AC data

AC data is necessary for small signal characterization and parameter extractions. Standard AC measurements of high-frequency bipolar devices are 2-port network, Vector Network Analyzer, VNA, measurements of scattering, S-parameters. The S-parameter 2-port VNA network translates well to the linearized, hybrid-π model of Figure 1.9 for characterization of small-signal bipolar behavior.

S-parameter measurements of high frequency bipolar devices are typically taken by probing a RF configured test structure of the bipolar device at wafer/chip level on a precise RF probe station. A 50 Ω impedance environment is maintained throughout an RF probed measurement setup. 50 Ω impedance termination, at the device, is obtained by making RF probe contact to the ground-signal-ground, G-S-G, metal bondpads on the chip surface. The two-port measurement reference plane is set to the bondpad surface by a probe-tip calibration method. For RF measurements of less than 20 GHz, probe-tip calibration is done using a standard short, open, load (50Ω), thru (SOLT) calibration technique and calibration chip of standards [49]. Calibration and measurement accuracy is further enhanced by measuring an open “dummy” RF test structure and subtracting its parasitic effects from the device measurements. By using on- wafer open calibration test structures, the 2-port measurement reference plane is moved to the surface metallization above the device terminals [49]. Modeling and characterization accuracy is greatly improved since the AC measurement is now starting very close to the indicated B, E, and C terminals indicated on the model overlay of the device cross-section in Figure 6.2.

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The research lab of Georgia Tech has the specialized cryogenic temperature equipment to take RF measurements at “on-wafer/chip” level, in a cryogenic temperature environment. Dr. John Cressler’s research group developed this capability. Their group took all the SiGe RF measurements at Georgia Tech as part of the NASA, EDTP project [46], “SiGe Integrated Electronics for Extreme Environments.” The RF measurements were taken by probing an RF configured SiGe HBT test structure layout on the SiGe chip, in a custom probe station manufactured by Lakeshore. The RF probe station is equipped with a cryogenic temperature chamber which houses the chip level chuck pedestal and RF probes.

RF measurements were taken at the same four ambient temperatures: 300K, 223K, 162K and 93K, at which the DC measurements were taken. The 2-port S-parameter SiGe HBT measurement setup [50] is diagramed in Figure 5.28. The HBT is connected and biased in a common-emitter configuration for all RF measurements. The base terminal of the HBT receives both DC bias and Port 1 RF signal through RF probe contact to the base signal bondpad. The collector terminal receives DC bias and Port 2 RF signal through the RF probe contact to the collector signal bondpad. The emitter terminal is connected to DC/RF ground through both RF probes. Each RF probe makes contact to the two ground/emitter bondpads when it makes contact to the signal pad. The ground/emitter pads sandwich the signal pads. The G-S-G pad layout configuration provides a 50 Ω RF termination to both the base terminal and the collector terminal of the transistor. The emitter is shorted to the substrate at the chip level in the RF test structure circuit. On chip metallization connects the emitter bondpad to the entire backside of the chip and thereby the HBT substrate. Surface access of the backside is through a deep P+ plug implant as shown in the device cross-section of Figure 5.1.

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Figure 5.28 AC data configuration for S-Parameter measurements

AC measurements were taken by DC biasing the HBT in the linear active operating region. The S-parameter measurements over wide frequency range at each DC operating point. The operating points were over a range of VBE bias values with a constant VBC bias applied and were selected to correspond with Gummel measurements. The collector voltage bias, VC, was synchronized by a 1V offset to the applied base voltage, VB. This voltage offset provided a constant applied base-collector terminal voltage, VBC, of -1V. At each DC bias point the four S- parameters: S11, S21, S12, and S22 were measured over a frequency range of 1 GHz to 30 GHz

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in 1 GHz steps. The VBE bias range was adjusted for each ambient temperature. The applied VBE needed to generate an IC of approximately 100µA on the low end and less than 4 or 5 mA on the high end. The applied VBE increased as temperature decreased to keep the device biased in the modeling range.

Interpretation of modeling information from direct S-parameter measurements is limited. Small-signal characterization and the parameter influences on AC behavior are better adapted to 2-port h-parameter (hybrid) and 2 port y-parameter networks [51]. Fortunately, 2-port S- parameter VNA measurements can be well represented as h-parameter and y-parameter networks. The y-parameters are used to de-embed the parasitics of the bondpads and metal connections from the device measurements. By converting the S-parameters of both measurements to y-parameters the open structure’s y-parameters can be subtracted from the y- parameters of the measured device. This results in y-parameters of the device behavior only, without pad parasitics. The y-parameters are then converted back to S-parameters, yielding de- embedded S-parameter device data [50]. All AC modeling and characterization work was done with de-embedded S-parameters measurements.

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Figure 5.29 S21dB and S12dB on the left. S11 and S22 on the right in the Smith chart. De- embedded S-parameters measured at ambient temperature, 162K.

HBT DC biased in linear region at VBE= 1.03V and VBC= -1V.

The 2-port h-parameter network of Figure 5.30 has a direct relationship to the small-signal hybrid-π bipolar model of Figure 1.9 [10]. The frequency response of the small-signal current gain, βAC, is relatable to h21. The cutoff frequency, fT, is defined as the frequency at which βAC=1.

Figure 5.30 H21dB vs. Log(Frequency). Ambient temperature, 162K

h11=input impedance I1=h11I1 + h12V2 h21=forward current gain V2=h21I1 + h22V2 h12=reverse voltage gain

h22=output admittance

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The cutoff frequency, fT, can be found by extrapolating the straight line curve of h21dB to the x- axis. The βAC=1 occurs at this interception frequency. The h21dB values form a straight line with a slope of 20dB/decade. For consistency with the modeling and characterization however, fT was determined by selecting a single frequency, 10 GHz, and using the relationship of . Therefore in an ambient temperature of 162K the modeled HBT has a fT of 62.2GHz when biased at VBE=1.03V. fT was extracted for each VBE bias point from the S- parameter measurements at the four ambient temperatures. fT was plotted as a function of VBE for all temperature as shown in Figure 5.32.

Figure 5.32 fT vs. Base-Emitter Voltage for ambient temperatures: 300K, 223K, 162K, 93K.

Each temperature is indicated and defined by color.

There is an increase of approximately 200mV in VBE operating voltage as temperature decreases as shown in Figure 5.32 when comparing peak fT bias points.

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A more common and useful form for modeling is to define fT in terms of the collector current as is shown in Figure 5.33. fT versus Log(IC) is plotted for each of the four ambient temperatures.

Figure 5.33 fT vs. Log(Collector Current). Data for ambient temperatures: 300K, 223K,

162, 93K are indicated and defined by color.

The increase of fT as temperature decreases is attributed to the contribution of the Germanium bandgap effects. The base transit time, τB, and emitter transit time, τE, decrease with

temperature due to the exponential relationship of , as defined in Equations (2.20)

and (2.21)[21]. The measured AC data indicates that the maximum fT is occurring at slightly higher IC values as the temperature decreases. This slight increase is attributed to the Kirk effect beginning at slight higher IC values due to the saturation velocity decreasing with temperature[52]. At 93K, both βF in Figure (5.27) and fT in Figure (5.33) exhibit a steep rolloff at high collector currents. This behavior is attributed to high-level injection heterojunction

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barrier effects at the base-collector heterojunction interface [52]. The impact to HBT performance is controlled by the process design of the amount of bandgap offset energy at the base-collector heterojunction interface, , defined in Figure 2.6 [21]. The epilayer collector doping at this interface is also critical to the rolloff and beginning of the Kirk effect [52].

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6 Factors influencing the ambient temperature model parameter extractions

The primary objective of this cryogenic temperature SiGe model development process was to develop one model that represented DC and AC measured behavior from 300K to 93K. The single expansive temperature, SET, model was developed to represent the DC quasi-saturation and linear regions of operation as well as the AC small signal behavior, over this wide temperature range, as explained in Section 1.1 and illustrated in Figure 1.3.

In order to reach our primary objective, four ambient “at temperature” models were optimized and fitted to the data of the previous chapter. The primary factors found to influence the ambient temperature model parameter extraction approach are summarized in this chapter. The four ambient temperature models/parameters and the fitted model results are presented in Chapter 7. Each ambient temperature model has a unique model parameter set, but uses the same modified Mextram model equations. The code modifications needed to support the ambient temperature region were minimal. The ambient temperature model developed in this work differs from the standard Mextram 504.7 model. The standard model was modified with the addition of non-ideality factor parameters and the expansion of certain numerical ranges in the 504.7 code.

The four ambient temperature model parameter sets provided the temperature behavior of the model parameters over the expansive temperature range. The development of the SET model in Chapter 8 was based on the ambient models’ parameter behavior. The SET model/parameter extraction approach required two development steps:

1st _{Step - Develop four, ambient temperature, “at temperature”, SiGe model/parameter} sets. Each model/parameter set was developed by fitting the same model equations to the DC and AC device data measured at that ambient temperature. Therefore, any

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changes in the model equations for one temperature would have to be applicable to the other three temperatures. The primary factors which influenced the development of the four ambient temperature models will be discussed in this chapter. The fitting of model parameters for each ambient temperature model are discussed in Chapter 7. 2nd _{Step - Develop temperature equations and corresponding parameter values which} represent the parameters’ behavior throughout the four ambient temperature parameter sets. Create one SET model parameter set by combining: 300K ambient model parameter set, the modified Mextram model equations, and the temperature shifting model equations/parameters that represent the expansive temperature range. The results of creating the SET model are presented in Chapter 8.

Development of the four ambient temperature models required a common parameter extraction approach. Each model was fitted to the same modified Mextram model equation code. The device electrical performance at the four ambient temperatures had some common characteristics and trends. However, at colder ambient temperatures the performance exhibited some unique behaviors, as discussed in Chapter 5. Several primary factors were found to describe this unique performance. A common parameter extraction approach was used to include these primary factors. The SiGe HBT’s electrical performance over a wide temperature range influenced the modification of the Mextram model equations and model parameter extractions. The primary factors influencing the four ambient temperature model/parameters sets reviewed in this chapter are:

 Identification of the Mextram configuration features needed to represent the SiGe device structure and definition of the corresponding model parameters.

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 Definition of model parameters associated with physical device characteristics. (Section 6.3)

 Determination of the 504.7 temperature parameter values from process. (Section 6.4)

 Utilization of SiGe model equations instead of Si model version. (Section 6.5)

 Determination of the model operating conditions to be fitted for each ambient temperature. (Section 6.6)

 Model parameters defined by physical device characteristics  Bias and frequency range

 Self-heating effects

 Addition of model parameters representing non-ideality factors, NF and NR  Modifications of the standard Mextram 504.7 code for ambient models.

(Section 6.7)

 Expansion of the 504.7 numerical control for low temperature ambient modeling  Addition of parameters, NF and NR

 Expansion of parameter ranges, and changing variables to parameters