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# Method of Characterizing and Modeling Two-State Device Mismatch and Across-Chip Variation

IP.com Disclosure Number: IPCOM000197735D
Publication Date: 2010-Jul-20
Document File: 5 page(s) / 82K

## Publishing Venue

The IP.com Prior Art Database

## Abstract

Disclosed is a method of modeling a two-value (for a fixed device dimensions) mismatch and Across-Chip Variation (ACV) problem.

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Page 1 of 5

Method of Characterizing and Modeling Two -State Device Mismatch and Across -Chip Variation

To create the shallow junctions with low resistivity required in the recent technology nodes, engineers need an anneal technique that generates a high temperature in very short time. Laser spike anneal (LSA) is such a technique. Semiconductor industry and others started to use laser spike anneal (LSA) in semiconductor manufacturing at 65 and 45 nm technology nodes.

One side effect that LSA has on a device's variation is a loss of correlation between certain device characteristics. For example, for polysilicon and diffused resistors manufactured with LSA, measured data at 45 nm silicon-on-insulator (SOI) technology reveals a loss of correlation between the resistance values of two resistors placed a few mm (2 mm, 5 mm, 10 mm, 15 mm, etc.) apart. In other words, the value of mismatch or across-chip variation (ACV) for such resistors can be characterized as two discrete values. For two closely placed resistors (say, distance < 0.2 mm), the mismatch in resistance value is

,

)

,

(

)

σ ≡

=

Δ

(

A

P

m

σ0 L

W

R

r

n

n

W

n

L

(1.1)

where R

n is the nominal resistance value (same for all resistors of the size dimensions),

σ(Δr) is the standard deviation of resistance difference, Δr = r

i - r

j

, between the i

and

j

th

th

resistors, A

P is the area proportionality constant for resistance r, and W

n and L are the

dimensions of each resistor. For ACV (say, distance >= 0.2 mm),

.

)

,

(

)

σ( 2

20 acv

n

m

n

L

=

W

+

R

Δr σ

σ

(1.2)

Known approaches use a switch in resistor's model. For one value of the switch, ACV is turned-off, and mismatch is modeled. In another value of the switch, ACV is turned-on, but mismatch can not be modeled at the same time. Overall, three variations (single device's total variation, mismatch among adjacent devices, and ACV between two separated devices) are not modeled simultaneously.

The solution presented here is a method of modeling a two-value (for a fixed device dimensions) mismatch and across-chip variation (ACV) problem. The method leads to a valid and satisfactory solution for a statistical variable or for a device's characteristic in which:

1. Single-device's standard deviation does not vary with, e.g., its distances to other devices (or whether an ACV switch is turned on or off), and

2. Single-device's tolerance, mismatch, and ACV can be simultaneously and correctly modeled.

1

Page 2 of 5

In addition, disclosed is a method of characterizing a device's ACV for all device dimensions using a general relation which can be represented in a Simulation Program with Integrated Circuit Emphasis (SPICE) model.

Requirements for a good device model describing both mismatch and ACV are: [see also Figure]

All instances must have the same mean value,

All instances must have the same and distance-independent standard deviation, and

The mismatch and ACV among a set of concerned devices can be accurately and conveniently describe...