3.2 Small Signal Equivalent Circuit Parameter Extraction
 
The HEMT can be described by an equivalent circuit model shown in  Figure 3.1. To extract the model parameters from measured S­parameters a value for each parameter of the model is assumed and S­parameters are calculated based on the equivalent circuit. The chosen values are then optimized by minimizing the differences between the calculated and the measured S­parameters.
 

The transit frequencies f_T and f_max can be traced back to equivalent circuit parameters. From the intrinsic device the well known approximation for the current gain cut-off frequency f_T can be derived as
 

.

(10)

 
Extrinsic values of g_m and C_GS can be calculated by g_m = g_mi /(1+g_miR_s) and C_GS = C_GSi (1+g_mR_s). In the active bias region of a HEMT (V_DS > 0.5 V and V_GS > V_T) C_GDi is only about 15 % of C_GSi. Therefore f_T can also be approximated using the extrinsic g_m and the extrinsic total gate capacitance C_G = C_GS + C_GDi in (10).

According to [37, 38] f_max can also be approximated with equivalent circuit parameters by:
 

.

(11)

 
For measuring purposes the devices are embedded in a network of coplanar lines and contacting pads. These will be not included in the simulation area as described in Chapter 5. The contacting network can be neglected in first order for DC measurements but must be taken into account when simulated and measured RF parameters such as f_T and f_max are compared. Thus, the parasitic elements L_G, L_D, L_S, C_PG and C_PD have to be included in the equivalent circuit model.

Based on the equivalent circuit the parameters can be extracted from measured S­parameters. In the extraction procedure it is difficult to distinguish between the parasitic pad capacitances C_PG and C_PD and the gate source capacitance C_GS because they are connected in parallel and therefore only their sum can be determined reliably. In first order C_PG and C_PD are the only capacitances which do not scale with the gate width L_w. This can be used to extract these values in a different way.

The measured value of f_T includes all capacitances. The total capacitance can be determined rearranging (10) to
 

.

(12)

 
As g_m, C_GS and C_GD scale linearly with L_w and both C_PG and C_PD are constant for all the devices the sum C_PG + C_PD can be determined by extrapolating C_tot to L_w = 0. The calculated C_tot using measured g_m and f_T for different bias points is shown in  Figure 3.2. The intercept for all linear fits is very close to about 25fF. This value is used for parameter extraction of all measured devices. More details of this deembedding procedure are described in [39].
 

The schematic of the extrinsic device used for simulation is shown in  Figure 2.1 It corresponds to the intrinsic device indicated by the dashed box in  Figure 3.1 and the parasitic resistances R_S, R_G, and R_D. The deembedded device parameters will be the basis for comparison between measured and simulated data.
 

• 3.3 Determination of Capacitances by Quasi Static Approximation

   
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