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Contents

3

Enhancements in Sentaurus Device

7

More Flexibility in Sentaurus Mesh

Unified Coordinate System

Numeric Performance Enhancements

8

Usability Enhancements in Sentaurus

Workbench

Latest Edition

After a challenging 2009, we entered 2010 with a renewed sense of optimism and normalcy in our industry. Many of the IC industry segments are projecting growth this year, and our customers are hard at work developing products and honing their market strategies.

To support these activities, I am pleased to announce the release of TCAD Sentaurus Version D-2010.03, and I invite you to browse through its many enhancements and new capabilities described in this newsletter. For example, we continue to increase the functionality, robustness, and performance of 3D simulation to address the rising complexity and inherent threedimensionality of many device technologies, from advanced strained-silicon CMOS and memory applications to power devices and image sensors. In addition, we address new physics in process and device simulation required at the leading-edge nodes, while also incorporating state-of-the-art numeric algorithms to improve simulation efficiency.

I trust that you will take advantage of this new version of TCAD Sentaurus for your simulation work. If you have any questions, we would be pleased to hear from you.

I hope you enjoy this edition of TCAD News and, as always, a heartfelt thank you for your continued support.

With best regards,

Terry Ma

VP Engineering, TCAD

Contact TCAD

For further information and inquiries: tcad_team@synopsys.com

the spheres have been absorbed into the structure using MGOALS3D. This type of operation significantly enhances the structuregeneration capabilities of MGOALS3D by combining it with the versatility of Sentaurus Structure Editor. One possible application of this technique is to define lenses with different shapes for simulating image sensors.

Figure 4. Polyhedra insertion from TDR file: (top) MGOALS3D geometry and externally generated polyhedra, and (bottom) the resulting geometry.

Returning to the SRAM flow simulation, polyhedra operations are used to create the SiGe pockets and elevated source and drain regions, as shown in Figure 5.

Figure 5. The new polyhedra operation is used to incorporate source/drain features in the 6T SRAM as shown in Figure 4: (top) before and (bottom) after polyhedra insertion.

The polyhedra for the SiGe pockets are described as a set of faces, with each face defined by a set of points with assigned coordinates. For convenience, two new “silicon-like” materials are defined to describe the SiGe pockets and the raised source/ drain regions. The polyhedra are inserted by replacing silicon and gas with the newly defined material. The Tcl-based Alagator input language is very useful in these operations.

The halo implantations are simulated with the Monte Carlo model. The analytic model is used for all other implantation steps. Dopant diffusion is simulated with the three-phase segregation model using the default model parameters. Mechanical stress is simulated and accounts for multiple stress sources. PMOS stress is due to lattice mismatch as a result of the 40% germanium concentration in theSiGepocketsandthesacrificialpolysilicon

Figure 6. Stress distribution in 6T SRAM cell; stress component along the channel is shown.

gate removal. NMOS stress is generated by the stressed metal gate and via, and by stress memorization applied to the source and drain regions.Thefinallongitudinalchannelstresses are of the order of 2 GPa compressive for PMOS and 1 GPa tensile for NMOS. The final stress distribution is shown in Figure 6.

The simulation of such a complex structure showcases the improved robustness in 3D structure generation with Sentaurus Process Version D-2010.03. The geometric operations described above simplify the structuregeneration process, contributing to cleaner geometries and higher simulation success rates. Other updates to MGOALS include:

•The robustness of the mesh generator has been improved, enabling the simulation of very complex structures.

•The core functions used by 3D etching and deposition have been further optimized, shortening the simulation time.

•The boundary repair functionality has been optimized, eliminating some unnecessary repairs and improving the quality of the final results. In addition, the repair function has been extended to work in 2D, improving the reliability of structure generation in 2D.

•Thefulllevel-setmethodhasbeenenhanced to eliminate residues or gaps previously produced at the boundary between the material being etched or deposited, and the adjacent materials.

•Etching of thin layers has been improved

through the addition of an analytic mode. This new algorithm improves the performance of the etching process both in terms of size and speed.

Collectively, these new features extend the well-established capabilities of Sentaurus Process to enable 3D simulation of more complex structures with unprecedented flexibility and robustness.

Enhancements to Diffusion Models

~ Mobile Impurities and Ion-Pairing ~

The ion-pairing model accounts for the pairing of positively and negatively charged dopant ions [4][5][6]. Ion-pairing reduces the diffusivity of dopants where the concentration of dopants of the opposite type is large. The ion-pairing model assumes that positively charged donors can bind with negatively charged acceptors to form neutral pairs. The ion-pairing model is significant because it allows the dependency of the impurity diffusivity to be modeled in both n-type and p- type materials. In particular, it can reduce the effective diffusivity of boron in n-type materials without affecting its diffusivity at high p-type concentrations.

The model reduces the mobile concentration of dopant species by the following factors:

where:

• Nd and Na are the total concentrations of electrically active donors and acceptors, respectively.

• Np is the concentration of ion pairs.

• fpd and fpa are the ion-pairing factors for donors and acceptors, respectively.

The concentration of ion pairs Np is given by:

Np = ½[(Nd + Na + Ω) –

√(Nd + Na + Ω)2 – 4NdNa]

The parameter Ω is given by:

Ω = Ion.Pair.Omega · ni

where Ion.Pair.Omega is a parameter for a given material; the default value for silicon and polysilicon is 6.0 [4]. The ion-pairing model is enabled or disabled for each material

with the Ion.Pair parameter; by default, it is disabled for all materials.

~ Nitrogen Diffusion Model ~

The binding energy of nitrogen interstitials is comparable to the formation energy of a silicon self-interstitial. Moreover, substitutional nitrogen is only marginally thermodynamically stable in the lattice. Since the migration energy of nitrogen interstitials is relatively small (~0.5 eV), nitrogen interstitials are fast diffusers. Therefore, nitrogen interstitials rarely dissociate into self-interstitials and substitutional nitrogen. Nitrogen interstitials can react and form nitrogen dimers that diffuse with a migration energy ~2.4 eV [7]. The NeutralReact diffusion model is used for the diffusion of nitrogen monomers and dimers. The dimer is formed by the reaction:

NI + NI < > N2

In this reaction, NI represents the monomer (nitrogen interstitial), and N2 denotes the dimer (Ni)2, which has the solution name

NDimer.

The stable clusters associated with nitrogen atoms are Ns–V, Ni–Ns, and Ns–Ns [8], which are symbolized by NV, N2V, and N2V2 in Sentaurus Process. The NeutralCluster model simulates the reactions for the clusters, in which all the binding energies are calculated from ab initio data.

~ ComplexCluster Activation Model ~

The ComplexCluster model is an extension of the TSUPREM-4™ ACT.FULL activation model.ThereactionoftheComplexCluster model is as follows:

n1X + n2Y + n3P1 + n4e < >

Xn1Yn2P2,m1 + m2P3 + m3e

where:

• X and Y denote two different dopant species.

• Xn1Yn2P2,m1 is a complex cluster.

• P1, P2, and P3 denote point defects, either silicon self-interstitial or vacancy.

• e represents an electron.

The reaction is formulated by:

Theboron–carbon–interstitial(BCI)clustering model is defined by:

~ Vacancy-Clustering Model ~

Recently, vacancy engineering has been investigated extensively to achieve shallow junctions with low sheet resistance. Some techniques used in vacancy engineering include the formation of a vacancy-rich layer using a high-energy silicon implant [9] or the formation of voids as a vacancy source using a helium implant [10][11]. To simulate these processes, the 1Moment, 2Moment, and full dynamics of vacancy-clustering are used. Small vacancy clusters can grow to large vacancy clusters and become voids.

The 1Moment model simulates the formation and dissolution of vacancy clusters or voids by solving a single equation to calculate the total number of vacancies bound in clusters.

The 2Moment model calculates the first two moments of the size distribution of vacancy clusters, that is, the number of clusters and the number of vacancies contained in the clusters. By setting the defect cluster model to Full, the TSUPREM-4-style transient small vacancy cluster model is used. The full dynamics of vacancy-clustering are modeled so that small vacancy clusters can grow to large vacancy clusters or voids.

~ Fast Anisotropic Diffusion ~

ThenewAlagatorfunctiondiag(fx,fy,fz) defines a multiplication factor for diffusivity as a diagonal tensor. The arguments fx, fy, and fz can be any solution-dependent expression. The function diag() can replace aniso() when the off-diagonal elements of the tensor are negligible, with the benefit of a faster simulation speed.

Monte Carlo Implantation

Monte Carlo (MC) implantation is a versatile technique that has applications in many situations where table-based analytic implantation is not suitable. With this release, the flexibility of MC implantation is enhanced with two new features.

~ Improved Binary Collision Approximation Damage Model ~

During implantation, energetic ions penetrate the target and lose their energy through collisions with atoms and electrons. For cases when the ion energy remains well above the displacement threshold, known as the ballistic regime, the ion trajectories can be appropriately simulated using the binary collision approximation (BCA). However, as the ion energy approaches the displacement threshold, the ion enters the thermal regime where multiple interactions with target atoms become important.

Molecular dynamics (MD) simulations demonstrate that energy transfers among atoms in this low-energy regime can lead to amorphous pockets, thereby generating more damage than conventional BCA models. The improved BCA (iBCA) damage model incorporates MD simulation results within the framework of BCA.

The iBCA damage model implemented in Sentaurus MC implantation is based on the work of Santos et al. [12], which uses a combination of the two traditional BCA approaches for damage generation. As in the full-cascade BCA, ion and recoil trajectories are followed to generate damage at the atomic level and to provide the individual positions of Frenkel pairs.

In addition, the energy deposited in the lattice is taken into account. This energy is used to generate thermally disordered atoms following a scheme similar to the modified Kinchin–Pease approach. Since the residual deposited energies that are being considered are always in the low-energy regime, the local character of damage generation is guaranteed.

Furthermore, the damage efficiency proposed [12] accounts for phase transformation (melting) and heat dissipation through the dependency of the parameters on the number of energetic neighbors.

This damage model typically generates much more damage than the conventional full-cascade model. With proper calibrations, this damage model can better predict the amorphous layer thicknesses, especially for heavy species implants. This model also captures the nonlinear effects on damage generation due to the proximity of several energetic atoms, and it is essential for molecular implants.

To activate this model, specify iBCA in the implant command or activate the global switch: pdbSet MCImplant iBCA 1.

~ Plasma Immersion Ion Implantation ~

Plasma immersion ion implantation is a promising technique for silicon processing due to its very high throughput. Sentaurus Process has implemented a simple MC model for plasma immersion ion implantation.

In this model, Sentaurus MC implantation samples the energy and tilt distributions for each particle using the specified average and standard deviation of the energy and the tilt angle. The default distribution is Gaussian for both the energy and tilt angle.

TCAD News March 2010

When the implant energy and tilt angle are determined for each particle, the particle is traced in a typical MC manner. The model is enabled with the parameter plasma in the implant command. In addition to the normal parameters, such as energy and tilt, you also must specify the standard deviation of the implant energy (en.stdev) or the standard deviation of the tilt angle (tilt.stdev) or both. For example:

implant <dopant> plasma dose=<n> \ energy=<n> en.stdev=<n> tilt=<n> \ tilt.stdev=<n> sentaurus.mc

where the parameters energy and tilt are the average energy and average tilt, respectively. If the specified en.stdev and tilt.stdev are both zero, the plasma implant is reduced to a conventional implant.

Figure 7 shows a comparison of plasma and conventional implantation. As expected, a prominent feature of plasma implantation is that with the increasing standard deviation, the peak of the profiles broadens. In addition, the surface concentration becomes higher due to low-energy particles, and the profile tails become deeper due to high-energy particles.

Depth [µm]

Figure 7. Comparison of plasma and conventional implantation for 5 keV boron.

Enhancements in Sentaurus Process Kinetic Monte Carlo

Sentaurus Process Kinetic Monte Carlo (SentaurusProcessKMC)VersionD-2010.03 includes two major improvements for the simulation of amorphization: bond-mediated (transient) diffusion of dopants in amorphous silicon and orientation-dependent solid phase epitaxial regrowth (SPER) with facet formation and strain dependency. Oxidation and silicidation support also has been improved by allowing boundary movement. Other minor modifications include improved deatomization in areas of low particle density, more charge states for particles, and extra reactions for amorphous pockets.

~ Indirect Diffusion of Dopants in Amorphous Silicon ~

A model for the diffusion of dangling bonds and floating bonds in amorphous silicon and its interactions with dopants is introduced in this release [13]. The model is activated by setting KMC aSi amorphous.bond to true. The initial concentration of dangling bonds and floating bonds in amorphous silicon as well as their respective diffusivities can be specified by users. In this model, a dopant (boron) can exist in two different states: an immobile fourfold-coordinated B4 or a highly mobile threefold-coordinated B3.

B4 and B3 are associated with B and Bi in amorphous silicon, respectively. The reaction B4 + Dangling Bond <–> B3 is modeled as B + I <–> Bi, and its parameters are set with

KMC aSi B Dm Bi and KMC aSi B Em Bi for B3 diffusivity, and with KMC aSi B Eb Bi and KMC aSi B Eb Bi for B3–B4 binding.

To simulate the transient behavior of boron diffusion in amorphous silicon, extra dangling bonds are created per impurity introduced in amorphous silicon. This number of dangling bonds is specified with the parameter KMC aSi B gamma and is typically 1. The annihilation of dangling bonds by interacting with floating bonds also is simulated and, in the model notation for amorphous silicon, is

the familiar I + V –> Ø. Finally, the formation of various clusters, agglomerating impurities and bonds in amorphous silicon, can be specified by using the existing clustering mechanism that has been extended to amorphous silicon.

Figure 8 shows the amorphous–crystalline interface of a line-shaped amorphized region in a (011) silicon substrate for different annealing times. The presence of SiO2 or gas atthetopcornerspreventstherecrystallization there and forms (111) planes, while the strain at the bottom corners distorts the lattice and locally slows down the recrystallization.

Figure 8. Amorphous–crystalline interface of a line-shaped amorphized region in a (011) silicon substrate at different annealing times (as a percentage of the total annealing time for SPER to recrystallize the whole sample): (top) 25%, (middle) 33%, and (bottom) 50%.

~ Orientation-dependent SPER Including Facet Formation and Strain Dependency ~

The simulation of solid phase epitaxial regrowth (SPER) is critical for advanced semiconductor processing. It is well known that SPER velocity depends on the substrate orientation, with velocity ratios of 20:10:1 for surface orientations (100), (110), and (111), respectively [14]. A new model that tracks the crystalline lattice (generically called lattice KMC) has been introduced [15]. The model assumes that the recrystallization rate for different orientations depends on the quality of the available crystalline template. In particular, it assumes that each atom in the amorphous phase needs to form two undistorted bonds with the crystal. This is modeled using three different prefactors to simulate the different frequencies at which atoms in the amorphous phase join the crystalline one: K(1), K(2), and K(3) for atoms having two undistorted bonds, needing an atom to join in a cluster, or needing two atoms to form a cluster, respectively. The model has been implemented by defining the silicon lattice with a particular orientation and assigning each silicon atom in the lattice a “crystalline” or an “amorphous” flag according to the initial locations of crystalline and amorphous regions. Each “amorphous” atom has a given frequency:

ν = K(n) x exp[–(E + |εxy|λ)/kBT ]

to be transformed into a crystalline atom. The quality of the crystalline template degrades when distortion is present, and this is modeled by increasing the SPER activation energy by λ|εxy|, where λ is a strain-coupling parameter.

~ Boundary Movement During Oxidation and Silicidation ~

Boundary movement during oxidation and silicidation now is allowed during KMC simulations. This new feature is active by default. If users do not want the material structure to change during diffusion, Grid DoNotMove.Reaction must be set to 1.

~ Deatomization in Areas of Low Concentration ~

Theoutputofaparticularfieldtobedeatomized by kmc deatomize can be increased slightly in areas of low concentration. This is performed by setting, in the Parameter Database Browser, KMC Smooth.Field

<field> and KMC Smooth.Weight, where

Smooth.Field specifies the minimum number M of particles to be accounted for, to display a concentration in the node. If there

are N particles in that node, where N < M, the effective volume of the node increases until the particles are found or some maximum is reached.

When extra M – N particles are found in the volume VR, the total concentration will be:

N/Vorig + Smooth.Weight × (N – M)/VR

This technique is not intended to accurately conserve the total dose but to fill nodes that have zero concentration with concentrations depending on the distance to the nearest particles.

~ New Charge States ~

Up to triple negative and positive charges for point defects and double negative and positive charges for impurity-paired defects are allowed.

~ New Amorphous Pocket Reactions ~

Reactions involving the creation of IV pairs at amorphous pockets are allowed. For example, by setting the reaction KMC Si B

ReactionsClusterI BV,Bi to true, an amorphous cluster In is allowed to react with an incoming mobile BV. The reaction is In +

BV –> In–1V + Bi.

Enhancements in Sentaurus Device

Orientationand Stress-dependent Mobility

A new electron stress channel mobility model has been introduced to address advanced technologies where both high stress and multiple interface orientations affect carrier mobility. The model gives an automatic dependency of Sentaurus Device mobility on channel/substrate MOSFET orientation and on arbitrary stress. One of the key applications for this model is FinFET simulation.

The orientation dependency of the model is based on a previously developed multivalley transportoptionandmultivalleymodifiedlocaldensity approximation (MLDA) model [16]. The stress-dependent conduction band structure is computed using a two-band k.p model [17]. Accounting for three ∆2 valleys in the silicon conduction band structure, the mobility tensor µ^ is represented as the sum of all valley contributions in the following typical form:

where:

• ni /n is a local valley occupation.

• τi /τ0 is the ratio between the stressed and unstressed momentum relaxation times based on a modified Dhar bulk model.

•(^mi)–1 is the valley inverse conductivity mass tensor computed in the valley energy minima of the k.p bands.

All three terms are stress dependent, with the stress dependency inserted through a stress-induced energy shift of the valley energy minima and the change to the effective mass. The channel/substrate orientation dependency in the model mainly comes through the terms ni /n and (^mi)–1. In particular, the local valley occupation is computed using the multivalley MLDA model, and so the

Effective Field [V/cm]

Figure 9. Relative electron mobility change in <100>/(100) NMOSFET induced by uniaxial <100> stress as a function of effective field at the tensile strain of 0.1% (lines: model simulation results and symbols: experimental data).

channel quantization becomes dependent on the interface orientation and stress in a consistent way. The MLDA valley quantization masses are computed also from the k.p bands and by rotation of the inverse mass tensor to obtain the quantization mass along the normal vector to the closest interface. Computation of the MLDA valley carrier density ni is a numeric integration over the energy, and it is generalized to account for the band nonparabolicity for each valley separately.

InSentaurusDevice,themodelisimplemented as a tensor factor to the standard local TCAD mobility (which is consistent with other stressrelated models) and is synchronized with the auto-orientation Lombardi model option also released in this version (see Mobility Model Enhancements). The model was checked against experimental and simulation data from Uchida et al. [18][19]. With one set of model parameters, it shows a good agreement for multiple channel/substrate orientations and a wide range of stress conditions. Comparisons between the model and the data [18][19] are shown in Figure 9 and Figure 10.

Figure 10. Relative electron mobility change in <110>/(110) NMOSFET induced by uniaxial <110> stress as a function of channel carrier density at the tensile strain of 0.1% (lines: model simulation results and symbols: experimental data).

Mobility Model for Thin Layers

The channel mobility in bulk MOSFETs has usually been modeled as a function of the normal electric field since it determines the channel-layer thickness and its degree of quantization. On the other hand, advanced transistors such as ultrathin-body SOI MOSFETs, double-gate FETs, and FinFETs have silicon layers whose thickness can be as small as a few nanometers. The mobility in such a thin silicon layer depends explicitly on the layer thickness because of geometric quantization. As a result, mobility models for bulk MOSFETs are not suitable for these advanced transistors.

Sentaurus Device now supports a physicsbased thin-layer mobility model that accounts for the explicit dependency on the layer thickness. For the mobility degradation due to acoustic phonon scattering and surface roughness scattering, the Lombardi model has been extended as a function of the layer thickness, ensuring that the thin-layer mobility model is reduced to the Lombardi model when the layer thickness is sufficiently large. In addition, the thin-layer mobility model introduces mobility degradation terms due to thickness fluctuations and surface optical phonons [20], which become important when the layer thickness is less than 5 nm.

Sentaurus Device extracts the layer thickness for each point automatically. Since layer thickness is an ambiguous term in all but the simplest geometries, users can overwrite the extracted value with an explicit specification. As an example, Figure 11 shows a FinFET structure with the corresponding extracted thickness. In the corners and the wedge at the base of the fin, the extracted thickness becomes small, which reflects the proximity of more than one interface.

Figure 12 shows the mobility on a horizontal plane located at the middle height of the fin,

DopingConcentration [cm–3] 1.0x10+20

1.0x10+19

1.0x10+18

1.0x10+17

1.0x10+16

LayerThickness [µm] 0.06

0.05

0.04

0.03

0.01

0.00

Figure 11. (Top) Example FinFET with 10 nm wide fin; the fin is lowly doped and covered by a 3 nm nitride dielectric, which is not shown. (Bottom) Extracted layer thickness.

eMobility [cm2/Vs]

Figure 12. Mobility on a horizontal cut plane at half height of the FinFET: (left) Vg = 0 V and (right) Vg = 1 V.

for a 0 V and 1 V gate bias, and 0 V sourcedrain bias. At 0 V, the mobility throughout the channel is nearly uniform, as it is determined mainly by the geometric quantization. At 1 V, the mobility is determined by the electric field and the profile resembles that of bulk MOSFETs: high mobility in the center of the channel where the electric field is low, and low mobility at the interfaces where the electric field is high.

Mobility Model Enhancements

~ Mobility Flexibility ~

It is now possible to specify more than one

DopingDependence or Enormal mobility model in the same simulation. This may be useful, for example, when you need to include additional degradation components that are created as physical model interface (PMI) models into the total mobility calculation. When more than one model is specified as an

option to DopingDependence or Enormal, they are combined using Matthiessen’s rule.

~ Coulomb-Scattering Degradation Components ~

Three mobility degradation components due to Coulomb scattering are available in Sentaurus Device: NegInterfaceCharge,

PosInterfaceCharge, and Coulomb2D. They account for mobility degradation due to negative interface charge, positive interface charge, and ionized impurities near the interface, respectively.

The interface charge components can be used to account for mobility degradation due to interface charge created as the result of processing conditions or from degradation. The Coulomb2D component can be used to introduce additional mobility degradation due to ionized impurities, which may be necessary to better match the mobility roll-off seen in experimental µeff versus Eeff curves.

These degradation components can be specified separately or in combination

with each other as options to the keyword Enormal. If specified, they are combined with other Enormal mobility models using Matthiessen’s rule.

~ Named Parameter Sets for Lombardi Model ~

Sentaurus Device now allows parameter sets for the Lombardi model to be named. These named parameter sets can be selected for use through the command file. The default parameter set for the Lombardi model has the base name of EnormalDependence. This is an unnamed parameter set. To name a parameter set, follow the base name with the parameter set name inside double quotation marks.

~ Orientation-dependent Lombardi Parameters ~

To facilitate simulations that account for surface orientation dependency of mobility, three named parameter sets for the Lombardi model are now available in the parameter file:

• EnormalDependence "100" {...}

• EnormalDependence "110" {...}

• EnormalDependence "111" {...}

These parameter sets represent Lombardi model parameters for surface orientations of (100), (110), and (111), respectively. To select them for use in a simulation, specify the

ParameterSetName=<name> option for

Lombardi in the command file.

Alternatively, an AutoOrientation option for Lombardi is available that automatically switchesbetweentheseparametersetsbased on the orientation of the nearest interface. This feature can be used to accurately model mobility in devices such as FinFETs, where the surface orientation can be different on the top and side interfaces.

~ Single-Trap Capabilities and Trap Randomization ~

Sentaurus Device now allows the keyword SingleTrap to be specified as part of the Trap specification to mimic the behavior of a single-carrier trap or single fixed-charge trap. When SingleTrap is specified, the trap location snaps to the node that is closest to the trap coordinates specified by the user. In addition, the trap concentration is computed automaticallysuchthatafilledtrapcorresponds to one electronic charge. An arbitrary number of SingleTrap specifications is allowed.

Moreover, the spatial distribution of traps can be randomized by including the keyword Randomize in the Trap specification. If

Randomize and SingleTrap are specified together, the location of the single trap is randomized.IfRandomizeisspecifiedwithout SingleTrap, the original concentration of traps at each node, as determined from the Trap specification, is randomized.

For example, randomized single traps can be used in conjunction with structures containing random discrete dopants to statistically characterize random telegraph signal (RTS) magnitudes for threshold-voltage shift. RTS threshold-voltage shifts can be understood by considering the trapping and de-trapping of a single-electron trap near the silicon–oxide interface. Anomalously large RTS threshold-voltage shifts have been explained by the unlucky occurrence of an electron trap in a dominant current percolation path that is created around the potential barriers associated with discrete dopants [21][22][23].

Now, consider an n-channel MOSFET with L = 20 nm and W = 32 nm. Sentaurus Mesh is used to create 200 structures where the doping profiles for both acceptors and donors have been randomized from a single continuously doped structure [24]. For each structure,SentaurusDeviceisusedtosimulate the Id–Vg characteristics with and without a filled electron trap randomly placed in the channel region at the silicon–oxide interface.

Electron Trap

Electron Trap

Figure 13. Electrostatic potential at silicon–oxide interface for two structures with randomly placed single-electron trap.

For the 200 structures, the threshold-voltage shift between the no-trap case and the filledtrap case is extracted. Figure 13 shows the electrostatic potential at the silicon–oxide interface for two such structures that include a random single-electron trap.

Figure 14 shows a histogram of normalized occurrences versus threshold-voltage shift. The results indicate that large thresholdvoltage shifts are possible, but there is an approximately exponential decrease in the likelihood of such events.

100

Figure 14. Frequency histogram for thresholdvoltage shifts due to RTS.

It is interesting to analyze the results for a case where a large threshold-voltage shift is observed. Figure 15 shows internal device characteristics for such a case. It shows 3D surface plots of conduction band energy in the channel region at a distance 11 Å below the interface when the gate is biased at the threshold voltage. The colored contours show electron density. The top plot shows results without the electron trap. The bottom plot shows results that include the randomly placed electron trap at the interface.

Peaks in conduction band energy, which are due to the presence of nearby discrete acceptor dopants, represent barriers to current flow (the electrons prefer conduction paths in the valleys). Red contours indicate regions of high electron density, which occur primarily at the source and drain edges. In the top plot, there is the beginning of a dominant current path that occurs in the conduction band energy valley in the foreground. In the bottom plot, the unlucky placement of the single-electron trap in the middle of this current path produces an additional potential barrier that inhibits conduction and results in a large threshold-voltage shift compared to the no-trap case.

Source

Drain

eDensity [cm3] 3.6e+18

2.9e+18

2.2e+18

1.4e+18

7.2e+17

0.0e+00

Source

Drain

Figure 15. Conduction band energy contour with superimposed electron density color bands for structure (top) without single-electron trap and (bottom) with single-electron trap.

Dipole Interfaces

The continual scaling of advanced CMOS process technologies has led to complicated gate structures composed of several insulating materials including, for example, high-k hafnium-based dielectrics. Recent experimentalresultshaveclearlydemonstrated that dipole-layer formation at high-k–SiO2 interfaces can result in significant shifts of the threshold voltage. The areal density difference of oxygen atoms causes the generation of such immobile dipole interface charges. In simulations, these dipole interface charges have been integrated as fixed (monopole) charges, distributed over a sufficiently thin insulator region, and inserted in the device structure. However, this way of accounting for the effect of the dipole layer is artificial.

With Version D-2010.03, a dipole interface model for insulator–insulator interfaces is available. It describes the charge densities of the immobile interface dipoles with infinitesimally small layer thickness, leading to discontinuities of the electrostatic potential across such dipole interfaces. The model simplifies device-structure generation as it makes the introduction of the charge-carrying insulator regions dispensable.

Figure 16 illustrates dipole modeling using spatially distributed monopole charges and the dipole interface model. The left figure shows the artificial region between the high-k and SiO2 regions. The spatial distribution of the electrostatic potential in the monopole charge modeling is continuous (middle figure); while for the dipole interface model, the discontinuities are visible (right figure). The electric fields differ locally, especially at the end of the artificial regions.

Extension of Spherical Harmonic Expansion to Full Band Structure

Sentaurus Device Version C-2009.06 includedahot-carrierinjectionmodelbasedon the first-order spherical harmonics expansion (SHE) of the Boltzmann equation with analytic band structures. As the hot-carrier injection depends on the tail part of the carrier-energy distribution, the simulation results can be sensitive to the employed band structure.

In this release, Sentaurus Device supports general user-defined band structures for the

TCAD News March 2010

which a perturbative, nonparabolic correction can be added, and a confined version of the two-band k∙p approach. For holes, a confined version of the six-band k∙p approach can be used. The full in-plane dispersion is computed for each subband and this dispersion can be saved to a TDR file for visualization. Figure 20 shows the in-plane dispersion of the topmost valence subband for three different surface orientations in a bulk MOS capacitor.

k y

-0.1

–

0.2

(111)/<112>

k y

-0.1

Figure 20. Subband dispersion of topmost valence subband for different sets of surface orientation/kx-direction.

~ Mobility Calculations ~

The inversion-layer mobility is computed using a deterministic approach by evaluating the Kubo–Greenwood integral over each subband:

This approach combines the subband dispersion (Eν) from the subband calculation, along with a microscopic relaxation time (τ) that is determined by user-selectable scattering models. Scattering models for elastic acoustic phonon-scattering, inelastic intervalley phonon-scattering, and surface roughness scattering are available. Surface roughness scattering can be screened using a scalar Lindhard dielectric function.

Using the Kubo–Greenwood approach, all three components of the in-plane mobility tensor can be computed enabling a full characterization of in-plane anisotropy. Alternatively, the diagonal component of the mobility tensor along a particular direction can be computed to simulate the mobility along a fixed channel direction.

As an example of an electron mobility calculation,Figure21comparesthecomputed

to enhance its computation speed and functionality. The new features are designed to meet the challenges of simulating CMOS image sensors (CISs) and solar cells in a more efficient and consistent manner. Two new major implementations are the dispersive model and the message passing interface (MPI) distributed-computing parallelization of the finite-difference time-domain (FDTD) kernel.

~ Dispersive Model ~

Different models have been introduced to model dispersive materials over a bandwidth: Debye, Drude, Lorentz, and Drude–Lorentz. To solve them, an auxiliary differential equation is discretized and appended to the explicit scheme of the FDTD methodology. On the other hand, if only a single frequency (for example, the sine-cosine formulation) is involved, a mathematically rigorous singledipole Drude dispersive model can be used.

The dispersive model is intended to handle situations where the extinction coefficient is larger than the refractive index, as commonly observed in metals at optical frequencies. Since for reasons of stability the mesh density of a dispersive material must be increased, dispersive models must be used only when necessary. This means that in typical CIS applications, the dispersive model must be applied only to the metal interconnects.

The dispersive model has been tested with a two-layer (air-gold) structure, and the results are in good agreement with analytic calculations. The application of the dispersive model to the metal interconnects in a onepixel CIS structure is shown in Figure 26.

Z

Y X

Optical Generation [cm–3 s–1]

2.0e+22

2.8e+21

3.8e+20

5.3e+19

7.2e+18 1.0e+18

Figure 26. Optical generation simulated by setting the metal interconnects as (left) a dispersive material and (right) a perfect electric conductor.

~ MPI Parallelization ~

CIS-pixel development engineers often need to simulate large, multipixel structures with FDTD to assess crosstalk. With this release, significant speed improvements for such large FDTD simulations can be achieved by simultaneously applying two strategies: domain decomposition and distributed computing. The FDTD problem is decomposed into numerous subdomains, and each subdomain problem is distributed to be solved by a separate process.

The information exchange between the subdomain problems is limited to boundary values of the fields. Such an adaptation reduces the bandwidth of communication in the solution process, thereby avoiding the memory-bus bandwidth limitations in the multithreading approaches for such a class of problem.

The new distributed-computing capability of EMW (EMW MPI) is built on the message passing interface (MPI) platform. The concept ofMPIreliesonthemanagementofinformation exchanges between the processes. A process is an executable job that solves a subdomain problem, and a master process controls the information exchanges between the different processes. The MPI controller distributes the processes to run on different machines and CPUs. The best assignment is to restrict one process to one CPU core. Nonetheless, a process is a virtual concept, so users can

declare more processes than CPU cores, in which case, resources will be shared and performance will degrade.

In EMW MPI, each MPI process also can spawnmultiplethreadstosolvethesubdomain problem, and this is referred to as the hybrid mode.

The optimal deployment of EMW MPI is on a specialized cluster of machines with InfiniBand interconnections. A representative cluster composed of 16 hosts/machines, with each host/machine containing four dual-core CPUs (2.41 GHz AMD Opteron) and 16 GB DRAM, giving a total of 64 cores, was used to test the speedup factors of a one-pixel and a four-pixel CIS structure.

As shown in Figure 27, a speedup factor of 20 times is achieved for the four-pixel case when distributing the simulation over 32 processes.

Figure 27. Speedup characteristics for one-pixel and four-pixel CIS structures using new MPI distributed-computing method.

~ EMW MPI on a Network with IP Connections ~

It is possible to use EMW MPI on a network of machines with IP connections, but performance will be limited by the bandwidth of the IP network. However, as long as the computation volume of each subdomain problem is much greater than the information (boundary field values) exchange volume, it is possible to attain optimal performance within the distributed-computing infrastructure.

The advantages of the MPI methodology are that there is no limit to the size of the problem thatcanbesolvedandscalabilityismaintained. One drawback of MPI distributed computing is the requirement for load-balancing. This means that all subdomain problems must finish computation at approximately the same time, so that the next computation step can be initiated. In other words, the computation speed depends on the slowest process member. Therefore, it is important to run the MPI job on a dedicated cluster or network of machines.

~ Other EMW Features ~

A common complex refractive index (CRI) library has been constructed to serve as a common module for various Sentaurus tools such as Sentaurus Device and Sentaurus Mesh. Figure 28 shows the assimilation of the module with other tools. Such integration ensures a consistent framework of the CRI

CRI Library

Figure 28. Layout of CRI library and its interface with other tools.

computation across different tools. The CRI library also provides an additional CRI model interface, analogous to the PMI in Sentaurus Device, which allows users to write their own routines for computing the refractive index and extinction coefficient.

Physical Model Interface

The physical model interface (PMI) of Sentaurus Device enables users to write their own custom models using C++. Examples include models for mobility, recombination, and energy gap. Header files are provided that definethebaseclassforeachPMI.Aparticular model is then implemented as functions in a derived class. An auxiliary cmi tool compiles the C++ source code and produces a shared object file. Sentaurus Device loads the shared object code at run-time to evaluate the custom model.

The popularity of PMI among users is rising for a number of reasons:

•New models can be implemented and verified quickly.

•The confidentiality of proprietary models can be protected.

•The performance of PMI models is comparable to that of built-in models.

The success of the PMI has encouraged Synopsys to offer, as an alternative, a simplified PMI that provides improvements in two important areas compared to the standard PMI:

•Instead of multiple functions for the model and the derivatives with respect to all variables, the simplified PMI only requires a single function to evaluate the model, eliminating the time-consuming and error-prone work of implementing multiple derivative functions.

•Compared to the standard PMI, which always evaluates a model in normal precision (64 bits), the simplified PMI also supports extended-precision floating-point arithmetic.

To enable these improvements, the simplified PMI provides a new data type pmi_float as a substitute for double. This new data type supports automatic differentiation: The derivatives of a model are computed simultaneously with the model itself.

Furthermore, the new data type pmi_float supports extended-precision floating-point arithmetic. The accuracy of the value of a variable of type pmi_float is identical to the accuracy selected for the Sentaurus Device simulation. Therefore, PMI models now can provide the same accuracy as built-in models.

The simplified PMI is an ideal solution for users who want a quick turnaround for prototyping. The added user-friendliness involves some computational overhead, which in most cases will result in a negligible reduction in performance. However, when a new PMI model has been validated, it can be easily translated back to the standard PMI for performance-critical applications. As another benefit, a user model can be implemented using both the standard and the simplified interfaces. In this case, Sentaurus Device picks the standard PMI for normalprecision arithmetic (best performance) and the simplified PMI for extended-precision arithmetic (best accuracy).

More Flexibility in Sentaurus Mesh

Over the past several releases, Sentaurus Mesh has become the standard meshgeneration engine for Sentaurus Process and Sentaurus Device. In this release, the flexibility of Sentaurus Mesh is extended with two new features.

Support of Layer Generation

In this release, some Noffset3D functionality is available in Sentaurus Mesh. Parameters

such as hlocal, factor, and maxlevel

Project Refresh

Refreshing projects (the F5 key) has been enhanced. Now, it updates not only the node status but also the extracted variables. This provides significant time-savings when monitoring the progress of a running project as it is no longer necessary to reload the whole project for this purpose.

Configuring Node Status Colors and Font Attributes

Now, users can redefine the default colors used to indicate node status. The adjustment of the standard color scheme to allow for better visual distinction of colors on-screen is performed in user preferences (Table >

Node Status Color).

In addition, users can configure font attributes of the project view for the currently open project (View > Table Options > Change Table Font). The next time the project is loaded, the applied font settings take effect. Users can choose the system default fonts that Sentaurus Workbench detects automatically or they can select the specific font from the dialog box. Applying a particular font to new projects can be set up in user preferences (Table > Font).

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