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18 //////////////////////////////////////////////////////
19 // Calibration class for set:ITS //
20 // Specific subdetector implementation is done in //
21 // AliITSCalibrationSPD //
22 // AliITSCalibrationSDD //
23 // AliITSCalibrationSSD //
24 //////////////////////////////////////////////////////
26 #include <Riostream.h>
29 #include "AliITSCalibration.h"
32 ClassImp(AliITSCalibration)
34 //______________________________________________________________________
35 AliITSCalibration::AliITSCalibration():
43 // Default Constructor (300 microns and 80 volts)
48 //______________________________________________________________________
49 AliITSCalibration::AliITSCalibration(Double_t thickness):
57 // Default Constructor
59 fdv = thickness/80.0; // 80 volts.
64 //______________________________________________________________________
65 AliITSCalibration::AliITSCalibration(const AliITSCalibration &ob):
67 fDataType(ob.fDataType),
71 fGeVcharge(ob.fGeVcharge),
72 fResponse(ob.fResponse)
78 //______________________________________________________________________________
79 AliITSCalibration& AliITSCalibration::operator= (const AliITSCalibration& source)
83 this->~AliITSCalibration();
84 new(this) AliITSCalibration(source);
90 //______________________________________________________________________
91 Double_t AliITSCalibration::MobilityElectronSiEmp() const {
92 // Computes the electron mobility in cm^2/volt-sec. Taken from SILVACO
93 // International ATLAS II, 2D Device Simulation Framework, User Manual
94 // Chapter 5 Equation 5-6. An empirical function for low-field mobiliity
95 // in silicon at different tempeatures.
101 // The Mobility of electrons in Si at a give temprature and impurity
102 // concentration. [cm^2/Volt-sec]
103 const Double_t km0 = 55.24; // cm^2/Volt-sec
104 const Double_t km1 = 7.12E+08; // cm^2 (degree K)^2.3 / Volt-sec
105 const Double_t kN0 = 1.072E17; // #/cm^3
106 const Double_t kT0 = 300.; // degree K.
107 const Double_t keT0 = -2.3; // Power of Temp.
108 const Double_t keT1 = -3.8; // Power of Temp.
109 const Double_t keN = 0.73; // Power of Dopent Consentrations
111 Double_t tT = fT,nN = fN;
113 if(nN<=0.0){ // Simple case.
114 if(tT==300.) return 1350.0; // From Table 5-1 at consentration 1.0E14.
115 m = km1*TMath::Power(tT,keT0);
118 m = km1*TMath::Power(tT,keT0) - km0;
119 m /= 1.0 + TMath::Power(tT/kT0,keT1)*TMath::Power(nN/kN0,keN);
123 //______________________________________________________________________
124 Double_t AliITSCalibration::MobilityHoleSiEmp() const {
125 // Computes the Hole mobility in cm^2/volt-sec. Taken from SILVACO
126 // International ATLAS II, 2D Device Simulation Framework, User Manual
127 // Chapter 5 Equation 5-7 An empirical function for low-field mobiliity
128 // in silicon at different tempeatures.
134 // The Mobility of Hole in Si at a give temprature and impurity
135 // concentration. [cm^2/Volt-sec]
136 const Double_t km0a = 49.74; // cm^2/Volt-sec
137 const Double_t km0b = 49.70; // cm^2/Volt-sec
138 const Double_t km1 = 1.35E+08; // cm^2 (degree K)^2.3 / Volt-sec
139 const Double_t kN0 = 1.606E17; // #/cm^3
140 const Double_t kT0 = 300.; // degree K.
141 const Double_t keT0 = -2.2; // Power of Temp.
142 const Double_t keT1 = -3.7; // Power of Temp.
143 const Double_t keN = 0.70; // Power of Dopent Consentrations
145 Double_t tT = fT,nN = fN;
147 if(nN<=0.0){ // Simple case.
148 if(tT==300.) return 495.0; // From Table 5-1 at consentration 1.0E14.
149 m = km1*TMath::Power(tT,keT0) + km0a-km0b;
152 m = km1*TMath::Power(tT,keT0) - km0b;
153 m /= 1.0 + TMath::Power(tT/kT0,keT1)*TMath::Power(nN/kN0,keN);
157 //______________________________________________________________________
158 Double_t AliITSCalibration::DiffusionCoefficientElectron() const {
159 // Computes the Diffusion coefficient for electrons in cm^2/sec. Taken
160 // from SILVACO International ATLAS II, 2D Device Simulation Framework,
161 // User Manual Chapter 5 Equation 5-53. Einstein relations for diffusion
162 // coefficient. Note: 1 cm^2/sec = 10 microns^2/nanosec.
168 // The Diffusion Coefficient of electrons in Si at a give temprature
169 // and impurity concentration. [cm^2/sec]
170 // const Double_t kb = 1.3806503E-23; // Joules/degree K
171 // const Double_t qe = 1.60217646E-19; // Coulumbs.
172 const Double_t kbqe = 8.617342312E-5; // Volt/degree K
173 Double_t m = MobilityElectronSiEmp();
176 return m*kbqe*tT; // [cm^2/sec]
178 //______________________________________________________________________
179 Double_t AliITSCalibration::DiffusionCoefficientHole() const {
180 // Computes the Diffusion coefficient for Holes in cm^2/sec. Taken
181 // from SILVACO International ATLAS II, 2D Device Simulation Framework,
182 // User Manual Chapter 5 Equation 5-53. Einstein relations for diffusion
183 // coefficient. Note: 1 cm^2/sec = 10 microns^2/nanosec.
189 // The Defusion Coefficient of Hole in Si at a give temprature and
190 // impurity concentration. [cm^2/sec]
191 // and impurity concentration. [cm^2/sec]
192 // const Double_t kb = 1.3806503E-23; // Joules/degree K
193 // const Double_t qe = 1.60217646E-19; // Coulumbs.
194 const Double_t kbqe = 8.617342312E-5; // Volt/degree K
195 Double_t m = MobilityHoleSiEmp();
198 return m*kbqe*tT; // [cm^2/sec]
200 //______________________________________________________________________
201 Double_t AliITSCalibration::LorentzAngleHole(Double_t B) const {
202 // Computes the Lorentz angle for electrons in Si
203 // Input: magnetic Field in KGauss
204 // Output: Lorentz angle in radians (positive if Bz is positive)
205 // Main Reference: NIM A 497 (2003) 389–396.
206 // "An algorithm for calculating the Lorentz angle in silicon detectors", V. Bartsch et al.
208 const Double_t krH=0.70; // Hall scattering factor for Hole
209 const Double_t kT0 = 300.; // reference Temperature (degree K).
210 const Double_t kmulow0 = 470.5; // cm^2/Volt-sec
211 const Double_t keT0 = -2.5; // Power of Temp.
212 const Double_t beta0 = 1.213; // beta coeff. at T0=300K
213 const Double_t keT1 = 0.17; // Power of Temp. for beta
214 const Double_t kvsat0 = 8.37E+06; // saturated velocity at T0=300K (cm/sec)
215 const Double_t keT2 = 0.52; // Power of Temp. for vsat
218 Double_t muLow=kmulow0*TMath::Power(tT/kT0,keT0);
219 Double_t beta=beta0*TMath::Power(tT/kT0,keT1);
220 Double_t vsat=kvsat0*TMath::Power(tT/kT0,keT2);
221 Double_t mu=muLow/TMath::Power(1+TMath::Power(muLow*eE/vsat,beta),1/beta);
222 Double_t angle=TMath::ATan(krH*mu*B*1.E-05); // Conversion Factor
225 //______________________________________________________________________
226 Double_t AliITSCalibration::LorentzAngleElectron(Double_t B) const {
227 // Computes the Lorentz angle for electrons in Si
228 // Input: magnetic Field in KGauss
229 // Output: Lorentz angle in radians (positive if Bz is positive)
230 // Main Reference: NIM A 497 (2003) 389–396.
231 // "An algorithm for calculating the Lorentz angle in silicon detectors", V. Bartsch et al.
233 const Double_t krH=1.15; // Hall scattering factor for Electron
234 const Double_t kT0 = 300.; // reference Temperature (degree K).
235 const Double_t kmulow0 = 1417.0; // cm^2/Volt-sec
236 const Double_t keT0 = -2.2; // Power of Temp.
237 const Double_t beta0 = 1.109; // beta coeff. at T0=300K
238 const Double_t keT1 = 0.66; // Power of Temp. for beta
239 const Double_t kvsat0 = 1.07E+07; // saturated velocity at T0=300K (cm/sec)
240 const Double_t keT2 = 0.87; // Power of Temp. for vsat
243 Double_t muLow=kmulow0*TMath::Power(tT/kT0,keT0);
244 Double_t beta=beta0*TMath::Power(tT/kT0,keT1);
245 Double_t vsat=kvsat0*TMath::Power(tT/kT0,keT2);
246 Double_t mu=muLow/TMath::Power(1+TMath::Power(muLow*eE/vsat,beta),1/beta);
247 Double_t angle=TMath::ATan(krH*mu*B*1.E-05);
250 //______________________________________________________________________
251 Double_t AliITSCalibration::SpeedElectron() const {
252 // Computes the average speed for electrons in Si under the low-field
253 // approximation. [cm/sec].
259 // The speed the holes are traveling at due to the low field applied.
261 Double_t m = MobilityElectronSiEmp();
263 return m/fdv; // [cm/sec]
265 //______________________________________________________________________
266 Double_t AliITSCalibration::SpeedHole() const {
267 // Computes the average speed for Holes in Si under the low-field
268 // approximation.[cm/sec].
274 // The speed the holes are traveling at due to the low field applied.
276 Double_t m = MobilityHoleSiEmp();
278 return m/fdv; // [cm/sec]
280 //______________________________________________________________________
281 Double_t AliITSCalibration::SigmaDiffusion3D(Double_t l) const {
282 // Returns the Gaussian sigma^2 == <x^2+y^2+z^2> [cm^2] due to the
283 // defusion of electrons or holes through a distance l [cm] caused
284 // by an applied voltage v [volt] through a distance d [cm] in any
285 // material at a temperature T [degree K]. The sigma diffusion when
286 // expressed in terms of the distance over which the diffusion
287 // occures, l=time/speed, is independent of the mobility and therefore
288 // the properties of the material. The charge distributions is given by
289 // n = exp(-r^2/4Dt)/(4piDt)^1.5. From this <r^2> = 6Dt where D=mkT/e
290 // (m==mobility, k==Boltzman's constant, T==temparature, e==electric
291 // charge. and vel=m*v/d. consiquently sigma^2=6kTdl/ev.
293 // Double_t l Distance the charge has to travel.
297 // The Sigma due to the diffution of electrons. [cm]
298 const Double_t kcon = 5.17040258E-04; // == 6k/e [J/col or volts]
300 return TMath::Sqrt(kcon*fT*fdv*l); // [cm]
302 //______________________________________________________________________
303 Double_t AliITSCalibration::SigmaDiffusion2D(Double_t l) const {
304 // Returns the Gaussian sigma^2 == <x^2+z^2> [cm^2] due to the defusion
305 // of electrons or holes through a distance l [cm] caused by an applied
306 // voltage v [volt] through a distance d [cm] in any material at a
307 // temperature T [degree K]. The sigma diffusion when expressed in terms
308 // of the distance over which the diffusion occures, l=time/speed, is
309 // independent of the mobility and therefore the properties of the
310 // material. The charge distributions is given by
311 // n = exp(-r^2/4Dt)/(4piDt)^1.5. From this <x^2+z^2> = 4Dt where D=mkT/e
312 // (m==mobility, k==Boltzman's constant, T==temparature, e==electric
313 // charge. and vel=m*v/d. consiquently sigma^2=4kTdl/ev.
315 // Double_t l Distance the charge has to travel.
319 // The Sigma due to the diffution of electrons. [cm]
320 const Double_t kcon = 3.446935053E-04; // == 4k/e [J/col or volts]
322 return TMath::Sqrt(kcon*fT*fdv*l); // [cm]
324 //______________________________________________________________________
325 Double_t AliITSCalibration::SigmaDiffusion1D(Double_t l) const {
326 // Returns the Gaussian sigma^2 == <x^2> [cm^2] due to the defusion
327 // of electrons or holes through a distance l [cm] caused by an applied
328 // voltage v [volt] through a distance d [cm] in any material at a
329 // temperature T [degree K]. The sigma diffusion when expressed in terms
330 // of the distance over which the diffusion occures, l=time/speed, is
331 // independent of the mobility and therefore the properties of the
332 // material. The charge distributions is given by
333 // n = exp(-r^2/4Dt)/(4piDt)^1.5. From this <r^2> = 2Dt where D=mkT/e
334 // (m==mobility, k==Boltzman's constant, T==temparature, e==electric
335 // charge. and vel=m*v/d. consiquently sigma^2=2kTdl/ev.
337 // Double_t l Distance the charge has to travel.
341 // The Sigma due to the diffution of electrons. [cm]
342 const Double_t kcon = 1.723467527E-04; // == 2k/e [J/col or volts]
344 return TMath::Sqrt(kcon*fT*fdv*l); // [cm]
346 //----------------------------------------------------------------------
347 Double_t AliITSCalibration::DepletedRegionThicknessA(Double_t dopCons,
350 Double_t voltBuiltIn)const{
351 // Computes the thickness of the depleted region in Si due to the
352 // application of an external bias voltage. From the Particle Data
353 // Book, 28.8 Silicon semiconductor detectors equation 28.19 (2004)
354 // Physics Letters B "Review of Particle Physics" Volume 592, Issue 1-4
355 // July 15 2004, ISSN 0370-2693 page 263. First equation.
357 // Double_t dopCons "N" doping concentration
358 // Double_t voltage "V" external bias voltage
359 // Double_t elecCharge "e" electronic charge
360 // Double_t voltBuiltIn=0.5 "V_bi" "built-in" Voltage (~0.5V for
361 // resistivities typically used in detectors)
365 // The thickness of the depleted region
367 return TMath::Sqrt(2.0*(voltage+voltBuiltIn)/(dopCons*elecCharge));
369 //----------------------------------------------------------------------
370 Double_t AliITSCalibration::DepletedRegionThicknessB(Double_t resist,
373 Double_t voltBuiltIn,
374 Double_t dielConst)const{
375 // Computes the thickness of the depleted region in Si due to the
376 // application of an external bias voltage. From the Particle Data
377 // Book, 28.8 Silicon semiconductor detectors equation 28.19 (2004)
378 // Physics Letters B "Review of Particle Physics" Volume 592, Issue 1-4
379 // July 15 2004, ISSN 0370-2693 page 263. Second Equation.
381 // Double_t resist "rho" resistivity (typically 1-10 kOhm cm)
382 // Double_t voltage "V" external bias voltage
383 // Double_t mobility "mu" charge carrier mobility
384 // (electons 1350, holes 450 cm^2/V/s)
385 // Double_t voltBuiltIn=0.5 "V_bi" "built-in" Voltage (~0.5V for
386 // resistivities typically used in detectors)
387 // Double_t dielConst=1.E-12 "epsilon" dielectric constant = 11.9 *
388 // (permittivity of free space) or ~ 1 pF/cm
392 // The thickness of the depleted region
394 return TMath::Sqrt(2.8*resist*mobility*dielConst*(voltage+voltBuiltIn));
396 //----------------------------------------------------------------------
397 Double_t AliITSCalibration::ReverseBiasCurrent(Double_t temp,
398 Double_t revBiasCurT1,
400 Double_t energy)const{
401 // Computes the temperature dependance of the reverse bias current
402 // of Si detectors. From the Particle Data
403 // Book, 28.8 Silicon semiconductor detectors equation 28.21 (2004)
404 // Physics Letters B "Review of Particle Physics" Volume 592, Issue 1-4
405 // July 15 2004, ISSN 0370-2693 page 263.
407 // Double_t temp The temperature at which the current is wanted
408 // Double_t revBiasCurT1 The reference bias current at temp T1
409 // Double_t tempT1 The temperature correstponding to revBiasCurT1
410 // Double_t energy=1.2 Some energy [eV]
414 // The reverse bias current at the tempeature temp.
415 const Double_t kBoltz = 8.617343E-5; //[eV/K]
417 return revBiasCurT1*(temp*temp/(tempT1*tempT1))*
418 TMath::Exp(-0.5*energy*(tempT1-temp)/(kBoltz*tempT1*temp));
420 //----------------------------------------------------------------------
421 void AliITSCalibration::Print(ostream *os) const {
422 // Standard output format for this class.
424 *os << fdv << " " << fN << " " << fT << " ";
426 // printf("%-10.6e %-10.6e %-10.6e %-10.6e \n",fdv,fN,fT,fGeVcharge);
429 //----------------------------------------------------------------------
430 void AliITSCalibration::Read(istream *is) {
431 // Standard input format for this class.
433 // ostream *is Pointer to the output stream
439 *is >> fdv >> fN >> fT >> fGeVcharge;
442 //----------------------------------------------------------------------
444 ostream &operator<<(ostream &os,AliITSCalibration &p){
445 // Standard output streaming function.
447 // ostream *os Pointer to the output stream
457 //----------------------------------------------------------------------
458 istream &operator>>(istream &is,AliITSCalibration &r){
459 // Standard input streaming function.
461 // ostream *os Pointer to the output stream
470 //----------------------------------------------------------------------