left
image shows prominent side lobes at diagonal locations for a 1:1.5 pitch.
The absence of side lobes at the edge proves that the position of the
first secondary maxima overlaps with the primary minima of the adjacent
hole. The center image shows side lobes at horizontal and vertical
locations for a 1:3 pitch. At this pitch and hole size, the first
secondary maximas of the adjacent holes overlap at the horizontal and
vertical locations, producing side lobes. Resist erosion around the via is
caused by Gibb’s phenomenon. The right image shows an isolated via, where
there is no interaction of secondary maxima. The first ring is a wall
caused by minimal resist erosion due to minimum electric field at the
feature boundary. The second ring is resist erosion caused by first
secondary maxima around the mother feature. |
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| 6. Intensity profile for
a 180 nm space and hole (s =0.31, NA=0.68,
l=248 nm). |
There are two different mechanisms behind side-lobe formation in high-transmission attPSMs: the background field and Gibb's phenomenon of field overshoot at a discontinuity. The forbidden pitch for a particular feature size and shape should be investigated in connection with location and intensity of side lobes, and the most affected pitches should be avoided. Higher-transmission masks have more propensity for side lobing, so should be avoided for via patterns because the ratio of first ripple to central maxima is much higher for a contact hole than it is for a trench pattern.
| Author Information |
| Moitreyee Mukherjee-Roy is a member of the technical staff at the Institute of Microelectronics . She is leading pattern transfer and PECVD groups for dual-damascene copper processes. She has a master's degree in materials science and engineering from the University of Kentucky. She worked previously at Texas Instruments, developing logic and DRAM products. |
| Navab Singh is a senior research engineer on the pattern transfer team at the Institute of Microelectronics. He has master's degrees in physics and solid-state materials from the Indian Institute of Technology Delhi. He worked previously as a photolithography engineer, developing 0.15 µm DRAM and DDR technologies. |
| References |
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