Driving MOSFET in battery powered circuit

[igru25]

Hello all,

I have prepared following circuit and I have troubles with MOSFET driving.

Circuit info:

• VDD = 2.8V (two fully charged NiMH AA batteries)
• NE555N replaced by ST555CN (CMOS, from 2V power supply)
• IRLZ44Z replaced by IRL3705N
• Q2 MOSFET activated 1-2 times per minute for 0.1 second (duty = 0.2-0.4%).

The problem:

I have prepared breadboard test circuit and there is no enough voltage in batteries to fully open the MOSFET Q2 using totem-pole configuration. Solenoid M1 is too slow, Q2 is not fully open.
I tried four batteries and circuit worked as expected. But I must save weight and I cannot use four batteries. Two light 3V Lithium-ion cells - is an option, but too expensive.

I have two beginner questions:

1. Can I utilize the booster output (15.8V) to drive Q2 MOSFET and how can I do it efficiently?
2. Can I utilize the booster output to power CMOS 555 timer and how can I do it efficiently? I think if battery voltage drops below 2V - timer will not work.

I can imagine voltage divider - from booster output to supply totem-pole and timer - but it is not efficient. Am I right?
May be programmable voltage reference TL431 using booster output as input? Is it efficient way?

I need most efficient way to save battery power.

Please suggest.

Thank you in advance.