Shot Noise Models for Sequential Processes and the Role of Lateral Mixing
Download
1 / 18

Estimates of the Number of Required Events - PowerPoint PPT Presentation


  • 48 Views
  • Uploaded on

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Estimates of the Number of Required Events' - levana


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

Shot Noise Models for Sequential Processes and the Role of Lateral MixingA.R. Neureuther, F. Pease, L. Yuan , K. Baghbani Parizi, H. Esfandyarpour, W.J. Poppe, J.A. Liddle and E.H. AndersonEIPBN June 1, 2005 This research was supported in part by SRC under grant SRC 2005-OC-460, DARPA under grant DARPA W911NF-04-1-0304, industry and the UC Discovery SMART grant ELE03-10160, and by instructional use of the LBNL nanowriter.


Estimates of the number of required events

100 Lateral Mixing

1000

10,000

Estimates of the Number of Required Events

  • Acid Generation Bottleneck

  • Statistics for Multi-Step Processes

  • Experiments on Contact Printing

  • Mechanisms of Linewidth Variation

Clear the Feature

Linewidth Control

# Events

Neureuther

Sutherland

Smith

Kruit

Pease


Acid generation bottleneck
Acid Generation Bottleneck Lateral Mixing

Kozawa group study of PHS at Osaka University:

  • Conditions

    Exposure dose = 10 uC/cm2

    75 keV electron beam.

    PHS Density = 1.2 g/cm3

  • Results

    Believe much of the energy is deposited in the resin and then generates acid

    Acid Density = 0.022/nm3= 2.2 x 1019/cm3

    Generation Rate is 0.035 acids/nm @ 75 KeV

Can be less than one acid per electron!

See Ming Yu et. al, SPIE 2005


Relating acid to energy deposition
Relating Acid to Energy Deposition Lateral Mixing

Everhart Hoff experiment model:

for 5 KeV < E < 25 KeV

=> Result : 0.42 eV/nm per electron @ 75 Kev

  • From Kozawa group result, we have:

    0.42 / 0.035 = 11.9 eV/acid


Energy per acid ev acid
Energy per Acid (eV/Acid) Lateral Mixing

eV/acid probably depends 2X to 4X on exposure type

Data from Rau SPIE 98, V3333/p1413 and Brainard SPIE 05



Sequential multiple step poisson processes
Sequential Multiple-Step Poisson Processes Electron Lithography

The following are approximate counts for a 100 keV e-beam exposure of a 5nm layer of resist


Statistics for a 3 sequential poisson processes
Statistics for a 3 Sequential Poisson Processes Electron Lithography

  • Generating Function

  • Average

  • Variance

  • Relative variance


Physical interpretation of 3 step process
Physical Interpretation of 3-Step Process Electron Lithography

  • Noise power contribution from the total number of each species is additive inversely to number of events!

  • For 400 electrons, 40 acid and 5,000 depotections the acid contribution clearly dominates!

  • The discrete number of electrons and deprotections do contribute and make the relative variance (0.1664) slightly larger than that from the acid alone (0.158).

  • The result agrees with the amplifier noise and gain model described in the text by Oliver Wells


Electron Electron Lithography

Acid

+

Deprotection

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

MF

Lateral Mixing Effects and Shot Noise


N=400 Electron Lithography

N=400

N=400

N=400

H / T

H / T

H / T

H / T

R

Inside

Left

Inside

Right

MFS = 50 nm

MFS/4 = 12.5

MFS/4 = 12.5

MFS/4 = 12.5

MFS/4 = 12.5

R

Parallel Process Model

Uncertainty in lateral sorting will add noise

*K is the number of electron source for each line width.


Experiments on contact printing
Experiments on Contact Printing Electron Lithography

Collaborative Experiments on the LBNL Nanowriter with A. Liddle and E. Anderson on exploratory EUV resists from R. Brainard of Shipley and G. Wallraff, of IBM

100 KeV, IBM KRS-XPS Resist, 40nm contacts at 70 uC/cm2, when the dose to clear large areas is 30uC/cm2


Electrons per Contact Printed Electron Lithography

Ave = 4500

Stdev ~ 500-1000

Low slope => StDev/AVE = 0.11-.22 => N = 20-80

Requires about 4500 regardless of size!

But NEFFECTIVE is under 100!


Source of low n effective in experiment
Source of Low N Electron LithographyEFFECTIVE in Experiment?

  • A thin 5 nm layer at the top of the resist appears to inhibit the dissolution and to lead to a punch through type behavior

  • A further reduction in the average acid present may be due to outgassing

  • Other factors such as lateral diffusion and beam wobble may also be contributing

SEM of a 50 nm line


Resist Profiles Show both LER and LWV Electron Lithography

Shipley UVII-HS (KrF)

By Williamson and used in Yuan SPIE 04

150 nm scale

10-30 nm scale

Gradual linewidth change

Divots and bumps


Resist is similar to mechanical fracture of silicon
Resist is Similar to Mechanical Fracture of Silicon Electron Lithography

Cut-Set silicon surface

10 nm rms

After hydrogen anneal

0.1 nm rms

From Talk by Nathan Cheung


Resist fracture model of lwv
Resist Fracture Model of LWV Electron Lithography

Exposure and reaction makes polar inhomogenities

Polar developer penetrates and causes pressure/stress

Mechanical fracture follows path of least strength/stress


Conclusions
Conclusions Electron Lithography

  • Data from the literature was combined to quantitatively model acid generation indicating that an acid bottleneck in 10-20 nm volumes and one acid per 6-25 eV of deposited energy

  • Noise from sequential Poisson processes can be combined as sqrt (1/N1 + 1/N2 + 1/N3) but parallel lateral mixing processes increase the noise by adding the noise of sorting

  • An 100 KeV e-beam experiment on thin IBM KRS-XPS resist showed minimum contacts of 20 nm, a dose to open several times larger than DCLEAR, about 4500 electrons per contact, NEFFECTIVE less than 100, and effects of surface acid reduction

  • The well know linewidth variation (LWV) that occurs over (100 nm) distances that are larger than the line-edge roughness (LER) (10 nm) feature size may have contributions from the mechanical fracture and benefit from multiple exposure pixels


ad