Module dopes.data_analysis.diode
Functions
def depletion_length(doping_in, doping_out, Vbias=0, temp=300)
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def depletion_length(doping_in, doping_out, Vbias=0,temp=300): """ Function to calculate the depletion length in a pn junction args: \n\t- doping_in (scalar): the doping in the region for which the depletion length has to be calculated \n\t- doping_out (scalar): the doping in the adjacent region for which the depletion length has to be calculated \n\t- Vbias (scalar): the bias voltage of the pn junction \n\t- temp (scalar): the temperature return: \n\t- a scalar with the depletion length calculated in one region """ kB = 1.38e-23 # J/K q = 1.602e-19 # C epsilon_0 = 8.8542e-12 # F/m epsilon_si = 11.7 phi_0 = kB * temp / q * np.log(doping_in * doping_out / sc.intrinsic_concentration(temp)**2 ) return np.sqrt(2 * epsilon_si * epsilon_0 / q * doping_out / doping_in / (doping_in + doping_out) * (phi_0 - Vbias))
Function to calculate the depletion length in a pn junction
args:
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doping_in (scalar): the doping in the region for which the depletion length has to be calculated
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doping_out (scalar): the doping in the adjacent region for which the depletion length has to be calculated
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Vbias (scalar): the bias voltage of the pn junction
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temp (scalar): the temperature
return:
- a scalar with the depletion length calculated in one region
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def ideal_diode(Vbias, Is, n=1, temp=300)
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def ideal_diode(Vbias,Is,n=1, temp=300): """ Function to calculate the current in an ideal diode args: \n\t- Vbias (scalar or sequence): the bias voltage of the diode \n\t- Is (scalar): the saturation current of the diode \n\t- n (scalar): the ideality factor of the diode, 1 for radiative recombination, 2 for SRH recombination \n\t- temp (scalar): the temperature return: \n\t- a scalar or sequence with same dimension as Vbias """ kB = 1.38e-23 # J/K q = 1.602e-19 # C return Is * (np.exp(q * Vbias / (n * kB * temp)) -1 )
Function to calculate the current in an ideal diode
args:
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Vbias (scalar or sequence): the bias voltage of the diode
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Is (scalar): the saturation current of the diode
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n (scalar): the ideality factor of the diode, 1 for radiative recombination, 2 for SRH recombination
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temp (scalar): the temperature
return:
- a scalar or sequence with same dimension as Vbias
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def j_radiative(Vbias, mu_n, mu_p, tau_n, tau_p, ND, NA, ln, lp, temp=300)
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def j_radiative(Vbias,mu_n,mu_p,tau_n,tau_p,ND,NA,ln,lp,temp=300): """ Function to calculate the radial contribution to the current density in a silicon pn junction args: \n\t- Vbias (scalar): the bias voltage of the pn junction \n\t- mu_n (scalar): the mobility of the electrons \n\t- mu_p (scalar): the mobility of the holes \n\t- tau_n (scalar): the lifetime of the electrons \n\t- tau_p (scalar): the lifetime of the holes \n\t- ND (scalar): the donor doping concentration in the n region \n\t- NA (scalar): the acceptor doping concentraion in the p region \n\t- ln (scalar): the length of the cathode (n-doped region) \n\t- lp (scalar): the length of the anode (p-doped region) \n\t- temp (scalar): the temperature return: \n\t- a scalar with the radiative current density calculated """ b_rad = 4.76e-15 # cm3/s - low-impurity value entre 1 et 10 kB = 1.38e-23 # J/K q = 1.602e-19 # C Dn = kB * temp / q * mu_n Dp = kB * temp / q * mu_p Ln = np.sqrt( Dn * tau_n ) Lp = np.sqrt( Dp * tau_p ) ld_n = depletion_length(ND, NA, Vbias) ld_p = depletion_length(NA, ND, Vbias) ni = sc.intrinsic_concentration(temp) n_p0=ni**2/NA p_n0=ni**2/ND coeff_radial = Dn * n_p0 / Ln / np.tanh( (lp-ld_p) / Ln ) + Dp * p_n0 / Lp / np.tanh( (ln-ld_n) / Lp ) + ni**2 *b_rad* (ld_p + ld_n) return q * ( coeff_radial * (np.exp(q * Vbias/ ( kB * temp)) - 1 ) )
Function to calculate the radial contribution to the current density in a silicon pn junction
args:
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Vbias (scalar): the bias voltage of the pn junction
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mu_n (scalar): the mobility of the electrons
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mu_p (scalar): the mobility of the holes
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tau_n (scalar): the lifetime of the electrons
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tau_p (scalar): the lifetime of the holes
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ND (scalar): the donor doping concentration in the n region
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NA (scalar): the acceptor doping concentraion in the p region
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ln (scalar): the length of the cathode (n-doped region)
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lp (scalar): the length of the anode (p-doped region)
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temp (scalar): the temperature
return:
- a scalar with the radiative current density calculated
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def j_srh(Vbias, ND, NA, tau=1e-07, temp=300)
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def j_srh(Vbias,ND,NA,tau=1e-7,temp=300): """ Function to calculate the Shockley-Read-Hall contribution to the current density in a pn junction args: \n\t- Vbias (scalar): the bias voltage of the pn junction \n\t- ND (scalar): the donor doping concentration in the n region \n\t- NA (scalar): the acceptor doping concentraion in the p region \n\t- tau (scalar): the global lifetime associated to the SRH mechanism \n\t- temp (scalar): the temperature return: \n\t- a scalar with the SRH current density calculated """ kB = 1.38e-23 # J/K q = 1.602e-19 # C ld_n = depletion_length(ND, NA, Vbias) ld_p = depletion_length(NA, ND, Vbias) ni = sc.intrinsic_concentration(temp) x=(ld_p + ld_n) # approximation by considering only the depletion region without diffusion mechanism, gives an upper limit as the effective length is always below coeff_SRH = q * ni * x / (2 * tau) return ( coeff_SRH * (np.exp(q * Vbias/ (2 * kB * temp)) - 1 ) )
Function to calculate the Shockley-Read-Hall contribution to the current density in a pn junction
args:
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Vbias (scalar): the bias voltage of the pn junction
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ND (scalar): the donor doping concentration in the n region
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NA (scalar): the acceptor doping concentraion in the p region
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tau (scalar): the global lifetime associated to the SRH mechanism
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temp (scalar): the temperature
return:
- a scalar with the SRH current density calculated
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def two_diodes(Vbias, Is1, Is2, n1=1, n2=2, temp=300)
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def two_diodes(Vbias,Is1,Is2,n1=1,n2=2, temp=300): """ Function to calculate the current for a two diodes model args: \n\t- Vbias (scalar or sequence): the bias voltage of the diode \n\t- Is1 (scalar): the saturation current of the first diode \n\t- Is2 (scalar): the saturation current of the second diode \n\t- n1 (scalar): the ideality factor of the first diode, 1 for radiative recombination, 2 for SRH recombination \n\t- n1 (scalar): the ideality factor of the second diode, 1 for radiative recombination, 2 for SRH recombination \n\t- temp (scalar): the temperature return: \n\t- a scalar or sequence with same dimension as Vbias """ kB = 1.38e-23 # J/K q = 1.602e-19 # C return Is1 * (np.exp( q * Vbias / (n1 * kB * temp)) -1 ) + Is2 * (np.exp( q * Vbias / (n2 * kB * temp)) -1 )
Function to calculate the current for a two diodes model
args:
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Vbias (scalar or sequence): the bias voltage of the diode
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Is1 (scalar): the saturation current of the first diode
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Is2 (scalar): the saturation current of the second diode
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n1 (scalar): the ideality factor of the first diode, 1 for radiative recombination, 2 for SRH recombination
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n1 (scalar): the ideality factor of the second diode, 1 for radiative recombination, 2 for SRH recombination
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temp (scalar): the temperature
return:
- a scalar or sequence with same dimension as Vbias
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def two_diodes_with_resistances(Vbias, Is1, Is2, n1=1, n2=2, temp=300, Rs=0, Rsh=inf)
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def two_diodes_with_resistances(Vbias,Is1,Is2,n1=1,n2=2, temp=300, Rs=0, Rsh=float("inf")): """ Function to calculate the current for a two diodes model by taking into account the series and shunt resistances args: \n\t- Vbias (scalar or sequence): the bias voltage of the diode \n\t- Is1 (scalar): the saturation current of the first diode \n\t- Is2 (scalar): the saturation current of the second diode \n\t- n1 (scalar): the ideality factor of the first diode, 1 for radiative recombination, 2 for SRH recombination \n\t- n1 (scalar): the ideality factor of the second diode, 1 for radiative recombination, 2 for SRH recombination \n\t- temp (scalar): the temperature \n\t- Rs (scalar): the serie resistance \n\t- Rsh (scalar): the shunt resistance return: \n\t- a scalar or sequence with same dimension as Vbias """ kB = 1.38e-23 # J/K q = 1.602e-19 # C if isinstance(Vbias, (int,float)): # x0=np.min((two_diodes(Vbias,Is1,Is2,n1,n2, temp),Vbias/Rs)) I = fsolve(lambda x:Is1 * (np.exp( q * (Vbias - Rs * x) / (n1 * kB * temp)) -1 ) + Is2 * (np.exp( q * (Vbias - Rs * x) / (n2 * kB * temp)) -1 ) + (Vbias - Rs * x ) / Rsh - x,x0=0) else: I=np.zeros(len(Vbias)) i=0 i=0 for v in Vbias: # x0=np.min((two_diodes(v,Is1,Is2,n1,n2, temp),v/Rs)) I[i] = fsolve(lambda x : Is1 * (np.exp( q * (v - Rs * x) / (n1 * kB * temp)) -1 ) + Is2 * (np.exp( q * (v - Rs * x) / (n2 * kB * temp)) -1 ) + (v - Rs * x ) / Rsh - x,x0=0) i+=1 return I
Function to calculate the current for a two diodes model by taking into account the series and shunt resistances
args:
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Vbias (scalar or sequence): the bias voltage of the diode
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Is1 (scalar): the saturation current of the first diode
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Is2 (scalar): the saturation current of the second diode
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n1 (scalar): the ideality factor of the first diode, 1 for radiative recombination, 2 for SRH recombination
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n1 (scalar): the ideality factor of the second diode, 1 for radiative recombination, 2 for SRH recombination
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temp (scalar): the temperature
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Rs (scalar): the serie resistance
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Rsh (scalar): the shunt resistance
return:
- a scalar or sequence with same dimension as Vbias
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