Electronic – Control latching pulse-solenoid-valve with MOSFET Array

Read my blog entry "Byte and Switch" -- it covers this exact scenario.

The short answer is that you need a freewheeling diode to conduct the current when the MOSFET turns off; the solenoid has inductance that stores energy in the magnetic field, and when you turn the MOSFET off the inductance will generate however much voltage is necessary to continue flow of that current. The resulting voltage pulse will cause breakdown in the MOSFET which causes the damage you are seeing.

You should also add a couple of resistors, one from microcontroller output to ground, to make sure it's off when your microcontroller is in reset, and the other from the microcontroller to the MOSFET gate, to add some resistive isolation between your power switch and your microcontroller.

edit: I just noticed you're using a BS170 MOSFET. Have you looked at the datasheet? This is a poor choice for a MOSFET used as a power switch from a microcontroller.

First of all, the MOSFET is specified at 10V Vgs. You're supplying it from a 5V microcontroller. You need to make sure you use MOSFETs that are "logic level" and have on-resistance specified at 4.5V or 3.3V Vgs. (I suggest you not use ultra-low voltage MOSFETs as there's a possibility of it turning on weakly when you think it is off.)

More importantly, it's a small TO-92 MOSFET specified at 5 ohms max Rdson at 10V Vgs. This MOSFET is fine for very small loads like LEDs drawing a few milliamps. But solenoids generally draw tens or hundreds of milliamps, and you need to calculate I2R loss in your MOSFET for the current load it draws, and make sure that it doesn't cause your transistor to overheat. Look at the thermal resistance R theta J-A on the datasheet and you can estimate how much temperature rise there is in the part.

Use a MOSFET in the 20V-60V range that has a lower on-resistance -- as I said in my comment, we need to know how much current your solenoid draws if we're going to help you.

You must model the solenoid valve as a resistor (33\$\Omega\$ in your case) in series with an inductor. If you like you can include a bit of parallel capacitance, but the resistance is required.

Otherwise the simulated current after a long time will be limited only by the MOSFET (maybe to something like 30A) and the voltage will approach zero.

For the operation time of the valve, you can consult the data sheet. Normally they will specify it without a diode, so whatever time you get with the zener will be a bit longer. You can guess that the difference in the current through the coil will give you an idea of the operation time, but there is no guarantee that even if the coil current drops to 10% or 5% of normal that the mechanical parts will have moved in that time. Some valves are fairly complex ('pilot valves', for example that operate indirectly), and the inductance of electromechanical systems often varies significantly during operation.

Edit: Below is a PSPICE simulation I did with similar parameters to yours (I used a 1N4740 Zener and a PHD23NQ10T,118 MOSFET to save me time). Green trace is the gate drive signal (before the resistor), red is the MOSFET drain. As you can see the MOSFET drain rises to a peak voltage of around 24V.

In the below close-up, you can see where the bulk of the energy is dissipated and the ringing afterward. The violet trace is the coil current (scaled so you can see it on the same graph).