differential equations – How to NDSolve stiff ODE?

I want to solve this ODE.

   k = 10^13;
   H = 10^-5;
    \[Chi][z_] := \[Pi]/4 + ArcTan[3/10 (34 - H*z)];
    \[ScriptA][z_] := E^(H*z);
  s = NDSolve[
  {A''[t] + ((\[ScriptA]'[t]/\[ScriptA][t] - 2 (I*k)/\[ScriptA][t])*
        A'[t] + 20*k/\[ScriptA][t]*\[Chi]'[t] A[t]) == 0, A[0] == 1, 
   A'[0] == 0},
  {A[t], A'[t], A''[t]}, {t, 0, 65*10^5}]

I tried below, but failed:

Thanks for your all suggestions!