Large BS170 drain current in off mode

Hi,

I have some basic knowledge of electronics, but I'm having trouble trying to get some real design to work. One of the things that do not work as expected is the BS170 MOSFET I'm trying to use. I know, it's not a very sophisticated part, but I have a few of them lying around and I thought they would be able to assist my learning.

Anyway, I connect the gate and source of the BS170 both to the ground, and the drain to a 330 ohm resistor, connected to 3.6 V. When I then measure the potential of the drain, it's at 2.85 V, which means it draws a current of (3.6-2.85)/330 = 2.3 mA. Thus, the drain-source resistance is about 1.2 kohm. My expectation was a much larger 'off' resistance (say

100 kohm or more).

I cannot relate anything on the data sheet

formatting link

ds/BS%2FBS170.pdf) to my observation. I tried with another BS170, which gave about the same results. Is my expectation wrong? Apparently, it is, but what is the right explanation? And, how can I deduce this from the data sheet? Then, how to solve this? Should I just use another transistor, or is there some common way to handle this?

In my case, I connected a LED to the drain and it didn't shut off. I can, of course, put a resistor in parallel, but that would increase power dissipation and would reduce the LEDs brightness when turned on.

Thanks for any insight!

Koen