Dose Planning:

How To Use:

  1. Choose a "Field Size", "Dot" count, and "Shot Pitch" that satisfies your resolution requirements.  Resultant pixel size is printed in information tab at the bottom of the widget.  It appears to be best to try to stay with the 600µm, 60k combination if possible.
  2. Input your resist and substrate parameters
    1. Take a guess on the clearing dose for your resist.  The "Large Area Clearing Dose" is depends on substrate.  The "Small Area Clearing Dose" is substrate independent.  I find that 550nm of ZEP520a has a "Small Area Clearing Dose" of 116uC/sqcm when developed with 30s of o-Xylene. 
    2. Input the backscatter coefficient for your layer stack.  Typical values are around 0.5.
    3. Input your pattern area
    4. Input a value for the BEAMER Base Dose.
  3. Examine the resulting parameters
    1. Is the process window (green bar) in the "Discretized PEC Optimized Dose Received" sufficiently large?
    2. Is the current reasonable?
    3. Is the write time insufferably?  Note that this write time includes none of the overhead incurred by driving to different fields.  Experience has shown that up to double the "PEC Write Time" can be incurred.
  4. Adjust the "Beamer Base Dose" to optimize.  Adjusting down will
    1. Decrease the write time.
    2. Increase the write current
    3. Decrease the dose resolution
    4. Decrease the process window
  5. Test several calibration doses by choosing one of the list of available doses printed under "Beamer PEC Values" and placing it in the "BEAMER Cal Dose" and examining the "CalDose Received" plot.   The "Beamer PEC valuse are the doses in BEAMER Units that will be permitted by the Elionix and will be reproduced faithfully without rounding.
    1. It is good to have one "low" dose.  A low dose will have several exposed features not fully develop.  The threshold for full development is indicated by the red line.
    2. It is good to have one "high" dose.  A high dose will have skirts of unexposed regions develop.
  6. In your BEAMER flow
    1. Put the "Beamer PEC Values" as the allowed doses in the BEAMER PEC Module.
    2. Put the "BEAMER Base Dose" in the Beamer Export Module
    3. Use the FDA Module to expose one of the cal patterns (linked below) with the low and high cal doses found above along with your PEC corrected pattern.
  7. Set your write current on the Elionix to the value indicated under Current

Calibration CAD files.  All files are saved at 1um.  The file "calMark150.dxf" will fit comfortably in a 150um write field.  For reference, the pinwheels are 25um, 50um, 100um, and 200um in diameter for each file respectively.



BEAMER Theory:

The fundamental problem of EBeam Lithography that BEAMER attempts to solve is that of Proximity Effect (PE).  When we expose a "large" square pattern with a given dose, we not only get that dose, but we also get a diffuse cloud of electron back-scatter.  This BS will also serve to expose the resist.  In general, the back-scattered cloud is of low intensity and typically large.  It only becomes appreciable when the pattern is large enough that a given exposed point will feel the effect of the back-scatter from all nearby exposed points.  In comparison, for a "small" isolated exposure area, the received dose will simply be the applied dose.  While there is still back-scatter, it is of negligible intensity due to the lack of contributing points.  Therefore, when we apply a dose to a small isolated area, the received dose will be the delivered dose (current*time/area).  However, when we apply the same dose to a large area, the received dose will also include the backscatter (BS) to yield (1 + BS)(current*time/area).  The size, shape, and magnitude of the backscatter is completely a function of the substrate layer stack.  Due to this, we can expect that the Small Area Critical Dose (SACD) will be larger than the Large Area Critical Dose (LACD).  In fact, for a backscatter magnitude of BS, we can say that LACD = SACD/(1+BS).

EBeam resists require a certain critical dose (CD) to either breakdown (positive resists) or polymerize (negative resists).  This is an intrinsic quantity of the resist and should not depend on the substrate at all.  However given the ubiquity of Silicon and the comparative ease of measuring large features over small ones, the CD is often quoted as being the LACD.  The SACD, since it removes all back-scatter effects, theoretically the same as the CD.  While initially convenient in terms of brute-force optimization of exposed samples, the LACD is complicated because it underestimates the CD of the resist and will change as the layer stack of the substrate changes.

From a practical perspective, we want to have the largest possible process window.  On every edge, there will be a half that we wish unexposed that will receive some dose from the local back-scatter, and a half which we do want exposed that will receive the delivered dose and the local back-scatter.  The goal of BEAMER is to maximize the difference of these two values and center them on the CD.  If our sample had no BS, this would result in exposing the sample with a value of 2*CD.

Let us consider the three extreme cases: isolated small "hole" in a large exposure, the edge at an isolated small exposure, the edge at half-space.  It is useful here to use the concept of Delivered Dose (DD) and Received Dose (RD).  The DD will be the dose coming from the electron beam column and be can be calculated by noting the electron beam current, exposure area, and exposure time.  In contrast, the RD will potentially be larger due back-scatter in the exposed regions.  Addionally, there will be RD in the unexposed regions as well due to back-scatter.


Since the exposed region is large, there will an backscatter everywhere.  The hole is small so the lack of exposure in this region does not significantly effect the magnitude of the backscattered cloud.  The received dose (RD) for the exposed regions DD*(1+BS).  The received dose for the unexposed hole will be DD*BS.  It follows that if we want to center this difference on CD (ie CD = ((DD*BS)+(DD*(1+BS))/2, then the we want DD = 2*CD/(1+2 BS).


The local backscattered cloud at the edge of a half space will have magnitude of BS/2 so that exposed region will have an RD of DD(1+BS/2) and unexposed region will have an RD of DD(BS/2).  Again, maximizing the process window on the edge will mean splitting the difference between these on the CD (ie CD = ((DD(1+BS/2)+DD(BS/2))/2).  Therefore, we want the DD on the edge of a half-space to be DD = 2 CD/(1+BS).

Dense Lines and Spacings:

If we consider a dense pattern of lines and spaces such that 50% of the total area is exposed and the backscatter is blurred so that there exists a uniform cloud, then the RD would be DD(1+BS/2) on an exposed stripe and DD(BS/2) on an unexposed stripe.  Similar to the edge above, the ideal DD = 2 CD (1+BS) = 2 LACD.  It is for this reason that the BEAMER manual recommends exposing a dense pattern of lines and spaces as it directly yields the LACD.  However, this process involves measuring the resulting line widths using an SEM with a high degree of accuracy.

Isolated Exposure:

In an isolated small exposure, the local basckatter will be neglible.  The exposed region will have an RD of DD and the unexposed surround region have an RD of 0.  Again, we want to split this difference on the CD (ie CD = (DD + 0)/2).  Therefore, we want the DD on the isolated small exposure to be CD*2.

A given pattern isn't made of the three extreme features, but rather has a range of features which possess attributes of all.  The beauty of BEAMER is how it algorithmically interpolates between these extremes.

It should be noted, that BEAMER has its own dose scale in what we will call BEAMER Units (BU).  This is normalized so that 1[BU] = 2*LACD.  It is not based on the intrinsic resist CD.  However, we can easily see that the CD is at 1/(2*(1+BS))[BU].  I believe this was done so that in the extreme case of exposing a large area with no backscatter, the ideal dose will be 1[BU].

Elionix Theory:

The Elionix is a complicated and expensive machine.  Our objective is to use it to get our desired exposure in the shortest amount of time possible.  While a complete in depth discussion of all the Elionix's working is beyond the scope of this document, there are a couple key features that need to be understood in order to properly interface the Elionix with BEAMER.

A pattern in the Elionix is made up of a set of polygons.  Each polygon can be though of as having a specified dose.  Polygons (and vector graphics in general) are a memory efficient method of handling large very detailed patterns.  These are converted on the fly into raster images and written by the tool.  Of vital importance is the pixel size in that raster image.  This is found by dividing the field size (in microns) by the field size in dots. In practice, the files only contain information about the dose time as the current on the machine is set manually via the aperture and the way the beam is focused on it.  The dose delivered to a dot (pixel) in Coloubms can be calculated by multiplying the (dot area)*current/time.  While the current on the Elionix is a continuous variable, the time is not.  The time must fall on discrete values which change based on the size of your field in dots (20kDots, 60kDots, and 240kDots).  The timer rules go as follows

  •   20kDots: n*0.15(us/dot)
  •   60kDots: n*0.05(us/dot)
  •   240kDots: n*0.0125(us/dot)

where n=0 or n={2,3,4,...}.  Note, n=1 is not allowed.

Herein lies the fundamental tradeoff: time resolution vs time.  You can expose at high currents and achieve low write times, but you will not have very many allowed dose values that are useful.

In general, the current is fixed by choosing a setting from the "Beam Memory."  This will prompt the tool to place one of several apertures at a back focal plane of the electron column and to set the focus value on that aperture.  The aperture appears as a point source for the downstream system, but the brightness of that pointsource depends on how well the electrons are focused on the hole.  It follows that if the setting of 1nA and 5nA share the same physical aperture and differ only in their focus values, an intermediate focus could be set to achieve a current 2.34nA if desired.

Combining BEAMER and the ELIONIX:

There is an inherent tradeoff posed by the discretized timer values and Proximetry Effect Correction (PEC)  In the limit of very small currents, the required times to achieve the DD will grow so that allowed timer values will approach a continous variable and fine gradiations in DD are possible.  However, this will yield very long write times.  On the other hand, if we crank up the current, our write time will be fast, but our available write times might be spaced too far apart to achieve good PEC.

This brings up the fundamental question that we attempt to answer here:  Given a CD for the resist and a substrate backscatter, what current and timer value will yield fastest write time while still having a wide process window.  Following that, what are the Elionix allowed doses in BUs to plug into BEAMER for PEC.  Furthermore, how much time should I schedule for the tool.  The following aplet attempts to answer all of these.

You choose:
  * field size in kDots
  * field size in microns
  * the critical dose (and whether this value is based on the intrinsic SACD or the LACD)
  * Total Backscatter.
  * BEAMER Base Dose.  Lower values decrease write time.  (this is input into the export module of BEAMER)
  * exposure area

From there, the code will show you
  * (First graphics column) the size of your process window (green bar) without PEC based on a uniform DD at the properly calibrated value.  For BS values above 1, there may be no process window.  Top row is the DD and the bottom is the RD.  The process window is defined as the difference between the smallest RD of intended exposure and the largest RD or uninteded exposure.
  * (Second graphics column) the size of your process window if idealized PEC is utilized.
  * (Third graphics column) the size of your process window when only Elionix allowed timer values are utilized.
  * The allowed timer values in BUs.  This can be input into the PEC module in BEAMER
  * Pixel Size
  * The resulting current
  * the write time assuming all large areas (shorter time) to assuming isolated small features (longer time).


Determining Exposure Values:

As a part of my pattern, I always write an underexposed and an overexposed calibration pattern.  If these are tuned properly, they can yield rich information about the magnitude and nature of the backscatter.  The goal of the underexposed pattern is to get only the large features to clear the CD.  The goal of the over exposed pattern is to have some of the isolated holes clear the CD.  Using another app (or photoshop), one can then simulate the process for various backscatter parameters to precisely measure the CD, BS and backscatter width.  Toward these ends, this app includes two additional columns which allows one to find these values.  These are found in BUs so that the dose of these structures can be set using the FDA module in BEAMER.  It is up to the user to choose a dose from the allowed timer values in BEAMER units.