I have a controller which has an active low input and an internal pull-up resistance of 200k tied 0.8V. I would like to use a BJT as a switch for the microcontroller to control the controller input. When there is a 3.3V output from the microcontroller, it will trigger a pull-down to ground the controller input.
The problem here is I am puzzled by choosing a value for R3. After I performed the calculation, the outcome is a very small current and very large resistor. How should I correlate this back to the BJT datasheet? Am I doing this right? The BJT I am using is an NPN BC847BW.

simulate this circuit – Schematic created using CircuitLab
I did below calculation.
Ic = 0.8V / 200K = 4uA
Using 1/10 of Ic rule of thumb:
Ib = Ic / B = 4uA / 10 = 0.4uA
R3 = (Vbb - Vbe) / Ib = (3.3 - 0.7) / 0.4uA = 6.5Mohm

