Electronics Workforce Development System Photolithography Module
Introduction Photolithography Module This module will teach students the different types of microlithographic systems being used today, their advantages and disadvantages, photoresist types and properties, photolithography alignment systems and their characteristics, optical effects in proximity and projection systems such as near-field and far-field diffraction, resolution, numerical aperture, depth of field, etc. It is complemented by a series of hands-on laboratory experiments. Module Design The Photolithography module was prepared to form a part of the Semiconductor Manufacturing Technology I course at Valencia Community College based on recent needs identified by high-technology business and industry representatives. The module is designed to be used in conjunction with the book by Peter Van Zant. Microchip Fabrication. 4 th ed. New York: McGraw-Hill, 2000. As such, it contains an extensive outline of the topics to be covered in the course, as well as additional material from other references. This module is one of a series of modules that form part of the Electronics Workforce Development System. About the Electronics Workforce Development System The Electronics Workforce Development System is aiming to increase the number of skilled technicians available in the engineering/electronics field. The focus of this system is to improve the quality of courses in basic mathematics, science and engineering core courses as well as more specialized engineering technology courses that yield technicians needed by the electronics industry. After completing their education, community college graduates may elect to immediately seek employment in the engineering technology field or choose to pursue a four-year degree. Valencia Community College, Hillsborough Community College, Brevard Community College and Seminole Community College have an articulation agreement with the University of Central Florida to offer a Bachelor of Science degree program in Electrical Engineering Technology (BSEET) or Engineering Technology (BSET). About the NSF The National Science Foundation (NSF), through the Advanced Technological Education (ATE) program has provided support for this project to strengthen science and mathematics preparation of technicians being educated for the high-performance workplace of advanced technologies. Focusing on both national and regional levels, the ATE centers and projects result in major improvements in advanced technological education, serve as models for other institutions and yield nationally usable educational products. For further information regarding this module, please contact: William Morales, wmorales@valencia.cc.fl.us i
Course Information Photolithography Module Course Outcome Summary Title Photolithography Module part of course EST 1300 Semiconductor Manufacturing Technology I Course Number EST 1300 Credits 3 Organization Valencia Community College Developer William Morales Development Date 03/19/02 Instructional Level Associate in Science (A.S.) Instructional Area Electronics Engineering Technology Types of Instruction (SMT I course) Instructional Type Contact Hours Outside Hours Credits Classroom 3 3 Laboratory Totals 3 3 Target Population This course has been designed for students enrolled in the Electronics Engineering Technology (EET) program leading to an A.S. Prerequisites None Course Description This module will teach students the different types of microlithographic systems being used today, their advantages and disadvantages, photoresist types and properties, photolithography alignment systems and their characteristics, optical effects in proximity and projection systems such as nearfield and far-field diffraction, resolution, numerical aperture, depth of field, etc. It is complemented by a series of hands-on laboratory experiments. Textbooks Van Zant, Peter. Microchip Fabrication. 4 th ed. New York: Mc Graw-Hill, 2000. Supplies EMS Semiconductor Manufacturing Equipment (supply is required) ii
Photolithography Syllabus Note: This module was designed to be a two-week section of the course EST 1300 Semiconductor Manufacturing Technology I. Course Information Title Photolithography Module part of course EST 1300 Semiconductor Manufacturing Technology I Course Number EST 1300 Credits 3 Organization Valencia Community College Instructor William Morales Office 9-220 Phone (407) 582-1945 E-mail wmorales@valenciacc.edu Fax (407) 582-1900 Office Hours TBA Prerequisites None Course Description This module will teach students the different types of microlithographic systems being used today, their advantages and disadvantages, photoresist types and properties, photolithography alignment systems and their characteristics, optical effects in proximity and projection systems such as nearfield and far-field diffraction, resolution, numerical aperture, depth of field, etc. It is complemented by a series of hands-on laboratory experiments. Textbooks Van Zant, Peter. Microchip Fabrication. 4 th ed. New York: Mc Graw-Hill, 2000. Supplies EMS Semiconductor Manufacturing Equipment (supply is required) iii
Material to be Covered in Photolithography Section of Course: Session Lesson Topic 1 The Electromagnetic Spectrum: Characteristics of electromagnetic radiation at different wavelengths, introduction of the concepts of period and frequency of a wave 2 10 Types of Microlithography: Photolithography, Electronbeam lithography, X-ray and Ion-beam lithography 3 10 Photoresists: characteristics of photoresists, positive and negative resists, spin coating and soft bake 4 8, 10 Wafer Exposure Systems: Light sources, alignment systems, contact, proximity and projection printing principles 5 10 Exposure System Optics: Near-field and far-field diffraction effects, resolution, numerical aperture (NA), depth of focus (DOF), the modulation transfer function (MTF) and spatial coherence 6 8 Photomasks: light-field and dark-field masks, composition, use and properties iv
Core Abilities and Indicators Matrix Core Ability 1. Thinks Critically 2. Learns Efficiently 3. 4. 5. Applies Knowledge Successfully Communicates Effectively Works Well With Others Indicator 1. Learner is able to link information from multiple fields into a coherent picture of the whole. 2. Learner is capable of abstract thought and theoretical insight. 3. Learner can identify a problem and come up with multiple solutions. 4. Learner can break down a problem into its constituent parts and analyze each part. 5. Learner can evaluate the problem and determine an appropriate solution for a particular situation. 1. Learner takes responsibility for his/her own learning. 2. Learner identifies and studies relevant facts. 3. Learner organizes information effectively. 4. Learner presents knowledge clearly and concisely. 5. Learner uses the appropriate resources to enhance the learning process. 1. Learner understands the relationship between theoretical concepts and their practical application. 2. Learner can evaluate the limitations of applying abstract knowledge to real-world solutions. 3. Learner can evaluate the usefulness of theoretical insight to practical applications. 4. Learner is able to extrapolate the solution to future applications from situations encountered. 5. Learner can successfully solve real-world problems with knowledge acquired conceptually. 1. Learner is able to express him/herself concisely. 2. Learner is able to convey complex technical information in an understandable manner. 3. Learner communicates effectively using the written word. 4. Learner knows how to present data using the best tools available. 5. Learner is able to summarize the most important fact or idea of a given topic. 1. Learner can work cooperatively. 2. Learner can communicate with others effectively. 3. Learner is a team player. 4. Learner can assume responsibility in a group environment. 5. Learner is sensitive to the opinion of others. v
Competencies and Performance Standards Matrix Competency Criteria Conditions Learning Objectives 1. Understand what the Electromagnetic Spectrum Is Performance will be satisfactory when: 1. Learner understands what an electromagnetic wave is. 2. Learner clearly grasps the concepts of frequency and period of a wave and can calculate both. 3. Learner knows qualitatively the different types of electromagnetic radiation and their common uses. Competence will be demonstrated through: 1. Homework problems. 2. Written examination. 1. Develop an appropriate understanding of the properties of each type of radiation. 2. Articulate the physical variables that describe a wave. Competency Criteria Conditions Learning Objectives 2. Understand the Different Microlithographic Processes Performance will be satisfactory when: 1. Learner can name the different types of microlithographic systems currently in use. 2. Learner understands the advantages and disadvantages of each method. 3. Learner can effectively communicate how each of the different processes work. 4. Learner is capable of discussing the theoretical limitations of each method. Competence will be demonstrated through: 1. In-class exercises. 2. Out-of-class research. 3. Written examination. 1. Develop a clear understanding of the tradeoffs involved in using different lithographic schemes. 2. List manufacturing processes that will favor one lithographic method over another. 3. Comprehend why photolithography is still the most popular form of lithography today. vi
Competency Criteria Conditions Learning Objectives 3. Develop a Working Knowledge of Photoresists Performance will be satisfactory when: 1. Learner understands what a photoresist is and what it is used for. 2. Learner clearly grasps the similarities and differences between positive and negative photoresists. 3. Learner can communicate effectively the main characteristics of a photoresist. 4. Learner is able to discuss the different steps involved in the photoresist spin coating and the soft bake process. Competence will be demonstrated through: 1. Practical lab experiments. 2. Written examination. 3. Homework assignments. 1. Develops knowledge of where the different soft bake types are used and why. 2. Articulate other process variables that can affect the photolithography process, in addition to exposure. Competency Criteria Conditions Learning Objectives 4. Study and Understand Wafer Exposure Systems Performance will be satisfactory when: 1. Learner can list the two different types of light sources used and their properties. 2. Learner is able to discuss the three main types of alignment systems and their advantages and disadvantages. 3. Learner possesses a clear understanding of the difference between scanning projection systems and step-and-repeat projection systems. Competence will be demonstrated through: 1. In-class demonstrations. 2. Homework assignments. 3. Laboratory exercises. 1. Understands the history of wafer exposure systems. 2. Understands where each system can be applied in an appropriate way. vii
Competency Criteria Conditions Learning Objectives 5. Understand Issues Associated with Exposure System Optics Performance will be satisfactory when: 1. Learner has understood the difference between farfield and near-field diffraction effects. 2. Learner possesses a clear understanding of how diffraction effects limit the resolution of proximity and projection printing systems. 3. Learner can explain each of the parameters used to characterize printing systems such as: resolution, NA, DOF and MTF. Competence will be demonstrated through: 1. Active class participation. 2. Laboratory exercises. 3. Written assignments. 1. Acquire a qualitative and quantitative understanding of the characteristics desired in a proximity/projection system. 2. Understands theoretical limits to the projection lithography process. Competency Criteria Conditions Learning Objectives 6. Understand the Use and Types of Photo Masks Performance will be satisfactory when: 1. Learner is able to explain the use of the photo mask in the optical lithography system. 2. Learner can distinguish between the different types of masks (light vs. dark field) and their characteristics. 3. Learner is capable of expressing the advantages of using phase-shifting masks. Competence will be demonstrated through: 1. Homework problems. 2. Examinations. 1. Knows the suitability of each mask, depending on photoresist used. 2. Understands the effect of the mask upon the system resolution and other parameters. viii
Table of Contents Lesson Title Page 1 The Electromagnetic Spectrum 2 2 Types of Microlithography 5 Photolithography 6 Electron-beam Lithography 8 X-ray Lithography 9 Ion-beam Lithography 11 3 Photoresists 13 Introduction 14 Photoresist Spin Coating 17 Soft Bake 20 4 Wafer Exposure Systems 22 Light Sources 23 Alignment Systems 25 Contact Printing 26 Proximity Printing 27 Projection Printing 28 5 Exposure System Optics 31 Diffraction Effects in Photolithography 32 Resolution of Projection Systems 36 The Numerical Aperture 38 Depth of Focus 40 The Modulation Transfer Function 42 Spatial Coherence 43 6 Photo Masks 45 References 48
Lesson 1 The Electromagnetic Spectrum 2
The Electromagnetic Spectrum The term electromagnetic spectrum is used to refer to the many different kinds of electromagnetic radiation, which are classified according to their frequency or wavelength. They all propagate at the same speed, i.e. the speed of light, through a vacuum. Types of Electromagnetic Waves: Gamma rays: Have the shortest wavelengths (less than 10pm) and are the most penetrating of all electromagnetic radiations. Exposure to intense gamma radiation can be lethal. They are emitted as a result of atomic nuclei transitions and elementary particle decay. 3
X-rays: Wavelengths vary from 0.01nm to 10nm and are typically produced when electrons are decelerated. X-rays can easily penetrate soft tissue. Ultraviolet: Range in wavelength from 1nm to 400nm and are produced mainly from thermal sources (blackbody radiation.) Exposure can cause sunburn, and prolonged exposure can cause skin cancer. Visible Light: Has wavelengths from about 400nm (violet) to about 700nm (red). The Sun emits its most intense radiation in the visible range. This is the only region of the electromagnetic spectrum that humans can see. Visible Light Spectrum Infrared: Wavelengths from about 700nm to about 1mm are in the infrared region. Bodies that are at a temperature between 3K and 3000K emit most of their radiation in the infrared; therefore it is sometimes called heat radiation. Microwaves: Microwaves are short radio waves with wavelengths in the 1mm to 1m range. They are used extensively in communications and are commonly produced by electromagnetic oscillators. Radio Waves: Have wavelengths longer than 1m. They are used in AM, FM and TV broadcasts. In nature, radio waves are emitted by trapped electrons spiraling in a magnetic field (synchrotron radiation). 4
Lesson 2 Types of Microlithography 5
Photolithography UV Light Source Mask Projection Lenses Conventional UV Photolithography Photolithography, also called optical lithography, is the most common type of lithographic system employed in semiconductor manufacturing today. It uses ultraviolet (UV) light (436nm or 365nm) or extreme ultraviolet (248nm or 193nm) to develop a substance called a photoresist or resist. Advantages: Wafer High throughput ( 50 wafers/hr) High resolution ( 0.10 m at a wavelength of 193nm EUV) Established technology 6
Disadvantages: Equipment is expensive (for projection systems) due to the very high quality optical components needed ( $10 million per system) Diffraction effects limit the minimum allowable resolution EUV Source (Laser) Mask Reflecting Optics EUV Photolithography System Wafer EUV Photolithography uses the same principles as conventional UV lithography except that the wavelength of the light is shorter. This requires the use of metal reflectors to concentrate and project the mask image onto the wafer, since the light will not pass through ordinary lenses at these short wavelengths. Another characteristic is that the masks used in this type of system consist of mirrors that reflect or absorb the light. 7
Electron-beam Lithography Source Mask Electromagnetic Coils to Focus Beam Aperture to Minimize Scattered Electrons E-beam lithography uses electrons instead of electromagnetic waves as its source. The wavelength of electrons is on the order of 4x to 5x shorter than that of UV light and therefore a higher level of resolution is made possible. Advantages: Very high resolution ( 1 angstroms) Greater depth of focus (DOF) than photolithographic systems Direct patterning without a mask is possible 8
Disadvantages: Low throughput ( 5 wafers/hr at 0.1 m resolution) Electron scatter effects present High cost (several million dollars per system) Commercial E-beam System X-ray Lithography Source: Synchrotron Mask Wafer In X-ray lithography, X-rays are used because they have a much smaller wavelength than UV sources (0.4nm 50nm) and therefore higher resolution. However, even though X-ray systems 9
have been around since the 1970s, they have not gained commercial acceptance, primarily because of the continued evolution and improvement in optical systems. Advantages: Higher resolution than optical systems (<0.1 m) Higher throughput than E-beam lithography No depth of focus (DOF) constraint Immunity to organic contamination (fewer defects) Disadvantages: Penumbral effect blurs Lateral magnification errors Difficulty in making X-ray masks Geometry of X-ray Lithography Showing the Penumbral Blurring Effect ( ) 10
Ion-beam Lithography Ion Source Mask Electrostatic Coils to Focus Beam Wafer Ion-beam systems are very similar to E-beam systems, but the chief advantage of the ion-beam systems is their negligible scatter characteristics. Also, their depth of penetration is less and takes place over a well-defined range. Advantages: Higher resolution than optical, X-ray and E-beam lithography ( 0.02 m) No diffraction effects and less scatter than E-beam systems Disadvantages: Current densities 1 to 2 order of magnitude less than E-beam systems Chromatic aberrations are introduced due to large energy spread of the beam 11
Comparison of Electron (left) vs. Ion Beam (right) Scattering Profiles Types of Lithographic Methods 12
Lesson 3 Photoresists 13
Photoresists A photoresist is a compound designed to chemically react when exposed to light They are fabricated from hydrocarbon-based materials A solvent is used to control the viscosity of the photoresist There are two kinds of resist in use: Positive Photoresists Negative Photoresists Positive and Negative Photoresists 14
Positive Photoresists: Most commonly used resist type in semiconductor manufacturing today Absorbs energy in the form of light and reacts chemically to become more soluble in the developer solution Consists of: Photosensitive compound Base resin Organic solvent (to control viscosity) Have a better resolution than negative resists Are used with a dark-field mask Negative Photoresists: Used extensively up to the mid-1970s Absorbs energy in the form of light and reacts chemically to become less soluble in the developer solution Consists of: Polymer Photosensitive compound Have poorer resolution than positive photoresists; therefore, as feature size began to shrink, it fell into disuse Are used with light (clear) field masks Characteristics of Photoresists: The four most important characteristics of a resist are: Resolution: What are the smallest features that can be reproduced Adhesion: How well the resist adheres to the surface of the wafer 15
Sensitivity: Quantifies how much energy (light) is needed to expose the resist (make it react chemically); it is measured in mj cm -2 Contrast: Quantifies how well the resist is able to distinguish between the light and dark areas projected by the lens system The higher the sensitivity (smaller number) the better The photoresist contrast is given by the following equation: 1 E log E where, = photoresist contrast (dimensionless) E f = dose required to produce 100 percent film thickness E t = dose at which exposure begins to have an effect f t 16
Photoresist Spin Coating Goal is to apply a very thin and uniform layer of photoresist on top of the wafer Typical resist thickness is between 0.5 m and 1.5 m Typical required uniformity is 0.01 m ( 1 percent) This is accomplished by the spin coating process Wafer is held on a spinning chuck (rotating disk) by means of a vacuum In dynamic dispense systems, the resist is dispensed by means of a dropper or syringe-like delivery system, while at the same time, the wafer is spun at a low speed ( 500rpm) To assure a very thin and uniform coating, after all resist has been dispensed, the wafer is spun at a high rate (from 1500rpm to as high as 6000rpm) 17
Photoresist Spin Coating with Moving Arm Dispense The thickness of the resist layer is determined by: Resist viscosity Spinner velocity (rpm) Surface tension Drying characteristics The formula for calculating the resist thickness is: where, k = spinner constant ( 80-100) p = percent of solids in resist w = rotational speed (in thousands of rpm) t kp w 2 1 2 18
The spinner acceleration is also an important parameter in determining the final thickness of the resist Artifacts introduced by the spin coating process: Striations: Variations in resist thickness resulting from non-uniform drying Edge beads: Rise in the thickness of the resist at the edge of the wafer In moving-arm dispensing, the dispensing arm moves slowly from the center of the wafer towards its periphery Moving-arm dispensers can achieve a more uniform coating thickness while using less resist per wafer 19
Soft Bake Process used to evaporate the solvent from the photoresist Since solvent was added to control the viscosity of resist during spin coating, it is no longer needed If solvent is left in photoresist, it can interfere in the exposure process There are four main types of systems used to evaporate the solvent: Hot Plate: In this system, a hot plate is used to heat up the wafer from below. The wafer then heats the photoresist and the solvent is evaporated. One of the advantages of this process is that the heating takes place from the bottom of the resist to the top. This prevents solvent from being trapped underneath heated resist. Hot plate heating is fast and reliable. A typical cycle might be 75 C to 85 C for 45 seconds. Convection Oven: Hot Plate Soft Bake The wafer is enclosed in a convection oven where heated air or nitrogen is circulated using blowers. The heating of the resist occurs from the top down. This can result in trapped solvent inside the resist. It is also slower than hot 20
plate heating. A typical process might be 90 C to 100 C for 20 minutes. Infrared Oven: In this method, intense infrared radiation is applied to the surface of the wafer. The IR radiation travels through the photoresist without heating it and strikes the wafer. The wafer then heats up, and the evaporation of the solvent begins. Since the wafer is the one that is heated, the process is similar to hot plate heating in the sense that the temperature increases from the bottom up. This eliminates the possibility of solvent being trapped in resist. Microwave Oven: Microwave heating is very similar to IR heating but progresses at a faster rate. Typical process time is well under one minute. The fast heating time means that the solvent can be evaporated just after spin coating. Typical Dissolution Rate vs. Temperature Curve 21
Lesson 4 Wafer Exposure Systems 22
Light Sources High Pressure Mercury (Hg) Arc Lights: Historically, have been used as the primary light source in UV photolithographic systems Lamps consume about 1kW of power Mercury has several emission lines in the UV range: G-line (436nm) H-line (405nm) I-line (365nm) In the early 90s, systems using the G-line were the most common for photolithography applications. As the decade progressed however, they were gradually replaced with equipment operating at the I- line. Hg Arc Lamp 23
Excimer Laser Excimer Lasers: Used where shorter UV wavelengths (DUV and EUV) are required Essentially monochromatic (single wavelength) sources Principal lasers used are: KrF (248nm) ArF (193nm) KrF lasers are typically used in the microelectronics industry for feature sizes 0.18 m Typical output specifications for a KrF laser are 10W of average optical power delivered at a 1kHz repetition rate. ArF lasers are used for feature sizes in the 0.13 m range and below ArF lasers, although offering a shorter wavelength (higher resolution), offer less output power ( 5W optical power at 1kHz repetition) than KrF lasers 24
Alignment Systems The Three Alignment Systems at a Glance: Contact Printing: Mask is placed in direct contact with the photoresist layer on the wafer. Mask size = image size. Not limited by diffraction effects. Proximity Printing: Mask and wafer are separated by a small distance ( 5-25 m). Mask size = image size. Limited by nearfield (Fresnel) diffraction. Projection Printing: Image of mask is projected on to wafer by lenses. Mask size is 4x-5x greater than the image size. Limited by far-field (Fraunhofer) diffraction. 25
Light Intensity Produced by the Three Exposure Methods Contact Printing Oldest and simplest method of photolithography Mask is in direct contact with the photoresist layer on the wafer With mask in direct contact with the wafer, diffraction effects are eliminated Method is capable of high-resolution printing Equipment is relatively inexpensive The contact that occurs between the mask and the wafer causes damage to both and results in high defect rates The high defect rates mean this system cannot be used for highvolume production Requires a mask that is the same size as the image to be formed on the wafer 26
Proximity Printing Mask and wafer are separated by a gap of approximately 5-25 m. This introduces near-field (Fresnel) diffraction effects, which reduce resolution when compared with contact printing. Since the mask and the wafer are not in contact, this method avoids damage to either and reduces the number of defects produced. Because of diffraction effects, it is not possible to make features smaller than 2 m with UV sources. Proximity printing equipment is much cheaper than projection printing equipment. Requires a mask that is the same size as the image to be formed on the wafer (1x mask). This increases mask manufacturing and verification complexity. 27
Projection Printing Most common exposure method used today Achieves high resolutions without the problems of mask-wafer interaction Resolution is limited by far-field (Fraunhofer) diffraction effects High throughput (50 wafers/hr typical) Expensive ( $10 million) Modern Projection Lithography System 28
There are two main types of projection printing systems: Scanning Projection Printing: A narrow slit of light (aperture) is introduced into the light path The slit makes it easier to correct optical aberrations of the projection system The image of the entire mask is then scanned across the wafer Step-and-repeat Projection Systems: Most common projection system used today In step-and-repeat systems (steppers), a small portion of the wafer (only a few cm 2 ) is imaged and projected at a time The wafer is then physically moved so the next portion of the wafer can be exposed The process is then repeated until the entire surface of the wafer is exposed 29
Modern steppers use automatic pattern recognition and alignment system Approximately one to five seconds to align and expose Different Types of Projection Lithography Systems and their Variations 30
Lesson 5 Exposure System Optics 31
Diffraction Effects in Photolithography Diffraction: An Example of Diffraction Diffraction results when light (or any other wave) passes through a narrow aperture (slit), where the aperture dimensions are comparable to that of the wavelength of the light There are two methods to calculate diffraction effects, depending on the distance between the aperture and the image plane (mask to wafer distance): Near-field or Fresnel diffraction; When distance between aperture and image plane is small Far-field or Fraunhofer diffraction: When the distance between the aperture and image plane is large Diffraction effects limit the minimum size of features that can be printed with photolithography methods 32
Near-field (Fresnel) Diffraction (Contact and Proximity Printing) When the mask and wafer are separated by a small gap the resulting light intensity pattern on the wafer has several distinct characteristics: The intensity increases gradually near the edges, broadening the area of exposed resist when compared to the mask The intensity of light inside the mask aperture is non-uniform (ringing) The first characteristic means that there will be a limit to the minimum size feature we can print with proximity lithography. It is given by the equation: W min where, W min = minimum resolvable feature size = wavelength of light g = gap separation g 33
The equation above is valid for < g < W 2 /. Since in proximity printing the gap separation g is from 5 m to 25 m, it turns out that at ultraviolet (UV) wavelengths the minimum feature size is in the order of a few m. Far-Field (Fraunhofer) Diffraction (Projection Printing) Single-Slit Diffraction: Single-slit Diffraction Generated by a Laser If light is passed through a slit of width b and is then focused by lens onto a screen, the intensity pattern at the screen surface is given by the following equation: 34
I( ) I 0 sin 2 2 ( bsin )/ where, I( ) = intensity at angle I 0 = intensity at = 0 b = slit width = wavelength of light The width of the central maximum increases as the slit width is decreased. Diffraction at a Circular Aperture: Circular Aperture Diffraction Geometry If light is made to travel through a very small circular aperture, the result is a diffraction pattern similar to the one shown at right, which was produced using a laser. Because of diffraction effects, the image consists of a bright center disk surrounded by a series of increasingly faint diffraction rings. This image is known as an Airy disk, in honor of 19 th century scientist Sir George Airy who was the first to derive a mathematical expression for the central intensity maximum. 35
The diameter of the central maximum (q1) is given by: q f 1.22 1. 2a 22 1 where, a = the radius of the obstruction d = the diameter of the obstruction f d It is apparent that as the aperture diameter decreases, the diameter of the central maximum increases. Resolution of Projection Systems and Rayleigh s Criterion Resolution of Two Point Sources When we try to image two point sources (similar to trying to image two adjacent features on a mask), what is the minimum distance between the sources that will still enable them to be resolved? The geometry of the setup is shown in the figure above. 36
The image formed will be of two Airy disks (see the figure below.) As we move the two sources together, it becomes harder and harder to distinguish the combined image from that of a single source (figure below): Rayleigh s criterion for the resolution of the two images occurs when the center of one of the Airy disks is at the first minimum of the other Airy disk. Using this criterion, the formula for the resolution (R) of two point sources becomes: R 1. 22 f d 37
The above expression is equal to the resolving power of the projection lens and limits the minimum feature size that can be imaged by the projection system. The Numerical Aperture (NA) Looking at the figure above, it is possible to express Rayleigh s criterion in a different form. If f >> d then we can make the approximation: nsin d 2 f where, n = the index of refraction of the medium between the sources and the image plane (for lithography systems the medium is air and therefore, n = 1) angle = the maximum acceptance angle that can be focused by the lens 38
Substituting the above expression into Rayleigh s criterion, we get: R 0.61 0.61 k nsin NA 1 NA The term n sin is called the Numerical Aperture (NA) of the lens and is a measure of its ability to collect light. Since the equation for the resolution was derived for a circular aperture, in photolithography the constant value of 0.61 is usually replaced by k 1 in order to reflect the different shapes found on the mask. A typical value for k 1 is between 0.6 and 0.8. Typical UV Projection Lens Assembly 39
It is apparent that to improve resolution we can do two things: Reduce the wavelength of light (increase its frequency) Increase the Numerical Aperture (NA) of the lens The first option is the reason why modern optical lithography uses UV and deep-uv sources (with wavelengths of 436nm and below) to project the mask image onto the wafer, since UV provides a higher resolution than visible light. Larger lenses have a higher NA, and therefore, can also increase the resolution of the optical system. Depth of Focus (DOF) Geometry for Depth of Focus (DOF) Calculation Rayleigh s criterion for depth of focus is that the path difference between the axial ( = 0) rays and the rays at the edge of the entrance aperture be less than /4. 40
The path difference of the two rays can be calculated by means of the figure above as: 4 cos If we assume that the angle is small, we can replace cos by a power series and truncate the series after the quadratic term: 1 cos 4 1 1 Since is small, we can make the substitution sin = NA into the expression above to obtain the DOF, 2 2 2 2 DOF 0.5 NA 2 k 2 NA 2 The factor k 2 is introduced in order to take into account varying process parameters and different feature sizes. As can be seen, a larger NA means a smaller DOF and vice versa. Therefore, there is a reduction in the DOF when trying to improve the optical resolution R by increasing the NA of the projection system. 41
The Modulation Transfer Function (MTF) Because of diffraction effects, a series of equally spaced lines and spaces on the mask will not produce a perfectly white and black image on the wafer. This effect is shown below: A good measure of the contrast in the image is the Modulation Transfer Function (MTF), defined as: MTF I I MAX MAX I I MIN MIN where, I = the intensity of light at the image plane Generally speaking, an MTF value of 0.5 or above is needed for a good exposure. As the feature size decreases (lines get closer together), the contrast decreases as shown in the figure below. 42
Graph of the MTF vs. Feature Size The value of MTF vs. feature size is also dependent on the degree of spatial coherence of the illumination. This is discussed below. Spatial Coherence The spatial coherence of a source is the degree to which light from the source is in phase. It determines the angular spread of light from the source. A point source would be considered completely coherent ( = 0), while a source of infinite extend would be completely incoherent ( = ). The degree of spatial coherence ( ) of a source is given by the following equation: light_ source_ diameter condenser_ lens_ diameter s d NA NA condenser projection 43
A graph of the MTF vs. the degree of spatial coherence of the source is shown below. Spatial Coherence vs. MTF An increasing amount of spatial coherence results in a decrease of the MTF for large features but an improvement in the MTF for small features. This is, almost always, a good tradeoff. Modern projection imaging systems have a spatial coherence of between 0.4 and 0.7, with a value near 0.7 considered the optimum. 44
Lesson 6 Photo Masks 45
Photo-Masks Photo-masks are usually made using an E-beam lithography process There are several substrate (clear) materials in use: Quartz Low expansion (LE) glass Sodalime glass Opaque materials used are: Chrome (Cr) Emulsion Iron oxide (Fe 2 O 3 ) The Cr on quartz mask type is necessary when performing deep UV photolithography A master mask is usually made of quartz substrate and then transferred to cheaper LE or sodalime glass to be used in production lithography systems Masks come in two polarities: Light field: Mostly clear, drawn features are opaque Dark field: Mostly opaque, drawn features are clear 46
Phase-shift masks are used to enhance the resolution of optical lithography Phase-shift masks can also be used to increase the depth of focus (DOF) at the regular resolution Phase-shift Mask Construction Resolution Enhancement by Use of a Phase-shift Mask 47
References Baker, R. Jacob, Harry W. Li and David E. Boyce. CMOS Circuit Design, Layout and Simulation. New York: IEEE Press, 1998. Kuecken, John A. Fiberoptics. Blue Ridge Summit, PA: Tab Books, Inc., 1980. Plummer, James D., Michael Deal and Peter B. Griffin. Silicon VLSI Technology. Upper Saddle River, NJ: Prentice Hall, 2000. Resnick, Robert, David Halliday and Kenneth S. Krane. Physics. 2 nd ed. New York: John Wiley and Sons, 1992. Thompson, Larry F., C. Grant Wilson and Murrae J. Bowden, eds. Introduction to Microlithography. 2 nd ed. Washington, DC: American Chemical Society, 1994. Van Zant, Peter. Microchip Fabrication. 4 th ed. New York: McGraw Hill, 2000. 48