# Contact Edge Roughness (CER)

**Contact edge roughness of nano-particles**

Lacerm provides a mean to inspect nano-particles after they have been formed either by a top-down or a bottom-up method. The parameters, e.g. the contact edge roughness, the mean diameter, the deviation of the diameters, which often decide the quality of the sample, can be extracted.

## The example here shows the SEM image of metal particles on a silicon wafer, which was fabricated by EB lithography and lift-off technique. It only detects the edges of the particles avoiding the debris around and the holes on particles. These are two things can come along during a lift-off process. Power spectral density (PSD) measurement in the metrology of nano-particles is new, and it can be calculated with a single click here.

## Contact Holes - Cross Section

## Contact Edge Roughness

In lithography metrology and also in the fabrications of nano-devices, an array of holes is often created on a photoresist layer on top of a substrate (left picture illustrates the cross-section of such sample). A photoresist is an organic or inorganic polymer which is sensitive to photons (also electrons). Recently, there has been a lot of attention in hybrid-photoresists which are the mixtures of both organic and inorganic materials. Mean CER and the deviation of CERs are among the main parameters which are used to evaluate the performance of the photoresist. Lacerm can measure these two parameters from a large area covering many holes in no time (right picture).

**Metrics**

Similar to the case of line-space patterns, CER and Mean-CER of nano-particles and contact holes are defined in the same way.

Assume that we have detected *n* holes, the number of points on the edge of i^{th} holes is *N*_{i} (*i* = 1,...,n) , and Δ*x*_{ij} is the edge residual of point *j* on hole *i*.

**1) CER**

Contact edge roughness is defined as 3 times the standard deviation *σ* (CER = 3**σ*).

σ=1N0-1∑j=1N0∆xj-μ2

where N_{0} is the total number of all points *N*_{0}* = N*_{1}* + N*_{2}* + ... + N*_{n}, Δ*x*_{j} is the edge residual of the j^{th} point of the total points of *n* holes, and *µ* is the average of Δ*x*_{j}.

**2) Mean CER**

The standard deviation σ_{i} of the i^{th} hole is defined as

σi=1Ni-1∑j=1Ni∆xij-μi2,

where *µ*_{i} is the average of Δ*x*_{ij}.

Contact edge roughness of the i^{th} hole CER_{i} is defined as 3 times its standard deviation *σ*_{i}. CER_{i} = 3**σ*_{i}*.*

Mean CER is then defined as the average of CER_{i} (i = 1,...,n).

**3) CER Deviation**

CER deviation is the deviation of CER_{i} (i = 1,...,n).

**4) Diameter**

Diameter is the mean diameter of the holes.

**5) Diameter Deviation**

Diameter deviation is the deviation of the diameters of the holes.