Here is how to get a fit to the curve form you give to the data set. Given the great deal of pattern in the data, it can be reproduced in a relatively compact form. And some of the pattern is a bit disconcerting in terms of the discreteness of the values and the way the time is recorded. There are 2 identical times repeated for "odd" times, and 3 identical times repeated for "even" times. Finally, I needed to remove the times that were zero because of the use of the Log
function on time
in the function.
(* Reproduce data from a compacted form *)
time = Flatten[Table[If[i == 1000, i, If[OddQ[i], {i, i}, {i, i, i}]], {i, 1000}]];
ch1Table = {{0, 3}, {1, 1}, {0, 14}, {1, 1}, {0, 3}, {1,
1}, {0, 2}, {1, 4}, {0, 3}, {1, 2}, {0, 4}, {1, 1}, {0, 3}, {1,
3}, {0, 22}, {1, 1}, {0, 14}, {1, 2}, {0, 3}, {1, 2}, {0, 5}, {1,
1}, {0, 3}, {1, 2}, {0, 4}, {1, 2}, {0, 2}, {1, 2}, {0, 12}, {1,
2}, {0, 4}, {1, 2}, {0, 14}, {1, 1}, {0, 2}, {1, 4}, {0, 2}, {1,
1}, {0, 5}, {1, 1}, {0, 3}, {1, 3}, {0, 1}, {1, 1}, {0, 1}, {1,
1}, {0, 8}, {1, 2}, {0, 7}, {1, 3}, {0, 18}, {1, 2}, {0, 2}, {1,
2}, {0, 8}, {1, 1}, {0, 4}, {1, 3}, {0, 2}, {1, 3}, {0, 14}, {1,
1}, {0, 8}, {1, 2}, {0, 9}, {1, 2}, {0, 1}, {1, 2}, {0, 14}, {1,
1}, {0, 3}, {1, 1}, {0, 6}, {1, 1}, {0, 9}, {1, 1}, {0, 2}, {1,
1}, {0, 16}, {1, 2}, {0, 1}, {1, 3}, {0, 4}, {1, 1}, {0, 12}, {1,
3}, {0, 2}, {1, 1}, {0, 11}, {1, 1}, {0, 2}, {1, 3}, {0, 18}, {1,
2}, {0, 2}, {1, 1}, {0, 10}, {1, 1}, {0, 3}, {1, 3}, {0, 3}, {1,
1}, {0, 14}, {1, 1}, {0, 3}, {1, 1}, {0, 15}, {1, 2}, {0, 3}, {1,
2}, {0, 8}, {1, 2}, {0, 4}, {1, 1}, {0, 18}, {1, 3}, {0, 22}, {1,
2}, {0, 3}, {1, 2}, {0, 8}, {1, 3}, {0, 1}, {1, 2}, {0, 3}, {1,
1}, {0, 4}, {1, 1}, {0, 10}, {1, 2}, {0, 2}, {1, 1}, {0, 14}, {1,
3}, {0, 3}, {1, 3}, {0, 3}, {1, 1}, {0, 8}, {1, 2}, {0, 2}, {1,
1}, {0, 31}, {1, 1}, {0, 3}, {1, 1}, {0, 3}, {1, 2}, {0, 14}, {1,
3}, {0, 1}, {1, 1}, {0, 6}, {1, 1}, {0, 4}, {1, 1}, {0, 7}, {1,
1}, {0, 1}, {1, 1}, {0, 17}, {1, 1}, {0, 1}, {1, 2}, {0, 8}, {1,
1}, {0, 13}, {1, 2}, {0, 12}, {1, 2}, {0, 20}, {1, 2}, {0, 1}, {1,
4}, {0, 1}, {1, 1}, {0, 10}, {1, 2}, {0, 2}, {1, 2}, {0, 4}, {1,
2}, {0, 3}, {1, 1}, {0, 24}, {1, 3}, {0, 2}, {1, 2}, {0, 7}, {1,
2}, {0, 4}, {1, 1}, {0, 3}, {1, 1}, {0, 1}, {1, 1}, {0, 2}, {1,
1}, {0, 16}, {1, 1}, {0, 4}, {1, 1}, {0, 14}, {1, 1}, {0, 3}, {1,
2}, {0, 3}, {1, 1}, {0, 4}, {1, 2}, {0, 2}, {1, 3}, {0, 2}, {1,
1}, {0, 4}, {1, 1}, {0, 4}, {1, 1}, {0, 10}, {1, 1}, {0, 14}, {1,
2}, {0, 3}, {1, 2}, {0, 3}, {1, 1}, {0, 4}, {1, 2}, {0, 7}, {1,
3}, {0, 18}, {1, 1}, {0, 13}, {1, 1}, {0, 4}, {1, 3}, {0, 2}, {1,
3}, {0, 11}, {1, 2}, {0, 1}, {1, 1}, {0, 8}, {1, 1}, {0, 25}, {1,
1}, {0, 2}, {1, 2}, {0, 2}, {1, 4}, {0, 3}, {1, 2}, {0, 8}, {1,
3}, {0, 1}, {1, 1}, {0, 1}, {1, 2}, {0, 12}, {1, 1}, {0, 3}, {1,
2}, {0, 15}, {1, 2}, {0, 1}, {1, 1}, {0, 1}, {1, 1}, {0, 13}, {1,
3}, {0, 1}, {1, 3}, {0, 5}, {1, 1}, {0, 3}, {1, 1}, {0, 47}, {1,
3}, {0, 3}, {1, 2}, {0, 3}, {1, 1}, {0, 9}, {1, 2}, {0, 19}, {1,
5}, {0, 1}, {1, 6}, {0, 1}, {1, 14}, {0, 2}, {1, 2}, {0, 2}, {1,
3}, {0, 4}, {1, 1}, {0, 3}, {1, 2}, {0, 4}, {1, 1}, {0, 6}, {1,
2}, {0, 1}, {1, 7}, {0, 3}, {1, 2}, {0, 1}, {1, 1}, {0, 4}, {1,
8}, {0, 2}, {1, 2}, {0, 3}, {1, 2}, {0, 4}, {1, 1}, {0, 1}, {1,
8}, {2, 4}, {3, 1}, {4, 1}, {5, 2}, {6, 1}, {7, 1}, {8, 1}, {9,
1}, {11, 1}, {12, 1}, {14, 1}, {16, 1}, {18, 1}, {20, 1}, {22,
1}, {24, 1}, {27, 1}, {29, 1}, {32, 1}, {35, 1}, {38, 1}, {41,
1}, {43, 1}, {46, 1}, {49, 1}, {52, 1}, {55, 1}, {58, 1}, {60,
1}, {63, 1}, {66, 1}, {69, 1}, {71, 1}, {73, 1}, {75, 1}, {77,
1}, {79, 1}, {81, 1}, {82, 1}, {84, 1}, {85, 1}, {87, 1}, {88,
1}, {89, 1}, {90, 1}, {91, 1}, {92, 1}, {93, 2}, {94, 1}, {95,
2}, {96, 3}, {97, 1}, {98, 9}, {99, 3}, {98, 3}, {99, 1}, {98,
3}, {97, 3}, {96, 2}, {95, 2}, {94, 2}, {93, 2}, {92, 1}, {91,
1}, {90, 2}, {89, 1}, {88, 1}, {87, 1}, {86, 1}, {85, 1}, {84,
1}, {83, 1}, {82, 1}, {80, 1}, {79, 1}, {78, 1}, {77, 1}, {76,
1}, {74, 1}, {73, 1}, {72, 1}, {71, 1}, {70, 1}, {68, 1}, {67,
1}, {66, 1}, {65, 1}, {64, 1}, {63, 1}, {62, 1}, {61, 1}, {60,
1}, {59, 1}, {58, 1}, {56, 2}, {55, 1}, {54, 1}, {52, 2}, {51,
1}, {50, 1}, {49, 1}, {48, 1}, {47, 2}, {46, 1}, {45, 1}, {44,
1}, {43, 1}, {42, 2}, {41, 1}, {40, 1}, {39, 1}, {38, 1}, {37,
1}, {36, 1}, {35, 1}, {34, 2}, {33, 1}, {32, 1}, {31, 1}, {30,
1}, {29, 1}, {28, 2}, {27, 1}, {26, 1}, {25, 1}, {24, 2}, {23,
1}, {22, 1}, {21, 1}, {20, 1}, {19, 1}, {18, 1}, {17, 2}, {16,
1}, {15, 1}, {14, 1}, {13, 2}, {12, 2}, {11, 2}, {10, 2}, {9,
2}, {8, 3}, {7, 1}, {6, 3}, {5, 2}, {4, 3}, {3, 2}, {2, 5}, {1,
4}, {0, 7}, {-1, 8}, {0, 1}, {-1, 17}, {0, 17}, {1, 23}, {2,
33}, {1, 8}, {2, 1}, {1, 3}, {2, 4}, {1, 6}, {2, 2}, {1, 3}, {2,
1}, {1, 4}, {2, 7}, {1, 13}, {2, 1}, {1, 16}, {2, 1}, {1, 3}, {2,
13}, {1, 1}, {2, 9}, {1, 1}, {2, 9}, {1, 1}, {2, 4}, {1, 1}, {2,
22}, {3, 2}, {2, 2}, {3, 3}, {2, 6}, {3, 27}, {4, 2}, {3, 1}, {4,
3}, {3, 2}, {4, 4}, {3, 1}, {4, 17}, {5, 1}, {4, 12}, {5, 4}, {4,
1}, {5, 1}, {4, 10}, {5, 1}, {4, 3}, {5, 3}, {4, 16}, {3, 1}, {4,
4}, {3, 1}, {4, 4}, {3, 1}, {4, 3}, {3, 4}, {4, 2}, {3, 2}, {4,
3}, {3, 1}, {4, 3}, {3, 25}, {2, 2}, {3, 4}, {2, 1}, {3, 25}, {4,
2}, {3, 29}, {4, 2}, {3, 2}, {4, 3}, {3, 1}, {4, 16}, {5, 2}, {4,
4}, {5, 2}, {4, 2}, {5, 2}, {4, 4}, {5, 5}, {4, 2}, {5, 1}, {4,
1}, {5, 39}, {4, 1}, {5, 4}, {4, 1}, {5, 2}, {4, 9}, {5, 1}, {4,
16}, {3, 3}, {4, 3}, {3, 1}, {4, 6}, {3, 1}, {4, 1}, {3, 2}, {4,
2}, {3, 4}, {4, 1}, {3, 55}, {4, 1}, {3, 13}, {4, 1}, {3, 72}, {2,
1}, {3, 14}, {2, 2}, {3, 3}, {2, 2}, {3, 1}, {2, 3}, {3, 3}, {2,
3}, {3, 3}, {2, 1}, {3, 3}, {2, 7}, {3, 3}, {2, 2}, {3, 4}, {2,
2}, {3, 1}, {2, 15}, {3, 1}, {2, 18}, {3, 1}, {2, 10}, {3, 1}, {2,
9}, {3, 1}, {2, 43}};
ch1 = Flatten[
Table[Table[ch1Table[[i, 1]], {j, ch1Table[[i, 2]]}], {i,
Length[ch1Table]}]];
data = Table[{time[[i]]/100000000, -ch1[[i]]/250}, {i, Length[time]}];
(* Define function to fit *)
UGLog[t_] := Umax Exp[-1/2 (Log[t/τ]/σ)^2] + a Exp[(t - μ)^2/γ]
(* Find parameter estimates *)fitCH1 =
NonlinearModelFit[data,
UGLog[t], {{b, 0}, {Umax, -0.397}, {τ, 0.00000578}, {σ,
0.0252}, {a, -0.017}, {μ, 0.000008}, {γ, 0.000001}}, t,
MaxIterations -> 300]
(* Show fit *)
Show[{ListPlot[data, PlotRange -> Full],
Plot[fitCH1[t], {t, 0.000001, 0.00001}, PlotRange -> Full,
PlotStyle -> Red]}, ImageSize -> Large]
(* Show residuals *)
ListPlot[fitCH1["FitResiduals"], ImageSize -> Large]
with the following results:

and the following residuals:

The residuals have a great deal of pattern so I wouldn't call this a great fit.
Table[DataList[[i,2]];
? $\endgroup$NonlinearModelFit
. $\endgroup$ComplexFit
package but still do not want complex numbers, then you should add a constraint to prevent these appearing, or give better initial guesses. $\endgroup$