**For a more complete discussion of this material, please see:**

Jason Lewis, PhD Dissertaion: "Far-Infrared
and Sub-Millimeter Microbolometer Detectors," The University of
Texas at Austin, 1994.

Abstracted versions of some of our related publications and talks available here on our Web site:

- Dean P. Neikirk, slides used in the talk "Micro-sensors
- what happens when you make "classical" devices "small":
integrated bolometric radiation detectors" (big file, about 700K)

- D. P. Neikirk, D. B. Rutledge, and W. Lam, "Far-Infrared
Microbolometer Detectors,"
*Int. J. Infrared Millimeter Waves*, vol. 5, pp. 245-277, 1984.

- S.M.Wentworth, R.L. Rogers, J.G. Heston, and D.P. Neikirk, "Twin-slot multi-layer
substrate-supported antennas and detectors for terahertz imaging,"
First International Symposium on Space Terahertz Technology, University
of Michigan, Ann Arbor, Mich., March 5-6, 1990, pp. 201-213.

- J. M. Lewis, D. P. Neikirk, and S. M. Wentworth, "Low
growth temperature GaAs microbolometers,"
*15th International Conference on Infrared and Millimeter Waves*, R. J. Temkin ed., Dec. 10-14, 1990, pp. 398-400.

- S. M. Wentworth and D. P. Neikirk, "A
Transition Edge Microbolometer (TREMBOL) for Far-Infrared Detection,"
*SPIE Conference on Superconductivity Applications for Infrared and Microwave Devices*, Orlando, FL, 1990.

One key figure of merit to consider when designing and optimizing microbolometer performance is responsivity (

The signal voltage for a microbolometer can be related to the incident power by using a simple circuit expression for responsivity, given by

(2.14)

where

According to equation 2.14, the responsivity can be optimized by maximizing the product of

A microbolometer will experience heating due to the bias current as well as from incident power. By far, most of the power will come from the bias source across the detector. The maximum allowable temperature rise above ambient (

(2.15)

due to the maximum allowable dc bias power (

(2.16)

where Z

(2.17)

Since the power dissipated in the detector is mostly due to joule heating from the bias source,

(2.18)

The maximum allowable detector bias current (

(2.19)

The second term in equation 2.14 can be broken down into the following physical constants

(2.20)

where

(2.21)

(2.22)

and

(2.23)

For a conventional bolometer,

Substituting equations 2.19 and 2.20 into equation 2.14 reveals a new expression which relates to the physical constants to microbolometer responsivity for the thermally limited case.

(2.24)

The bracketed terms are related, and cannot be varied independently. For convention bolometers, this relation can be reduced to

(2.25)

The relations in equations 2.24 and 2.25 can be useful in evaluating the potential detector materials and configurations. The square root dependence on

The relations above also indicate that an improvement in responsivity would result from an increase in the thermal impedance of the detectors. It has been shown experimentally that preventing the detector from contacting the substrate by use of air-bridges increases the responsivity of a microbolometer by increasing the thermal impedance of the detector [Neikirk, 1984 #1]. This method was reported to have increased responsivity by a factor of five, and the sensitivity was improved by a factor of four. Choosing detector materials to minimize thermal conductivity would also serve to increase thermal impedances. This criterion would tend to favor semiconductor or oxide materials over metallic detector materials. Choosing a high resistance detector may also be an easy way to increase responsivity. Even though this term has a square root dependence for the thermally limited case, it would be easy to find a detector material with a resistivity of many orders of magnitude higher than bismuth. For conventional microbolometers, the detector resistance is fixed in order to be impedance matched to the antenna. For composite structures, this restriction does not apply. The strong linear dependence of

Another mechanism which may limit responsivity by limiting the driving current through the detector may be device failure due to electromigration. The current density may also be limited in the case of superconducting microbolometers. In this case, it is assumed that the maximum allowable current is determined by the maximum allowable current density through the detector element, rather than a maximum allowable temperature rise. Although electromigration damage is generally dependent on temperature in most systems, this analysis will assume that the increase in temperature due to the bias current will be small and thus have a negligible effect on the maximum current density.

Equation 2.26 shows an expression for responsivity that is algebraically identical to equation 2.14.

(2.26)

The maximum allowable current (

(2.27)

where

(2.28)

where

(2.29)

For the case of the air-bridge bolometer [Neikirk, 1984 #1], the thermal impedance will be independent of the detector length (see section 2.1.2). For a given detector material, the length of the airbridge will determine the maximum responsivity of the device.

For moderately long substrate supported microbolometers, the thermal impedance is primarily determined by heat flow directly into the substrate. An empirical approximation for this case was presented in section 2.1.3, and is shown in equation 2.11. By using equation 2.11 to approximate

(2.30)

This equation will over estimate the responsivity for short detector lengths due to the fringe mechanism of heat loss described in section 2.1.4.

These relations show that for bolometers in which bias current is limited by current density, there is a linear dependence on

Experiments have shown that typical bismuth microbolometers with the following properties can be operated reliably for long periods of time at 2 milli-amps. The devices become unreliable at around 3 to 5 milli-amps.

length |
4 um |

width | 2 um |

thickness | 1500 Å |

resistance | ~ 100 [Omega] |

responsivity | ~ 20 volts/watt |

a | ~ 0.003 K^{-1} |

Table 2.4 Operating parameters for a typical bismuth microbolometer

For the dimensions listed in table 2.1, the current density at 0.003
amps would be 10^{6} amps/cm^{2}, which suggests the possibility
that failure may be due to electromigration damage.

The temperature rise due to the bias current can be approximated by using

(2.31)

This estimates a 20 C temperature rise above ambient (~300 K) when biased
at about 0.003 amps. This temperature of ~45 C is much lower that the melting
point of bismuth (544 C), which makes it unlikely that failure is due to
melting of the bismuth element. Failure due to oxidation is also unlikely
if these temperatures are accurate.

Though the observations shown here are not entirely conclusive, they do
suggest that electromigration is the most likely mechanism for limiting
current in bismuth microbolometers.

**2.2.5 Electric Field Breakdown**

Composite microbolometers have an extra vulnerability that does not exist
with conventional microbolometers, in that voltage differences between the
heater and the detector element will result in high electric fields within
the dielectric that separates the two elements. The likelihood of accidentally
stressing the dielectric may be reduced by grounding one lead of the antenna
to one of the detector leads. The dielectric will also experience electric
fields due to the detector bias voltage. The electric circuit for electric
fields induced by the bias voltage is illustrated in figure 2.9. The highest
fields will be at **E _{1}**, where they will be roughly

(2.32)

where

Figure 2.9 Electrical circuit for a composite microbolometer
showing the distribution of

electric field within the dielectric.

If electric field-induced breakdown is the limiting factor, then the
maximum responsivity can be given as

(2.33)

where **V _{BD}** is the breakdown voltage of the device.

This behavior would be more likely for high resistance detectors where high bias voltages (> 10 V) could be used without dissipating much power. For a dielectric thickness of 1000 Å, only 10 volts would be needed to produce an electric field of 10

Another issue which affects microbolometer operation and can limit responsivity is stability under constant bias conditions. Using a higher bias across the detector will generally increase responsivity and thus will result in a larger signal. A linear relationship between bias current and responsivity is described in equation 2.14. and implies that it will be linear as long as the other parameters (

It is important to remember that there are two components of power that are dissipated in the detector. The incident radiation received from the antenna is one component dissipated in the detector, and will be considered an independent variable for this analysis. The other component is power dissipated from the bias current, which will normally be much higher than the incident power. The key point is that incident power (

Table 2.5 shows the conditions which result in positive or negative feedback.

Bias type |
Temp. Coeff. of Resistance |
Type of Feedback |

constant current | a > 0 | positive |

constant current | a < 0 | negative |

constant voltage | a > 0 | negative |

constant voltage | a < 0 | positive |

For example, under constant current bias and a positive coefficient of resistance (

Experience has shown that some operating conditions can result in unstable positive feedback where runaway current destroys the device. Instabilities even in large area (100 um x 1000 um) superconducting Bi-Sr-Ca-Cu-O bolometers when operated at high currents have been reported [Lewis, 1989 #5], although these devices were large enough to dissipate a 10 volt bias without destroying themselves. Superconducting devices could be voltage biased in order to avoid positive feedback; however, destructively high currents could occur if the device temperature drifts too close to the superconducting state. In these cases, the maximum bias conditions are lower than what would be predicted when positive feedback effects are ignored. In order to better understand and predict the maximum stable bias, an analysis is given here.

The following definitions will be used for this discussion:

r = small signal responsivity =

I

Z = Thermal Impedance

[Delta]V

P

[Delta]P

From the above definitions,

The incremental increase in power dissipated in the detector (joule heating) caused by the increased bias voltage can be expressed as:

This increase in power in the detector then causes another incremental increase in detector voltage that can be expressed as:

Further iterations of the incremental increases in bias voltage due to feedback can be expressed as:

[Delta]V

The total increase in detector voltage due to feedback can then be expressed as:

(2.38)

By using the following relation:

for (A < 1) (2.39)

the total feedback voltage can then be expressed as

(2.40)

From this relation it is apparent that the following must be true for stable operation:

r . I

Another form of this relation looks like:

(2.42)

These results suggests that high resistance detectors would be more stable
than low resistance detectors. This criterion should be considered when
modeling low resistance detectors, such as superconducting microbolometers.
However, if high resistance detectors are integrated with a composite microbolometer
structure, operation may be limited by electric field breakdown in the dielectric
between the heater and the detector.

**References**

1. D. P. Neikirk, W. W. Lam, and D. B. Rutledge, "Far-Infrared Microbolometer
Detectors," International Journal of Infrared and Millimeter Waves,
**5**, 245 - 278 (3 1984).

2. S. M. Wentworth, "Far-Infrared Microbolometer Detectors", Doctoral
Dissertation, University of Texas at Austin, 1990

3. V. M. Abrosimov, B. N. Ergorov, and M. A. Krykin, "Size Effect of
Kinectic Coefficients in Poly Crystalline Bismuth Films," Sov. Phys.
JETP, **37**, 113-116 (1 1973).

4. D. P. Neikirk, and D. B. Rutledge, "Air-bridge Microbolometer for
Far-infrared Detection," Appl. Phys. Lett., **44**, 153-155 (15
January 1984).

5. J. M. Lewis, "Optical Detectors Based on Superconducting Bi-Sr-Ca-Cu-Oxide
Thin Films", Undergraduate Thesis, Massachusetts Institute of Technology,
1989