The VEE current required by an LCD is very small. I have many times used the TC7660 chip to invert the +5V supply to -5V for use in biasing the LCD module (for those modules that have a VEE connection).

To adjust the LCD contrast I'll then hook up a series connection of a 1K resistor from +5V followed by a 5K trimmer resistor and then connected to yet another 1K resistor to the charge pumped -5V rail. The wiper of the trimmer connects to the base of a PNP transistor. The collector of the PNP goes to the -5V rail and the emitter of the transistor goes to the VEE pin of the LCD module. The PNP transistor acts like an emitter follower buffer to eliminate variation of LCD contrast that can occur if the VEE pin is just connected to the variable resistor.

If one wants to vary the VEE voltage in a dynamic manner a good approach can be to use a PWM out put from the microcontroller which switches a transistor on and off that gates a variable duty cycle of -5V to the VEE pin. Capacitors added to the VEE pin filter the duty cycle of the PWM signal to an average DC potential.

Michael Karas