EP1285395A1 - Semi-physical modeling of hemt dc-to-high frequency electrothermal characteristics - Google Patents
Semi-physical modeling of hemt dc-to-high frequency electrothermal characteristicsInfo
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- EP1285395A1 EP1285395A1 EP01937188A EP01937188A EP1285395A1 EP 1285395 A1 EP1285395 A1 EP 1285395A1 EP 01937188 A EP01937188 A EP 01937188A EP 01937188 A EP01937188 A EP 01937188A EP 1285395 A1 EP1285395 A1 EP 1285395A1
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- European Patent Office
- Prior art keywords
- model
- semi
- gate
- physical
- bias
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Classifications
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- H—ELECTRICITY
- H01—ELECTRIC ELEMENTS
- H01L—SEMICONDUCTOR DEVICES NOT COVERED BY CLASS H10
- H01L22/00—Testing or measuring during manufacture or treatment; Reliability measurements, i.e. testing of parts without further processing to modify the parts as such; Structural arrangements therefor
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/30—Circuit design
- G06F30/36—Circuit design at the analogue level
- G06F30/367—Design verification, e.g. using simulation, simulation program with integrated circuit emphasis [SPICE], direct methods or relaxation methods
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
- G01R31/28—Testing of electronic circuits, e.g. by signal tracer
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
- G01R31/28—Testing of electronic circuits, e.g. by signal tracer
- G01R31/316—Testing of analog circuits
Definitions
- the present invention relates to a method for modeling a semiconductor device and more particularly to a method of modeling the thermal and electrical characteristics of a semiconductor device which utilizes a semiphy scial device model coupled with an analytical thermal resistance model to self consistently solve for the channel temperature and internal charge/electrical field structure of the semiconductor device.
- HEMT technology provides RF components that have unparalleled, high performance characteristics at high frequencies (microwave to millimeter wave) and high power levels. As such, HEMTs are known to be used in various RF applications. Unfortunately, high power level applications also require high levels of DC power dissipation that elevates the HEMT components to high temperature levels.
- DC power dissipation that elevates the HEMT components to high temperature levels.
- Finite element thermal simulations are used to simulate the lay out dependent thermal conducting characteristics of a semiconductor device.
- the simulation may be accomplished either by simulating the two dimensional cross section of the device lay out and then assuming semi-infinite thermal conditions in the orthogonal direction; so called quasi-three dimensional modeling; or fully simulating the three dimensional device layout. Because the full three dimensional approach requires much more computational power and sophisticated software, the quasi-three dimensional approach is known to be in more common use. A typical example of this approach is shown in
- Fig. 1 which depicts a finite element mesh for a HEMT device layout.
- the device layout is typical of all HEMT devices.
- Finite element thermal simulations are known to provide accurate estimations of a devices thermal conduction.
- the main draw back with this method is the inability to couple the calculated channel temperature of the device back to an electrical simulation in order adjust the electrical characteristics of the device.
- this approach assumes a heat source, typically DC power dissipated within the intrinsic device which remains constant.
- the DC power dissipation also changes with temperature.
- the so-called self heating effect must be taken in account.
- the full electrothermal characteristics canbe simulated from so-called physical device simulators.
- Physical device simulators are known to utilize comprehensive knowledge about material characteristics and basic device physics to simulate the physical operation within the structure of the device.
- simulators are based upon finite element or Monte Carlo approaches- although the finite element approach is usually employed for electrothermal simulations that also incorporate thermal conduction.
- these tools use the physical structure to simulate performance, the correspondence between the simulated electrothermal performance and the devices physical characteristics are relatively strong.
- the ability of device simulators to accurately model real, measured high frequency electrical characteristics is relatively inaccurate.
- simulation tools are able to achieve fairly useable modeling of DC characteristics but cannot be used for accurate high frequency simulations.
- there is a need for an electrothermal semiconductor device model which provides relatively accurate results at high frequencies.
- the present invention relates to a method for modeling semiconductor devices which utilizes a semiphysical device model coupled with an analytical thermal resistance model to self consistently solve for the channel temperature and internal charge/electric field structure of the semiconductor device.
- the method in accordance with the present invention can realistically simulate the response of electrical performance to temperature and vice versa of a semiconductor device.
- FIG. 1 illustrates a known finite element mesh for a HEMT device layout.
- FIG.2 is a graphical illustration illustrating the measured semi-physical modeled
- FIG. 3 is similar to FIG. 2 but at an ambient temperature of 25°C.
- FIG. 4 is a graphical illustration illustrating the measured vs semi-phyically modeled DC-IV characteristics at an ambient temperature of 25°C for a self heating large periphery 8 fingered 600 ⁇ m gate periphery device cell.
- FIG. 5 is schematic diagram of an exemplary small signal equivalent circuit model for a HEMT device.
- FIG. 6 is a sectional view of an exemplary HEMT illustrating the rough translation of the physical origins for each of the equivalent circuit elements illustrated in the small signal circuit model in FIG. 1.
- FIG. 7 is a cross-sectional view of a HEMT illustrating the regions in the HEMT which correspond to the various circuit elements in the small signal equivalent circuit model illustrated in FIG. 5.
- FIG.8 is an example of a relatively accurate measured-to-model I-V characteristics using the semi-physical modeling method in accordance with one aspect of the present invention.
- FIG.9 is a elevational view illustrating an epi stack for an exemplary HEMT.
- FIG. 10 is a cross-sectional view of a HEMT and an exemplary epi stack.
- FIG. 11 is a blown up diagram of the cross-sectional parameters pertaining to the T-gate geometry for the exemplary epi stack illustrated in FIG. 7.
- FIG. 12 is a diagram of an electric conductance model used in the semi-physical example.
- FIG. 13 is a Smith chart illustrating the measured vs modeled S -parameters S 11 , S12 and S22 simulated in accordance with the method in accordance with the present invention.
- FIG. 14 illustrates the measured vs modeled values for the S21 parameter.
- FIG. 15 is similar to FIG. 14 but for the S12 S-parameter.
- FIG. 16 represents an exemplary S-parameter microscope in accordance with the present invention.
- FIG. 17 illustrates the internal and external regions of an exemplary HEMT device.
- FIG. 18 is similar to FIG. 16 but illustrates the approximate locations of the model elements in the HEMT FET device illustrated is FIG. 16.
- FIG. 19 is a schematic diagram of a common source FET equivalent circuit model.
- FIG. 20 is an illustration of specific application of the S-parameter microscope illustrated in FIG. 16.
- FIG. 21 is similar to FIG. 16 which demonstrates the inability of known systems to accurately predict the internal charge and electrical field structure of a semiconductor device.
- FIG. 22 is a plan view of a four-fingered, 200 ⁇ m GaAs HEMT device.
- FIG.23 is a graphical illustration illustrating the measured drain-to-source current I ds as a function of drain-to-source voltage Vds for the sample FET device illustrated in FIG. 22.
- FIG. 24 is a graphical illustration illustrating the drain-to-source current I ds and transconductance G m as a function of the gate-to-source voltage V gs of the sample FET device illustrated in FIG. 22.
- FIG. 25 is a Smith chart illustrating the measured SI 1, S 12 and S22 parameters from frequencies of 0.05 to 40.0 GHz for the FET device illustrated in FIG. 22.
- FIG. 26 is a graphical illustration of the magnitude as a function of angle for the
- FIG. 27 is a graphical illustration of a charge control map of the charge and electric field distribution in the on mesa source access region shown with R s as a function bias in accordance with the present invention.
- FIG. 28 is a graphical illustration of a charge control map of charge and electric field distribution in the on-mesa drain access region shown with R d as a function of bias in accordance with the present invention.
- FIG.29 is a graphical illustration of a charge control map for the non-quasi static majority carrier transport, shown with Rj as a function of bias in accordance with the present invention.
- FIG. 30 is a graphical illustration of a charge control map for gate modulated charge and distribution under the gate, shown with Cgs and Cgt as function of bias in accordance with the present invention.
- FIG. 31 is a plan view of an exemplary ⁇ -FET with two gate fingers.
- FIG. 32 is a plan view of a ⁇ -FET with four gate fingers.
- FIG. 33 is an illustration of a ⁇ -FET parasitic model in accordance with the present invention.
- FIG. 34 is an illustration of an off-mesa parasitic model for a ⁇ -FET in accordance with the present invention.
- FIG. 35 is an illustration of an interconnect and boundary parasitic model in accordance with the present invention for the ⁇ -FET with four gate fingers as illustrated in FIG. 32.
- FIG. 36 is an illustration of an inter-electrode parasitic model in accordance with the present invention.
- FIG. 37 is a schematic diagram of the inter-electrode parasitic model illustrated in FIG. 36.
- FIG. 38 is an illustration of an on-mesa parasitic model in accordance with the present invention.
- FIG. 39 is a schematic diagram of the on-mesa parasitic model illustrated in FIG. 41.
- FIG. 40 is an illustration of an intrinsic model in accordance with the present invention.
- FIG. 41 is a schematic diagram of the intrinsic model illustrated in FIG. 40.
- FIG. 42 A is an exemplary device layout of a ⁇ -FET with four gate fingers.
- FIG. 42B is an equivalent circuit model for the ⁇ -FET illustrated in FIG. 42A.
- FIG. 43 is a single finger unit device cell intrinsic model in accordance with the present invention.
- FIG. 44 is similar to FIG. 43 and illustrates the first level of embedding in accordance with the present invention.
- FIG. 45 is similar to FIG. 43 and illustrates the second level of embedding in accordance with the present invention.
- FIG. 46 is an equivalent circuit model of the ⁇ -FET illustrated in FIG. 42A in accordance with the present invention.
- FIG. 47 is similar to FIG. 45 and illustrates the third level of embedding in accordance with the present invention.
- FIG. 48 is similar to FIG. 45 and illustrates the fourth level of embedding in accordance with the present invention.
- FIG. 49 is similar to FIG. 45 and illustrates the fifth level of embedding in accordance with the present invention.
- FIG. 50A and 50B is a flow chart of a parameter extraction modeling algorithm that forms a part of the present invention.
- FIGS. 51 and 52 represent the error metric in accordance with the present invention.
- FIG 53A is a Smith chart illustrating the measured versus the initial model solutions for the Sll, S12 and S22 S-parameters from frequencies from 0.05 to 40.0 GHz.
- FIG. 53B is a graphical illustration of angle versus magnitude for the initially modeled S-parameter S21 from frequencies of 0.05 to 40 GHz.
- FIG. 54A is a Smith chart illustrating the measured versus simulated S- parameters Sll, S12 and S22 for frequencies 0.05 to 40 GHz for the first extraction optimization cycle.
- FIG. 54B is a graphical illustration of magnitude as a function of angle for the measure and first optimized model S-21 parameter for frequencies 0.05 to 40 GHz for the first optimization cycle.
- FIG. 55 A is a Smith chart illustrating the measure as a function of the final model solution for S-parameters Sll, S12 and S22 for frequencies 0.05 to 40 GHZ for the final solution.
- FIG. 55B is a graphical illustrations of the magnitude as a function of an angle for S-parameter S21 for the final model solution from frequency 0.05 to 40 GHz.
- FIG. 56 is a graphical illustration of the semi-physically modeled vs measured small signal Gm.
- FIG. 57 is a graphical illustration of the semi-physically simulated bias dependence of the small-signal output conductance Rds.
- FIG. 58 is a graphical illustration of the semi-physically simulated bias dependence of the small signal gate-source and gate-drain capacitance Cgs and Cgd.
- FIG. 59 is a graphical illustration of the semi-physically simulated bias dependence of the small signal gate source charging resistance Ri.
- FIG. 60 is a graphical illustration of the semi-physically bias dependence of the small signal source and drain resistance Rs and Rd.
- FIG.61 is a graphical illustration of the measured vs modeled bias dependent gain at 23.5 Ghz for a K-band MMIC amplifier.
- FIG 62A and 62B are graphical illustration of the extracted parameters from measured device I-V's for process control monitor testing.
- FIG. 63 is a graphical illustration of the measured vs semi-physically simulated process variation for Gmpk and Vspk.
- Fig. 64 is a graphical illustration of the measured vs semi-physically simulated process variation for Idpk and Gmpk.
- FIG. 65 is a graphical illustration of the measured vs semi-physically simulated process variation for frnax and Vpo.
- FIG. 66 is a graphical illustration of the measured/extracted vs semi-physically simulated process variation for the small signal equivalent model Rds and Gm.
- FIG. 67 is a graphical illustration of the measured/extracted vs semi-physically simulated process variation for the small signal equivalent model Cgs and Gm.
- FIG. 68 is a graphical illustration of the measured vs semi-physically simulated physical dependence for Imax as a function of physical gate length.
- Fig. 69 is a graphical illustration of the measured/extracted model vs semi- physically simulated physical dependence for Rds as a function of physical recess undercut width.
- the model in accordance with the present invention utilizes a semi physical device model that is coupled to an analytical thermal conductance model as a means of simulating the electrothermal performance characteristics of a semiconductor device.
- a semiphysical model for HEMT devices is demonstrated that is able to relatively accurately represent small signal, noise, non-linear and large signal characteristics.
- the following procedure is utilized:
- the semiphysical HEMT model may be extended to perform full electrothermal device simulations.
- a semiphysical model mentioned in step 1 is discussed below.
- step 2 reported thermal properties of the material systems used for the HEMT technology are incorporated into an appropriate material related expression of the semiphysical device model. These properties may be obtained from "GaAs, ALAs and AlxGal-xAs Materials Parameters For Use and Research and Device Applications" by S. Adachi, J.Appl. Phys, vol. 58, No. 3, August 1985, hereby incorporated by reference.
- step number 3 the DC I-V and bias dependent S-parameters are measured for a standard device lay out across several base plate temperatures; for example -25°C, 25°C, 125°C and 200°C.
- step 4 S-parameter microscopy is employed for each set of temperature dependent data.
- step 5 a temperature compensation co-efficient is developed from reported material thermal dependance relationships, for example, as shown below.
- TCF is applied to the appropriate semiphysical charge
- FIG. 3 demonstrates the enhanced semiphysical device model now able to accurately simulate I-V characteristics at 200°C
- Figure 4 demonstrates the accuracy of the I-V simulation at 25°C.
- step 6 the analytical thermal conduction expression is as set forth in "Precise Technique Finds FET Thermal Resistance” by H. Cooke, “Microwaves and RF". August 1986.
- step 7 gate length, which is taken to be the length of the heat- generating region in Cooke's expressions, is replaced by a semiphyically modeled 5 XSAT expression provided below.
- the temperature compensation coefficient is modified to operate between the 5 "channel temperature” rather the “ambient temperature” as generally shown by the equations provided below.
- TCF is a temperature coefficient determined through complete, uniform heating of the device sample.
- base-plate heating is used to heat the device sample, it can be assumed that base-plate temperatures are roughly equal to the "chamiel temperature", or rather the temperature of the device is the same as the surrounding environment.
- self-heating areas adjacent to the device's heat sources, or that region approximately under the gate, are heated to higher temperatures than the base-plate. As a result, the device becomes hotter than its surrounding environment. In this regime, "channel temperature" must be used to gauge how hot the intrinsic device gets.
- SEMI PHYSICAL MODEL Semi-physical device modeling represents both the physical device characteristics and measured characteristics, which can be used to simulate RF performance through physically-based device models.
- the semi-physical model is an analytical model based upon empirical expressions that model the physics of HEMT operation, hence the terminology "semi-physical".
- the model incorporates real process parameters, such as gate length recess etch depth, recess undercut dimensions, passivation nitrite thickness, and the like.
- the semi-physical model is able to maintain relatively good measured to model accuracy while accounting for the effects of process variations on the device performance.
- the semi-physical model provides model elements for the standard small signal equivalent circuit model or FET is illustrated in FIG. 5.
- FIG. 6 is a rough translation of the physical origins for each of the equivalent circuit elements in the small-signal equivalent circuit model illustrated in FIG. 5.
- FIG. 7 is a cross-sectional drawing of an exemplary HEMT device structure.
- the model elements are derived from small signal excitation analysis of the intrinsic charge and electric fields within the device.
- the simulated small signal model elements represent a relatively accurate physical equivalent circuit description of a physical FET.
- the general methodology for the semi-physical modeling of intrinsic charge, electrical conductance and the electrical field are as set forth below.
- the relationships between the conduction band offsets, electrical permitivities and material composition for the various materials in the epi stack are determined. These relationships can be performed analytically or by fitting simulated data from physical simulators.
- the basic electron transport characteristics in any of the applicable bulk materials in the epi stack are determined. Once the electron transport characteristics are determined, the undeleted linear channel mobility is determined either through material characterization or physical simulation.
- the Schottky barrier height value or expressions are determined. Once the Schottky barrier height value is determined, the semi-physical equations are constructed modeling the following characteristics: Fundamental-charge control physics for sheet charge in the active channel as controlled by the gate terminal voltage.
- the empirical terms of the semi- physical modeling equations are adjusted to fit the model I-V (current-voltage) characteristics against measured values. Subsequently, the empirical terms are interactively readjusted to achieve a simultaneous fit of measured C-V (capacitance- voltage) and I-V characteristics. Lastly, the empirical modeling terms are fixed for future use.
- FIG. 8 illustrates a set of relatively accurate measured-to-modeled I-V characteristics for a HEMT using the semi-physical modeling discussed herein.
- FIG. 8 illustrates the drain-to- source current I ds as a function of the drain-to-source voltage V ds for various gate biases, for example, from 0.4V to -1.0V.
- solid lines are used to represent the semi-physical model while the Xs are used to represent measured values.
- a close relationship exists between the measured values and the modeled parameters.
- FIG. 11 relates to a blown up T-gate characteristic which is correlated to the parameters identified in Table 1.
- the semi-physical modeling of the intrinsic charge and electric field within the HEMT device is initiated by determining the relationships between the conduction band offset, electric permitivities and material composition for the various materials in the epi stack.
- Material composition related band offset and electric permitivity relationships may be obtained from various references, such as "Physics of Semiconductor Devices," by Michael Shur, Prentice Hall, Englewood Cliffs, New Jersey 1990.
- the basic electron transport characteristics, for example, for the linear mobility of electron carriers in the bulk GaAs cap layer may be determined to be 1350cm 2 /Vs, available from "Physics of Semiconductor Devices", supra.
- the linear mobility of electron carriers in the undeleted channels is assumed to be 5500cm s.
- This value may be measured by Hall effect samples which have epi stacks grown identically to the stack in the example, except for some differences in the GaAs cap layer.
- the Schottky barrier height is assumed to be 1.051 volts, which is typical of platinum metal on a AlGaAs material.
- Threshold Voltage ⁇ o M ⁇ b - ⁇ E 0 - V ⁇
- Ns represents the model sheet carrier concentration within the active channel.
- Ns' represents the ideal charge control law and is modeled as a semi- physical representative of the actual density of state filling rate for energy states within the channel v. gate voltage.
- the gate-to-channel voltage used for the charge control, Vgt is a function of the Schottky barrier height, conduction band offsets and doping in the epi stack as is known in the art.
- Gate-Drain Control Region «d [ ⁇ m] (L g 2 + ⁇ L d )* ⁇ ta ⁇ h[10(L 0 /2-X D ,)]+1 ⁇ /2
- FIG. 12 is a schematically illustrates how electrical conductance in the source and drain access regions are modeled in the example.
- Equivalent circuit element Cgs and Cgd takes the form of delta(Nsn)/delta(Vgs)*Lgn, where delta (Nsn) is the appropriate charge control expression, and Lgn is the gate source or gate drain charge partitioning boundary length.
- Equivalent circuit element Ri Lgs/(Cgschannel * vs) where Cgs channel is the portion of gate source capacitance attributed to the channel only, and vs is the saturated electron velocity.
- Cds is taken to be the sum of the appropriate fringing capacitance Semi-Physical models, or can take the form of delta(Nsd)/delta(Vds')*Xsat, were Nsd is the charge control expression for charge accumulation between the appropriate source and drain charge boundaries, and Xsat is the length of the saturated region, if in saturation.
- Table 3 represents a comparison of the values for a high frequency equivalent circuit model derived from equivalent circuit model extraction from and semi-physical modeling for the sample illustrated in Table 2.
- results of the semi-physical modeling method produce a small-signal equivalent circuit values which are relatively more accurate than the physical device simulator in this case. Furthermore, given the differences in the parasitic embedding, treatment of the two approaches, the results given in Table 2 yield much closer results than a comparison of equivalent circuit values.
- Table 3 lists the values of parasitic elements used in the model derivations.
- the modeled results that are simulated using the semi-physically derived equivalent circuit model very accurately replicate the measured high frequency, S-parameter data.
- C gsf [fF/ ⁇ m] Cg s ⁇ rf C f . fotra1 SiNF + Cgsf Source + Cgsf Pad
- Empirical Fringing capacitance-bias shaping expression '-'f-forml [] ⁇ 1 - tanh[ KC (K ( V gs - VC (0n + V ds MC tL )] ⁇ /
- Gate-Source Non-quasistatic charging resistance L g s 2 W g /[C BsCh anW 0 V s ]
- FIG. 60 shows the semi-physically simulated bias dependence of the on-mesa parasitic access resistances Rs and Rd.
- the following example verifies how the semi-physical small-signal device model is able to provide accurate projections for bias-dependent small-signal performance.
- the same semi-physical device model as used in the previous examples was used because the example MMIC circuit was fabricated utilizing the same HEMT device technology.
- the bias-dependence small-signal gain and noise performance of a two-stage balanced K-band MMIC LNA amplifier is replicated through microwave circuit simulation using small signal and noise equivalent circuits that were generated by the semi-physical model.
- the results of the measured and modeled results are shown below in Table 4. As seen from these results, the Semi-Physical device model was able to accurately simulate the measured bias-dependent performance, even though the bias variation was quite wide.
- the following example verifies how the Semi-Physical small-signal device model is able to provide accurate projections for physically dependent small-signal performance
- the same Semi-Physical device model as used in the previous examples was used.
- physical process variation was input into the Semi-Physical device model in terms of statistical variation about known averages, cross-correlation, and standard deviations.
- the goal of this exercise was to replicate the measured DC and small-signal device variation.
- the degree of accurate replication indicates the degree to which the Semi-Physical model is physically accurate.
- FIG. 18 shows schematically the kind of data that is extracted and recorded from measured device I-V's during PCM testing.
- Figures 63, 64 AND 65 shows how accurately the simulated results match with measured process variation.
- Figure 63 shows how the Semi-Physically simulated Vgpk and Gmpk match with actual production measurements.
- Figure 64 shows how simulated Idpk and Gmpk match, also.
- Figure 65 shows how simulated Imax and Vpo also match very well. Small-signal S-parameter measurements are also taken in process for process control monitoring. These measurements are used to extract simple equivalent circuit models that fit the measured S-parameters.
- Figures 66 and 67 show how accurately the simulated results match with measured/extracted process variation for the small-signal model parameters.
- Figure 66 shows how the Semi-Physically simulated Rds and Gm match very well with actual extracted model process variation.
- the S-parameter (SPM) method utilizes bias dependent S-parameter measurements as a form of microscopy to provide qualitative analysis of the internal charge and electrical field structure of the semiconductor device heretofore unknown.
- Pseudo images are gathered in the form of S-parameter measurements extracted as small signal models to form charge control maps.
- finite element device simulations have heretofore been used to calculate the internal charge/electric field of semiconductor devices, such methods are known to be relatively inaccurate.
- the S- parameter microscopy provides a relatively accurate method for determining the internal charge and electric field within a semiconductor device. With accurate modeling of the internal charge and electric field, all of the external electrical characteristics of semiconductor devices can be relatively accurately modeled including its high frequency performance.
- the system is suitable for making device technology models that enabled high frequency MMIC yield analysis forecasting and design for manufacturing analysis.
- S-parameter microscopy is similar to other microscopy techniques in that SPM utilizes measurements of energy reflected to and from a sample to derive information. More particularly, SPM is based on transmitted and reflective microwave and millimeter wave electromagnetic power or S-parameters. As such, S-parameter microscopy is analogous to the combined operation of scanning and transmission electron microscopes (SEM and TEM). Scattered RF energy is analogous to the reflection and transmission of the electron beams in the SEM and TEMs. However, instead of using electron detectors as in the SEM and TEMs, reflectometers in a network analyzer are used in S-parameter microscopy to measure a signal. S- parameter microscopy is similar to other microscopy techniques in that both utilize; measurement of scattering phenomenon as data; include mechanisms to focus measurements for better resolution; and include mechanisms to contrast portions of the measurement to discriminate detail as shown in Table 6 below:
- RESULT Detailed "images" of device's internal charge and electric field structure.
- S-parameter microscopy does not relate to real images, but are used provide insight and qualitative detail regarding the internal operation of a device. More specifically, S-parameter microscopy does not provide visual images as in the case of traditional forms of microscopy. Rather, S- parameter microscopy images are more like maps which are computed and based on a non-intuitive set of measurements.
- FIG. 16 illustrates a conceptual representation of an S-parameter microscope, generally identified with the reference numeral 20.
- the S-parameter microscope 20 is analogous to a microscope which combines the principles of SEM and TEM. Whereas SEM measures reflections and TEM measures transmissions, the 2-port S- parameter microscope 20 measures both reflective and transmitted power.
- data derived from the 2-port S-parameter microscope contains information about the intrinsic and extrinsic charge structure of a device. More particularly, as in known in the art, SEM provides relatively detailed images of the surface of a sample through reflected electrons while TEM provides images of the internal structure through transmitted electrons. The reflective signals are used to form the external details of a sample while transmitted electrons provide information about the interior structure of a device.
- S-parameter microscopy utilizes a process of measuring reflective and transmitted signals to provide similar "images" of the charge structure of a semiconductor device.
- the internal and external electrical structure of a semiconductor device are commonly referred to as intrinsic device region 22 and extrinsic parasitic access region 24 as shown in FIG. 17.
- parasitic components associated with the electrodes and interconnects which are not shown. These are the so-called device "layout parasitics”.
- the ports 26 and 28 are emulated by S-parameter measurements.
- the S-parameter measurements for a specific semiconductor device, generally identified with the reference number 30, are processed to provide charge control maps, shown within the circle 32, analogous to images in other microscopy techniques.
- These charge control maps 32 are expressed in the form of equivalent circuit models.
- linear circuit elements are used in the models to represent the magnitude and state of charge/electric fields inside the semiconductor device 30 or its so-called internal electrical structure.
- the position of the circuit elements within the model topology is roughly approximate the physical location within the device structure, hence the charge control map represents a diagram of the device's internal electrical structure.
- the S-parameter microscope 20 in accordance with the present invention also emulates a lens, identified with the reference numeral 40 (FIG. 16).
- the lens 40 is simulated by a method for the extraction of a unique equivalent circuit model that also accurately simulates the measured S-parameter. More particularly, parameter extraction methods for equivalent circuit models that simulate S-parameters are relatively well known. However, when the only goal is accurately fitting measuring S-parameters, an infinite number of solutions exist for possible equivalent circuit parameter values. Thus, in accordance with an important aspect of the present invention, only a single unique solution is extracted which accurately describes the physical charge control map of the device. This method for unique extraction of equivalent circuit model parameters acts as a lens for focus the charge control map solution.
- the lens 40 is subsequently simulated by a filter that is based on an apparent layout parasitic embedding model.
- the layout parasitic embedding model consists of linear elements which simulate the effect of the device's electrodes and interconnects upon its external electrical characteristics.
- a Pi FET embedding model 42 is described below. This model effectively acts as a filter to remove the electrical structure of the extrinsic parasitic access contribution to the preliminary charge control map solution.
- the resultant, filtered charge control map solution represents a clearer "image", which shows only the electrical structure of the intrinsic device. This enhanced imaging is needed in order to achieve as accurate a view of the internal electric charge/field as possible.
- the S-parameter microscope 20 in accordance with the present invention is able to relatively accurately model the internal electric charge/field structure within a semiconductor device.
- an exemplary application of the S-parameter microscope is illustrated in detail below.
- an exemplary GaAs HEMT device with four gate fingers and 200 ⁇ m total gate periphery formed in a Pi-FET layout as generally illustrated in FIG. 22 and identified with the reference numeral 43 is used.
- the GaAs HEMT 43 is adapted to be embedded in a 100- ⁇ m pitch coplanar test structure to facilitate on wafer S-parameter measurement.
- the I-V characteristics for the device are measured.
- the drain source current Ids is plotted as a function of drain-to-source voltage Vds at various gate voltages Vgs as shown in FIG. 23.
- FIG.24 illustrates the drain-to-source current Ids as a function of gate voltage Vgs and transconductance Gm (i.e. the derivative of Ids with respect to Vgs) at different drain voltages Vds.
- Gm transconductance
- Table 7 shows the bias conditions in which S-parameters were measured.
- the S- parameters were measured from 0.05 to 40 GHz at each bias condition.
- F I G . 2 5 illustrates a Smith chart illustrating the measured S-parameters SI 1, S 12 and S22 for frequencies from 0.05 to 40.0 GHz.
- FIG. 26 is a graphical illustration of magnitude as a function of angles for the measured S-parameter S21 for frequencies from 40.05 to 40.0 GHz.
- the extracted small signal equivalent circuit values are obtained as illustrated in Table 8 for each S-parameter at each bias condition, using the extraction method discussed below.
- the values in Table 8 represent solutions that are close to the charge control map and represent physically significant solutions of the FET's electrical structure. However, the values represented in Table 8 contain the influence of external layout parasitics which are subtracted using a model for the embedding parasitics to obtain the most accurate charge control mapping to the intrinsic device characteristic.
- an embedding model is applied filter the extracted equivalent circuit model values and obtain values more representative of the intrinsic device.
- a PiFET embedding parasitic model is used to subtract capacitive contributions due to interelectrode and off-mesa layout parasitic influences. This filter essentially subtracts known quantities formed from the parameters Cgs, Cgd and Cds depending on the device layout involved. In this example, embedding of the inductive parameters is not necessary because these quantities are extrinsic and do not contribute to the charge control map of the intrinsic device.
- FIGS.27-30 illustrate the bias dependent charge control maps for the parameters RS, RD, RI, CGS and CGD as a function of bias. More particularly, FIG. 27 illustrates a charge control map of the charge and electric field distribution in the on-mesa source access region illustrated by the source resistance R s as a function of bias.
- FIG. 28 illustrates a charge control map of the charge and electric field distribution in the on-mesa drain access region illustrated by the drain resistance R d as a function of bias.
- FIG. 29 illustrates a charge control map for a non-quasistatic majority carrier transport illustrated by the intrinsic device charging resistance R ; as a function of gate bias for different drain bias points.
- FIG. 30 illustrates a charge control map for gate modulated charge and distribution under the gate shown with the gate capacitance CGS and CGD as a function of bias.
- the S-parameter microscope 20 may utilize a filter to provide a clearer charge control map for modeling the internal electric charge/field of a semiconductor device.
- the filter is illustrated in connection with the PiFET with multiple gate fingers, as illustrated in FIGS. 31 and 32, the principles of the invention are applicable to other semiconductor devices.
- PiFETs are devices in which the gate fingers and the edge of the active region resemble the greek letter ⁇ , as illustrated. Such PiFET layouts facilitate construction of multi fingered large periphery device cells, for example, as illustrated in FIG 32.
- the multi-finger semiconductor device is modeled as a combination of single finger device cells.
- Each single finger device cell is represented by a hierarchy of four models, which, in turn, are assembled together using models for interconnects to represent an arbitrary multifingered device cell, illustrated in Fig.33.
- the four models are as follows: off mesa or boundary parasitic model; interelectrode parasitic model; on-mesa parasitic model and intrinsic model.
- the off-mesa parasitic model is illustrated in FIG. 34. This model represents the parasitics that exist outside the active FET region for each gate finger. In this model, the fringing capacitance of each gate finger off the active device region as well as the off-mesa gate finger resistance is modeled.
- FIGS. 35-37 The interelectrode parasitic model and corresponding equivalent circuit are illustrated in FIGS. 35-37.
- This model represents parasitics between the metal electrodes along each gate finger.
- the following fringing capacitance parasitics are modeled for the gate-to-source air bridge; drain-to-source air bridge; gate-to-source ohmic; gate-to-drain ohmic and source-to-drain ohmic as generally illustrated in FIG.
- the on-mesa parasitic model and corresponding equivalent circuit are illustrated inFIGS.38 and39.
- This model represents that parasitics around the active FET region along each gate finger including various capacitance fringing parasitics and resistive parasitics.
- the gate-to-source side recess; gate-drain-side recess; gate- source access charge/doped cap; and gate-drain access charge/doped cap capacitance fringing parasitics are modeled.
- the gate metallization and ohmic contact resistive parasitics are modeled.
- the intrinsic model and corresponding equivalent circuit are illustrated in FIGS. 40 and 41.
- the intrinsic model represents the physics that predominately determine the FET performance.
- the DC and current voltage response can be determined by physics based analytical equations for magnitude and location of intrinsic charge which are generally know in the art, for example, as disclosed in 'TSTonlinear Charge Control in AlGaAs/GaAs Modulation-Doped FETs", by Hughes, et al, IEEE Trans. Electron Devices. Vol. ED-34, No. 8, August 1987.
- the small signal model performance is modeled by taking a derivative of the appropriate charge or current control equations to derive various terms such as RI, RJ, RDS, RGS, RGD, GM, TAU, CGS, CDS and CGD.
- control equations are generally known in the art and disclosed in detail in the Hughes, et al. reference mentioned above, hereby incorporated by reference.
- the noise performance may be modeled by current or voltage perturbation analysis "Noise Characteristics of Gallium Arsenide Filed-Effect Transistors" by H. Statz, et al. IEEE-Trans. Electronic Devices, vol. ED-21, No. 9, September 1974 and "Gate Noise in Field Effect Transistors at moderately High Frequencies" by A. Van Der Ziel, Pro. IEEE, vol 51 , March 1963 "Gate Noise in Field Effect Transistors at Moderately High Frequencies", by H. Statz, IEEE Trans. Electron
- FIGS. 42-49 An example of a parasitic model for use with the S-parameter microscopy discussed above is illustrated in FIGS. 42-49.
- a specific embodiment of a semiconductor device is illustrated and described, the principles of the present invention are applicable to various semiconductors devices.
- FIG. 42A a Pi-FET is illustrated. As shown, the PiFET has four gate fingers. The four fingered Pi-FET is modeled in FIG.42B .
- FIG 42B illustrates an equivalent circuit model for Pi-FET illustrated in FIG. 42A as implemented by a known CAD program, for example, LIBRA 6.1 as manufactured by Agilent Technologies.
- the equivalent circuit models does not illustrate all of the equivalent circuit elements or network connections involved with implementing the parasitic embedding models, but rather demonstrates a finished product.
- the actual technical information regarding the construction of the network and its equivalent circuit elements are normally provided in schematic view.
- An important aspect of parasitic modeling relates to modeling of multi-gate fingered devices as single gate finger devices.
- a single unit device cell refers to a device associated with a single gate finger.
- a four fingered Pi-FET as illustrated in FIG. 42A is modeled as four unit device cells.
- the four finger Pi-FET illustrated in FIG. 42A is modeled as a single finger unit device cell 100 with an intrinsic model 102, as shown in FIGS. 43 and 44.
- the Pi-FET intrinsic FET model 104 is substituted for the block 102 defining a first level of embedding.
- the parameter values for the Pi-FET intrinsic model are added together with the parameter values for the single fingered unit device cell intrinsic model.
- the intrinsic device model 104 may be developed by S-parameter microscopy as discussed above.
- the interconnect layout parasitic elements are added to the equivalent model by simply adding the model terms to the value of the appropriate circuit element to form a single unit device cell defining a second level of embedding.
- this device is used to construct models for multi-fingered devices.
- a Pi-FET with four gate fingers is modeled as four single finger device unit cells as shown in FIG. 46.
- the off-mesa layout parasitic elements are connected to the multi-fingered layout, defining a third level of embedding as illustrated in FIG. 47.
- These off-mesa layout parasitic elements are implemented as new circuit elements connected at key outer nodes of the equivalent circuit structure.
- a fourth level of embedding is implemented as generally illustrated in FIG. 48.
- an inductor model is connected to the sources of each of the various unit device cells to represent the metallic bridge interconnection, as generally shown in FIG. 48.
- a fifth level of embedding is implemented in which the feed electrodes model 114 and 116 are modeled as lumped linear elements (i.e. capacitors inductors) as well as the distributive elements (i.e. microstrip lines and junctions) to form the gate feed and drain connections illustrated in FIG. 53.
- the distributive elements are distributed models for microstrip elements as implemented in LIBRA 6.1.
- FIGS. 50-55 The method for determining FET equivalent circuit parameters as discussed above is illustrated in FIGS. 50-55. This method is based on an equivalent circuit model, such as the common source FET equivalent circuit model illustrated in FIG. 5.
- a model is initially generated in step 122.
- the equivalent circuit parameters are based upon measured FET S-parameters. Measurement of S-parameters of semiconductor devices is well known in the art.
- FIG. 53A is a Smith chart illustrating exemplary measured S-parameters SI 1, S12 and S22 for frequencies between 0.05 to 40 GHz.
- FIG. 53B represents a magnitude angle chart for the measured S-parameter S21 from frequencies from 0.05 to 40 GHz. After the S-parameters are measured, as set forth in step 124
- step 126 it is ascertained whether the measurements are suitable in step 126. This is either done by manually inspecting the test result for anomalies, or by algorithms to validate the test set. If the measurements are suitable, the S-parameter measurements are stored in step 128. A space of trial starting feedback impedance point values, for example, as illustrated in Table 9 is chosen. Then, a direct model extraction algorithm, known as the Minasian algorithm, is used to generate preliminary values for the equivalent circuit model parameters, for each value of starting feedback impedance. Such extraction algorithms are well known in the art, for example, as disclosed "Broadband Determination of the FET Small Equivalent Small Signal Circuit" by M. Berroth, et al., IEEE - MTT. Vol. 38, No. 7, My 1990.
- Model parameter values are determined for each of the starting impedance point values illustrated in Table 3.
- each impedance point in Table 9 is processed by the blocks 130, 132, etc. to develop model parameter values for each of the impedance point in order to develop an error metric, winch, in turn, is used to develop a unique small signal device model, as will be discussed below.
- the processing in each of the blocks 130, 132 is similar.
- only a single block 130 will be discussed for an exemplary impedance point illustrated in Table 9.
- the feedback impedance point 17 which correlates to a source resistance R s ohm of 1.7 ⁇ and a source inductance L s of0.0045pH is used.
- initial intrinsic equivalent circuit parameters and initial parasitic equivalent circuit parameter are determined, for example, by the Minasian algorithm discussed above and illustrated in Tables 10 and
- step 138 the simulated circuit parameters are compared with the measured S-parameters, for example, as illustrated in FIGS .54A and
- Each of the processing blocks 130 and 132 etc. goes through a fixed number of complete cycles, in this example, six complete cycles. As such, the system determines in step 140 whether the six cycles are complete.
- Each cycle of the processing block 130 consists of a direct extraction followed by an optimization with a fixed number of optimization iterations, for example 60.
- a fixed “distance” or calculation time which the model solution must be derived is defined.
- the algorithm implements a convergence speed requirement of the global error metric by setting up an environment where each trial model solution competes against each other by achieving the lowest fitting error over a fixed calculation time thus causing "race” criteria to be implemented where "convergence speed" is implicitly calculated for each processing block 130, 132 etc.
- the system determines whether the racing is done in step 140, the system proceeds to block 142 and optimizes model parameters.
- Various commercial software programs are available, for example, the commercially available, LIBRA 3.5 software as manufactured by HP-eesof may be used both for circuit simulation as well as optimizing functions. The optimization is performed in accordance with the restrictions set forth in Table 12 with the addition of fixing the feedback resistance R s to a fixed value. TABLE 12 Environment Used for Competitive Solution Strategy, as Implemented in this
- Table 13 illustrates the optimized intrinsic equivalent parameter values using commercially available software, such as LIBRA 3.5. These values along with the optimized parasitic values, illustrated in Table 14, form the first optimized model solution for the first extraction-optimization cycle (i.e. one of six). The optimized model parameters are then fed back to the function block 134 and 136 (FIG. 50A) and used for a new initial model solution. These values are compared with the measured S-parameter value as illustrated in FIGS. 54A and 54B. The system repeats this cycle for six cycles in a similar fashion as discussed above.
- the extraction-optimization algorithm makes the final optimization fitting error for each point implicitly carry information about both the measured to model fitting error and the speed of convergence. It does so by the fixed optimization time constraint which sets up a competitive race between the various trial model solutions.
- the final model for solutions are compared with the measured S-parameter values as shown in FIGS. 55 A and 55B. As shown, there is good correlation between the simulated model values and the measured S-parameters values thus verifying that the simulated model values represent a relatively accurate and unique small signal device model.
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