Question

Assume that you are using a piezoelectric material to build a micro/MEMS actuator beam in order to pick up a red-blood cell (with mass of ~1picogram or 10-12grams). If the dimensions of this actuator beam are length=100µm, width=10μm, and thickness=1μm, what is the minimal voltage you need to apply to this piezoelectric actuator in order to pick up the red-blood cell? Please write down all your assumptions used to estimate the voltage required.

Answer 1

Given :

Mass = 1 picogram or upto 10-12 grams (well they have given us the range of mass the actuator should able to pick-up)

Length = 100 um

Width = 10 um

Thickness = 1 um

We have to see the specification of sensor MEMS(Micro Electromechancial Sensor).

Formula Relating Pressure ,Voltage and few other parameters.

P=e33*eo*V/(kt*d33*t) ....................................(1)

P=pressure output, e33=relative dielectric, eo=permittivity in vacuum, V= voltage from piezoelectric Sensor, kt=coupling factor, d33=piezoelectric constant, t=thickness of piezoelectric layer.

First let's calculate force by using the info given so

F=M.g

F=0.012*10 ( Mass is given as 10-12 grams and we know gravity is 10 m /sec^2

F=0.12 N........ ................................................(2)

Now we know P = F/A........................................(3)

so to calculate area we will use above given information

Area = length *Width

Area = 100*10^-6*10*10^-6

Area = 10^-9 m^2................................................(4)

Now Putting Values from equation 2 and equation 4 in equation 3

P= 0.12*10^9

P= 12*10^7 Pascal.........................(5)

Now we have to assume different values as per the need.

So e33*eo = Electrical Permitivity

but Electrical Permitivity of Blood can be different at different frequencies i am taking frequency as 100MHZ

now e33*eo = 76.8

kt = 0.19

d33= 2 *10^-12 C/ N

t = 10^-6

So putting all the values in equation 1 we get

V=0.059*10^-11 Volts

The above value is calculated for m = 12 grams now you can replace value of m = 1 picogram in equation 2