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 gate-to-channel 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)

 
Here, e, n_s0, m, and v_sat are the permittivity of the semiconductor, the equilibrium electron sheet concentration, the low field mobility, and the saturation velocity in the channel respectively, and Dd_GC is the distance between the channel/barrier heterointerface and the maximum of the electron probability distribution in the channel.

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_0.2Ga_0.8As/In_0.2Ga_0.8As 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 cm²/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.
 
 

• 5.3.2 Fitting Procedure
• 5.3.2.1 Simulation of the Transfer Characteristics
• 5.3.2.2 Simulation of the Output Characteristics
• 5.4 Model Parameters used for Simulation
• 5.5 Investigated Parameters

   
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