Sentaurus Technology Template: DC and RF ...

Sentaurus Technology Template: DC and RF Characterization of HEMTs

Abstract The purpose of this Sentaurus TCAD simulation project is to provide a template setup for the DC and RF characterization of high electron mobility transistors (HEMTs). For HEMTs, the following simulations are performed: IdVgs, a family of IdVds curves, on-state and off-state breakdown, and RF analysis. The template is based on an InGaAs HEMT; however, the project structure and input files can be used for any HEMT with only minor modifications. For each of the simulated IV curves, relevant electrical parameters such as pinch-off voltage, transconductance, drain saturation current, and breakdown voltage are calculated. Furthermore, RF parameters such as ft and fmax, as well as other twoport network and RF gain parameters, are computed.

Synopsys and the Synopsys logo are registered trademarks of Synopsys, Inc. Copyright © 2007 Synopsys, Inc. All rights reserved.

Introduction This project provides standard templates for Sentaurus Device, which can be used to perform the most common types of simulation for the characterization and performance assessment of HEMTs. There are three different Sentaurus Workbench projects: ■

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A DC characterization project HEMT_DC, which performs an IdVgs simulation and computes a family of IdVds curves. A breakdown simulation project HEMT_BV, which computes the on-state and off-state breakdown.

Project setup: HEMT_DC The first Sentaurus Workbench template project performs device simulations relevant for the DC characterization of HEMT devices.

Sentaurus Device Sentaurus Device performs IdVgs and IdVds sweeps. The bias conditions and the number of sweeps are controlled using the following Sentaurus Workbench parameters: ■

Vgmin [V] defines the minimum gate voltage for the IdVgs or IdVds sweeps. Here, it is set to -1.5 for the IdVgs sweeps and to -0.8 for the IdVds sweeps.

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Vgmax [V] defines the maximum gate voltage for the IdVgs or IdVds sweeps. Here, it is set to 0.8.

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It is assumed that the user is familiar with the Sentaurus tool suite, in particular, Sentaurus Workbench, Sentaurus Structure Editor, Sentaurus Device, and Inspect. For an introduction and tutorials, refer to the Sentaurus training material.

Vd [V] defines the drain bias for the IdVgs sweeps and the final drain voltage for the IdVds sweeps. It is set to 0.05 for the low bias IdVgs sweep and to 1.5 for the high bias IdVgs sweep, as well as the IdVds sweeps.

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The focus of this project is to provide setups that can be used as they are or adapted to specific needs. The documentation focuses on aspects of the project setup. For details about tool uses and specific tool syntax, refer to the respective manuals.

IdVd = 0,1,2,3,... For IdVd = 0, an IdVgs sweep is performed. For IdVd = N, a family of N IdVds sweeps is simulated at gate biases equally spaced between Vgmin and Vgmax. Here, the parameter is set to 0 (IdVgs) and 5 (IdVds).

Inspect

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A small-signal simulation project HEMT_RF, which performs a two-port network analysis.

All three projects are based on an analytic InGaAs HEMT device structure, which is created using Sentaurus Structure Editor.

General simulation setup The simulations are organized in three Sentaurus Workbench projects. The tool flow of the projects are discussed here. The tool flow consists of Sentaurus Structure Editor, which creates the analytic HEMT structure; Sentaurus Device, which calculates the device characteristics; and the visualization tool Inspect. For each tool, the associated Sentaurus Workbench input parameters, as well as the extracted parameters, are discussed.

All projects

Inspect plots the respective IV characteristics and extracts: ■

Vtgm [V] is the threshold voltage, defined as the intersection of the tangent at the maximum transconductance gm with the Vgs axis.

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Vti [V] is the threshold voltage, defined as Vgs at which Id = 1 mA/mm.

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Idmax [mA/mm] is the maximum value of the IdVgs curve.

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Ron [kΩ mm] is the on-state resistance, extracted for Vgs = 0 V and Vds = 1 V.

Project setup: HEMT_BV

Sentaurus Structure Editor

The second Sentaurus Workbench template project performs on-state and off-state breakdown simulations of the HEMT device.

The analytic HEMT structure is defined with Sentaurus Structure Editor. The Sentaurus Structure Editor setup is identical for all three HEMT template projects.

Sentaurus Device

The generated structure, mesh, and doping information are stored in a TDR file, which is then passed to Sentaurus Device.

Copyright © 2007 Synopsys, Inc. All rights reserved.

Sentaurus Device performs breakdown simulations using two different methods. In the direct method, a large resistor is attached to the drain (load line) and the drain is ramped to a very high voltage. Depending on the gate bias, this yields the on-state or off-state breakdown. Alternatively, the draincurrent injection method [1] is used to perform an off-state 3

breakdown simulation. In this method, the drain current level is held constant while the gate is closed. To maintain the drain current, the drain voltage must rise sharply when the gate closes. When breakdown sets in, the drain voltage saturates.

Project setup: HEMT_RF

The bias condition and type of breakdown simulation are controlled using the Sentaurus Workbench parameters:

Sentaurus Device

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Vg [V]: Gate bias. For the on-state breakdown IdVds sweep, the bias is set to 0. For the off-state breakdown IdVds sweep, the bias is set to -1.5. For the draincurrent injection method, this parameter sets the end point of the gate voltage sweep. Here, the value –5 is used. Vd [V]: For the direct method, this parameter sets the end point of the drain bias sweep. Values of 200 and 400 are used for the on-state and off-state breakdown sweeps, respectively. For the drain-current injection method, this parameter is used pre-bias the drain, before switching to the current boundary condition. Here, a value of 0.1 is used. Rd [Ω μm]: This parameter sets the value of the drain contact resistance. In the direct method, the resistance is set to a high value in order to emulate a load line. Values of 1e4 and 1e5 are used for the on-state and off-state breakdown sweeps, respectively. For the drain-current injection method, this parameter is set to the regular drain contact resistance of 150. Id [mA/mm]: If this parameter is set to 0, the direct method is used. For a nonzero value, the drain-current injection method is used and the value gives the current level. Here, three different current levels are used (200, 300, and 500).

The third Sentaurus Workbench project is designed to investigate the RF characteristics of the HEMT device.

Sentaurus Device performs a small-signal analysis during an IdVgs sweep. The bias conditions and feedback circuit are controlled using the Sentaurus Workbench parameters: ■

Rfb [Ω μm]: For Rfb = 0, no external resistive feedback from drain to gate is considered. Otherwise, a resistor of the given magnitude between the drain electrode and the gate electrode is included in the circuit setup. Here, the values 0 and 1e5 are used.

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Vgmin [V] defines the minimum gate voltage for the IdVgs sweep. Here, it is set to -0.5.

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Vgmax [V] defines the maximum gate voltage for the IdVgs sweep. Here, it is set to 0.5.

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Vd [V] defines the drain bias for the IdVgs sweep. Here, it is set to 1.0.

Inspect The Sentaurus Workbench variable Extract controls which RF parameter Inspect plots and extracts: ■

IdVg: IdVgs and the DC transconductance are plotted.

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fmax: The maximum frequency of oscillation (fmax) is plotted as a function of bias for three different extraction methods: unit-gain-point, extract-at-dBPoint, and extract-at-frequency. The maximum fmax value over all bias points for the unit-gain-point method and the extract-at-dBPoint method is written to the Sentaurus Workbench Family Tree together with the bias point at which the maximum is reached.

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MUG: A family of Mason’s unilateral gain curves is plotted as a function of frequency for all bias points.

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MUG_b: A family of Mason’s unilateral gain curves is plotted as a function of bias for all frequencies.

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ft: The cut-off frequency (ft) is plotted as a function of bias for three different extraction methods: unit-gainpoint, extract-at-dBPoint, and extract-at-frequency. The maximum ft value over all bias points for the unit-gainpoint method and the extract-at-dBPoint method is written to the Sentaurus Workbench Family Tree together with the bias point at which the maximum is reached.

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h21: The RF parameter h21 is plotted as a function of frequency for a gate bias of 0 V. The plot shows the real and imaginary parts of h21 as well as the magnitude and phase.

Inspect Inspect plots the respective IV characteristics and extracts: ■

BVv [V]: Breakdown voltage defined as the maximum inner voltage on the drain. The inner voltage is measured at the device contact directly and does not include the voltage drop across the contact resistance.

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BVi [V]: Breakdown voltage defined as the inner drain voltage at which the drain current reaches a certain value. Here, a value of 1000 mA/mm is used.

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BVc [V]: Breakdown voltage determined using the drain-current injection method. Here, the breakdown voltage is defined as the drain voltage reached after the gate has been biased well below the pinch-off voltage. Here, a value of Vgs = –1.5 V is used.

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h21_b: The RF parameter h21 is plotted as a function of bias for a frequency of 1 GHz. The plot shows the real and imaginary parts of h21 as well as the magnitude and phase.

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fK1: A plot of the boundaries of the region of unconditional stability is shown. This boundary is defined as the isolines at which the Rollett stability factor (K) is one. If two boundaries exist for a given bias point, the low frequency line is red and the high frequency line is blue. To highlight in which regions the device is unconditionally stable, the isolines at which K=1.1 are also shown as green dashes.

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MSG: The maximum stable gain (MSG), the maximum available gain (MAG), and the Rollett stability factor (K) are plotted as a function of frequency for a gate bias of 0 V.

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MSG_b: MSG, MAG, and the Rollett stability factor (K) are plotted as a function of bias for a frequency of 1 GHz.

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Smith: The RF parameters s11 and s22 are plotted on a Smith chart for all frequencies and a gate bias of 0 V. Note that the frequency associated with a given point on the Smith chart can be identified by clicking the respective frequency label on the legend.

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Smith_b: The RF parameters s11 and s22 are plotted on a Smith chart for all bias points and a frequency of 1 GHz. Note that the bias associated with a given point on the Smith chart can be identified by clicking the respective bias label on the legend.

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S21S12: The RF parameters s21 and s12 are plotted on a polar plot for all frequencies and a gate bias of 0 V. Note that the frequency associated with a given point on the polar plot can be identified by clicking the respective frequency label on the legend. Export2CSV: The RF parameters Y, H, Z, and S are written to a text file using a comma-separated values (CSV) format, which can be read by any spreadsheet program. The file contains a header, which lists the number of bias and frequency points as well as the minimum and maximum bias points and frequencies. The header is followed by a table, which contains the frequency, the bias, and the real and imaginary parts of the respective components of the RF parameters matrix (for example y11, y12, y21, and y22). Two versions of the CSV file are written. One is sorted by frequencies and the other is sorted by bias points.

Tool-specific setups Sentaurus Structure Editor and Sentaurus Mesh Sentaurus Structure Editor is used to define the HEMT devices in a fully parameterized manner. Copyright © 2007 Synopsys, Inc. All rights reserved.

The HEMT layer structure is as follows (the actual names of the Scheme variables used in the parameterization of the HEMT structure are given in parentheses): ■

Substrate: 0.8 μm GaAs (HGaAsSub)

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Channel: 10 nm InGaAs (HChannel)

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Spacer: 34.5 nm AlGaAs (HSpacer)

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Cap layer: 30 nm GaAs (HGaAsCap)

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Passivation layer: 50 nm nitride (HPass)

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Location of delta-doping layer: 31 nm (YDelta)

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Thickness of delta-doping layer: 2 nm (DeltaThick)

The gate Schottky contact is etched into the top spacer layer. This gate recess is 15 nm deep (GRecess). The gate length is 0.25 μm (Lg). At each side of the gate, a 40 nm wide oxide layer isolates the gate from the cap layer (Wsp). The sheet doping concentration is 5.4 x 1012 cm–2 (SheetCharge). It is assumed that the dopants are in a tight Gaussian distribution, with a diffusion length given by the thickness of the delta-doping layer. Mole fractions and trap concentrations are defined in the input file of Sentaurus Device. To adjust details of the devices, users can modify the top section of the Sentaurus Structure Editor input file sde_dvs.cmd. For example, the width and sheet doping concentration of the delta-doping layer are defined by the Scheme variables: (define DeltaThick 0.002) ; [um] (define SheetCharge 5.4e12) ; [1/cm2]

Other geometric, doping, and meshing parameters are accessible in a similar manner. The meshing strategy is designed to result in a high-quality mesh without excessive node counts for a large range of geometric parameters. Most of the meshing strategy is defined using regular refinement boxes, which specify the allowed minimum and maximum mesh spacing within a specified area. It is the meshing algorithm that places the actual lines. For the deltadoping layer, a new feature is applied that allows users to place lines explicitly, by defined a list of x- and y-values at which a line is to be added. To use this feature, a stanza is added to the Sentaurus Mesh command file, which has the form: AxisAligned { xCuts = ( ) yCuts = ( ) }

Sentaurus Structure Editor calls a meshing engine to generate the structure files for Sentaurus Device. Sentaurus Mesh is called from within Sentaurus Structure Editor with: (sde:build-mesh "snmesh" "n@node@_half_msh")

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This command generates a device structure in TDR format, containing doping and grid data. Note that only half of the HEMT structure is created by Sentaurus Structure Editor and meshed with Sentaurus Mesh. It is subsequently reflected about the vertical axis to obtain the full device. The reflection is performed in Sentaurus Structure Editor by a system call to Sentaurus Data Explorer (tdx): (system:command "tdx -mtt -x -ren drain=source n@node@_half_msh n@node@_msh")

The option -x instructs Sentaurus Data Explorer to reflect the device along an axis defined by x = x min . The given half-structure has three contacts: drain, gate, and substrate, which are defined in sde_dvs.cmd. Of these, the gate and substrate contacts touch the axis of reflection and, upon reflection, are extended and thereby preserve their names. However, the drain contact in the reflected half is named drainmirrored by default. This contact is explicitly renamed to source with the Sentaurus Data Explorer command-line option -ren. The device obtained using Sentaurus Structure Editor is shown in Figure 1.

The mole fraction in the AlxGa(1–x)As spacer layer is set to x = 0.3 with: Physics(Material="AlGaAs"){ MoleFraction(xFraction=0.30 Grading=0) }

In the substrate layer, a donor trap concentration of 1016 cm–3 is defined with: Physics( Region="R.GaAsSub" ){ Traps( (Donor Conc=1e16 EnergyMid=0.61 fromCondBand eXsection=2.5e-18 hXsection=2.5e-16) ) }

Hydrodynamic transport is used for the electrons. Highfield mobility saturation is selected. Furthermore, Shockley–Read–Hall (SRH), Auger, and radiative recombination models are activated. For the breakdown simulations, the avalanche generation model is used as well. At the Ohmic source and drain contact, a contact resistance of 150 Ω μm is set, and the gate is defined as a Schottky contact with a Schottky barrier height of 0.9 eV and electron and hole recombination velocities of 107 cm/s: Electrode{ { Name="source" Voltage=0.0 Resistor= 150 } { Name="drain" Voltage=0.0 Resistor= 150 } { Name="gate" Voltage=0.0 Schottky Barrier=0.9 eRecVelocity=1.e7 hRecVelocity=1.e7 } ... }

Figure 1

HEMT device generated by Sentaurus Structure Editor. For better viewing, different scales are used for the x-axis and y-axis.

Sentaurus Device Sentaurus Device is used to simulate the various DC current-voltage as well as the RF characteristics. The mole fraction in the In(1–x)GaxAs channel is set to x = 0.75 with: Physics(Material="InGaAs"){ MoleFraction(xFraction=0.75 Grading=0) }

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Figure 2

Electron concentration under the gate at Vgs = –1.5 V and Vds = 1.5 V. The mesh in this critical area is shown. For better viewing, different scales are used for the x-axis and y-axis.


To suppress such artifacts, the energy relaxation time is effectively reduced in regions where the carrier density is less than RelTermMinDensity: Math{... ErrRef(Electron) = 1e7 ErrRef(Hole) = 1e4 RelTermMinDensity = 1e4 RelTermMinDensityZero = 1e7 }

For the IdVds sweeps (see Figure 4), first the gate is ramped to Vgmin and then to Vgmax. During the sweep from Vgmin to Vgmax, the solution is saved at a number of equidistant bias points. This number is set by the Sentaurus Workbench parameter IdVd. The solutions are reloaded one by one and a drain bias sweep is performed. 700

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Drain Current [mA/mm]

To track accurately the electron and hole concentrations, the error control parameter ErrRef(Electron|Hole) is reduced from the default value of 1010 cm–3 to 107 cm–3 for the electrons and 104 cm–3 for the holes. In regions with very low concentrations, such as the depletion region under the Schottky contact, the carrier temperature is not a welldefined quantity. It is possible that the numeric solution of the partial differential equation (PDE) results in nonphysically high temperatures in such regions, which can have a negative effect on convergence.

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Vgs = 0.8 V Vgs = 0.4 V Vgs = 0.0 V Vgs = -0.4 V Vgs = -0.8 V

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(RelTermMinDensityZero controls the reduction of the energy relaxation time in low density regions in which artificial cooling occurs.)

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DC characterization

Figure 4

For the IdVgs sweeps (see Figure 3), the gate and drain are first ramped together to the bias conditions defined by the Sentaurus Workbench parameters Vgmax and Vd. Then, the gate is ramped to the final bias point defined by the Sentaurus Workbench parameter Vgmin. (Note that, in HEMT devices, often faster convergence can be obtained by sweeping an open device into pinch-off, instead of starting at pinch-off.)

Breakdown simulations

Vds = 1.5 V Vds = 50 mV


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1.2

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Drain current as function of drain voltage for a gate bias of Vgs = –0.8, –0.4, 0.0, 0.4, and 0.8 V

For the breakdown simulations, two different methods are used. In the direct method (see Figure 5 on page 8), a large load-line resistor is attached to the drain contact and the drain is ramped to a very large value. After the onset of impact ionization, most of the voltage drop occurs across this resistor if the value chosen is sufficiently large. Therefore, this simple technique achieves an automatic switching from a voltage-controlled prebreakdown regime to a current-controlled post-breakdown regime. The breakdown IV characteristics can be seen by plotting the terminal current versus the inner contact voltage instead of the outer contact voltage. The appropriate value for the attached resistor is of the order of R = V/I at the onset of impact ionization. This technique is used here for the onstate as well as the off-state breakdown simulations. The values of the external resistor are defined using the Sentaurus Workbench parameter Rd. The external resistor is declared in the Sentaurus Device Electrode section with:

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0 -1.5

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Drain Voltage [V]

Electrode{... { Name="drain" Voltage=0.0 Resistor= @Rd@ } } -1

-0.5

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Gate Voltage [V] Figure 3

Drain current as function of gate voltage for a drain bias of Vds = 50 mV (blue) and 1.5V (red)


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function of the gate bias originates from the resistance of the substrate layer, which now carries most of the current.) 2500


RF characterization 2000

For the simulation of the RF characteristics, the same biasing and sweeping scheme as for the IdVgs simulation is used. At equidistant bias points, Sentaurus Device performs a small-signal analysis (AC) for various frequencies and it stores the small-signal admittances and capacitances for all contact-to-contact combinations (this data is equivalent to the Y-matrix). During postprocessing with Inspect, this data is used to determine the various RF parameters.

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500 On-state BV: Vgs = 0 V Off-state BV: Vgs = -1.5 V 0 0

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Drain Voltage [V] Figure 5

On-state and off-state breakdown calculated using the direct method: blue curve is IdVds at Vgs = 0 V (on-state breakdown) and red curve is IdVds at Vgs = –1.5 V (off-state breakdown)

With the drain-current injection method [1] (see Figure 6), the HEMT is first biased to a nonzero drain bias, given by the Sentaurus Workbench parameter Vd, in order to have a nonzero current flow. Then, the contact boundary condition is switched from voltage controlled to current controlled with: Set ( "drain" mode Current )

The drain current is ramped to a value given by the Sentaurus Workbench parameter Id. Finally, the gate is closed by ramping it to a large negative value, given by the Sentaurus Workbench parameter Vg.

Drain Voltage [V]

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Id = 500 mA/mm Id = 300 mA/mm Id = 200 mA/mm

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Gate Voltage [V] Off-state breakdown calculated using the drain-current injection method: drain voltage as function of gate voltage for a constant drain current level of Id = 500 (blue), 300 (green), and 200 (red) mA/mm

Near pinch-off, the channel resistivity rises sharply. To maintain the current level, the drain voltage must rise sharply. At some point, impact ionization sets in and the device resistivity stabilizes. Then, the drain voltage saturates. (The residual slope of the drain voltage as a

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drain=2 source=0 substrate=0) 1 0 ) { dc = 0 } 2 0 ) { dc = 0 } (1 2) { resistance = @Rfb@ }

If the Sentaurus Workbench parameter Rfb is set to a nonzero value, an external feedback resistor is also included in the circuit.

Quasistationary( ... Goal{ Parameter=vg.dc Voltage=@Vgmax@ } ){ ACCoupled( StartFrequency= 1e8 EndFrequency= 1e12 NumberOfPoints= 13 Decade Node(1 2) Exclude(vg vd) ACCompute( Time=(Range=(0 1) Intervals=20) ) ){ Poisson Electron Hole eTemperature } }

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Figure 6

System { HEMT hemt (gate=1 Vsource_pset vg ( Vsource_pset vd ( #if @Rfb@ != 0 Resistor_pset Rfb #endif }

The AC analysis is activated with the ACCoupled statement:

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A mixed-mode environment is required for AC simulation in Sentaurus Device, that is, instead of simulating an isolated HEMT, the HEMT is embedded in an external circuit. Here, a two-port network circuit configuration (see Figure 7 on page 10) is used, in which voltage sources are attached to the gate (port 1) and drain (port 2) terminals. All other terminals are grounded. The circuit is defined in the System section:

The ACCompute statement defines that the AC analysis will be performed at 21 evenly spaced bias points between the starting bias point Vgmin and the bias end point Vgmax. The frequency range is set from 100 MHz (1e8) to 1 THz (1e12). This range is sampled by 13 logarithmically distributed points (that is, 3 points/decade).

DC extractions with Inspect In the Sentaurus Workbench tool flow, Sentaurus Device is followed by the Sentaurus visualization tool Inspect. This


tool plots the corresponding IV characteristics and extracts relevant electrical parameters, as discussed in General simulation setup on page 3. The extractions are performed with the help of the Inspect library EXTRACT. The extraction routines are activated with: load_library EXTRACT

(Refer to the Inspect User Guide for more information about this library.)

ExtractVti

where Name defines the name of the extracted parameter, Curve refers to the name of the Inspect IdVgs curve, and Ilevel defines the drain current level at which the gate voltage is extracted. For example, the call: set Io 1 ; # [mA/mm] set Vti [ExtractVti Vti Id $Io]

results in output such as: DOE: Vti -1.076 Vti (Vg at Io=1.000e+00): -1.076 V

Scaling IV data Extracting maximum transconductance By default, for 2D simulations, Sentaurus Device uses the units of A/μm if no explicit AreaFactor is specified in the Physics section. For HEMT devices, it is common to use the units mA/mm. Rescaling to these units is performed with the utility routine cv_scaleCurve, which is part of the EXTRACT library. cv_scaleCurve Id 1 1e6 y

The first argument gives the name of the curve to be scaled, the second and third arguments give the scaling factors for the x-axis and the y-axis, and the last argument defines on which y-axis the scaled curve should be displayed (y or y2).

Extracting threshold voltage using transconductance method

The routine ExtractGm extracts the transconductance. The routine is called with:

maximum

ExtractGm

where Name defines the name of the extracted parameter, Curve refers to the name of the Inspect IdVgs curve, and Type can be either "nMOS" or "pMOS". For example, the call: set gm [ExtractGm gm Id "nMOS"]

results in output such as: DOE: gm 1.955e+02 gmb: 1.955e+02 mS/mm Max gmb is at Vg= -0.918 V

Extracting maximum y-value The routine ExtractVtgm extracts the threshold voltage using the maximum transconductance method. The routine is called with: ExtractVtgm

where Name defines the name of the extracted parameter as it appears in the Variable Values column of Sentaurus Workbench, Curve refers to the name of the Inspect IdVgs curve, and Type can be either "nMOS" or "pMOS". The routine passes the extracted value to Sentaurus Workbench and prints it to the log file. It also returns the value to Inspect. For example, the call: set Vt [ExtractVtgm Vtgm IdVg nMOS]

results in output such as: DOE: Vtgm -1.029 Vt (Max gm-B method): -1.029 V

Extracting threshold voltage using current level method

The routine ExtractMax extracts the maximum y-value of a given curve. The routine is called with: ExtractMax

where Name defines the name of the extracted parameter and Curve refers to the name of the Inspect IdVgs curve. For example, the call: set IdMax [ExtractMax IdMax Id]

results in output such as: DOE: IdMax 9.383e+01 Max: 9.383e+01

Extracting breakdown voltage The breakdown voltage can be defined as the maximum voltage that can be applied to a contact. The routine ExtractBVv extracts this value. The routine is called with: ExtractBVv

The routine ExtractVti extracts the gate voltage at which the drain current exceeds a given current level. The routine is called with:


where Name defines the name of the extracted parameter, Curve refers to the name of the Inspect curve, and the

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parameter Sign can take the values +1 (NMOS) or –1 (PMOS) and is used to distinguish between the different types of transistor. (In general, set Sign to –1 if the breakdown occurs at a negative bias.) For example, the call:

Loading Sentaurus Device small-signal data file The Sentaurus Device small-signal output file is loaded with the routine rfx_load: rfx_load "ACFileName=AC_@acplot@ Port1Name=1 \ Port2Name=2 BiasPortName=v(1) DeviceWidth=25"

set BVv [ExtractBVv BVv Id 1]

results in output such as: DOE: BVv 1.09e+01 BVv: 1.09e+01 V

The breakdown curve sometimes exhibits a pronounced snapback. In this case, another relevant definition is the bias voltage at which the current reaches a certain level. This type of extraction is performed with the routine ExtractBVi, which is called with: ExtractBVi

where Name defines the name of the extracted parameter, Curve refers to the name of the Inspect curve, and Ilevel refers to the mentioned current level. For example, the call: set BVi [ExtractBVi BVi Id 1000]

results in output such as:

The port names do not have to be numbers but they must agree with the node names defined in the Sentaurus Device System section. The parameter BiasPortName defines which port is biased and whether the biasing is a voltage or a current condition. The parameter DeviceWidth is optional. If present, the Y matrix is multiplied by this number. This allows users to specify the actual width of the device if no AreaFactor has been defined in Sentaurus Device. The device width is not very important when the main interest is the Y, Z, or H matrices and the derived gain parameters, since these parameters scale trivially with the device width. However, for the S matrix, the device width is very important because the reference impedance is 50 Ω. NOTE For a current condition, the syntax for BiasPortName is more complex. For example, if the name of the current source is vc and the name of the port is 2, the declaration would be: BiasPortName=i(vc,2)

DOE: BVi 4.094e+00 BVi: 4.094e+00 V

RF extractions with Inspect The RF parameter extractions are performed using the Inspect library RFX. The extraction routines are activated with:

In this case, however, Sentaurus Device must also be instructed to include the current at this node through this device in the small-signal data file. This is performed in the System section of the Sentaurus Device input file with, for example: System { HBT hbt (base=1 collector=2 emitter=0) Vsource_pset vb ( 1 0 ){ dc = 0 } Vsource_pset vc ( 2 0 ){ dc = 0 } ACPlot(v(1) v(2) i(vb 1) i(vc 2)) }

load_library RFX

(Refer to the Inspect User Guide for more information about this library.) The following routines of this library are used in this project. (Refer to the Inspect User Guide, Chapter 3, for a complete command reference and list of formulas used to compute the RF parameters. These formulas have been taken from the literature [2]–[5].)

Cutoff frequency (ft) The routine rfx_GetFt returns a list of ft values. For example, the following command returns the ft values using the unit-gain-point method: set ft0 [rfx_GetFt "Method=unit-gain-point \ Scale=1e9"]

The RFX library assumes a two-port network–like configuration such as shown in Figure 7. Port1

Port2 Two-Port Network

Figure 7

Schematic of two-port network

The optional Scale argument allows users to change the unit of ft. Here, the unit is set to GHz. The extraction routine supports three different methods to extract ft from the RF parameter h21: ■

Method=unit-gain-point With this method, the frequency at which h21 = 1 is returned.

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Method=extract-at-dBPoint With this method, the frequency at which h21 drops by a predefined amount of decibels (dB) is located. Then, it is assumed that the gain curve exhibits a 20 dB/decade decay at this point and, using this assumption, the unitgain-point is computed by extrapolation. The dB point at which the extrapolation is to be calculated is set, for example, to 10 dB using: set dBPoint 10 set ft10 [rfx_GetFt "Method=extract-at-dBPoint \ Parameter=$dBPoint Scale=1e9"]

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Method=extract-at-frequency With this method, the extrapolation of the gain to the unit-gain-point is performed by assuming that the 20 dB/ decade decay is established at a given frequency. To set the frequency used for the extrapolation, for example to 10 GHz, use: set frequency 1e10 set ft1e10 [rfx_GetFt \ "Method=extract-at-frequency \ Parameter=$frequency Scale=1e9"]

The rfx_load command creates automatically a list of all bias points, called rfx_BiasPoints, as well as a list of all frequencies, called rfx_Frequencies. To plot the ft values as a function of bias, create an Inspect curve as follows: cv_createFromScript ft0 $rfx_BiasPoints $ft0 y cv_display ft0 y

The transition between the flat low-frequency region of the gain curves to the 20 dB/decade slope at higher frequencies can be drawn out. In fact, sometimes, a clear 20 dB/decade slope is never reached. In this case, the extract-at-dBPoint method may give misleading results. (Often, the results can be improved by adjusting the dB point used for the extrapolation.) Sometimes, it is known beforehand that at a given frequency the gain curves fall off at a 20 dB/decade slope. In this case, the unit-gain-point can be determined by the extract-atfrequency method. However, the band of frequencies for which the 20 dB/decade slope assumption holds true can be very narrow and can depend on the bias conditions. This discussion shows that using solely one method may give inappropriate results. Therefore, it is recommended to always use all three methods concurrently. If the fmax or ft curves for all three methods agree well, the results can be trusted with a high level of confidence. If they give differing results, it is suggested to examine the underlying gain curves (that is, Mason’s unilateral gain or h21). In most cases, it is clear that the assumptions on which the extractions are based are not fulfilled. That is, the gain curve does not fall off with a clean 20 dB/decade slope at high frequencies.

60

ft [GHz]

50

40

unit-gain-point extract-at-frequency extract-at-dBPoint

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-0.4

-0.2

0

0.2

0.4

Gate Voltage [V]

Figure 8

NOTE Unfortunately, there is no single definition of ft and fmax that is appropriate under all circumstances. You may think that the direct search for the unit-gain-point should be the most appropriate definition. However, at high frequencies, additional parasitic elements may become dominant and may alter the 20 dB/decade slope near the unit-gain-point. Furthermore, in experiments, it is sometimes difficult to trace the gain curve to high enough frequencies to see the unit-gain-point directly. Therefore, extrapolating the experimental data to the unit-gain-point is common. In this case, the experiment may not ‘see’ the altered slope due to the parasitics (also some parasitics may not be included in the simulation). Therefore, for a comparison with experimental results, the extrapolation methods may be better.

Cutoff frequency ft as a function of gate bias, extracted with three different methods: unit-gain-point (blue), extract-at-frequency (green), and extract-at-dBPoint (red). This data is computed with a feedback resistor of 100 kΩ μm.

The problem is illustrated in Figure 9 on page 12 where the fmax curves for the HEMT device are shown. The unit-gainpoint method gives fmax values between 100 and 200 GHz. The other two methods predict substantially higher fmax values (400–600 GHz). Moreover, the extract-at-dBPoint method gives very noise results.

Maximum frequency of oscillation (fmax) The routine rfx_GetFmax returns a list of fmax values. It uses the same methods and control parameters as the routine rfx_GetFt. The main difference is that rfx_GetFmax operates on Mason’s unilateral gain instead of h21.


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to-drain capacitance result in a second-order pole in the gain (that is, a 40 dB/decade slope). Refer to the literature [6].

extract-at-dBPoint extract-at-frequency unit-gain-point -

600

For higher gate voltages, the gain curve exhibit a spike-like gain enhancement between 10 and 100 GHz. (This resonance is actually much narrower than the spacing frequency sample points used in the simulation.)

fmax [GHz]

500

400

300

200

100 -0.4

-0.2

0

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Gate Voltage [V] Figure 9

Maximum frequency of oscillation fmax as function of gate bias, extracted with three different methods: unit-gain-point (blue), extract-at-frequency (green), and extract-at-dBPoint (red). This data is computed without a feedback resistor.

The reason for this unusual behavior is better understood by looking at Figure 10, where the underlying Mason’s unilateral gain (MUG) curves are shown as a function of frequency. Clearly, these curves have a more complex shape than assumed (flat low-frequency region, followed by a 20 dB/decade slope).

Mason’s Unilateral Gain [dB]

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Identifying bias point or frequency index

Vgs = -0.5 Vgs = -0.4 Vgs = -0.3 Vgs = -0.2 Vgs = -0.1 Vgs = 0.0 Vgs = 0.1 Vgs = 0.2 Vgs = 0.3 Vgs = 0.4 Vgs = 0.5

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Internally, the RF extraction script stores the Y matrix as a function of bias and frequency in the form of a twodimensional array. To access an RF parameter for a given bias or frequency, the appropriate array index must be given. Use the routine rfx_GetNearestIndex to obtain the relevant index.

20 dB/decade

The routine operates on the list of bias points (rfx_BiasPoints) or the list of frequencies (rfx_Frequencies), which is created when loading the Sentaurus Device small-signal output file.

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0 8 10

For example, to find the index of the bias point closest to 0.025 V, use: 9

10

10

10 Frequency [Hz]

11

10

12

10

Figure 10 Mason’s unilateral gain as function of frequency for various gate voltages between Vgs = –0.5 and 0.5 V at a drain bias of Vds = 1 V. This data is computed without a feedback resistor. The black dashed line shows an ideal 20 dB/decade slope.

The topmost curves (–0.5 V < Vgs < 0 V) exhibit a 20 dB/ decade slope up to about 100 GHz, but then they fall off at 40 dB/decade. For this reason, the actual unit-gain-point is found at much lower frequencies than an extrapolation based on a 20 dB/decade slope predicts. Such behavior is typical for HEMTs where parasitic elements such as the gate-to-source resistance and the gate-

12

This feature is caused by a process in the channel under the gate: As the gate restricts the current flow in the channel, the parallel electric field rises. This raises the electron temperature and, due to high-field saturation, the effective mobility degrades, which in turn changes the charge and field distribution in the channel area under the gate. In HEMTs, the channel and the gate actually form a parasitic capacitor, which provides a RF signal feedback to the gate. The temperature response in the channel area is delayed with respect to changes in the parallel field. Consequently, the charge and field distribution response to an AC change in the gate voltage is phase shifted. Under certain conditions, this phase shift results in an increased power transfer from the gate to the drain. This causes the ‘resonance’ in MUG. (In the literature [6], it is shown that such resonances occur also in HEMT compact models if it is assumed that the transconductance element reacts with a delay to gate bias changes.)

set BiasPointIndex [rfx_GetNearestIndex \ Target=-0.025 $rfx_BiasPoints]

The Inspect log file contains information about the bias associated with the returned index: !rfx_GetNearestIndex: Nearest Index is 11. ! Corresponding value is 5.0E-02. ! Target value is 0.025.

The actual bias point can be accessed in the script with: set BiasPoint [lindex $rfx_BiasPoints \ $BiasPointIndex]


The identification of a frequency index works the same way. For example, to find the index for a frequency close to 1 GHz, use: set FrequencyIndex [rfx_GetNearestIndex \ Target=1e9 $rfx_Frequencies] set Frequency [lindex $rfx_Frequencies \ $FrequencyIndex]

Mason’s unilateral gain The routine rfx_GetMUG returns a list of Mason’s unilateral gain (MUG) values. For example, to compute the gain as a function of frequency at the fifth bias point index, use: set MUG [rfx_GetMUG "XAxis=frequency \ BiasOrFqIndex=5"]

To plot the gain curve as a function of frequency, create an Inspect curve as follows: cv_createFromScript MUG $rfx_Frequencies $MUG y cv_display MUG y

To plot the gain curve as a function of bias for a given frequency, for example 1 GHz, use: set FrequencyIndex [rfx_GetNearestIndex \ Target=1.e9 $rfx_Frequencies] set MUG [rfx_GetMUG "XAxis=bias \ BiasOrFqIndex=$FrequencyIndex"] cv_createFromScript MUG $rfx_BiasPoints $MUG y cv_display MUG y

To plot a family of gain curves, for example between the bias points on –0.5 V and 0.5 V, use a Tcl loop: set StartIndex [rfx_GetNearestIndex \ Target=-0.5 $rfx_BiasPoints] set EndIndex [rfx_GetNearestIndex \ Target=0.5 $rfx_BiasPoints] for {set i $StartIndex} {$i