Lower current through different transistors
The VGS problem:

The 2n7000 has a *VGS (Voltage Gate to Source) of 3 Volts Max. Meaning it is a low logic level Mosfet, and will have it's lowest RDS(on) (Resistance Drain to Source when On) at that voltage or above. It's great for a 3.3V signal.

The IRF540 has a much higher VGS, nearly 10 Volts for lowest RDS(on). It's VGS Threshold is listed as min 2.0 ~ max 4.0 Volts. This Threshold dictates the lowest voltage that will even turn it on (Passing just 250µA). Always assume the Max spec, 3.3V won't even turn it on. At Room Temperature, it won't be at all. Looking at it's VGS graph, at 5V, it will still pass around 10 Amps. Not the lowest resistance or maximum current capabilities, but fine for some folks. It's the go-to resistor for the Arduino crowd (Arduino Uno being 5V logic).

I can't find the 16NF06FP, but a STP16NF06 has similar stats to the IRF540.



The PIR Module:

The Sensor you have is a BIS00001 based PIR controller module. It's operating at 3.3V, and it's output is directly controlled by the BIS00001. It has limited current sourcing, and is Active High. It's output goes high when motion is sensed.



Driving it

Since you want to control a low side, N-Channel mosfet or transistor, you could hook it up directly and it will turn on the Load/LEDs when the sensor sees motion. But since you need to drive a larger Mosfet, you need an in-between. And since that in-between is also a low side, N-Channel mosfet or transistor, you will need to invert the logic. 

You will need 3 transistors or Mosfets total. The first two are just logic level switching, the last being the power driver. Q1 and M1 can both be transistors, or mosfets. I used one 2n3904 and one 2N7000, but you can replace them with any small switching transistor or n-fet.







simulate this circuit &ndash; Schematic created using CircuitLab

Alternatively, you can replace it with a P-Channel Mosfet and one transistor, no logic inverting needed. Again, the 2n7000 can work instead of the 2n3904 if you want.







simulate this circuit