5.3.1 Identification of the Most
Critical Parameters
A figure of merit for HEMTs is the maximum transconductance g_{m
max}. One of the most important parameters governing g_{m
max} is the gatetochannel separation d_{GC}.
The thickness of the epitaxial layers can be controlled very precisely
by MBE growth. The critical technological step which determines the magnitude
of d_{GC} is the gate recess. In the recess region it is
intended to remove the GaAs cap layer completely but to leave the AlGaAs
Schottky barrier intact. In practice, this etching can only be performed
with a finite selectivity, and the effective recess depth can vary a few
nanometers across the wafer or from on processing run to another. Therefore,
small deviations in the order of 2 nm of the actual d_{GC}
from the nominal values must be considered to be realistic. Deviations
of the gate length L_{G} from their nominal values are also
technological inevitable. These deviations highly depend on the used technology
to define the gate structure.
First the impact of the most important parameters on the intrinsic device
should be investigated using an analytical formula. The intrinsic g_{m
max int} (i. e. g_{m max} for vanishing source
resistance R_{S}) of a HEMT is given by [58]:
. 
(60)











The parameters m and v_{sat}
depend on the channel material whereas L_{G} and d_{GC}
are geometry quantities defined by process technology. The equilibrium
electron concentration n_{s0} depends on various parameters
such as doping concentration in the barriers, the distance of the doping
layer to the channel, and the height of the energy barriers. For practical
devices with typical values n_{s0} this will have almost
no influence on g_{m max int} as shown in Figure
5.15 but only determine the threshold voltage V_{T}.
In the following g_{m max int} will be plotted versus the
parameters m, v_{sat}, L_{G},
and d_{GC} to qualitatively analyze what has to be expected
for the measured and simulated devices investigated in Chapter
6. Typical values of an Al_{0.2}Ga_{0.8}As/In_{0.2}Ga_{0.8}As
HEMT used for the plots are given in Table
5.1. The parameters which are not varied actually are kept at these
constant values.
The magnitude of the material parameter m
can be determined by Hall measurements. The absolute measured values have
fairly large uncertainties because there is no standardized epitaxial Hall
structure. Figure
5.16 reveals that g_{m max int} is nearly independent
of m for L_{G} < 250
nm and m higher than about 4000 cm^{2}/Vs.
With increasing L_{G} the influence of m
increases.
The experimental determination of v_{sat} is even more
difficult than that of µ and can be done directly only for bulk material.
When the same material is used in a quantum well additional effects have
to be taken into account. These are the change in alloy scattering depending
on the growth technique, interface roughness, Coulomb scattering, electron
scattering and change in the v(E) characteristics due to quantization
effects. Today there are no models suitable for device simulation which
can describe these effects in AlGaAs/InGaAs quantum wells. It has to be
expected that v_{sat} is reduced significantly compared
to the bulk material values. Therefore especially v_{sat}
is considered to be a fitting parameter. In Figure
5.17 the dependency on v_{sat} is shown. Practical devices
operate in the saturation region when they reach their maximum g_{m}.
Therefore g_{m max int} is almost linearly dependent on
v_{sat} as expected.
The dependence of g_{m max int} on L_{G}
is plotted in Figure
5.18. For L_{G} < 250 nm only a small influence can
be observed. The decrease is almost linear for L_{G} > 500
nm. The expected reduction proportional to
occurs for gate lengths of several microns (not shown in Figure
5.18).
As shown in Figure
5.19 the dependence of g_{m max int} on (d_{GC}
+ Dd_{GC}) is only moderate for
values larger than about 30 nm. It appears that g_{m max int}
gets extremely sensitive to (d_{GC} + Dd_{GC})
for much smaller values which nowadays can be manufactured with an accuracy
below 2 nm. Considering (d_{GC} + Dd_{GC})
= 20 nm a reduction of 1 nm (which corresponds to only 4 atomic layers)
increases g_{m max int} by about 50 mS/mm. This establishes
d_{GC} as the most important technological parameter for
the transconductance of HEMTs with L_{G} below 1 µm
which are nowadays used for practical applications.
Next: 5.3.2 Fitting Procedure Up:
5.3 Determination of the Parameter Set for the Simulation
Previous: 5.3 Determination of the Parameter Set
for the Simulation
Helmut Brech 19980311