Pyroelectric Detector

The pyroelectric phenomenon, when absorbed energy causes a change in temperature and polarization within a pyroelectric material, is the basis of operation of some laser energy meters. The change in polarization manifests itself as a pyroelectric current, which can be measured by an ammeter circuit. Laser energy meters based on the pyroelectric phenomenon are used to calibrate of laser sources.

This 2D axisymmetric model demonstrates the operation of a pyroelectric detector based on a lithium niobate (LiNbO3) crystal sandwiched between two electrodes with connection to an external circuit. To represent the absorbed laser energy, an energy flux that varies with position and time is applied to the top surface of the disk. This model uses (i) the multiphysics interface and (ii) the interface. A time-dependent study solves for temperature evolution in the disk and the pyroelectric current generated.

Model Definition

A 25 μm-thick LiNbO3 crystal in the shape of a disk with a diameter of 3 mm is bonded to an electrically conductive base by a 40 μm thick ring-shaped silver (Ag) pad. Most material properties of the LiNbO3 and Ag domains are defined by material models from the material library and some properties need to be added manually. The pyroelectric coefficient of LiNbO3 was specified as −83 μC/(m2·K). The top and bottom surfaces of the crystal are coated with a thin metal layer, forming the top and bottom electrodes. The model geometry is fully parameterized to allow for easy changes in the device structure for future optimization.

This model uses the multiphysics interface, which automatically sets up the , , and interfaces together with , , and couplings. In the interface, a material model is assigned to the LiNbO3 domain. In the interface, a is applied to the base of the Ag pad. In the interface, an applied to the top surface of the disk represents the laser energy while a constant temperature of 293.15 K is assigned to the base of the Ag pad. These assignments can be seen in Figure 1.

Figure 1: A cross section of the 2D axi-symmetric model showing the material models and boundary conditions used. The disk is lithium niobate (purple) and the pad is silver (gray). The bottom surface of the disk is grounded (yellow) while the top electrode (red) is connected to an external circuit. A fixed constraint and T = 293.15 K is applied to the bottom of the silver pad.

To calculate output power, the device is connected to an external circuit using the interface. The terminals of the LiNbO3 disk is connected in parallel to the capacitor C1 with a capacitance value of Cext = 100 pF. The disk is also connected to the load R1 with resistance value of Rext = 0.1, 5.106, 5.107, or 109 Ω. The electrical power is calculated as the product of the voltage and current across R1. The circuit components are parameterized to allow for easy changes in the device structure for future optimization.

The model solves a multiphysics problem involving , , and couplings using a time-dependent study. In the first study, the model includes all couplings and is referred to as the full model. In the second study, the and couplings are disabled, and the model is referred to as pyroelectricity-only.

Results and Discussion

A plot of temperature and current through R1versus time is shown in Figure 2 with the temperature measured at the center of the disk.

Figure 2: Temperature and current through R1 versus time at the center of the disk.

Figure 3 shows a plot of voltage versus time with the voltage measurements taken across the load R1.

Figure 3: Voltage versus time. Voltage measurements taken across the load R1.

Figure 4 shows a plot of electric power versus time, with the electric power measurements taken through the load R1.

Figure 4: Electric power versus time. Electric power measurements taken through the load R1.

Figure 5 shows a comparison of the electric power between the full model and the pyroelectricity-only model. The electric power for the full model is about 8% less than for the pyroelectricity-only model.

Figure 5: Comparison of electric power between full model and pyroelectricity-only model.

MEMS_Module/Sensors/pyroelectric_detector

Modeling Instructions

Start by creating a new 2D axi-symmetric model with the Piezoelectricity and Pyroelectricity multiphysics interface and the Electrical Circuit interface.

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select .

Click .

In the tree, select .

Click .

Click

In the tree, select .

Click

Define and enter the values for the following global parameters.

Global Definitions

Parameters 1

In the window, under click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
r_el	1.4[mm]	0.0014 m	Radius of top electrode
r_s	0.25[mm]	2.5E-4 m	Width of standoff
r_d	1.5[mm]	0.0015 m	Radius of crystal
t_d	0.025[mm]	2.5E-5 m	Thickness of crystal
t_s	0.040[mm]	4E-5 m	Thickness of standoff
w_b	2[mm]	0.002 m	Width of laser beam
Qmax	500[W/m^2]	500 W/m²	Maximum laser power density
pulse	1[s]	1 s	Duration of laser pulse
C_ext	100[pF]	1E-10 F	Capacitance of C1
R_ext	1000[ohm]	1000 Ω	Resistance of R1

Define a rectangular function and an analytical function describing the shape of laser pulse.

Definitions

Rectangle 1 (rect1)

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type 0.2.

In the text field, type 1.

Analytic 1 (an1)

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type exp(-((r^2)/(2*(10000)^2))).

In the text field, type r.

Locate the section. In the table, enter the following settings:


Argument	Unit
r	um

Define the expression for the energy flux representing laser pulse using the functions previously defined.

Variables 1

In the window, right-click and choose .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Unit	Description
Flux	Qmaxan1(r)rect1(t/pulse)	W/m²	Power density distribution

Geometry 1

In the window, under click .

In the window for , locate the section.

From the list, choose .

Rectangle 1 (r1)

In the toolbar, click

In the window for , locate the section.

In the text field, type r_d.

In the text field, type t_d.

Rectangle 2 (r2)

In the toolbar, click

In the window for , locate the section.

In the text field, type r_s.

In the text field, type t_s.

Locate the section. In the text field, type r_d-0.3.

In the text field, type -t_p.

In the text field, type r_d-r_s.

In the text field, type -t_s.

Rectangle 3 (r3)

In the toolbar, click

In the window for , locate the section.

In the text field, type r_el.

In the text field, type t_d.

Click

Multiphysics

Pyroelectricity 1 (pye1)

In the window, under click .

Select Domains 1 and 3 only.

Add the lithium niobate model from the library.

Add Material

In the toolbar, click

to open the window.

Go to the window.

In the tree, select .

Click in the window toolbar.

In the toolbar, click

to close the window.

Materials

Lithium Niobate (mat1)

Next, enter missing properties for lithium niobate.

In the window for , locate the section.

In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Thermal conductivity	k_iso ; kii = k_iso, kij = 0	4.2	W/(m·K)	Basic
Heat capacity at constant pressure	Cp	628	J/(kg·K)	Basic
Coefficient of thermal expansion	{alpha11, alpha22, alpha33} ; alphaij = 0	{6.5e-6, 6.5e-6, 14.8e-6}	1/K	Basic
Total pyroelectric coefficient	{pET1, pET2, pET3}	{0,0,-8.3e-5}	C/(m²·K)	Pyroelectric

Setup the boundary conditions for the Electrostatics interface.

Electrostatics (es)

Charge Conservation, Piezoelectric 1

In the window, under click .

Select Domains 1 and 3 only.

Ground 1

In the toolbar, click

and choose .

Select Boundaries 2, 6, and 8 only.

Terminal 1

In the toolbar, click

and choose .

In the window for , locate the section.

Click

In the dialog box, type 3 in the text field.

Click .

In the window for , locate the section.

From the list, choose .

Charge Conservation 1

In the window, click .

In the window for , locate the section.

From the list, choose .

Solid Mechanics (solid)

Piezoelectric Material 1

In the window, under click .

Select Domains 1 and 3 only.

Setup the boundary conditions for the Solid Mechanics interface.

Fixed Constraint 1

In the toolbar, click

and choose .

Select Boundary 5 only.

Setup the boundary conditions for the Heat Transfer interface.

Heat Transfer in Solids (ht)

In the window, under click .

Heat Flux 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the q0 text field, type Flux.

Select Boundaries 3 and 9 only.

Temperature 1

In the toolbar, click

and choose .

Select Boundary 5 only.

Add the Electric Circuit interface, define the capacitor C_ext and the load R_ext and how they are connected to the detector terminals.

Electrical Circuit (cir)

In the window, under click .

Resistor 1 (R1)

In the toolbar, click

In the window for , locate the section.

In the table, enter the following settings:


Label	Node names
n	0

Locate the section. In the R text field, type R_ext.

Capacitor 1 (C1)

In the toolbar, click

In the window for , locate the section.

In the table, enter the following settings:


Label	Node names
p	1
n	0

Locate the section. In the C text field, type C_ext.

External I-terminal 1 (termI1)

In the toolbar, click

In the window for , locate the section.

In the text field, type 1.

Locate the section. From the V list, choose .

Add material model for silver.

Add Material

In the toolbar, click

to open the window.

Go to the window.

In the tree, select .

Click in the window toolbar.

In the toolbar, click

to close the window.

Materials

Ag - Silver (mat2)

Next, enter missing properties for silver.

Select Domain 2 only.

In the window for , locate the section.

In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Relative permittivity	epsilonr_iso ; epsilonrii = epsilonr_iso, epsilonrij = 0	1	1	Basic

Click the

button in the toolbar.

Mesh 1

Free Triangular 1

In the toolbar, click

Size 1

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Click

Add a time-dependent study using the full model to analyze effect of thermal expansion, piezoelectricity and pyroelectricity.

Study 1

Time Dependent, Full Model

In the window, under click .

In the window for , locate the section.

In the text field, type range(0,0.02,2).

In the text field, type Time Dependent, Full Model.

Click to expand the section. Select the check box.

Click

In the table, enter the following settings:


Parameter name	Parameter value list	Parameter unit
R_ext (Resistance of R1)	0.1 5e6 5e7 1e9	Ω

In the window, click .

In the window for , locate the section.

Clear the check box.

In the toolbar, click

Add a time-dependent study using the pyroelectricity-only model to analyze effect of pyroelectricity.

Add Study

In the toolbar, click

to open the window.

Go to the window.

Find the subsection. In the tree, select .

Click in the window toolbar.

Study 2

Time Dependent - Pyroelectricity Only

In the window for , type Time Dependent - Pyroelectricity Only in the text field.

Locate the section. In the text field, type range(0,0.02,2).

Locate the section. In the table, enter the following settings:


Physics interface	Solve for	Equation form
Electrostatics (es)	√	Automatic (Time dependent)
Solid Mechanics (solid)		Automatic (Stationary)
Heat Transfer in Solids (ht)	√	Automatic (Time dependent)
Electrical Circuit (cir)	√	Automatic (Time dependent)