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Chapter 1

Introduction of the Schottky emitter array system

1.1 Introduction

In this rapidly changing information age the next generation computing devices will have to perform better and faster. This requires smaller size of integrated circuits (or line width) on chips. The lithography technology holds the key in developing finer line widths for semiconductor devices. The general term lithography refers to a process in which a surface is patterned by first coating it with a “resist” material, then forming a desired stencil pattern in the resist coating, and finally transferring the pattern onto the surface. A variety of energy sources can be used for exposing the resist pattern such as photons, x-rays or electron beams. When photons in the visible light range are used, the process is referred to as photolithography. Photolithography is the main technique for micro structuring of electronic devices in microelectronics. Current photolithographic equipment uses 248nm and 193nm UV light of krypton fluorine excimer lasers and argon fluoride respectively.

The theoretical resolution of lithography is given by the well known Rayleigh equation

Wmin = Kλ / NA

where Wmin is the minimum line width, K is a process dependent parameter, λ is the wavelength, and NA is the numerical aperture of the projection optics. High resolution can be achieved by shrinking the wavelength and/or increasing NA. Since increasing NA to improve resolution is fundamentally tied to decreasing the depth of focus, DOF (=λ/NA

2

), shrinking the wavelength is most popular nowadays. The resolution limit of photolithography is extended to less than 37nm with the help of immersion lithography where the wavelength of light is reduced in a liquid medium, thus extended the life of photolithography technology in industry.

To further continue Moore’s law, feature sizes in the regime of sub-25nm are required. For the next generation sub-25nm tools the limit of photolithography will be an issue. Electron, UV, EUV and x-ray lithography are the only available techniques which can write features of size smaller than 25nm. But costly masks are associated with x-ray lithography and make it a very expensive technique. There is much more interest in deep-UV or extreme-UV lithography for the sub-25nm device generations. However, these techniques

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are facing some serious practical issues related to the radiation energy, which is capable of ionizing contaminants, and may result in mask defects, resist heating and vacuum problems.

Scanning electron lithography is widely popular in industry, as it does not require any mask. However its direct writing feature makes it too slow (low throughput) to be used for mass fabrication of chips and its application is limited to mask fabrication till today. The throughput is determined by the time required to deliver the beam current to the wafer to develop the exposed regions. The exposure time T is given by:

T= C.A.S/(I)

where C is pattern coverage, A is the total chip area of the wafer, S is the charge density required to expose the resist, I is the beam current. For example, a 300mm wafer, accommodating 100 chips of 25x25 mm2 with 50% coverage, a dose of 10µC/cm2 and a beam current of 15nA would correspond to an exposure time of 2.4 days. Therefore to decrease the exposure time, the sensitivity of the resist should be higher (i.e. lower dose) and the beam current should be as high as possible. However, increasing the sensitivity also increases the dose variation due to shot noise.

In chip making, it is also important to inspect the wafer for any possible defects. Usually this is done optically; however, this technique faces the same resolution limit as in optical lithography. As the dimensions of chips are shrinking, the defect size is also shrinking which presents new challenges for the defect detection as well. Electron microscopy is an alternative but throughput is an issue akin to electron lithography. The total inspection time can be given by:

Tinspect = C.A.τ

where τ is the pixel exposure time per pixel area.

The pixel exposure time is the most critical in electron beam inspection and is a function of beam current and beam diameter and influences the S/N ratio of the tool and contrast (∆S/S) of the image. Normally the contrast of defect is set at 0.1 [1] to detect a defect and the pixel exposure time should be sufficient to generate enough contrast. Any decrease in the feature size to be detected would result in more pixels to be scanned in a given area and a reduction in probe size or probe current. As a result, M times reduction in the defect size leads to M4 increase in the time to scan. The throughput can be increased with faster scanning which warrants more current in the beam else it will decrease the signal-to-noise ratio. For example, with a field of 512 × 512nm, a square pixel of 16nm side and with 1 µs pixel time, the time for inspection would translate to 9x10-3 cm2/hour [1]. The ITRS has defined the throughput requirement for inspection as: 3000 cm2/hour for 32nm node wafer ( ~ Four

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300mm wafers/hour). A concept of multi electron beam microscopy is reported in [2] to increase the throughput thereby enabling cost efficient manufacturing. The detection of 10nm defects on a wafer and a throughput of more than 1 wafer per hour is reported.

In both lithography and inspection the throughput can be increased by increasing the the reduced brightness which determines for a given beam angle and energy, the amount of current that can be put into given probe size. At very high current density, a strong negative space charge will be present near the emitter which may result in broadening of beam due to space-charge effects and energy spread due to Coulomb interactions. Figure 1.1 shows the beam current that can be put in a given spot size for different source brightness [2].

Fig. 1.1. Beam current vs. spot size characteristics for different source brightness (energy

spread= 0.5 eV) [2].

The above effect can be minimized by spreading the beam using multiple beams. There has been a constant drive throughout the world to make a device for parallel electron lithography systems. The multi-beam approaches offer the opportunity to improve throughput dramatically through the use of parallel writing/scanning with multiple beamlets. The current in a beamlet is given by :

2 2 beamlet

I = 0.25 B. ( .d )( .

π

π α

) (V)

where B is the reduced brightness, d is the diameter of the geometric probe,

α

is the half opening angle and V is the potential of the beam. The beamlet current (Ibeamlet) can be written

as total current (Itotal) divided by the number of beamlets (n). The above equation can be

written as:

2 2

total

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The above equation gives the relationship between number of beamlets and brightness of the source, given the total current needed for the lithography.

To increase the throughput and to capitalise its potential to write sub-25nm patterns, an array of electron beams, i.e. the incorporation of several electron beams into a single system, for lithography has been envisioned. Such a system can be possible with two configurations: (1) an array of electron source where each source delivers one beam (2) an array of electron source where each source delivers single or multiple beamlets.

The prerequisite for such a device is to incorporate an array of electron source into a single system. There have been several attempts to build such an array of electron source. A number of multiple electron-beam approaches are currently under evaluation for sub-25nm lithography, a review of these technologies is presented in [3,4]. An array of miniature electron beam columns was proposed by authors in [5,6,7] where an STM aligned field emission tip combined with micro-fabricated lenses has been incorporated to further reduce the size of the electron-optical columns. An array of such micro-columns can be used in parallel to achieve high throughput. Fig 1.2 shows the schematic drawing of such a system.

Fig 1.2. Arrayed micro-column technique as proposed in [5].

In [8] the authors report about a micro-column array in which each column, as fabricated by MEMS technology, contains a Schottky emitter and electron-optical elements to produce low energy electron beams, and such arrays of columns are then placed close to each other. A similar miniature micro-column is described in [9,10]. As each beam has its column, there is no cross-over of beams. However, there was a technical difficulty to increase the

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number of microcolumns to increase the throughput and resolution of the system. Also the beam variation from column to column resulted in non-uniformity of features at the wafer.

To ensure the quality of each beam, a multi-source single column system concept was proposed. The electron source in these systems can be photocathodes or microfabricated field emitter arrays [11-14] where the electron beams are demagnified using a single column. However, the fluctuation in current is high for field emitters and photocathodes which makes it unsuitable for lithography purposes. Also, the cross-over of beams poses a great challenge in such a systems which increases the Coulomb interactions.

Single source, single column systems overcome the problems of having an array of sources like above where the instability of the emission is an issue. Another alternative to the microcolumn concept is to split the emission of a single emitter into many sub-beams. In [15, 16] and [17] the authors have reported splitting of beams from a LaB6 emitter and a Schottky

emitter, respectively. The problem of the Coulomb interactions can be reduced by limiting the current by an aperture immediately behind the source and shortening the distance between source and aperture. In [18], the authors proposed a source module for multi-beam lithography/inspection using a single source. Using a Nova Nano 200 SEM optical column, with a multi-beam source module the authors in [19] have demonstrated the blanking of beamlets. A TU Delft spin off company Mapper Lithography [20], plans to use 13,000 beamlets for the next generation lithography tool. The 13,000 beam-lets will write sub 25nm features which will result in more than 10 wafers per hour. Currently the Mapper system is working with a single electron source which generates 110 beam-lets and writes 45nm features. The schematic of the current Mapper device is shown in Fig 1.3.

Fig.1.3. Schematic of the Mapper concept with a single source and column.

Electron Source Collimator lens

Aperture Array

Condenser lens array

Beam Blanker Array Beam Stop Array Beam Deflector Array Wafer

Fiber array Light

Glass lens

Projection lens array Electron Source Collimator lens

Aperture Array

Condenser lens array

Beam Blanker Array Beam Stop Array Beam Deflector Array Wafer

Fiber array Light

Glass lens

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Fig. 1.4. Schematic of the emitter array with multiple beams from multiple sources.

To accomplish the goal of more than 13,000 beam-lets on the wafer level, a source with high brightness and high emission current is needed which is not possible to obtain from the best commercially available sources. For example, I-type dispensor cathode has high emission current but low brightness whereas CNTs has high brightness but low emission current. Therefore a different source system is needed, the schematic of which is shown in figure 1.4. In this concept, a hybrid of the two concepts, i.e. an array of source where each beam from a source would be further split into multiple beamlets. It would consist of an emitter array, beam splitting and optical components. The main challenge in such a system is to get sufficient current density and uniformity of the beamlets. This thesis addresses the feasibility of the above concept and various challenges posed by such a system. The basic requirements for the above lithography machine are set by the following criteria on throughput, CD uniformity and overlay.

Throughput

To be industrially viable or to match the speed of optical lithography systems, the electron beam lithography system should match or exceed the throughput of an optical lithography system. The current industrial trend for the 22nm node and 300mm wafer size is to have 100 wafers per hour. If one takes into account redundancy, then the requirement goes up to 200 wafers/ hour.

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CD uniformity

The international roadmap for Semiconductors requires that the CD uniformity due to edge roughness, and other effects is around 10% of the line width. This is one of the most critical requirements as any variation in the beam quality will influence CD uniformity. For the case of 22nm feature size, the CD uniformity is defined to be 2.2 nm. For a spot size of 22nm, a 2.2nm variation would be caused by a 5% variation in the dose [20].

Overlays

Overlay is the term for how accurately each successive patterned layer is matched to the previous layers. The maximum overlay, that is the misplacement of the beam-let position on the wafer has to be within certain specific limit. The ITRS has a recommendation for overlays as well, and it is around 5nm for a 22nm feature. The mismatch between successive layers could arise from a change in the beam-let position at the wafer or from thermal expansion of the wafer. The change in beam-let position could result from drift in the source position or misalignment of electrodes with respect to the source. The thermal expansion of the wafer can result in overlay inaccuracy if each electron source delivers a different current on the resist and thus a different power resulting in differential heating among different fields.

1.2 Requirement for the array concept

For the next generation lithography tool, sub-25nm feature size is required and development of such a tool with sufficient throughput is in progress. Such a tool requires the following requirements on the wafer level. Based on these requirements, one can extract the requirements and tolerance for our electron source system.

Dose (d)

We need a certain amount of electrons to write the pattern on the resist, based on the sensitivity of the resist material. Due to the statistical nature of electron arrival, there is a variation in the number of electrons arriving in an area. The uncertainty (σ) in the number of electrons in an area A is given by N0.5 , where N is the number of electrons. As 5% (3 σ) variation in the total dose can be from shot noise, a minimum of 4000 electron [21] has to be deposited in a pixel. The resist sensitivity determined by the dose D is given by:

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Where N is the number of electrons required to define a feature of area A. For a node of 22nm or a pixel of 22nm x 22nm, it translates to 130µC/cm2.

Total current

Throughput (wafer per hour) can also be written as Throughput= (3600.I)/ (D.A.)

where I is the total current (C/s) delivered to the wafer, D is the required dose (C/ cm2), and A is the chip area (cm2 ). For a throughput of 20 wafers of 300mm with 69 fields of 26mm x 33mm, a dose of 130µC/cm2 with double scan, the total current I is calculated to be 855µA.

&o. of beam-lets (n) and Beam-let current (Ibeam-let)

The main factors that determine the minimum number of beams in a multi-beam lithography system is the amount of current put in a beam of a specific diameter, and the blanking speed. Due to brightness limitations, there is a limit to the amount of current put in a specific diameter of electron beam. Therefore the total amount of current to wafer has to be delivered to the wafer through many beamlets. Now based on the number of beam-lets or the electrons needed to expose the resist, one can determine the current needed per beam-let. Based on the total current and the total number of beam-lets, a probe current of 65nA is estimated.

If each beam is blanked individually, the data transfer rate of the pattern onto the wafer can be calculated as follows. A 300 mm wafer has approximately 1.22 x 1014 pixels of 22nm x 22nm. For better dose control, and to ensure CD uniformity, the CD element is usually subdivided into a smaller address grid of 20 x 20 [20], giving a total number of pixels of 5 x 1016 . For a total wafer writing time of 180 seconds (20 wafers per hour), the pixel rate must be 2.68 x 1014 pixels/s. For 13,000 beams a blanking rate of 20GHz is needed per beam which is possible by using current fibre optics technology.

Diameter of beam-let

For accurate and sharp images, the beam diameter ‘d’ must be small or equal to the minimum feature size. For throughput reason it is better to have as large beam diameter as possible to accommodate more current. With a minimum feature size of 22nm, the required beam diameter is 22nm.

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Brightness and Choice of electron emitter

To meet the above requirements the reduced brightness of the source has to be high to deliver enough current per beam-let. The probe current is related to the beam half-angle (α) and the diameter of the spot focused on the substrate (d) by the equation for Ibeamlet. To

maximize the probe current, each parameter cannot be altered independently as brightness regulates the other parameters. The brightness is mainly determined by the type of electron source and its operating parameters such as temperature and field.

Current can be increased by increasing the opening angle (α). However it would also contribute to the beam diameter increase. Since opening angle is related differently to chromatic aberration (linear) or spherical aberration (^3) and geometrical diameter (inversely proportional) an optimum angle has to be determined. For low energy beams, the probe size is dominated by the chromatic aberration of the last lens and the contribution from spherical aberration can be neglected. Therefore the opening angle is mainly determined by the chromatic aberration, which in turn is a function of energy spread, chromatic aberration coefficient and the beam energy.

For I=65nA, α=1.74E-2 rad, d=22nm,V=5kV, a gun brightness of more than 1 x 108A/m2 Sr V is required. The Schottky emitter has the potential of meeting the various requirements of the array system, which will be discussed shortly. The typical brightness of a Schottky emitter is around 108A/m2 Sr V. The basic characteristic of the Schottky emitter is the high brightness with high current stability.

A Schottky emitter consist of a sharp tungsten single crystal with the <100> direction with a reservoir of ZrO2 along the shaft. This reservoir forms ZrO complex at the tip surface

and lowers the work function of tungsten (100) from 4.2eV to around 2.9eV. The tip is spot welded on the polycrystalline tungsten heating filament as shown in figure 1.5 and heated to 1800K. To suppress the emission from the shaft, a suppressor electrode is present at -300V with respect to the tip. The tip protrudes from a hole in the suppressor (fig.1.6b). At a distance of typically 0.5 mm from the tip is an extraction electrode at about 5 kV. This generates a high electric field at the tip and lowers the potential barrier and increases the total emission in comparison to a thermionic emission. The field (F) and the voltage at the extractor electrode (Vext) are related by the following equation:

F = β Vext

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sup ext 1 cm LSA (1 V /V )(LTA - 0.0068) 0.758 0.366.LSA.(r) β = − −     

where LTA is the distance between the tip and the extractor, LSA is the distance between the suppressor and the extractor electrode and r is the tip radius (all units in cm). The current density of the Schottky emitter is determined by the temperature (T), field (F) and work function ( Φ) at the tip given by Schottky equation:

3/2 1/2 2 3 4. .m.e (KT) exp ( (e .F - ))

J=

h KT π Φ

Fig.1.5 Cross section of an FEI commercial single Schottky tip assembly [23].

(a) (b)

Fig.1.6 (a) Schottky emitter tip (b) Schematic of Schottky tip and electrode layout.

380µm 380µm 242µm 508µm s u p p re s s o r e x tr a c to r tip 380µm 380µm 242µm 508µm 380µm 380µm 242µm 508µm s u p p re s s o r e x tr a c to r tip

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&o. of Schottky emitters:

The emission current passing through the various electron optical components and the extractor results in the loss of emission current when it reaches the wafer level. The useful facet current from a Schottky emitter is around 50µA. If 10% of this current can be put into the beam-lets reaching the wafer, one will have 5µA per source. Given the total required current calculated above and the amount of useful current from a source, a minimum number of Schottky emitters would be 875/5 = 175 emitters.

1.3 Constraints on parameters

Any variation in the dose which may result from any change in beam current, or brightness or temperature would create a different dose and thus change the CD uniformity. In the following section we will discuss the various parameters that may affect the CD uniformity and overlay. We will set the allowable variation for various parameters which will directly affect the CD uniformity and overlays. The main factor which will contribute to the CD variation is the variation in the beam quality from tip to tip. The direct parameters to be considered are the change in the brightness and the change in the beam focussing position,

Then we have to check the various parameters which influence these two important parameters. The various primary parameters which would influence the change in brightness are the change in the field and temperature. The change in the field can happen due to a change in the position of the tip relative to the anode and the change in the shape of the tip [24]. The change in image position can be the result of a change in the position of the tip, bending of various lens electrodes etc. Since it takes several minutes to write a full wafer, the source or beam characteristic should not alter during that time. This sets the short term stability requirement of the beam. Since the beam is also used to produce large batches of wafers, the long term stability is also very important.

Change in Brightness:

Based on [20], Since 5% dose variation is allowed that would translate to 5% variation in current or 5% variation in brightness. However, the above variation in dose is for 10% variation in the spot size (probe size), not the geometrical spot size. Also if the variation in brightness is known beforehand, by varying the writing strategy, a beam brightness of 20% can be tolerated. The reduced brightness is a function of temperature and field at the tip. To check the maximum allowable brightness and to compare with the standard configuration as a reference, brightness is plotted versus temperature, tip radius, and tip-extractor distance. If

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each beam needs to give the same angular current density, ideally each tip should have the same diameter, temperature, and extraction voltage. Figure 1.7 presents the allowed variation in some of the parameters (temperature, tip radius and tip-extractor distance) for a 20% variation in the brightness. It can be seen that a tip radius variation of 50nm, a temperature variation of 30K, and a tip – extractor distance variation of up to 20-30µm is allowed to maintain a brightness variation of 20%.

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Fig.1.7 (a) Field vs. tip radius plot (b)

Brightness vs. temperature (c) Brightness vs. tip-extractor distance. The bars depict the change in 20% of brightness.

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Stable tip position

Sub-25 nano-meter lithography requires a small beam diameter combined with a high placement accuracy and beam current stability. To ensure the CD uniformity (within 10%), the spot size and the current in the beam-let should remain almost the same. This requirement

1700 1750 1800 1850 1900 1950 1800K B ri g h tn e s s ( a .u .) Temperature (K) 1770K

For 20% variation in brightness, at 0.5micron of tip radius

1830K 400 440 480 520 560 600 0 1x106 2x106 3x106 4x106 5x106 565nm 454nm Tip radius (nm) C u rr e n t d e n s it y ( A /m 2) vext= 5000V Vsup=-300V LSA=0.076cm LTA=0.05cm 440 460 480 500 520 540 560 580 +20% B ri g h tn e s s ( a .u .)

Tip-Ext distance (micron) -20%

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demands more stringent measures when an array of emitters is used for lithography. Any drift in the position of a tip will cause a corresponding drift in the image plane.

As the tungsten single crystal tip is spot welded on a filament, any morphological change is translated into a position drift of the tip. The change in the z position of the Schottky tip has a two-fold effect: first the field at the tip changes due to a change in the distance between tip and extractor which changes the current and the brightness, and second it also changes the electron optics and may result in defocus at the wafer level due to a change in distance at the source level. It can be estimated from simulation, given the tolerance in the brightness, that the maximum allowable change in the position of the tip in the z direction depending on the tip radius, and initial geometry configuration, is around 30 microns. However, the effect of defocusing would be more problematic in this case. Therefore the allowable z drift would be determined by the amount of allowable defocus (or change in beam size). The drift in x-y direction changes the alignment of the tip with respect to the electrodes, thus changing field as well. The typical x-y drift in the Schottky emitter is more than 25micron/year, which is more than the required specification. Given the virtual source size of 30nm, the magnification is one, the positional stability is around 1nm and long term stability is 100nm in x,y,z direction.

The specifications can be summarized as follows:

Beams from Schottky emitter array

• No. of Schottky emitter array > 175 • Pitch among Schottky emitters 1.5mm • Energy spread < 0.5 eV

• Angular current density sufficient for 100 beam-lets with 65nA

• Angular current density sufficiently uniform to allow beam-let to beam-let brightness variation < 20% (1-sigma)

• Current stability in time < 1% (1-sigma)

• Position stability x,y <10% (3- sigma) of virtual source size over 10 minutes.

• The virtual x-y positioning needs to be 50/M, (M=system magnification) in order to keep the correction within the over scan range.

• The z-positioning accuracy needs to be 100 nm /M2

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Beam-lets:

• Number of beam-lets > 13.000 • Pitch between beam-lets < 150 µm

• Current per beam-let 65 nA to be imaged into about 10 nm for the 22 nm half pitch node • Beam-let to beam-let current variation < 0.5 % (1-sigma) for a week

• Current stability in time < 1% (1-sigma) for hours

• Position stability x,y <10% (3-sigma) of virtual source size over 10 minutes..

• Maximum position drift over lifetime 50/M nm (3_sigma) (M is magnification of virtual source to wafer which is normally 1/5)

• Maximum position drift over life time z <100/M2

nm (3-sigma) • Parallelism beam-lets < 1M mrad

1.4 Challenges

Making Schottky emitters of 1mm diameter is the first challenge. To make 200 Schottky emitters with uniform beam quality is a big challenge, as a slight variation in tip radius or temperature may alter the beam uniformity. Therefore reproducibility of making Schottky emitters is one of the big challenges. With 200 Schottky emitters at 1800K in close proximity, another challenge is to maintain the thermo-mechanical integrity of various components in the design. With the typical total emission current of 200µA, an extractor voltage of 5 kV and 200 of such emitters, the power on the extractor would be 200 Watt. This power has to be cooled down to avoid positional uncertainties and alignment problems. Another challenge is to minimize the tip movement. This thesis addresses these challenges.

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Thesis outline

The main objective of the thesis is to develop and investigate the feasibility of Schottky emitter arrays for future generation parallel electron lithography and multi-beam inspection. Some design concepts were analysed and the information and knowledge gained is used for further re-processing of the design. The main aims of this project were:

1. Study the various requirements of the design.

2. Use the information gained above to refine the design and make a final design proposal, make estimations for the challenges and future outlook.

This thesis starts with a brief introduction of the requirements of the project (this Chapter 1). The subsequent chapters discuss the various constraints that are necessary to overcome, before such an array system can be made. The thesis has been divided into 2 parts. The first part is an initial study of the various requirements. The second part of the thesis discusses the feasibility of the Schottky array design. A schematic of the outline of this thesis is seen in Fig. 1.8.

The first part consists of a general investigation of the first ideas with reference to the various requirements (Chapter 1-5). First the requirement of controlling the temperature for each Schottky emitter is investigated and the miniature Schottky emitter is investigated. In Chapter 2, first the thermal model for the miniature Schottky emitter is investigated. Another requirement discussed is the reduction of the anode heating, and the wish to have a simpler system is discussed. Chapter 3 discusses about the concept of a suppressor-less Schottky emitter to operate the Schottky emitter at lower extraction potential which would reduce the thermal load on the extractor. Secondly, the stability requirement is addressed by investigating possible causes of the drift and possible ways to optimize it. Chapter 4 discusses the x,y stability of a standard Schottky emitter and possible ways to minimize it, with focus on the mechanism of the stability. In chapter 5, the feasibility study of using RTV as a spring is investigated. In chapter 6 the EDM fabrication of a miniature Schottky emitter is investigated.

In the second part of the thesis knowledge gained from the first part is applied to further re-assess the design (chapters 7-12). In chapter 7 the knowledge gained from the above investigations is discussed and the first design is re-assessed and few others designs are proposed. The first concept of realizing the preferred design is presented in chapters 8 and 9. Chapter 8 discusses the possibility of using polycrystalline tungsten in an array. Chapter 9 discusses the fabrication of such an array. Although the results presented in this chapter are

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preliminary, the scope of this chapter is large and could be developed into a new project. Chapter 10 summarises the design description of the proposed concept. Chapter 11 treats the various thermal and mechanical considerations for the design. A simulation is presented to estimate the tolerance level of the system. In addition, this chapter also contains a small note on the various challenges that might occur during the operation. Chapter 12 discusses the impact of the drift on the beam position at the lens level. Finally, summary is discussed with conclusions.

Figure 1.8: Schematic of the structure of this thesis

References:

1. A. Diebold, Current state of Defect Review by Electron Beam Tools: A White paper (Sematech, Houston, 2000).

2. H. M. P. van Himbergen et al., J. Vac. Sci. Technol. B 25, pp. 2521-2525 (2007). 3. PhD thesis, Yanxia Zhang (November 2008).

x,y,z temperature

Stability requirement and correction

Stability measurement Z spring RTV

Miniaturization issue

EDM miniature tip

Thermal issue

Thermal model

Suppressor-less configuration

Introduction

Conclusion First concept: control temperature and

x,y,z position Stability requirement Stability measurement Z spring RTV Miniaturization Thermal model -Thermal model

Design re-assessment, input from the previous study

Array fabrication

Recrystallization

WEDM array configuration

Feasibility study of the design

Design configuration Thermal modeling Beam stability due to extractor displacement

Possible array design and preferred design

Preferred design concept

Array fabrication

Recrystallization

WEDM array configuration Array fabrication

Recrystallization WEDM array configuration

Feasibility study of the design

Design configuration Thermal modeling Beam stability due to Feasibility study of the design

Design configuration Thermal modeling Virtual source stability

Array design Introduction Introduction Conclusion Summary Suppressor-less configuration

EDM miniature tip

Thermal management

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4. T.H.P. Chang et al, Microelectronic Engineering, 57–58 , 117–135, (2001). 5. T.H.P. Chang et al, J. Vac. Sci. Technol. B 10 2743 (1992).

6. H. S. Kim et al, J. Vac. Sci. Technol. B 12, 3413(1994) 7. H. S. Kim et al, J. Vac. Sci. Technol. B 13, 2468 (1995) 8. T. H. P. Chang et al, J. Vac. Sci. Technol. B 14, 3774 (1996). 9. J. P. Spallas et al, Microelectron. Eng. 83, 984 (2006). 10. L. P. Muray et al, J. Vac. Sci. Technol. B 24, 2950 (2006). 11. E.Yin et al, J. Vac. Sci. Technol. B 18, 3126(2000). 12. W. Barth et al., J. Vac. Sci. Technol. B 18, 3544(2000). 13. M.J.Wieland Microelec. Engi. 57-58, 155 (2001). 14. T.F.Teepen et al. J. Vac. Sci. Technol. B 23, 359 (2005).

15. M.Muraki and S.Gotoh, J. Vac.Sci.Technol.B 18(6), 2000, pp3061-3066 16. N.Shimazu, K.Saito and M.Fujinami, Jpn.J.Appl.Phys. 34, 1995, pp6689-6695 17. M.J.van Bruggen et al, J.Vac.Sci.Technol.B 23(6) 2005, pp2833-2839.

18. Yanxia Zhang, Pieter Kruit, Physics Procedia ,553 (2008)

19. A. M. Gheidari and P. Kruit, Techinical Digest of IVNC2009, page 183. 20. E. Slot et al, Proc. of SPIE, vol. 6921 (2008).

21. P.Kruit et al, J. Vac. Sci. Technol. B 22 2948-2955 (2004).

22. W. Swanson and G.A.Schwind in Handbook of Charged Particle Optics edited by Jon Orloff (CRC Press LLC, 1997).

23. www.fei.com

24. M.S.Bronsgeest et al. J. Vac. Sci. Technol. B. 26, 2073 (2008). 25. International Technology Roadmap for Semiconductor, www.itrs.net

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Chapter 2

Thermal model of miniaturized Schottky emitter for parallel

electron beam lithography

J. Vac. Sci. Technol. B 252, Mar/Apr 2007, page 504-507.

Abstract

For parallel electron beam lithography, an array of miniaturized Schottky emitters is proposed. The design of this miniaturized Schottky emitter unit is analyzed thermally to determine optimum power and filament dimensions. A numerical thermal analysis in steady state condition has been done and the temperature of the tip has been determined for different currents and heating filament dimensions. The model has been verified with some available experimental data. The optimized solution from the model will be used for fabrication of an array of miniaturized Schottky emitters.

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2.1 Introduction

To continue with Moore’s law, feature sizes in the regime of sub-32 nm are required in the next few years. Scanning electron beam lithography is widely used in laboratories around the world for features of that size. For direct writing on silicon wafers, it would also have the advantage of not requiring a mask. However, the present technology is too slow to be used for the volume fabrication of chips. To increase the throughput and to capitalize on its potential to write sub-32 nm patterns, an array of many electron beams into a single system is under development in several laboratories and companies [1]. Schottky emitters are known for their high brightness and high current stability and would be the ideal sources [2,3] but the total current from a single tip is limited. For use in parallel electron beam lithography, we are investigating the possibility of creating an array of Schottky emitters.

But the diameter of conventional Schottky emitters is too large to use in an array [3,4]. We are developing a miniaturized Schottky source of 1 mm diameter to incorporate in our array design consisting of 200 of such emitters. A Schottky source consists of a tiny single crystal W wire spot welded on a heating filament for heating up to 1800 K. The W is covered with ZrO. An extractor/anode at 1–5 kV sits at a distance of 0.1–1 mm from the tip. A suppressor electrode typically at −300 V with a hole of 0.380 mm is positioned around the tip to suppress thermal emission from the shanks. So, a basic emitter unit would consist of a base plate holding the array of miniaturized Schottky emitters, a suppressor electrode, and an extractor electrode. In such a system where 200 of such emitters are in close proximity to each other and to the electrodes, care needs to be taken for alignment between various electrodes and emitters. One of the reasons for misalignment could be the heating of various parts of the system. Several papers report on misalignment in various electron emitter units due to heating. Therefore for the design of a parallel electron lithography system an accurate estimate of the heat dissipation of the miniature Schottky emitter array is important.

Since there is no literature available on a thermal model of the Schottky emitter, a numerical thermal model has been developed to design a miniature Schottky emitter and determine its effect on the surroundings. The temperature of the tip was checked for various parameters such as heating current, diameter, and length of the heating filament. In this article, we present the numeric model for the temperature variation in the heating filament for various design parameters of the miniaturized Schottky emitter.

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2.2 Test structure and Problem statement

The geometry of the proposed structure is similar to a standard Schottky emitter [3,4] with no suppressor cap over it, though in a smaller scale. It consists of a monocrystalline W (100) tip mounted on heating filament. The heating filament is of polycrystalline tungsten. The resistive heating of the filament is determined by the diameter (i.e. cross sectional area) and length of the filament, specified by Dw and Lw respectively, shown in Fig. 2.1. The various

nodal points along the length of the heating filament are also shown in the figure. The support structure on which filament is to be fixed is of tungsten.

The heat dissipated by the filament has the undesirable effect of heating other elements in the system. By designing the dimensions of the heating filament and current etc, the emitter is to be optimized in such a way that the temperature at the tip should be at 1800 K, without raising the temperature in the surroundings significantly.

In selecting the proper heating filament material, electrical resistivity, emissitivity, and heat conductivity are of interest as these factors determine the amount of heat generation in the filament and heat dissipation to the surroundings. It is of interest to look for a material that has a high thermal and electrical resistivity and tungsten has been chosen in the example we present here. To determine the dimensions of the components of the emitter system, a thermal model is made to estimate the temperature at various nodes of heating filament and

Fig 2.1. Schematic diagram of Schottky emitter and positions of nodes across the filament

dx dx w w T1 Lw Dw L Dw L T20 T19 T2 T3 Tt ip w w T1 w w T1 Lw Dw L Dw L T20 T19 T2 T3 Tt ip Lw Dw L Dw L T20 T19 T2 T3 Tt ip

No. of nodal points n=20,

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the tip. The temperature is calculated by the heat balance equation i.e. thermal power generated by ohmic heating and liberated by radiation and conduction.

Since the material properties such as resistivity, thermal conductivity and emissitivity are temperature dependent; we have to create a loop in which we correct for the local filament properties after each update of the temperature calculation. Then the temperature of the tip was checked for various parameters like heating current, diameter and length of the heating filament. To check for the optimum operating power, radiation power for each configuration has also been checked.

2.3 Simulation method and mathematical formulation

The geometry in Fig. 2.1 is a simple geometry with cylindrical heating filament, so a simple numerical model is made. Since Schottky emitter is operated in high vacuum, only conduction and radiation are considered. The heat conduction is assumed to be one dimensional, steady state, and perpendicular to the cross sectional area of heating filament. The view factor for radiation to the surrounding is assumed to be unity for simplicity. The ambient temperature is assumed to be 300 K. The heat in the tungsten support structure is transferred through conduction only, which in turn transferred to the base plate. The base plate holding 200 of Schottky emitters would be cooled with water-cooling tubing, to maintain the temperature of 300 K. The parameters for the cooling mechanism have been estimated in terms of length, diameter, and number of tube and water pressure in the tube. In our simulation we calculated that for heat removal of 200 W by the two tubes of 0.5 mm internal diameter and water speed of 8 m/ s, the temperature difference between inlet and outlet water is approximately 15 K. And for one tube of 1 mm internal diameter and water speed of 10 m/ s, temperature difference between inlet and outlet water is approximately 10 K. Heat is generated in the filament by Ohmic heating (Joule heating). The following stationary heat balance equation is solved over one leg of the filament of the Schottky emitter:

( )

( )

( )

(

)

2 4 4

0

T T T b amb i heat radiation Joule heating conduction

d

dT

I

A

e

T

T

D

dx

dx

A

ρ

λ

σ

π

=

⋅ ⋅

+

+

⋅ ⋅

1

424

3

1444424444

3

1442443

Where, ( )T

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A Cross sectional area of heating filament (m2). dx Distance between adjacent nodes (m).

b

σ

Stephan Boltzman constant (W/(m2K4).

( )T

e Emissitivity at temperature T D Diameter of heating filament (m).

( )T

ρ Resistivity (Ωm) at temperature T

I Current(A).

The temperature at the clamping position of the filament (x=L), T20 is prescribed. At the tip

position (x=L) symmetry is assumed, assuming zero heat conduction: 0 0 wall T T at x dT at x L dx = = = =

Joule heating (Pj ) and heat conduction in the tip is neglected. The tip, however, radiates heat

to the surroundings (radiation power- Prad ) and therefore acts as a heat fin for the filament.

This is accounted for in the heat balance equation of the filament, by adding the radiating surface area of the tip to that of the filament at x=L. The actual tip temperature with respect to the clamping position of filament, T20, can be estimated using a fin formula:

(

)

(

)

20

1 cosh

tip amb amb

tip T T T T m L = + − ⋅ ⋅ , tip rad A P h m ⋅ ⋅ =

λ

where P denotes the tip perimeter, Atip the cross sectional area of tip and hrad the radiative

heat transfer coefficient. Material properties are evaluated at T20. The tip length and diameter

is taken as 1.2mm and 0.127mm respectively. From this expression it follows that in order to achieve a tip temperature of 1800K, T20 should be around 1833K.

To solve the equation numerically, the equation is made spatially discrete using a second order scheme. Twenty nodal points equidistantly spaced over the heating filament are used, where the last nodal point is at the tip location (x=L). The equations are solved using Mathcad [5]. Given a filament current and filament dimension, the filament temperature distribution is the result of the calculation.

The temperature dependence of thermal conductivity, emissitivity and electrical resistivity are taken into account. The resistivity and emissitivity are evaluated at the nodal temperature while conductivity is evaluated at the average of two adjacent nodal temperatures. The temperature dependence of various properties of tungsten used in the model are given below: Temperature dependence of electrical resistivity of tungsten [6]:

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ρ(Τ) = 4.6122+ 2.4498 . 10−2.(Τ)+3.5328 .10−6 . (Τ)2 −1.9686 .10−10. (Τ)3 µΩ cm Temperature dependence of heat conductivity of tungsten [7]:

λ(Τ)=174.9274−0.1067 . (Τ) + 5.0067 .10−5 . (Τ)2 −7.8349 . 10−9 . (Τ)3 W/(mK) Temperature dependence of total hemispherical emissivity of tungsten [8]

e(T)= - 0.0334+1.8524 . 10−4 . (Τ) − 1.954 . 10−8 . (Τ)2

It should be noted that if material properties are assumed to be constant in temperature and the radiation contribution negligible, the temperature of the filament is parabolic in profile, where the temperature increase of the tip with regard to the clamping position reads:

2 2 2 2 4 4 16 J

P L

I

L

T

D

D

π π

ρ

λ

λ

⋅ ⋅

∆ =

=

⋅ ⋅

⋅ ⋅

The above equation shows the sensitiveness of the temperature on the length and diameter of the filament. For a given length or diameter of filament, even a micrometer change in dimension can give a significant change in temperature. According to this simplified expression, to increase the temperature of the filament, the required heating power is proportional to the heat conductivity of the filament, the cross sectional surface area of the filament, and inversely proportional to the length of the filament, as intuition also predicts.

2.4 Simulation results

In the thermal model, important goals are to keep the tip temperature around the operating temperature of 1800K, and to keep the filament temperature, radiation power, and the power consumption as low as possible. Thermal analysis in steady state has been done for different filament dimensions and heating powers. Both these parameters have been optimized in this model; where filament dimensions and current can be varied to see its effect on temperatures of various nodes of filament.

In standard Schottky emitter the effective length of filament is difficult to determine owing to its large area of contact (more than 150 µm) with the filament post. Therefore after measuring the filament length under microscope, the length of filament is adjusted within 200 µm for approximation fit to the model. Various configurations for miniaturized Schottky emitter is considered and compared with standard Schottky emitter. The solutions are shown in table I and Fig 2.2. The first row of the table shows the emitter configuration of a standard Schottky emitter with measured diameter of 126 µm and length (after adjustment) of 5.72 mm and the current required7 (as per specification) to achieve tip temperature of 1800K. In this model, for configuration 1, 0.008 ampere increment gives an increment of 13-16 K,

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which is quite close to value of 10K, given in the FEI data sheet [9]. Since other configurations have different dimensions, the same “rule” cannot be applicable for others due to different degree of heat dissipation. Based on the temperature distribution and power consumption simulated above, the best operating parameter can be chosen. However, it is evident from Table 2.1 and Fig.2.2 that for some configurations there is excessive heating of the filament and for some it requires more power (Pj) to reach a tip temperature of 1800K.

Normally, it is desirable to have high electrical and thermal resistance. The thermal and electrical resistance along the filament length for different dimension are shown in Fig 2.3(a) and 2.3(b). From the figure it is evident that for configuration 5, both electrical and thermal resistance are higher and also consumes less power. The lowest power for the operation would be as low as 0.653 W to get the tip temperature of 1800K, which is much lower than 1.759W and 1.16W, which are the operating power of the Standard Schottky emitter and Low Power Schottky Emitters respectively [9].

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Table 2.1. Heating filament configurations to get the tip temperature of 1800 K of heating

filament for various configurations.

It can be seen that the final temperature at the tip is not directly dependent on power but the combination of heat generation and dissipation. The heat dissipation occurs through radiation and conduction to various elements and the support structure. Conduction between various elements constitutes the major portion of heat dissipation. Most of the radiated energy is emitted in the infrared regime. The heat dissipation through radiation constitutes a reasonable fraction of the total dissipated energy. The radiation power (Prad) for each

configuration is calculated and given in last column of Table 2.1. For configuration 1, because of its large surface area, the radiation power is quite high. Owing to their smaller surface area, configuration 2,3 and 4 radiate smaller fraction of the total power compared to configuration 1. For configuration 5 and 6, the radiation power is comparable to configuration 2, 3 and 4. Though configurations 5 and 6 have smaller area than configuration 2,3 and 4, the radiation power, which is proportional to T4, is relatively high due to higher temperature.

Since in our array design, we would place 200 of such emitters in close proximity, together with suppressor and extractor electrode, such an analysis would give an insight into heating of other electrodes. Heating of these electrodes by radiation can cause radial and axial expansion. As we want to minimize the heating of various electrodes, the absolute amount of radiation power is important which makes configuration 6 the optimum design configuration. In the proposed array design, 200 Schottky emitters will be arranged within the dimension of 30 x 30 -mm each beam from a source is further split into 100 beam-lets (Fig 2.4).

S.N Dw, Lw I (A) Pj (W) Prad(W) 1 126µm, 5.73mm 2.42 1.759 0.322 2 100µm, 2.5mm 3.22 2.114 0.155 3 70µm, 2.5mm 1.63 1.127 0.135 4 70µm, 2.0mm 1.995 1.335 0.121 5 50µm, 2.5mm 0.874 0.653 0.121 6 50µm, 2.0mm 1.06 0.76 0.111

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(a) (b)

Fig 2.3. (a)Thermal resistance and (b) electrical resistance for different filament

configurations

(a) (b)

Fig 2.4. (a) Schematic diagram of Schottky emitter array arrangement and (b) beam

trajectories.

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These beam-lets can be focused or deflected with the help of micro-lenses and deflector arrays similar to the design of van Bruggen et al [10], shown in Fig. 2.4.We are presently analyzing the feasibility of such an array. To meet the stringent alignment requirement and axial spacing between various electrodes and tip, a comparative analysis with different materials and thickness for the electrodes along with the analyses of the temperature profile and thermal expansion of various electrodes in either direction is in progress.

2.5 Conclusion

A numerical thermal modeling study is presented to optimize the problem of heat in a Micro-Schottky emitter array unit. This thermal model calculates temperatures in various parts of Schottky unit. Such analysis can give an estimate of the temperature of the tip for various configurations and thus enables us to tune various parameters to optimize the best design. Based on power consumption and heat dissipation by radiation, an optimum configuration has been determined.

References:

[1]. Not much of this development is available in the scientific literature. However, several concepts are presented on http://www.sematech.org/meetings/archives.htm.

[2]. D.W.Tuggle and L.W.Swanson, J. Vac. Sci. Technol. B 3, 220(1985).

[3]. H. S. Kim, M. L. Yu, E. Kratschmer, B. W. Hussey, M. G. R. Thomson, and T. H. P. Chang, J. Vac. Sci. Technol. B 13, 2468 (1995).

[4]. http://www.feibeamtech.com/pages/schottky.html. [5]. http://www.mathcad.com

[6]. J. W. Davis and S. Fabritsiev, ITER Material Properties Handbook, University of California, San Diego.

[7]. J. M. Davis, V. Barabash, and S. Fabritsiev, ITER Material Properties Handbook (IAEA, Viena, 1997), AM01-3112, No. 2, p. 1–2.

[8]. J. M. Davis and V. Barabash, ITER Material Properties Handbook (IAEA, Viena, 1997), AM01-3111, No. 3, p. 1–4.

[9]. FEI data sheet from the purchased Schottky emitter.

[10]. M. J. van Bruggen, B. van Someren, and P. Kruit, J. Vac. Sci. Technol. B 23, 2833 (2005).

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Chapter 3

Concept and operation of a Schottky emitter without suppressor

electrode

Journal of Vacuum Science and Technology-B (JVST-B), Vol.27, page.2426-2431 ( 2009).

Abstract

The Schottky electron emitter is the most frequently used electron source in electron microscopes. A suppressor electrode around the emitter is usually employed to prevent emission from the shank of the cathode. A concept of operating the Schottky emitter without the suppressor electrode is proposed with the aim of lowering the potential of the extractor electrode. Simulation results show that if the suppressor electrode is removed, then the same field as for the standard configuration can be obtained at the tip apex at an extraction voltage of 2265V instead of 5000V. The total emission from the shank region is calculated by estimating the emission area of the shank, taking into the account the different work functions of the crystal facets. The total emission for typical operating parameters is calculated to rise from 500µA to 668µA. The total emission from the shank and the filament of the Schottky emitter is measured experimentally in two different configurations which match with the simulated results. The measured total emission of 450 to 750µA confirms the idea that a Schottky emitter can be operated without suppressor, all the more so because the power at the extractor aperture is even reduced as a result of the lower acceleration voltage.

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3.1 Introduction

The Schottky emitter is known for its high brightness and current stability[1,2]. In a Schottky emitter, the useful emission comes from the W (100) facet at the very end of the tip. The emission from all the other parts of the tip (conical and cylindrical) called shank emission is suppressed by a suppressor electrode, which is usually an integral part of a Schottky emitter unit. The disadvantage of the suppressor electrode is that the negative potential at the suppressor electrode reduces the field at the apex of the emitter tip considerably. The potential of the extractor electrode has to be increased to compensate this reduced field. The typical potential applied to the extractor and suppressor electrodes are 5 kV and -300 V, respectively, for a tip-extractor distance of 500µm. There have been efforts to operate the Schottky emitter at lower extraction voltages for its application in an array of microcolumns [3,4]. To operate the Schottky emitter at low extraction voltage, the field at the tip should not change along with other parameters such as temperature and work function. The field at the tip has to be maintained to get the same angular current density and brightness. This can be done by bringing the extractor plate closer to the tip. In Ref. 5 Kim et al. discussed the operation of Schottky emitters below 1 kV of extractor voltage, which were operated at a tip-extractor distance of 50–100 µm with 1–2µm thick silicon extractors with an aperture of 5 µm. However, such small tip-extractor distance and aperture size require very stringent tip positional stability, for a slight tip movement can give rise to a considerable change in the total electron emission. Moreover, a Si extractor of 1–2 µm thickness in close proximity to the tip at 1800 K is susceptible to thermal effects.

To lower the potential of the extractor electrode it is proposed to operate the Schottky emitter without the suppressor electrode. This concept would have several advantages over the conventional Schottky emitter. There would be no issue of alignment of the tip with respect to the suppressor electrode. It would also make the whole Schottky emitter unit less voluminous. The lower extraction potential would result in lower heat dissipation on the extractor electrode, thus less susceptible to thermal drifts and outgassing. The suppressor-less Schottky emitter allows also for a higher tip radius emitter which has better emission and shape stability without increasing the extraction voltage beyond 5 kV. The above advantages would make it easier to construct a Schottky emitter array for multibeam lithography.

A suppressor electrode will have no influence on the electron optics as long as the field at the tip remains the same. It is shown in Ref. 6 that the angular intensity distribution is

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similar for different suppressor voltages if the field at the tip is kept constant by adjusting the anode voltage. Therefore, the Schottky emitter can be operated at much lower extraction voltage if there is no suppressor electrode at all. For the suppressor-less Schottky emitter configuration, it is important to know the total emission from the conical and cylindrical shank and the filament, which would be falling on the extractor in the absence of the suppressor electrode. The total emission current in the suppressor-less configuration has first been simulated and then measured in two different extractor configurations: with and without an aperture to distinguish between shank and facet current from the tip. The total emission from a typical Schottky emitter varies from ~ 40 to 500µA depending upon the operating conditions. The emission from the facet varies from 4 to 40µA.

3.2 Simulation method

CPO software [7] is commonly used for the modelling of electrostatic, magnetostatic and ray tracing problems. The CPO program uses a Boundary Element Method or Charge Density Method to approximate the partial derivatives for the potential and is suitable for problem with large scale difference in geometries of various electrodes. The various geometries of the electrodes i.e. emitter, suppressor electrode and extractor electrode are defined in the program. The geometry has a two-dimensional cylindrical symmetry around the emitter axis, shown in figure 3.1. In this configuration, the tip-extractor distance is 508µm, the bore diameter of extractor and suppressor electrodes are 380µm and the tip-suppressor distance is 242µm. The tip apex is approximated to a truncated hemisphere of radius 500nm. The radius of this hemisphere is considered the tip radius (r) and the truncated part (usually 0.3*r) is called facet of the tip. The emitter apex was positioned far away from the boundary as the potential at the domain boundary may affect the overall solution. In the beginning of the simulation, the emitter is grounded and the extractor and suppressor are biased at 5KV and –300V respectively. Subsequently the bias voltage at the extractor and suppressor are changed to estimate different electric fields at the apex of the tip.

The total shank emission has been calculated using the standard Schottky emission theory. With this theory the local current density on the surface can be calculated if the local temperature, field and work function (WF) are known. The field along the conical and cylindrical shank (figure 3.2a) is determined locally at the interval of 100nm by the simulation program. While calculating the current density from the conical shank, the work function of different crystallographic orientations i.e. the four W(100)/ZrO2 lobes (WF=2.95

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Fig 3.1. Standard Schottky emitter configuration, used for the simulation.

consideration. For the cylindrical shank, the work function of polycrystalline tungsten is considered. Then using the Schottky equation [8] for each 100nm wide ring, current density is calculated. The total emission has been estimated using the total surface area of the emitter excluding the ZrO2 lump. The diameter and length of the cylindrical shank is assumed to be

125µm and 1.12mm respectively. The length of the conical shank is estimated to be 265µm. The area of the four W(100) lobes on the conical shank has been estimated with the help of a SEM picture (figure 3.2b).

3.3 Simulation Results

The tip shape and the geometry used for the above simulation method were verified by comparing the field enhancement factor β, given by equation 1 [8] to the field enhancement factor obtained by simulation for the standard configuration with a suppressor.

sup ext 1 cm LSA (1 V /V )(LTA - 0.0068) 0.758 0.366.LSA.(r) β = − −      (1)

where LTA is the distance between the tip and the extractor, LSA is the distance between the suppressor and the extractor electrode and r is the tip radius (all units in cm). The electric field at the apex of the tip is studied for the standard Schottky tip shape and geometry (i.e. LSA=750µm, LTA=508µm, r=0.5µm, Vext=5KV, Vsup=-300V). The field values for the

380µm 380µm 242µm 508µm s u p p re s s o r e x tr a c to r tip 380µm 380µm 242µm 508µm 380µm 380µm 242µm 508µm s u p p re s s o r e x tr a c to r tip

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standard configuration, the suppressor- less configuration from the simulation and the theoretical field value using equation 1 are plotted in Fig 3.3. The β obtained from the equation 1 and from the simulated results matches within the accuracy of ±1.9%, thus validating our simulation.

(a) (b)

Fig 3.2. Standard Schottky emitter (a) Total shank region (b) the band of W(100) on the

conical shank.

For the standard configuration, the field at the centre of the apex can be deduced from Fig 3.3 to be 0.96 V/nm. The same field as that of a standard configuration can be achieved by lowering the extraction voltage to 2265V in the suppressor less configuration. The field at the apex without suppressor at the extraction voltage of 5KV is approximately 2.1V/nm. With zero suppressor voltage, the field of 0.96 V/nm can be obtained at the extractor potential of 4570V. The difference between zero suppressor voltage and no suppressor is considerable.

Figure 3.4 shows the equipotential lines around the apex of the tip in the standard and suppressor-less configuration. From the figures, it is evident that the line density increases as the suppressor electrode is removed. Since the tip is far from the boundary, the boundary effect in the simulation can be neglected. In the case of the suppressor-less geometry, the suppressor electrode is assumed to be at infinity at zero potential.

Conical Shank Cylindrical Shank Conical Shank Cylindrical Shank 24 .3µ m 24 .3µ m W(100) 24 .3µ m 24 .3µ m W(100)

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Fig 3.3. Field value obtained by CPO simulation and from equation 1 for various extractor

voltages.

(a) (b)

Figure 3.4. Simulated equipotential lines at Vext = 5kV and (a) Vsup = -300V (b) No

suppressor 1000 2000 3000 4000 5000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

Field for standard configuration

Suppresor less Vsup =0V

Vsup=-300V (slope (β)=209.6mm-1)

Field calculated using eqn 1 (slope(β)=205.7 mm-1)

(Valid above 3000V) F ie ld ( k V /m m ) Extractor voltage (V)

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The total shank emission for various configurations has been calculated and shown in table 3.1. The conical shank emission increases by more than 30% for the suppressor-less configuration at 2265V extractor voltage compared to the standard configuration as the increased field led to increased Schottky effect. However the total Joule heating (emission*Vext) of the extractor electrode would be less than that of the standard

configuration as the potential is reduced by more than 50%. The total cylindrical emission assuming there were no W(100) planes, is estimated to be only a few micro-amperes and therefore the increase is not significant in comparison to the emission from the conical part. However, if there were W(100) planes then the emission would be 4.22mA for 2265V of extractor voltage, as shown within the bracket in table 3.1. It has to be noted that in case of a standard configuration in the presence of a suppressor electrode, no emission from the cylindrical shank takes place. The following sections discuss the total emission and shank current measurements.

Table 3.1. Shank current estimation for various configurations

3.4 Experimental methods

The set-up consists of a Schottky emitter without its suppressor electrode and aligned to a molybdenum extractor plate in front of it. The tip extractor distance of 600µm and 850µm micron was maintained for two different configurations, shown in figure 3.5. In the first configuration the total emission current and current on the extractor plate is measured. In the second configuration, an extractor with an aperture of 380µm was placed to distinguish

Configuration (Vext,Vsup)

Conical shank current (A)

Cylindrical shank current (A) (with W(100) plane)

Std., 5000V, -300V 4.98 E-4 -

Std., 5000V, 0V 5.57 E-4 2.48 E-7 (2.62 E-3)

Suppressor-less, 5000V 11.3 E-4 5.26 E-7 (5.58 E-3)

Suppressor-less 2265V 6.68 E-4 3.98 E-7 (4.22 E-3)

Suppressor-less with coating of Mo, 2265V

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