Memosa-FVM  0.2
Public Types | Public Member Functions | Private Attributes | List of all members
TunnelingDiscretization< X, Diag, OffDiag > Class Template Reference

#include <TunnelingDiscretization.h>

Inheritance diagram for TunnelingDiscretization< X, Diag, OffDiag >:
Inheritance graph
[legend]
Collaboration diagram for TunnelingDiscretization< X, Diag, OffDiag >:
Collaboration graph
[legend]

Public Types

typedef NumTypeTraits< X >
::T_Scalar 		T_Scalar
 
typedef Array< T_Scalar > TArray
 
typedef Array< int > IntArray
 
typedef CRMatrix< Diag,
OffDiag, X > 		CCMatrix
 
typedef CCMatrix::DiagArray DiagArray
 
typedef CCMatrix::OffDiagArray OffDiagArray
 
typedef Array< X > XArray
 
typedef Array< Vector
< T_Scalar, 3 > > 		VectorT3Array
 

Public Member Functions

 TunnelingDiscretization (const MeshList &meshes, const GeomFields &geomFields, const Field &varField, const Field &conductionbandField, const ElectricModelConstants< T_Scalar > &constants, T_Scalar &fluxIn, T_Scalar &fluxOut)
 
void discretize (const Mesh &mesh, MultiFieldMatrix &mfmatrix, MultiField &xField, MultiField &rField)
 
- Public Member Functions inherited from Discretization
 Discretization (const MeshList &meshes)
 
virtual ~Discretization ()
 
 DEFINE_TYPENAME ("Discretization")
 

Private Attributes

const GeomFields & _geomFields
 
const Field & _varField
 
const Field & _conductionbandField
 
const ElectricModelConstants
< T_Scalar > & 		_constants
 
T_Scalar & _fluxIn
 
T_Scalar & _fluxOut
 

Additional Inherited Members

- Protected Attributes inherited from Discretization
const MeshList & _meshes
 

Detailed Description

template<class X, class Diag, class OffDiag>
class TunnelingDiscretization< X, Diag, OffDiag >

Definition at line 43 of file TunnelingDiscretization.h.

Member Typedef Documentation

template<class X , class Diag , class OffDiag >
typedef CRMatrix<Diag,OffDiag,X> TunnelingDiscretization< X, Diag, OffDiag >::CCMatrix

Definition at line 50 of file TunnelingDiscretization.h.

template<class X , class Diag , class OffDiag >
typedef CCMatrix::DiagArray TunnelingDiscretization< X, Diag, OffDiag >::DiagArray

Definition at line 51 of file TunnelingDiscretization.h.

template<class X , class Diag , class OffDiag >
typedef Array<int> TunnelingDiscretization< X, Diag, OffDiag >::IntArray

Definition at line 49 of file TunnelingDiscretization.h.

template<class X , class Diag , class OffDiag >
typedef CCMatrix::OffDiagArray TunnelingDiscretization< X, Diag, OffDiag >::OffDiagArray

Definition at line 52 of file TunnelingDiscretization.h.

template<class X , class Diag , class OffDiag >
typedef NumTypeTraits<X>::T_Scalar TunnelingDiscretization< X, Diag, OffDiag >::T_Scalar

Definition at line 47 of file TunnelingDiscretization.h.

template<class X , class Diag , class OffDiag >
typedef Array<T_Scalar> TunnelingDiscretization< X, Diag, OffDiag >::TArray

Definition at line 48 of file TunnelingDiscretization.h.

template<class X , class Diag , class OffDiag >
typedef Array<Vector<T_Scalar, 3> > TunnelingDiscretization< X, Diag, OffDiag >::VectorT3Array

Definition at line 54 of file TunnelingDiscretization.h.

template<class X , class Diag , class OffDiag >
typedef Array<X> TunnelingDiscretization< X, Diag, OffDiag >::XArray

Definition at line 53 of file TunnelingDiscretization.h.

Constructor & Destructor Documentation

template<class X , class Diag , class OffDiag >
TunnelingDiscretization< X, Diag, OffDiag >::TunnelingDiscretization ( const MeshList &  meshes,
const GeomFields &  geomFields,
const Field &  varField,
const Field &  conductionbandField,
const ElectricModelConstants< T_Scalar > &  constants,
T_Scalar &  fluxIn,
T_Scalar &  fluxOut 
)
inline

Definition at line 56 of file TunnelingDiscretization.h.

63  :
64  Discretization(meshes),
65  _geomFields(geomFields),
66  _varField(varField),
67  _conductionbandField(conductionbandField),
68  _constants(constants),
69  _fluxIn(fluxIn),
70  _fluxOut(fluxOut)
71  {}
Discretization::Discretization
Discretization(const MeshList &meshes)
Definition: Discretization.cpp:8
TunnelingDiscretization::_constants
const ElectricModelConstants< T_Scalar > & _constants
Definition: TunnelingDiscretization.h:385

Member Function Documentation

template<class X , class Diag , class OffDiag >
void TunnelingDiscretization< X, Diag, OffDiag >::discretize ( const Mesh &  mesh,
MultiFieldMatrix &  mfmatrix,
MultiField &  xField,
MultiField &  rField 
)
inlinevirtual

Implements Discretization.

Definition at line 73 of file TunnelingDiscretization.h.

References TunnelingDiscretization< X, Diag, OffDiag >::_conductionbandField, TunnelingDiscretization< X, Diag, OffDiag >::_constants, TunnelingDiscretization< X, Diag, OffDiag >::_fluxIn, TunnelingDiscretization< X, Diag, OffDiag >::_fluxOut, TunnelingDiscretization< X, Diag, OffDiag >::_geomFields, TunnelingDiscretization< X, Diag, OffDiag >::_varField, GeomFields::coordinate, ElectricModelConstants< T >::electron_trapdepth, ElectronSupplyFunction(), fabs(), FermiFunction(), Mesh::getBoundaryFaceGroups(), Mesh::getCellCells(), Mesh::getCells(), StorageSite::getCount(), CRConnectivity::getCount(), CRMatrix< T_Diag, T_OffDiag, X >::getDiag(), Mesh::getFaceCells(), MultiFieldMatrix::getMatrix(), StorageSite::getSelfCount(), H_SI, HBAR_SI, FaceGroup::id, K_SI, ME, PI, PositiveValueOf(), QE, FaceGroup::site, sqrt(), and GeomFields::volume.

75  {
76  #define DEBUG 0
77 
78  const StorageSite& cells = mesh.getCells();
79 
80  //const StorageSite& faces = mesh.getFaces();
81 
82  const int nCells = cells.getSelfCount();
83 
84  const TArray& conduction_band = dynamic_cast<const TArray&> (_conductionbandField[cells]);
85 
86  const TArray& cellVolume =
87  dynamic_cast<const TArray&>(_geomFields.volume[cells]);
88 
89  const VectorT3Array& cellCentroid =
90  dynamic_cast<const VectorT3Array& > (_geomFields.coordinate[cells]);
91 
92  const MultiField::ArrayIndex cVarIndex(&_varField,&cells);
93 
94  CCMatrix& matrix = dynamic_cast<CCMatrix&>(mfmatrix.getMatrix(cVarIndex,cVarIndex));
95 
96  const XArray& xCell = dynamic_cast<const XArray&>(_varField[cells]);
97 
98  TArray* ts = new TArray(cells.getCount());
99  *ts = 0;
100  TArray& transmission = *ts;
101 
102  XArray& rCell = dynamic_cast<XArray&>(rField[cVarIndex]);
103 
104  DiagArray& diag = matrix.getDiag();
105 
106  _fluxIn = 0.0;
107  _fluxOut = 0.0;
108 
109  const T_Scalar electron_effmass = _constants["electron_effmass"];
110  const T_Scalar temperature = _constants["OP_temperature"];
111  const T_Scalar electron_capture_cross = _constants["electron_capture_cross"];
112  //const T_Scalar voltage = _constants["voltage"];
113  //const T_Scalar substrate_voltage = _constants["substrate_voltage"];
114  //const T_Scalar membrane_voltage = _constants["membrane_voltage"];
115  const T_Scalar fermilevelsubstrate = -_constants["substrate_workfunction"] - _constants["substrate_voltage"];
116  //const T_Scalar fermilevelmembrane = -_constants["substrate_workfunction"] - _constants["membrane_voltage"];
117  //const T_Scalar& dielectric_ionization = _constants["dielectric_ionization"];
118  const int subID = _constants["substrate_id"];
119  //const int memID = _constants["membrane_id"];
120  const int nLevel = _constants["nLevel"];
121  const int normal = _constants["normal_direction"];
122  const int nTrap = _constants["nTrap"];
123 
124  const vector<double> electron_trapdepth = _constants.electron_trapdepth;
125  const vector<double> electron_trapdensity = _constants.electron_trapdensity;
126 
127  if (int(electron_trapdepth.size()) != nTrap || int(electron_trapdensity.size()) != nTrap)
128  throw CException ("trap depth vector size error!");
129 
130  T_Scalar fluxCoeff(0), fermilevel(0), scatterfactor(0);
131  //T_Scalar sourceTunneling(0);
132 
133  for(int c=0; c < cells.getCount(); c++){
134  transmission[c] = 0.0;
135  }
136 
137 
138 
139  //=======================================//
140  // tunneling from substrate to dielectric
141  //=======================================//
142 
143  //const T_Scalar energystep = 0.1 * fabs(substrate_voltage - membrane_voltage) / nLevel;
144  const T_Scalar energystep = 0.01;
145  const T_Scalar alpha = 4.0 * PI * (electron_effmass*ME) / pow(H_SI, 3.0);
146 
147  fermilevel = fermilevelsubstrate;
148 
149 #if DEBUG
150  shared_ptr<IntArray> mark(new IntArray(cells.getCount()));
151  *mark = 0;
152 #endif
153 
154  for (T_Scalar en = fermilevel-4.0; en <= fermilevel+4.0; en += energystep){
155 
156  const T_Scalar supplyfunction = ElectronSupplyFunction(en, fermilevel, temperature);
157 
158  const T_Scalar fermifunction = FermiFunction(en, fermilevel, temperature);
159 
160  //========= transmission coefficient calculation ==========//
161  // this scheme only works for Cartesian mesh
162 
163  foreach(const FaceGroupPtr fgPtr, mesh.getBoundaryFaceGroups())
164  {
165  const FaceGroup& fg = *fgPtr;
166 
167  if (fg.id == subID){
168 
169  const StorageSite& faces = fg.site;
170  const CRConnectivity& faceCells = mesh.getFaceCells(faces);
171  const CRConnectivity& cellCells = mesh.getCellCells();
172  const int nFaces = faces.getCount();
173 
174  for(int f=0; f<nFaces; f++){
175 
176  int c0 = faceCells(f,0); //the first cell adjacent to boundary
177  int c1 = faceCells(f,1); //boundary cell
178 
179  transmission[c1] = 1.0;
180 
181  int low = c1;
182  int me = c0;
183  int high = c0;
184 
185  for(int l=0; l< nLevel; l++){
186 
187  T_Scalar dX = cellCentroid[me][normal] - cellCentroid[low][normal];
188  T_Scalar factor = -2.0/HBAR_SI * sqrt(2.0*electron_effmass*ME*QE);
189  T_Scalar valueMe = PositiveValueOf( conduction_band[me] - en);
190  //T_Scalar valueLow = PositiveValueOf( conduction_band[low] - en);
191  //T_Scalar avg = (valueMe + valueLow) / 2.0;
192  T_Scalar avg = valueMe;
193  T_Scalar exponent = factor * sqrt(avg) * fabs(dX);
194 
195 #if DEBUG
196  (*mark)[me] = 1;
197 #endif
198  transmission[me] = transmission[low] * exp(exponent);
199 
200  const int nbc = cellCells.getCount(me);
201 
202  T_Scalar drmin = 0.0;
203  int neighborUp = 0;
204 
205  for(int nc = 0; nc < nbc; nc++){
206  const int neighbor = cellCells(me, nc);
207  const T_Scalar dr = cellCentroid[me][normal] - cellCentroid[neighbor][normal];
208  if (dr < drmin){
209  drmin = dr;
210  neighborUp = neighbor;
211  }
212  }
213 
214  if (neighborUp < nCells) {
215  high = neighborUp;
216  low = me;
217  me = high;
218  }
219  }
220  }
221  }
222  }
223 
224  //========= tunneling calculation ==========//
225 
226  for(int c=0; c<nCells; c++){
227 
228  for (int i=0; i<nTrap; i++){
229 
230  const T_Scalar stcap = electron_capture_cross * cellVolume[c];
231 
232  const T_Scalar endiff = en - (conduction_band[c]-electron_trapdepth[i]);
233 
234  // tunneling from substrate to traps
235 
236  if (en-conduction_band[c] < 0){ //this condition determines tunneling only happens close to contact
237 
238  if (endiff < 0)
239  scatterfactor = exp(-QE * fabs(endiff)/(K_SI*temperature));
240  else scatterfactor = 1.0;
241 
242  fluxCoeff = alpha * stcap * transmission[c] * supplyfunction *
243  fermifunction * scatterfactor * energystep * QE;
244 
245  _fluxIn += (fluxCoeff * (electron_trapdensity[i] - xCell[c][i]));
246  rCell[c][i] += (fluxCoeff * (electron_trapdensity[i] - xCell[c][i]));
247  diag[c](i,i) -= fluxCoeff;
248 
249  }
250  // tunneling from traps to substrate
251 
252  if(en - conduction_band[c] < 0){
253  if (endiff > 0)
254  scatterfactor = exp(-QE * fabs(endiff)/(K_SI*temperature));
255  else scatterfactor = 1.0;
256 
257  fluxCoeff = alpha * stcap * transmission[c] * supplyfunction *
258  (1-fermifunction) * scatterfactor * energystep * QE;
259 
260  _fluxOut += (fluxCoeff * (- xCell[c][i]));
261  rCell[c][i] += (fluxCoeff * (- xCell[c][i]));
262  diag[c](i,i) -= fluxCoeff;
263 
264  }
265  }
266  }
267  }
268 #if 0
269  //=======================================//
270  // tunneling from membrane to dielectric
271  //=======================================//
272  for(int c=0; c < cells.getCount(); c++){
273  transmission[c] = 0.0;
274  }
275 
276  fermilevel = fermilevelmembrane;
277 
278  for (T_Scalar en = fermilevel-4.0; en <= fermilevel+4.0; en += energystep){
279 
280  const T_Scalar supplyfunction = ElectronSupplyFunction(en, fermilevel, temperature);
281 
282  const T_Scalar fermifunction = FermiFunction(en, fermilevel, temperature);
283 
284  foreach(const FaceGroupPtr fgPtr, mesh.getBoundaryFaceGroups())
285  {
286  const FaceGroup& fg = *fgPtr;
287 
288  if (fg.id == memID){
289  const StorageSite& faces = fg.site;
290  const CRConnectivity& faceCells = mesh.getFaceCells(faces);
291  const CRConnectivity& cellCells = mesh.getCellCells();
292  const int nFaces = faces.getCount();
293 
294  for(int f=0; f<nFaces; f++){
295 
296  int c0 = faceCells(f,0);
297  int c1 = faceCells(f,1);
298 
299  transmission[c1] = 1.0;
300 
301  int low = c1;
302  int me = c0;
303  int high = c0;
304 
305  for(int l=0; l<nLevel; l++){
306 
307  T_Scalar dX = cellCentroid[me][normal] - cellCentroid[low][normal];
308  T_Scalar factor = -2.0/HBAR_SI * sqrt(2.0*electron_effmass*ME*QE);
309  T_Scalar valueMe = PositiveValueOf( conduction_band[me] - en);
310  T_Scalar valueLow = PositiveValueOf( conduction_band[low] - en);
311  T_Scalar avg = (valueMe + valueLow) / 2.0;
312  T_Scalar exponent = factor * sqrt(avg) * fabs(dX);
313  transmission[me] = transmission[low] * exp(exponent);
314 
315  const int nbc = cellCells.getCount(me);
316 
317  T_Scalar drmin = 0.0;
318  int neighborUp = 0;
319 
320  for(int nc = 0; nc < nbc; nc++){
321  const int neighbor = cellCells(me, nc);
322  const T_Scalar dr = cellCentroid[me][normal] - cellCentroid[neighbor][normal];
323  if (dr > drmin){
324  drmin = dr;
325  neighborUp = neighbor;
326  }
327  }
328  if (neighborUp < nCells) {
329  high = neighborUp;
330  low = me;
331  me = high;
332  }
333  }
334  }
335  }
336  }
337 
338  for(int c=0; c<nCells; c++){
339 
340  for(int i=0; i<nTrap; i++){
341 
342  const T_Scalar stcap = electron_capture_cross * cellVolume[c];
343 
344  const T_Scalar endiff = en - (conduction_band[c]-electron_trapdepth[i]);
345 
346  // tunneling from membrane to traps
347 
348  if (en-conduction_band[c] < 0){
349 
350  if (endiff < 0)
351  scatterfactor = exp(-QE * fabs(endiff)/(K_SI*temperature));
352  else scatterfactor = 1.0;
353 
354  fluxCoeff = alpha * stcap * transmission[c] * supplyfunction *
355  fermifunction * scatterfactor * energystep * QE;
356 
357  rCell[c][i] += (fluxCoeff * (electron_trapdensity[i] - xCell[c][i]));
358  diag[c](i,i) -= fluxCoeff;
359  }
360 
361  // tunneling from traps to membrane
362  if(en - conduction_band[c] < 0 ){
363  if (endiff > 0)
364  scatterfactor = exp(-QE * fabs(endiff)/(K_SI*temperature));
365  else scatterfactor = 1.0;
366 
367  fluxCoeff = alpha * stcap * transmission[c] * supplyfunction *
368  (1-fermifunction) * scatterfactor * energystep * QE;
369 
370  rCell[c][i] += (fluxCoeff * (-xCell[c][i]));
371  diag[c](i,i) -= fluxCoeff;
372  }
373  }
374  }
375  }
376 
377 #endif
378  //cout << _fluxIn << " " << _fluxOut << endl;
379  }
Mesh::getBoundaryFaceGroups
const FaceGroupList & getBoundaryFaceGroups() const
Definition: Mesh.h:187
CRConnectivity::getCount
int getCount(const int i) const
Definition: CRConnectivity.h:165
MultiFieldMatrix::getMatrix
Matrix & getMatrix(const Index &rowIndex, const Index &colIndex)
Definition: MultiFieldMatrix.cpp:42
FaceGroupPtr
shared_ptr< FaceGroup > FaceGroupPtr
Definition: Mesh.h:46
PI
#define PI
Definition: PhysicsConstant.h:10
StorageSite::getSelfCount
int getSelfCount() const
Definition: StorageSite.h:40
GeomFields::coordinate
Field coordinate
Definition: GeomFields.h:19
TunnelingDiscretization::T_Scalar
NumTypeTraits< X >::T_Scalar T_Scalar
Definition: TunnelingDiscretization.h:47
FaceGroup
Definition: Mesh.h:28
FermiFunction
const T FermiFunction(const T &energy, const T &fermilevel, const T &temperature)
Definition: ElectricUtilityFunctions.h:19
K_SI
#define K_SI
Definition: PhysicsConstant.h:12
TunnelingDiscretization::CCMatrix
CRMatrix< Diag, OffDiag, X > CCMatrix
Definition: TunnelingDiscretization.h:50
ME
#define ME
Definition: PhysicsConstant.h:16
sqrt
Tangent sqrt(const Tangent &a)
Definition: Tangent.h:317
HBAR_SI
#define HBAR_SI
Definition: PhysicsConstant.h:22
FaceGroup::id
const int id
Definition: Mesh.h:41
MultiField::ArrayIndex
pair< const Field *, const StorageSite * > ArrayIndex
Definition: MultiField.h:21
H_SI
#define H_SI
Definition: PhysicsConstant.h:14
QE
#define QE
Definition: PhysicsConstant.h:18
Mesh::getCellCells
const CRConnectivity & getCellCells() const
Definition: Mesh.cpp:480
TunnelingDiscretization::_constants
const ElectricModelConstants< T_Scalar > & _constants
Definition: TunnelingDiscretization.h:385
Mesh::getCells
const StorageSite & getCells() const
Definition: Mesh.h:109
GeomFields::volume
Field volume
Definition: GeomFields.h:26
PositiveValueOf
const T PositiveValueOf(T input)
Definition: ElectricUtilityFunctions.h:50
Mesh::getFaceCells
const CRConnectivity & getFaceCells(const StorageSite &site) const
Definition: Mesh.cpp:388
fabs
Tangent fabs(const Tangent &a)
Definition: Tangent.h:312
ElectronSupplyFunction
const T ElectronSupplyFunction(const T &energy, const T &fermilevel, const T &temperature)
Definition: ElectricUtilityFunctions.h:25
StorageSite::getCount
int getCount() const
Definition: StorageSite.h:39
ElectricModelConstants::electron_trapdepth
vector< T > electron_trapdepth
Definition: ElectricBC.h:77
FaceGroup::site
StorageSite site
Definition: Mesh.h:40

Member Data Documentation

template<class X , class Diag , class OffDiag >
const Field& TunnelingDiscretization< X, Diag, OffDiag >::_conductionbandField
private

Definition at line 384 of file TunnelingDiscretization.h.

Referenced by TunnelingDiscretization< X, Diag, OffDiag >::discretize().

template<class X , class Diag , class OffDiag >
const ElectricModelConstants<T_Scalar>& TunnelingDiscretization< X, Diag, OffDiag >::_constants
private

Definition at line 385 of file TunnelingDiscretization.h.

Referenced by TunnelingDiscretization< X, Diag, OffDiag >::discretize().

template<class X , class Diag , class OffDiag >
T_Scalar& TunnelingDiscretization< X, Diag, OffDiag >::_fluxIn
private

Definition at line 386 of file TunnelingDiscretization.h.

Referenced by TunnelingDiscretization< X, Diag, OffDiag >::discretize().

template<class X , class Diag , class OffDiag >
T_Scalar& TunnelingDiscretization< X, Diag, OffDiag >::_fluxOut
private

Definition at line 387 of file TunnelingDiscretization.h.

Referenced by TunnelingDiscretization< X, Diag, OffDiag >::discretize().

template<class X , class Diag , class OffDiag >
const GeomFields& TunnelingDiscretization< X, Diag, OffDiag >::_geomFields
private

Definition at line 382 of file TunnelingDiscretization.h.

Referenced by TunnelingDiscretization< X, Diag, OffDiag >::discretize().

template<class X , class Diag , class OffDiag >
const Field& TunnelingDiscretization< X, Diag, OffDiag >::_varField
private

Definition at line 383 of file TunnelingDiscretization.h.

Referenced by TunnelingDiscretization< X, Diag, OffDiag >::discretize().

The documentation for this class was generated from the following file: