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SEMI E115-0302 E © SEMI 2002 2 complex con j ugate of a load im pedance of 2.0 – j20 ohms woul d be 2.0 + j20 ohms. 5.2.2 device under test (DUT) — t he matching network to be tested. 5.2.3 harmoni c frequency — the harm…

SEMI E115-0302

TEST METHOD FOR DETERMINING THE LOAD IMPEDANCE AND

EFFICIENCY OF MATCHING NETWORKS USED IN SEMICONDUCTOR

PROCESSING EQUIPMENT RF POWER DELIVERY SYSTEMS

This test method was technically approved by the Global Metrics Committee and is the direct responsibility

of the North American Metrics Committee. Current edition approved by the North American Regional

Standards Committee on March 30, 2002. Initially available at www.semi.org June 2002; to be published

July 2002. Previously published March 2002.

This document was editorially modified in May 2002 to correct an errata. A change was made in Section

1.1.

1 Purpose

1.1 The purpose of this document is to define a test

method used to determine the load impedance and

efficiency of matching networks used in RF power

delivery systems for semiconductor processing

equipment.

2 Scope

2.1 This document specifies the testing procedures and

test equipment required for determining the load

impedance and power efficiency of a matching network

based on the positions of the tuning elements in the

matching network.

2.2 The primary focus for this specification is

semiconductor processing equipment including, but not

limited to, the following tool types:

• Dry etch equipment,

• Film deposition equipment (CVD and PVD).

2.3 This standard does not address any safety or

performance issues related to RF emissions or electrical

codes (e.g., Underwriter’s Laboratory, Inc. (UL), the

National Electrical Code (NEC



), Federal

Communications Commission (FCC)). It is the

responsibility of the users of this standard to conform to

the appropriate local codes and regulations as applied to

this type of equipment, some of which are covered by

referenced documents.

2.4 This standard does not purport to address safety

issues, if any, associated with its use. It is the

responsibility of the users of this standard to establish

appropriate safety and health practices and determine

the applicability of regulatory limitations prior to use.

3 Limitations

3.1 This standard addresses RF Matching Networks

used in RF systems that primarily operate in the

frequency range of 0.2–100 MHz. It does not address

higher frequency RF systems or microwave systems.

3.2 This standard is meant for analyzing matching

networks that are designed to operate at fixed frequency

with a 50-ohm input impedance.

3.3 International, national, and local codes, regulations

and laws should be consulted to ensure that the

equipment and procedures meet regulatory

requirements in each location.

4 Referenced Standards

4.1 SEMI Standards

SEMI E113 — Specification for Semiconductor

Processing Equipment RF Power Delivery Systems

4.2 IEEE Standards

IEEE-STD-383 — IEEE Standard for Type Test of

Class 1E Electrical Cables, Field Splices, and

Connections for Nuclear Power Generating Stations

4.3 Military Standards

MIL-PRF-39012D — General Specification for

Connectors, Coaxial, Radio Frequency

5 Terminology

5.1 Abbreviations and Acronyms

5.1.1 CVD — Chemical Vapor Deposition

5.1.2 PVD — Physical Vapor Deposition

5.1.3 VSWR — Voltage Standing Wave Ratio

5.2 Definitions of Terms

5.2.1 complex conjugate load impedance — the

complex conjugate load impedance has the same real

part of the load impedance and the negative of the

reactive part of the load impedance. For example, the

1 Institute of Electrical and Electronics Engineers, IEEE Operations

Center, 445 Hoes Lane, P.O. Box 1331, Piscataway, New Jersey

08855-1331, USA. Telephone: 732.981.0060; Fax: 732.981.1721

2 Available through the Naval Publications and Forms Center, 5801

Tabor Avenue, Philadelphia, PA 19120-5099, USA. Telephone:

215.697.3321

SEMI E115-0302

complex conjugate of a load impedance of 2.0 – j20

ohms would be 2.0 + j20 ohms.

5.2.2 device under test (DUT) — the matching network

to be tested.

5.2.3 harmonic frequency — the harmonic frequencies

are defined as integer multiples of the fundamental

frequency. For example, the second harmonic of 13.56

MHz is 27.12 MHz.

5.2.4 “L” type matching network — this type of

network consists of a tuning element that is connected

to ground, which is often a variable capacitor, and

another tuning element that is in series with the output

connection. The series section of the “L” matching

network typically consists of an inductor and a

capacitor, one of which is variable.

5.2.5 load and tune position — for some matching

networks, the tuning elements are referred to as the

Load Position and the Tune Position. This terminology

is common for “L” type matching networks, which

have a tuning element that is connected to ground and

another tuning element that is in series with the output

connection. The Load Position corresponds to the

tuning element that is grounded and is associated with

matching to the real part of the load impedance. The

Tune Position corresponds to the tuning element that is

in series with the output and is associated with

matching to the reactive part of the load impedance.

5.2.6 load impedance — the load impedance is the

impedance to which a matching network is matched.

5.2.7 load impedance simulator — the Load

Impedance Simulator is a device that presents a load

impedance to which a matching network can match.

Details of a typical Load Simulator can be found in the

Related Information section of this test method.

5.2.8 matched input impedance — a matched load

impedance is defined as typically having a magnitude

of 50 ± 3.3 ohms at a phase angle of up to ± 3.8

degrees. In other words, the load is considered matched

if the reflection coefficient is no greater than 0.032 at

any phase angle.

5.2.9 matching network — the device used to

transform the impedance of the load (chamber/chuck)

to match the impedance of the generator/cable

assembly, which is typically 50 ohms.

5.2.10 power efficiency — the ratio of the power

exiting the matching network divided by the power

entering the matching network.

5.2.11 S-parameters — the scattering matrix used to

describe a network. The reflection coefficient is the

S11 parameter and the transmission coefficient is the

S21 parameter.

5.2.12 tuning element position — the position of the

tuning element is defined as the output voltage or

output encoder value that corresponds to the position of

a variable tuning element in a Matching Network. For

example, the voltage from a rotary potentiometer on the

rotating shaft of a variable capacitor (the “Tuning

Element”) would be referred to as the capacitor’s

“Position”. In this example, the position/voltage

corresponds to a certain shaft location or position.

6 Test Apparatus

6.1 RF Vector Network Analyzer — The Network

Analyzer is used to measure the load impedance and

efficiency of the matching network. The Network

Analyzer requires vector capability so that both the

magnitude of phase of the reflection coefficient and

transmission coefficient can be measured at the

operating frequency. The Network Analyzer shall have

an up-to-date calibration per the manufacturer.

6.2 Coaxial Output Adapter — An adapter to convert

the output connection of the matching network to a

standard coaxial interface is required for some of the

tests.

6.3 RF Adapters and Terminations — Various adapters

may be necessary to convert between different types of

coaxial connectors (e.g., type N to type HN adapters,

etc.). All adapters used shall have the same nominal

characteristic impedance as the system, which is

typically 50 ohms. For some measurements, additional

coaxial cable assemblies are used. These cable

assemblies shall also be of the same nominal

characteristic impedance as the system. Standard

terminations are also used, such as shorts, opens, and

precision 50-ohm loads.

6.4 RF Load Impedance Simulator — A device that

can be attached to the output of the DUT to act as a

load for the DUT is required for some of the

measurements. The load simulator shall have an

impedance range to match a minimum of 80% of the

tuning space of the matching network to be tested.

7 Safety Precautions

7.1 Work should be conducted in accordance with local

safety requirements and test device manufacturer

recommended safety procedures. The tests described in

this document involve using low output power test

instrumentation (typically less than 10 milli-Watt).

7.2 The area immediately surrounding the Test Setup

shall be keep free and clear of unnecessary equipment

and materials.

SEMI E115-0302

8 Test Setup for Determining Load Impedance

and Efficiency

8.1 Two test methods are described for analyzing

matching networks. The first method for determining

the load impedance and efficiency measures the

complex conjugate of the load impedance and then

corrects for the matching network losses to determine

the load impedance and efficiency. A schematic of the

Test Setup is shown in Figure 1. The method uses a

Network Analyzer to measure the reflection coefficient,

which is related to the load impedance, and the

transmission coefficient, which is related to the

efficiency. The Test Setup for this approach consists of

the Network Analyzer, the matching network to be

tested (DUT), coaxial test cables, and the appropriate

adapters (if any) to connect the DUT to the Network

Analyzer.

8.2 The second method for determining the load

impedance and efficiency uses a Load Impedance

Simulator attached to the output of the matching

network. A schematic of the Test Setup is shown in

Figure 2. The Test Setup for this approach consists of

the Network Analyzer, the matching network to be

tested (DUT), the load simulator, coaxial test cables,

the appropriate adapter (if any) to connect the DUT to

the Network Analyzer, and the appropriate adapter to

connect the load simulator to the DUT.

8.3 Prior to making any measurements, the Network

Analyzer shall be turned on and allowed to warm up

before the testing is to take place. This time will allow

for electronics to come to a stable operating condition

for the measurements.

9 Test Procedure for Determining Load

Impedance and Efficiency

9.1 Two test procedures can be used to determine the

load impedance and efficiency of the matching

network. The first method is designed for “L” type

matching networks, where the losses are dominated by

the loss resistance of the inductor that is in series with

the load impedance. For the case where there are finite

losses in the shunt capacitor, the capacitor losses can be

lumped in with the inductor losses without introducing

significant error (usually less than 0.5% for typical

values of < 0.1 ohms). Lumping the total losses into an

overall series loss will also cause a slight shift in the

reactive part of the impedance, but the magnitude of the

shift is on the same order as the impedance

measurement uncertainty and can be ignored.

9.2 The second method is designed for other matching

network types and uses a load simulator to determine

the load impedance and efficiency.

9.3 Test Method 1 for Determining Matching Network

Load Impedance and Efficiency

9.3.1 This test method shall be used for “L” type

matching networks of the type shown schematically in

Figure 1, where the losses in the network are dominated

by the loss resistance of the inductor, RLOSS. The

efficiency for this type of matching network is given as

Eff =

RLOAD

RLOAD + RLOSS

(1)

where RLOAD refers to the real part of the load

impedance and RLOSS refers to the losses of the

matching network.

9.3.2 For this type of network, the real part of the

complex conjugate impedance, Re(Zout*), contains the

real part of the load impedance plus twice the loss

resistance, RLOSS.

Re(

RLOAD + 2RLOS

(2)

9.3.3 The load impedance, therefore, is equal to the

complex conjugate impedance less twice the loss

resistance (along with the sign change of the reactive

part of the conjugate impedance). For example, if the

conjugate impedance is measured as 3 + j20 and

RLOSS is determined to be 0.5 ohms, then the load

impedance is 2 – j20 ohms.

9.3.4 The efficiency of the matching network and the

loss resistance, RLOSS, can be determined by

measuring both the transmission coefficient, S21, and

the reflection coefficient, S11, in the Test Setup shown

in Figure 1. Note that the reflection coefficient

measurement, S11, is equivalent to measuring the

complex conjugate impedance. If the matching

network is considered as a test load with an impedance

equal to the complex conjugate impedance, then the

loss resistance is found by measuring the efficiency of

the test load. This efficiency, Effm, can be expressed as

Effm =

Re(

out*) − RLOSS

Re(Zout*)

(3)

where Re(Zout*) is the real part of the complex

conjugate load impedance, Zout*. The measured

efficiency, Effm, can be determined from the S21 and

S11 measurements (as shown later in this section).

Thus, the measurements of Re(Zout*) and Effm can be

used to determine RLOSS as

)1(*)Re( EffmZoutRLOSS −×

(4)

and the load impedance and power efficiency of the

matching network can then be determined from

Effc =

Re(

out*) − 2RLOSS

Re(Zout*) − RLOSS

(5)