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I need solve this equation, but i have problems with singularity/stiff

ni = 1.4*(10^10);
q = 1.602*(10^-19); 
eps = 8.854*(10^-14)*11.7;
tensione = NDSolve[{-eps*V''[x] == 10 (2/Pi) ArcTan[(x - 1/2) 10^(3)] 
q*ni*Exp[V[x]] + q*ni*Exp[-V[x]], V[0] == -1, V[1] == 1}, V[x], x]

NDSolve::ndsz: At x == 2.3590299026264842`*^-6, step size is effectively 
zero; singularity or stiff system suspected.

I want eliminate or bypass the problem. Thanks for your help.

J. M.'s missing motivation
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Amos Varca
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  • Possible duplicate: https://mathematica.stackexchange.com/questions/72725/how-to-avoid-ndsolvendsz-problem-singularity-problem/72769#72769 -- You'll have to find good starting initial conditions. – Michael E2 Sep 28 '17 at 12:43
  • Note also that your code does not match the formula. Which is correct? – Michael E2 Sep 28 '17 at 12:44
  • Hi Michael, I guess that you are talking about Vth. However I have the same problem. But I want to thank you for the duplicate. – Amos Varca Sep 28 '17 at 13:29

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