Help solving this integral equation?

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Arka Bhattacharya
评论： Arka Bhattacharya 2023-4-6
Hi I need help solving the above integral equation. Here f is Fermi Dirac distribution and Nt is Gaussian distribution. n_total, N_0 and N_T are all non values. I need to solve for E_f. Any help is appreciated.
N_T=@(E) N_t*exp(-E.^2/(2*E_t^2));
f=@(E) 1/(1+exp((E-Ef)/(k*T)));

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采纳的回答

Walter Roberson
Walter Roberson 2023-4-6
Ran in:
syms E E_F E_t eta_total k N_0 N_t t
N_T = N_t * exp(-E.^2/(2*E_t^2))
N_T = 
f = 1/(1+exp((E-E_F)/(k*t)))
f = 
eta_mobile = int(N_0 * f, E, -inf, 0)
eta_mobile = 
eta_trap = int(N_t*f, E, 0, inf)
eta_trap = 
eqn = eta_total == eta_mobile + eta_trap
eqn = 
lr = lhs(eqn) - rhs(eqn)
lr = 
specific_lr = subs(lr, [eta_total, N_0, N_t, k, t], [101, 17, 33, 87, 5])
specific_lr = 
fun = matlabFunction(specific_lr, 'vars', E_F)
fun = function_handle with value:
@(E_F)-integral(@(E)1.7e+1./(exp(E_F.*(-1.0./4.35e+2)+E./4.35e+2)+1.0),-Inf,0.0)-integral(@(E)3.3e+1./(exp(E_F.*(-1.0./4.35e+2)+E./4.35e+2)+1.0),0.0,Inf)+1.01e+2
sol = fsolve(fun, 1)
Warning: Minimum step size reached near x = -Inf. There may be a singularity, or the tolerances may be too tight for this problem.
Warning: Minimum step size reached near x = -Inf. There may be a singularity, or the tolerances may be too tight for this problem.
No solution found. fsolve stopped because the problem appears regular as measured by the gradient, but the vector of function values is not near zero as measured by the value of the function tolerance.
sol = 1
  1 个评论
Arka Bhattacharya
Arka Bhattacharya 2023-4-6
Thanks for the answer. After exchanging the limits of integral for eta_mobile and eta_trap, I was able to get a solution.

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