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17 //////////////////////////////////////////////////////
18 // Calibration class for set:ITS //
19 // Specific subdetector implementation is done in //
20 // AliITSCalibrationSPD //
21 // AliITSCalibrationSDD //
22 // AliITSCalibrationSSD //
23 //////////////////////////////////////////////////////
25 #include "Riostream.h"
26 #include "AliITSCalibration.h"
28 ClassImp(AliITSCalibration)
30 //______________________________________________________________________
31 AliITSCalibration::AliITSCalibration(){
32 // Default Constructor
34 fdv = 0.000375; // 300 microns and 80 volts.
40 //______________________________________________________________________
41 AliITSCalibration::AliITSCalibration(Double_t thickness){
42 // Default Constructor
44 fdv = thickness/80.0; // 80 volts.
50 //______________________________________________________________________
51 AliITSCalibration::AliITSCalibration(const AliITSCalibration &ob) : TObject(ob) {
53 // Copies are not allowed. The method is protected to avoid misuse.
54 Error("AliITSCalibration","Copy constructor not allowed\n");
57 //______________________________________________________________________
58 AliITSCalibration& AliITSCalibration::operator=(const AliITSCalibration& /* ob */){
59 // Assignment operator
60 // Assignment is not allowed. The method is protected to avoid misuse.
61 Error("= operator","Assignment operator not allowed\n");
65 //______________________________________________________________________
66 Double_t AliITSCalibration::MobilityElectronSiEmp() const {
67 // Computes the electron mobility in cm^2/volt-sec. Taken from SILVACO
68 // International ATLAS II, 2D Device Simulation Framework, User Manual
69 // Chapter 5 Equation 5-6. An empirical function for low-field mobiliity
70 // in silicon at different tempeatures.
76 // The Mobility of electrons in Si at a give temprature and impurity
77 // concentration. [cm^2/Volt-sec]
78 const Double_t km0 = 55.24; // cm^2/Volt-sec
79 const Double_t km1 = 7.12E+08; // cm^2 (degree K)^2.3 / Volt-sec
80 const Double_t kN0 = 1.072E17; // #/cm^3
81 const Double_t kT0 = 300.; // degree K.
82 const Double_t keT0 = -2.3; // Power of Temp.
83 const Double_t keT1 = -3.8; // Power of Temp.
84 const Double_t keN = 0.73; // Power of Dopent Consentrations
86 Double_t tT = fT,nN = fN;
88 if(nN<=0.0){ // Simple case.
89 if(tT==300.) return 1350.0; // From Table 5-1 at consentration 1.0E14.
90 m = km1*TMath::Power(tT,keT0);
93 m = km1*TMath::Power(tT,keT0) - km0;
94 m /= 1.0 + TMath::Power(tT/kT0,keT1)*TMath::Power(nN/kN0,keN);
98 //______________________________________________________________________
99 Double_t AliITSCalibration::MobilityHoleSiEmp() const {
100 // Computes the Hole mobility in cm^2/volt-sec. Taken from SILVACO
101 // International ATLAS II, 2D Device Simulation Framework, User Manual
102 // Chapter 5 Equation 5-7 An empirical function for low-field mobiliity
103 // in silicon at different tempeatures.
109 // The Mobility of Hole in Si at a give temprature and impurity
110 // concentration. [cm^2/Volt-sec]
111 const Double_t km0a = 49.74; // cm^2/Volt-sec
112 const Double_t km0b = 49.70; // cm^2/Volt-sec
113 const Double_t km1 = 1.35E+08; // cm^2 (degree K)^2.3 / Volt-sec
114 const Double_t kN0 = 1.606E17; // #/cm^3
115 const Double_t kT0 = 300.; // degree K.
116 const Double_t keT0 = -2.2; // Power of Temp.
117 const Double_t keT1 = -3.7; // Power of Temp.
118 const Double_t keN = 0.70; // Power of Dopent Consentrations
120 Double_t tT = fT,nN = fN;
122 if(nN<=0.0){ // Simple case.
123 if(tT==300.) return 495.0; // From Table 5-1 at consentration 1.0E14.
124 m = km1*TMath::Power(tT,keT0) + km0a-km0b;
127 m = km1*TMath::Power(tT,keT0) - km0b;
128 m /= 1.0 + TMath::Power(tT/kT0,keT1)*TMath::Power(nN/kN0,keN);
132 //______________________________________________________________________
133 Double_t AliITSCalibration::DiffusionCoefficientElectron() const {
134 // Computes the Diffusion coefficient for electrons in cm^2/sec. Taken
135 // from SILVACO International ATLAS II, 2D Device Simulation Framework,
136 // User Manual Chapter 5 Equation 5-53. Einstein relations for diffusion
137 // coefficient. Note: 1 cm^2/sec = 10 microns^2/nanosec.
143 // The Diffusion Coefficient of electrons in Si at a give temprature
144 // and impurity concentration. [cm^2/sec]
145 // const Double_t kb = 1.3806503E-23; // Joules/degree K
146 // const Double_t qe = 1.60217646E-19; // Coulumbs.
147 const Double_t kbqe = 8.617342312E-5; // Volt/degree K
148 Double_t m = MobilityElectronSiEmp();
151 return m*kbqe*tT; // [cm^2/sec]
153 //______________________________________________________________________
154 Double_t AliITSCalibration::DiffusionCoefficientHole() const {
155 // Computes the Diffusion coefficient for Holes in cm^2/sec. Taken
156 // from SILVACO International ATLAS II, 2D Device Simulation Framework,
157 // User Manual Chapter 5 Equation 5-53. Einstein relations for diffusion
158 // coefficient. Note: 1 cm^2/sec = 10 microns^2/nanosec.
164 // The Defusion Coefficient of Hole in Si at a give temprature and
165 // impurity concentration. [cm^2/sec]
166 // and impurity concentration. [cm^2/sec]
167 // const Double_t kb = 1.3806503E-23; // Joules/degree K
168 // const Double_t qe = 1.60217646E-19; // Coulumbs.
169 const Double_t kbqe = 8.617342312E-5; // Volt/degree K
170 Double_t m = MobilityHoleSiEmp();
173 return m*kbqe*tT; // [cm^2/sec]
175 //______________________________________________________________________
176 Double_t AliITSCalibration::SpeedElectron() const {
177 // Computes the average speed for electrons in Si under the low-field
178 // approximation. [cm/sec].
184 // The speed the holes are traveling at due to the low field applied.
186 Double_t m = MobilityElectronSiEmp();
188 return m/fdv; // [cm/sec]
190 //______________________________________________________________________
191 Double_t AliITSCalibration::SpeedHole() const {
192 // Computes the average speed for Holes in Si under the low-field
193 // approximation.[cm/sec].
199 // The speed the holes are traveling at due to the low field applied.
201 Double_t m = MobilityHoleSiEmp();
203 return m/fdv; // [cm/sec]
205 //______________________________________________________________________
206 Double_t AliITSCalibration::SigmaDiffusion3D(Double_t l) const {
207 // Returns the Gaussian sigma^2 == <x^2+y^2+z^2> [cm^2] due to the
208 // defusion of electrons or holes through a distance l [cm] caused
209 // by an applied voltage v [volt] through a distance d [cm] in any
210 // material at a temperature T [degree K]. The sigma diffusion when
211 // expressed in terms of the distance over which the diffusion
212 // occures, l=time/speed, is independent of the mobility and therefore
213 // the properties of the material. The charge distributions is given by
214 // n = exp(-r^2/4Dt)/(4piDt)^1.5. From this <r^2> = 6Dt where D=mkT/e
215 // (m==mobility, k==Boltzman's constant, T==temparature, e==electric
216 // charge. and vel=m*v/d. consiquently sigma^2=6kTdl/ev.
218 // Double_t l Distance the charge has to travel.
222 // The Sigma due to the diffution of electrons. [cm]
223 const Double_t kcon = 5.17040258E-04; // == 6k/e [J/col or volts]
225 return TMath::Sqrt(kcon*fT*fdv*l); // [cm]
227 //______________________________________________________________________
228 Double_t AliITSCalibration::SigmaDiffusion2D(Double_t l) const {
229 // Returns the Gaussian sigma^2 == <x^2+z^2> [cm^2] due to the defusion
230 // of electrons or holes through a distance l [cm] caused by an applied
231 // voltage v [volt] through a distance d [cm] in any material at a
232 // temperature T [degree K]. The sigma diffusion when expressed in terms
233 // of the distance over which the diffusion occures, l=time/speed, is
234 // independent of the mobility and therefore the properties of the
235 // material. The charge distributions is given by
236 // n = exp(-r^2/4Dt)/(4piDt)^1.5. From this <x^2+z^2> = 4Dt where D=mkT/e
237 // (m==mobility, k==Boltzman's constant, T==temparature, e==electric
238 // charge. and vel=m*v/d. consiquently sigma^2=4kTdl/ev.
240 // Double_t l Distance the charge has to travel.
244 // The Sigma due to the diffution of electrons. [cm]
245 const Double_t kcon = 3.446935053E-04; // == 4k/e [J/col or volts]
247 return TMath::Sqrt(kcon*fT*fdv*l); // [cm]
249 //______________________________________________________________________
250 Double_t AliITSCalibration::SigmaDiffusion1D(Double_t l) const {
251 // Returns the Gaussian sigma^2 == <x^2> [cm^2] due to the defusion
252 // of electrons or holes through a distance l [cm] caused by an applied
253 // voltage v [volt] through a distance d [cm] in any material at a
254 // temperature T [degree K]. The sigma diffusion when expressed in terms
255 // of the distance over which the diffusion occures, l=time/speed, is
256 // independent of the mobility and therefore the properties of the
257 // material. The charge distributions is given by
258 // n = exp(-r^2/4Dt)/(4piDt)^1.5. From this <r^2> = 2Dt where D=mkT/e
259 // (m==mobility, k==Boltzman's constant, T==temparature, e==electric
260 // charge. and vel=m*v/d. consiquently sigma^2=2kTdl/ev.
262 // Double_t l Distance the charge has to travel.
266 // The Sigma due to the diffution of electrons. [cm]
267 const Double_t kcon = 1.723467527E-04; // == 2k/e [J/col or volts]
269 return TMath::Sqrt(kcon*fT*fdv*l); // [cm]
271 //----------------------------------------------------------------------
272 Double_t AliITSCalibration::DepletedRegionThicknessA(Double_t dopCons,
275 Double_t voltBuiltIn)const{
276 // Computes the thickness of the depleted region in Si due to the
277 // application of an external bias voltage. From the Particle Data
278 // Book, 28.8 Silicon semiconductor detectors equation 28.19 (2004)
279 // Physics Letters B "Review of Particle Physics" Volume 592, Issue 1-4
280 // July 15 2004, ISSN 0370-2693 page 263. First equation.
282 // Double_t dopCons "N" doping concentration
283 // Double_t voltage "V" external bias voltage
284 // Double_t elecCharge "e" electronic charge
285 // Double_t voltBuiltIn=0.5 "V_bi" "built-in" Voltage (~0.5V for
286 // resistivities typically used in detectors)
290 // The thickness of the depleted region
292 return TMath::Sqrt(2.0*(voltage+voltBuiltIn)/(dopCons*elecCharge));
294 //----------------------------------------------------------------------
295 Double_t AliITSCalibration::DepletedRegionThicknessB(Double_t resist,
298 Double_t voltBuiltIn,
299 Double_t dielConst)const{
300 // Computes the thickness of the depleted region in Si due to the
301 // application of an external bias voltage. From the Particle Data
302 // Book, 28.8 Silicon semiconductor detectors equation 28.19 (2004)
303 // Physics Letters B "Review of Particle Physics" Volume 592, Issue 1-4
304 // July 15 2004, ISSN 0370-2693 page 263. Second Equation.
306 // Double_t resist "rho" resistivity (typically 1-10 kOhm cm)
307 // Double_t voltage "V" external bias voltage
308 // Double_t mobility "mu" charge carrier mobility
309 // (electons 1350, holes 450 cm^2/V/s)
310 // Double_t voltBuiltIn=0.5 "V_bi" "built-in" Voltage (~0.5V for
311 // resistivities typically used in detectors)
312 // Double_t dielConst=1.E-12 "epsilon" dielectric constant = 11.9 *
313 // (permittivity of free space) or ~ 1 pF/cm
317 // The thickness of the depleted region
319 return TMath::Sqrt(2.8*resist*mobility*dielConst*(voltage+voltBuiltIn));
321 //----------------------------------------------------------------------
322 Double_t AliITSCalibration::ReverseBiasCurrent(Double_t temp,
323 Double_t revBiasCurT1,
325 Double_t energy)const{
326 // Computes the temperature dependance of the reverse bias current
327 // of Si detectors. From the Particle Data
328 // Book, 28.8 Silicon semiconductor detectors equation 28.21 (2004)
329 // Physics Letters B "Review of Particle Physics" Volume 592, Issue 1-4
330 // July 15 2004, ISSN 0370-2693 page 263.
332 // Double_t temp The temperature at which the current is wanted
333 // Double_t revBiasCurT1 The reference bias current at temp T1
334 // Double_t tempT1 The temperature correstponding to revBiasCurT1
335 // Double_t energy=1.2 Some energy [eV]
339 // The reverse bias current at the tempeature temp.
340 const Double_t kBoltz = 8.617343E-5; //[eV/K]
342 return revBiasCurT1*(temp*temp/(tempT1*tempT1))*
343 TMath::Exp(-0.5*energy*(tempT1-temp)/(kBoltz*tempT1*temp));
345 //----------------------------------------------------------------------
346 void AliITSCalibration::Print(ostream *os) const {
347 // Standard output format for this class.
349 *os << fdv << " " << fN << " " << fT << " ";
351 // printf("%-10.6e %-10.6e %-10.6e %-10.6e \n",fdv,fN,fT,fGeVcharge);
354 //----------------------------------------------------------------------
355 void AliITSCalibration::Read(istream *is) {
356 // Standard input format for this class.
358 // ostream *is Pointer to the output stream
364 *is >> fdv >> fN >> fT >> fGeVcharge;
367 //----------------------------------------------------------------------
369 ostream &operator<<(ostream &os,AliITSCalibration &p){
370 // Standard output streaming function.
372 // ostream *os Pointer to the output stream
382 //----------------------------------------------------------------------
383 istream &operator>>(istream &is,AliITSCalibration &r){
384 // Standard input streaming function.
386 // ostream *os Pointer to the output stream
395 //----------------------------------------------------------------------