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Geng(SMH)_CH06.qxd 04/04/2005 19:37 Page 6.9

PLASMA PROCESS CONTROL

PLASMA PROCESS CONTROL 6.9

reduces the voltage on the transmission line to

V()−= V 1 = V rf [ + Γ ()]
−
l
1
l
rf + 1 +Γ (− l)
1 1 −Γ (− l) 2
Accordingly the current on the transmission line to
I()−= V rf [ − Γ ()]
−
1
l
l
2 Z o
The time-averaged power at the input is then described by
P av,in = 1 ℜ{ V I } = 1 ℜ{ Z I I }
in in
in in in
2 2
V −
2
P av,in = 1 ℜ{( l I − l)} = 1 V | | 2 1 [ − | Γ l − ( ) | ]
(
)
2 2 Z o
The reflection coefficient is zero when the load (in this case Z ) is equal to the characteristic
in
impedance of the transmission line, Z . When this occurs the time-averaged power at the input
o
achieves a maximum
P = P = V | | 2
av,in max
2 Z
o
The matching network usually has at least one tunable element since the impedance range of the
plasma can vary based on power, pressure conditions, and chemistry of the discharge. The tunable
element(s), usually a capacitor, of the matching network adjusts the impedance of the matching net-
work to a load impedance that is within the operating specification of the RF generator. In mathe-
matical terms, the matching network arrives to an impedance value that is a near equivalent to the
complex conjugate of the plasma impedance. This cancels the phase component difference and
requires a scaling of the impedance magnitude. When the matching network is tuned to the optimal
load impedance of the RF generator, the transfer of power into the discharge is maximized.
The tuning operation of the matching network is accomplished by circuitry that is internal to the
matching network. The circuitry of the matching network has an RF detector and associated elec-
tronics that measure the impedance magnitude and phase. These measurements are used as feedback
elements to command the tunable element(s) of the matching network. Traditionally, this has been
28
accomplished with analog and mixed signal circuitries. This has some limitations due to the non-
linear equations that describe the transfer of power based on impedance. A more novel approach uses
29
a digital controller with fuzzy logic to command the tunable element. Today, the industry is expe-
riencing the advent of solid-state matching networks to replace the passive elements of the traditional
matching network. A matching network using a pin-diode configuration is one such example. 30
Another alternative to matching the impedance of the plasma to the RF source impedance is to
31
use a fixed match with an RF generator that has an agile frequency. Auto frequency tuning has the
major benefits of speed, cost, and reliability by eliminating the movable tuning elements found in
traditional matching networks. To use auto frequency tuning, it is necessary to incorporate a match-
ing network with a fixed impedance between the generator and chamber. This matching network
must be designed so that the process window of impedance can be tuned within a reasonable fre-
quency range (typically ±10 percent for mid frequency and +5 percent for high frequency). The oper-
ation of auto frequency tuning generators is analogous to the operation of a tunable matching
network. The tunable matching network adjusts the real and imaginary components of the imped-
ance to a tune range within the operating specification of the RF generator. In the case of auto fre-
quency tuning generators, the fixed match converts the real component of the impedance and the auto

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