def contact_phin(cell: PVCell, bound: Boundary,
pot: Potentials) -> Tuple[f64, f64]:
n = physics.n(cell, pot)
Jn = current.Jn(cell, pot)
return Jn[0] - cell.Snl * (n[0] - bound.neq0), Jn[-1] + cell.Snr * (
n[-1] - bound.neqL)
def comp_shr(cell: PVCell, pot: Potentials) -> Array:
ni = physics.ni(cell)
n = physics.n(cell, pot)
p = physics.p(cell, pot)
nR = ni * jnp.exp(cell.Et) + n
pR = ni * jnp.exp(-cell.Et) + p
return (n * p - ni**2) / (cell.tp * nR + cell.tn * pR)
def contact_phin_deriv(cell: PVCell,
pot: Potentials) -> Tuple[f64, f64, f64, f64]:
n = physics.n(cell, pot)
dJn_phin_maindiag, dJn_phin_upperdiag, dJn_phi_maindiag, dJn_phi_upperdiag = current.Jn_deriv(
cell, pot)
return dJn_phin_maindiag[0] - cell.Snl * n[0] , dJn_phin_upperdiag[0] , \
dJn_phi_maindiag[0] - cell.Snl * n[0] , dJn_phi_upperdiag[0] , \
dJn_phin_maindiag[-1] , dJn_phin_upperdiag[-1] + cell.Snr * n[-1] , \
dJn_phi_maindiag[-1] , dJn_phi_upperdiag[-1] + cell.Snr * n[-1]
def comp_rad_deriv(cell: PVCell,
pot: Potentials) -> Tuple[Array, Array, Array]:
n = physics.n(cell, pot)
p = physics.p(cell, pot)
DR_phin = cell.Br * (n * p)
DR_phip = cell.Br * (-n * p)
DR_phi = jnp.zeros_like(pot.phi)
return DR_phin, DR_phip, DR_phi
def comp_auger_deriv(cell: PVCell,
pot: Potentials) -> Tuple[Array, Array, Array]:
ni = physics.ni(cell)
n = physics.n(cell, pot)
p = physics.p(cell, pot)
DR_phin = (cell.Cn * n) * (n * p - ni**2) + (cell.Cn * n +
cell.Cp * p) * (n * p)
DR_phip = (-cell.Cp * p) * (n * p - ni**2) + (cell.Cn * n +
cell.Cp * p) * (-n * p)
DR_phi = (cell.Cn * n - cell.Cp * p) * (n * p - ni**2)
return DR_phin, DR_phip, DR_phi
def pois_deriv_eq(cell: PVCell, pot: Potentials) -> Tuple[Array, Array, Array]:
ave_dgrid = (cell.dgrid[:-1] + cell.dgrid[1:]) / 2.
ave_eps = (cell.eps[1:] + cell.eps[:-1]) / 2.
n = physics.n(cell, pot)
p = physics.p(cell, pot)
dchg_phi = -n - p
dpois_phi_ = -ave_eps[:-1] / cell.dgrid[:-1] / ave_dgrid
dpois_phi__ = (ave_eps[:-1] / cell.dgrid[:-1] +
ave_eps[1:] / cell.dgrid[1:]) / ave_dgrid - dchg_phi[1:-1]
dpois_phi___ = -ave_eps[1:] / cell.dgrid[1:] / ave_dgrid
return dpois_phi_, dpois_phi__, dpois_phi___
def comp_shr_deriv(cell: PVCell,
pot: Potentials) -> Tuple[Array, Array, Array]:
ni = physics.ni(cell)
n = physics.n(cell, pot)
p = physics.p(cell, pot)
nR = ni * jnp.exp(cell.Et) + n
pR = ni * jnp.exp(-cell.Et) + p
num = n * p - ni**2
denom = cell.tp * nR + cell.tn * pR
DR_phin = ((n * p) * denom - num * (cell.tp * n)) * denom**(-2)
DR_phip = ((-n * p) * denom - num * (-cell.tn * p)) * denom**(-2)
DR_phi = (-num * (cell.tp * n - cell.tn * p)) * denom**(-2)
return DR_phin, DR_phip, DR_phi
def plot_charge(design: PVDesign, pot: Potentials, filename=None):
n = scales.density * physics.n(design, pot)
p = scales.density * physics.p(design, pot)
x = scales.length * design.grid * 1e4
plt.plot(x, n, label="electron", color="lightcoral")
plt.plot(x, p, label="hole", color="cornflowerblue")
plt.yscale("log")
plt.xlabel("position / μm")
plt.ylabel("density / cm$^{-3}$")
plt.legend()
plt.xlim(0, x[-1])
plt.tight_layout()
if filename is not None:
plt.savefig(filename)
plt.show()
def pois_deriv(cell: PVCell,
pot: Potentials) -> Tuple[Array, Array, Array, Array, Array]:
ave_dgrid = (cell.dgrid[:-1] + cell.dgrid[1:]) / 2.0
ave_eps = 0.5 * (cell.eps[1:] + cell.eps[:-1])
n = physics.n(cell, pot)
p = physics.p(cell, pot)
dchg_phi_n = -n
dchg_phi_p = -p
dchg_phi = -n - p
dpois_phi_ = -ave_eps[:-1] / cell.dgrid[:-1] / ave_dgrid
dpois_phi__ = (ave_eps[:-1] / cell.dgrid[:-1] +
ave_eps[1:] / cell.dgrid[1:]) / ave_dgrid - dchg_phi[1:-1]
dpois_phi___ = -ave_eps[1:] / cell.dgrid[1:] / ave_dgrid
dpois_dphin__ = -dchg_phi_n[1:-1]
dpois_dphip__ = -dchg_phi_p[1:-1]
return dpois_phi_, dpois_phi__, dpois_phi___, dpois_dphin__, dpois_dphip__
def comp_rad(cell: PVCell, pot: Potentials) -> Array:
ni = physics.ni(cell)
n = physics.n(cell, pot)
p = physics.p(cell, pot)
return cell.Br * (n * p - ni**2)
def comp_auger(cell: PVCell, pot: Potentials) -> Array:
ni = physics.ni(cell)
n = physics.n(cell, pot)
p = physics.p(cell, pot)
return (cell.Cn * n + cell.Cp * p) * (n * p - ni**2)