def enforce_minimum_piezo_dimensions(x0):
c = cantilever_divingboard(*x0)
min_pr_thickness = 30e-9
min_pr_length = 1e-6
min_pr_width = 500e-9
return min(c.l_pr - min_pr_length, c.w_pr - min_pr_width, c.t_pr - min_pr_thickness)
def enforce_minimum_dimensions(x0):
c = cantilever_divingboard(*x0)
min_thickness = 1e-6
min_length = 20e-6
min_width = 500e-9
return min(c.l - min_length, c.w - min_width, c.t - min_thickness)
def enforce_minimum_dimensions(x0):
c = cantilever_divingboard(*x0)
min_thickness = 1e-6
min_length = 20e-6
min_width = 500e-9
return min(c.l - min_length, c.w - min_width, c.t - min_thickness)
def enforce_minimum_piezo_dimensions(x0):
c = cantilever_divingboard(*x0)
min_pr_thickness = 30e-9
min_pr_length = 1e-6
min_pr_width = 500e-9
return min(c.l_pr - min_pr_length, c.w_pr - min_pr_width,
c.t_pr - min_pr_thickness)
def enforce_positive_dimensions(x0):
c = cantilever_divingboard(*x0)
return min(c.l, c.w, c.t, c.l_pr, c.w_pr, c.w_gap, c.t_pr)
def optimize_cantilever(x0):
c = cantilever_divingboard(*x0)
return c.force_resolution()
c = cantilever_divingboard(*x0)
min_pr_thickness = 30e-9
min_pr_length = 1e-6
min_pr_width = 500e-9
return min(c.l_pr - min_pr_length, c.w_pr - min_pr_width,
c.t_pr - min_pr_thickness)
def enforce_positive_resolution(x0):
c = cantilever_divingboard(*x0)
return c.force_resolution()
def enforce_minimum_natural_frequency(x0):
c = cantilever_divingboard(*x0)
min_natural_frequency_hz = 50e3
print 'Force resolution: %f' % c.force_resolution()
return (c.omega_vacuum_hz() - min_natural_frequency_hz)
c1 = cantilever_divingboard(*x)
print 'Cantilever L/W/T: %f %f %f' % (c1.l * 1e6, c1.w * 1e6, c1.t * 1e6)
print 'Piezo L/W/T: %f %f %f' % (c1.l_pr * 1e6, c1.w_pr * 1e6, c1.t_pr * 1e6)
print 'Resistance: %f' % log10(c1.resistance())
print 'Doping Concentration: %f' % c1.N
print 'Force resolution: %f' % c1.force_resolution()
print 'Natural freq: %f' % c1.omega_vacuum_hz()
# fmin_tnc and blfs won't work, because they don't provide enough constraint flexibility
w = 1e-6
l = 400e-6
l_pr = 1 # estimated from SEM in paper
w_pr = 1
t_pr = 1
w_gap = 1
freq_min = 1e1
freq_max = 1e5
V_bias = 5
N = 4e19
beta = 0.7
c = cantilever_divingboard(freq_min, freq_max, l, w, t, l_pr, w_pr, w_gap,
t_pr, V_bias, N)
# For L = 400e-6
c.l = 400e-6
c.w = 0.1e-6
print c.omega_damped_hz()
c.w = 0.5e-6
print c.omega_damped_hz()
c.w = 1e-6
print c.omega_damped_hz()
c.w = 5e-6
print c.omega_damped_hz()
def enforce_positive_dimensions(x0):
c = cantilever_divingboard(*x0)
return min(c.l, c.w, c.t, c.l_pr, c.w_pr, c.w_gap, c.t_pr)
def enforce_minimum_natural_frequency(x0):
c = cantilever_divingboard(*x0)
min_natural_frequency_hz = 50e3
print 'Force resolution: %f' % c.force_resolution()
return (c.omega_vacuum_hz() - min_natural_frequency_hz)
l = 400e-6
l_pr = 1 # estimated from SEM in paper
w_pr = 1
t_pr = 1
w_gap = 1
freq_min = 1e1
freq_max = 1e5
V_bias = 5
N = 4e19
beta = 0.7
c = cantilever_divingboard(freq_min, freq_max,
l, w, t,
l_pr, w_pr, w_gap, t_pr,
V_bias, N)
# For L = 400e-6
c.l = 400e-6
c.w = 0.1e-6
print c.omega_damped_hz()
c.w = 0.5e-6
print c.omega_damped_hz()
c.w = 1e-6
print c.omega_damped_hz()
c.w = 5e-6
from cantilever_divingboard import *
# Agressive
# Minimal thickness and width
# Moderative
# Conservative
v_all = linspace(1, 100, 101)
for v_test in v_all:
c = cantilever_divingboard( l = 80e-6, w = 500e-9, t = 1e-6,
l_pr = 10e-6, w_pr = 500e-9, w_gap = 1e-6, t_pr = 100e-9,
V_bias = v_test, N = 4e17, freq_min = 1e0, freq_max = 1e2)
print "Resolution (pN): %f Freq (kHz): %f" % (c.force_resolution(), c.omega_damped_hz()/1000)
def enforce_minimum_natural_frequency(x0):
c = cantilever_divingboard(*x0)
min_natural_frequency_hz = 50e3
print 'Force resolution: %f' % c.force_resolution()
return (c.omega_vacuum_hz() - min_natural_frequency_hz)
def enforce_positive_resolution(x0):
c = cantilever_divingboard(*x0)
return c.force_resolution()
def enforce_maximum_piezo_dimensions(x0):
c = cantilever_divingboard(*x0)
return min(c.l - c.l_pr, c.w - c.w_pr, c.t - c.t_pr)
from cantilever_divingboard import *
def optimize_cantilever(x0):
c = cantilever_divingboard(*x0)
print x0
return c.force_resolution()
x = optimize.anneal(func = optimize_cantilever,
x0 = ( 150e-6, 1e-6, 5e-6,
10e-6, 1e-6, 1e-6, 1e-6, 3., 1e15))
c1 = cantilever_divingboard(*x)
print 'Cantilever L/W/T: %f %f %f' % (c1.l*1e6, c1.w*1e6, c1.t*1e6)
print 'Piezo L/W/T: %f %f %f' % (c1.l_pr*1e6, c1.w_pr*1e6, c1.t_pr*1e6)
print 'Resistance: %f' % log10(c1.resistance())
print 'Doping Concentration: %f' % c1.N
print 'Force resolution: %f' % c1.force_resolution()
print 'Natural freq: %f' % c1.omega_vacuum_hz()
def enforce_maximum_piezo_dimensions(x0):
c = cantilever_divingboard(*x0)
return min(c.l - c.l_pr, c.w - c.w_pr, c.t - c.t_pr)
def optimize_cantilever(x0):
c = cantilever_divingboard(*x0)
print x0
return c.force_resolution()
def enforce_positive_resolution(x0):
c = cantilever_divingboard(*x0)
return c.force_resolution()
from cantilever_divingboard import *
# We need to scale the parameters before applying the optimization algorithm
# Normally there are about 20 orders of magnitude between the dimensions and
# the doping concentration, so this is a critical step
# Run the script
freq_min = 1e3
freq_max = 1e5
omega_min = 100e3
initial_guess = (50e-6, 1e-6, 1e-6,
30e-6, 1e-6, 1e-6, 500e-9, 5., 1e15)
constraints = ((30e-6, 100e-6), (500e-9, 20e-6), (1e-6, 10e-6),
(2e-6, 100e-6), (500e-9, 5e-6), (500e-9, 20e-6), (30e-9, 10e-6),
(1., 10.), (1e15, 4e19))
x = optimize_cantilever(initial_guess, constraints, freq_min, freq_max, omega_min)
c = cantilever_divingboard(freq_min, freq_max, x)
c.print_performance()
def brute_force():
n = 10 # Number of points to check in each dimension
# ASML
# 0.45 micron resolution
# ??? alignment resolution
f_min = 1e2
f_max = 100e3
bandwidth = 100e3
# Others
doping = logspace(16, 19, n)
bias = linspace(0., 10., n)
# Cantilever dimensions
length = linspace(10e-6, 100e-6, n)
width = linspace(0.45e-6, 10e-6, n) # Min = ASML resolution for frontside DRIE
thickness = linspace(100e-9, 10e-6, n) # Min = stability to survive water entry?
# For each iteration we'll check that the piezo dimensions are valid first, so match upper limit to length/width/thickness
piezo_length = linspace(0.45e-6, max(length), n)
piezo_width = linspace(0.45e-6, max(width), n)
piezo_gap = linspace(0.45e-6, 10e-6, n)
piezo_thickness = linspace(100e-9, max(thickness), n)
# Define limits of iteration
ii_max = len(doping)
jj_max = len(bias)
kk_max = len(length)
ll_max = len(width)
mm_max = len(thickness)
nn_max = len(piezo_length)
oo_max = len(piezo_width)
pp_max = len(piezo_gap)
qq_max = len(piezo_thickness)
# results = zeros((ii_max, jj_max, kk_max, ll_max, mm_max, nn_max, oo_max, pp_max, qq_max), dtype = Float)
min_resolution = 10000.
for ii in range(0, ii_max-1):
for jj in range(0, jj_max-1):
for kk in range(0, kk_max-1):
for ll in range(0, ll_max-1):
for mm in range(0, mm_max-1):
for nn in range(0, nn_max-1):
for oo in range(0, oo_max-1):
for pp in range(0, pp_max-1):
for qq in range(0, qq_max-1):
doping_level = doping[ii]
bias_voltage = bias[jj]
l = length[kk]
w = length[ll]
t = length[mm]
l_pr = length[nn]
w_pr = length[oo]
w_gap = length[pp]
t_pr = length[qq]
# Check dimensions are okay, if not skip onto the next for loop iteration
if (l_pr >= l) or (w_pr >= w) or (t_pr >= t) or (bias_voltage == 0):
continue
print bias_voltage
c1 = cantilever_divingboard(l, w, t, l_pr, w_pr, w_gap, t_pr, V_bias = bias_voltage, N = doping_level)
# print 'Cantilever L/W/T: %f %f %f' % (c1.l*1e6, c1.w*1e6, c1.t*1e6)
# print 'Piezo L/W/T: %f %f %f' % (c1.l_pr*1e6, c1.w_pr*1e6, c1.t_pr*1e6)
# print 'Doping: %f' % log10(c1.N)
# print 'Resistance: %f' % c1.resistance()
# print "Integrated noise: %f" % (c1.integrated_noise()*1e8)
# print "Sensitivity: %f" % c1.force_sensitivity()
# print 'Force resolution: %f' % (c1.force_resolution()*1e12)
# print 'Natural freq: %f' % c1.omega_vacuum_hz()
# print '\n'
if (c1.omega_vacuum_hz() > bandwidth):
# results[ii, jj, kk, ll, mm, nn, oo, pp, qq] = c.force_resolution()
# print c1.force_resolution()*1e12
if (c1.force_resolution() < min_resolution):
min_resolution = c1.force_resolution()
return min_resolution
from cantilever_divingboard import *
# Agressive
# Minimal thickness and width
# Moderative
# Conservative
v_all = linspace(1, 100, 101)
for v_test in v_all:
c = cantilever_divingboard(l=80e-6,
w=500e-9,
t=1e-6,
l_pr=10e-6,
w_pr=500e-9,
w_gap=1e-6,
t_pr=100e-9,
V_bias=v_test,
N=4e17,
freq_min=1e0,
freq_max=1e2)
print "Resolution (pN): %f Freq (kHz): %f" % (c.force_resolution(),
c.omega_damped_hz() / 1000)
