The aspect ratio is not really an issue. But for sure, it affects the TC of the output current. A simple example. Please, consider again: ID1 equal to `X`, and ID2 equal to `10*X`. In another words, the aspect ratio is S1/S2 = 10. Consider now that each 1 degree celcius causes an increase of ID1 increase by `Y`. So the TC1 is Y/degrees. Due to the current mirror gain, for 1 degree of change in ID1, ID2 changes by 1*10 = 10. Therefore, if you consider that TC = deltaID/deltaTEMP, for the same change in the temperature, the variation in ID2 is 10 times bigger. Then, TC2 = 10*TC1.
Added after 2 hours 5 minutes:
Hi!
Regarding the slope... you dont need to be worry about it.
The advantage of this circuit is to provide gm constant.
The transconductance of one NMOS biased with a copy of the PTAT Current - through a current mirror - will be proportional ( or equal) to gm of the device in the internal loop of the PTAT circuit. It will be constant over the temperature range.
Because this..... the GBW of your circuit will be also constant.
This consideration neglects the temperature coefficient of the resistor; when the transconductance is inversely proportional to the resistance.
Moreover, usually this circuit is used with an external resistor. In such way, you can guarantee the desired gm. Otherwise, variation of until 20% in the value of the resistor will change the designed gm.
This is my point of view. Lets discuss.
Best wishes,