GB2453966A

GB2453966A - Measuring surface emissivity and temperature of a material using infrared imaging

Info

Publication number: GB2453966A
Application number: GB0720796A
Authority: GB
Inventors: Christopher Hunter Oxley; Gwynne Arthur Evans; Richard Henry Hopper
Original assignee: De Montfort University
Current assignee: De Montfort University
Priority date: 2007-10-23
Filing date: 2007-10-23
Publication date: 2009-04-29
Anticipated expiration: 2027-10-23
Also published as: GB2453966B; GB0720796D0

Abstract

A method of measuring the surface emissivity and consequently the temperature of a first material 2 that is substantially transparent to infrared radiation. The first material 2 is temporarily or permanently mounted on a surface of a second material 7 of known emissivity. The infrared radiation emitted from the first material 2 is then measured using infrared imaging, and then the surface emissivity of the first material 2 is calculated using the measured infrared radiation emission, a spreading factor and the surface emissivity of the second material. The method is particularly suitable for measuring the surface emissivity and temperature of thin semiconductor devices.

Description

TITLE

Method of Measuring Surface Emissivity

DESCRJPTION

Technical Field

The present invention relates to thermal mapping of materials and provides an improved method of measuring the surface emissivity of a material. The method is particularly suitable for measuring the surface emissivity of a semiconductor.

Background Art

Infrared (IR) imaging is a relatively simple and non-invasive method of measuring the temperature of an object. In IR imaging the infrared radiation emitted from a point of the surface of the object will be collected and measured by a microscope. As will be understood by those skilled in the art, for the purpose of infrared imaging infrared radiation may be considered to be any electromagnetic radiation with a wavelength greater than 2pm and less than 5j.tm. Once the infrared radiation has been collected and measured, this information will then be analysed to provide an estimate of the temperature of the surface of the material. By measuring the temperature of many points across the surface of an object it is possible to build up a temperature profile of the object. IR imaging is particularly useful in mapping the thermal profile of semiconductor electronic devices that are in use as it is a passive method and may provide a substantially real-time image of the thermal profile of a device.

In order to obtain an estimate of the temperature of a material using IR imaging it is necessary to know the emissivity of a surface of the material. The surface emissivity of a material is defined as the ratio of the energy radiated by the material to the energy that would be radiated by an ideal black body at the same temperature. Therefore, if an accurate value of the surface emissivity of an object and the energy it is radiating are known then the surface temperature of the object may be estimated with a reasonable degree of accuracy. Currently, the surface emissivit-y of a material is measured by heating an object formed from the material to a known temperature, measuring the JR radiation emitted by the object and comparing it to the JR radiation that would be emitted by an ideal black body at the same temperature.

The ability to accurately measuie the thermal profile of semiconductor devices is becoming increasingly important as accurate thermal mapping may provide validation of thermal software models and a more reliable prediction of the life expectancy of such devices. Unfortunately, the majority of semiconductor electronic devices are at least partially transparent to JR radiation. That is, if infrared radiation is directly incident upon a surface 50% or more of that radiation will be transmitted through the thickness of the device without being absorbed. This can lead to inaccuracies in measuring the emissivity and consequently the surface temperatures of devices when JR imaging is used. This is because the IR radiation detected as being emitted from the surface will be affected by internal reflections of the radiation and emissions from within the material.

The current method of overcoming these problems and measuring the thermal profile of such devices is to coat a front surface of the device with a high emissivity material that is not transparent to the wavelengths of JR radiation used in infrared imaging, such as carbon, prior to IR imaging. However, this can result in a loss of temperature resolution across the surface of the material as the high emissivity material will act to conduct and spread heat across the surface. Furthermore, coating functional devices with a high emissivity material is not a preferred method as it may affect the function of the devices and is therefore only suitable for examining test specimens.

Therefore, there is a need for a new method of JR imaging that allows the surface temperature of a material to be measured. Preferably the method will enable the surface temperature of thin semiconductor devices to be accurately and non-invasively measured. There is a particular need for such a method which does not rely upon coating the material with a high emissivity material.

It is known that in thin semiconductor devices the emissivity of the back surface of the device will have an effect on the temperature of the front surface measured by IR imaging. The magnitude of this effect is dependent upon the thickness of the device and the material upon which the back face is mounted. However, to date there has been no appreciation that this phenomenon could have practical value in the measurement or evaluation of the surface emissivity of the IR-transparent material itself.

Summary of Invention

The present invention provides a method of measuring the surface emissivity of a first material that is at least partially transparent to infrared radiation, comprising the steps of: measuring, using infrared imaging, the infrared radiation emitted from the first material when that first material is mounted on a surface of a second material of known surface emissivity; and calculating the surface emissivity of the first material using the measured infrared radiation emission, a spreading factor and the surface emissivity of the second material.

In respect of the present invention, a first material may be considered to be at least partially transparent to infrared radiation if, when infrared radiation of the wavelengths used in infrared imaging is directly incident upon the surface of the first material that is being analysed, 50% or more of that radiation is transmitted through the thickness of the material without being absorbed.

The infrared radiation emitted from the first material may be measured using conventional JR imaging means. Therefore, as will be appreciated by a person skilled in the art, it is preferable that any first material examined using the method of the present invention has substantially planar and parallel front and back surfaces.

According to an aspect of the present invention, when the infrared radiation emitted from the surface of the first material is measured using conventional means a single point on the surface will be analysed. The surface emissivity of that point may be calculated on the basis of the measured infrared radiation emission, a spreading factor and the surface emissivity of the second material using formulae (1) and (2) shown below. These formulae describe single path transmission and geometrical spreading of radiation within the material: (1) e1= em l+e2j2 2 F' -tfD2exp[_a(x2+y2+D2)o] () 2 2 22 [x +y +D] wherein: e1 is the corrected emissivily of the first material; em is the measured emissivity of the first material as calculated by conventional means; a is the infrared attenuation factor of the first material (rn'); D is the thickness of the thickness of the sample of the first material (m); e2 is the emissivity of the second material; F,2' is a spreading factor of the first material; x is a linear distance from the source of the radiation to the point on the surface being analysed in a first direction perpendicular to the thickness of the material (m); and y is a linear distance from the source of the radiation to the point on the surface being analysed in a second direction perpendicular to the thickness of the material and the first direction. (m) These formulae may be used to calculate the surface emissivity of any sample of a first material that is mounted on a surface of a second material. However, the formulae are particularly useful when the first material is at least partially transparent to infrared radiation in accordance with the present invention. The formulae may be especially useful when the first material is substantially transparent to infrared radiation.

In respect of the present invention, a first material may be considered to be at least substantially transparent to infrared radiation if, when infrared radiation of the wavelengths used in infrared imaging is directly incident upon the surface of the first material that is being analysed, 75% or more of that radiation is transmitted through the thickness of the material without being absorbed.

Formula (2) may be simplified using mathematical approximations. Generally, when the emissivity of a point on the surface of the first material is being measured using the method of the present invention the first material may be approximated to a single dimension and the x and y dimensions may be disregarded. This approximation is particularly valid when the sample of the first material has substantially planar and parallel front and back faces. According to this approximation the formula for the spreading factor of the first material simplifies to: F = exp(-aD) Therefore the formula for the corrected emissivity of the first material becomes formula (3): (3) e1= Cm I + e2 exp(-aD) As will be appreciated the formula for the corrected emissivity of the first material may be further simplified in the situations where exp(-cxD) is substantially equal to I. Situations where this may occur include when the first material is substantially transparent to infrared radiation and thus the relevant attenuation factor of the material is very small and/or when the sample of the first material is very thin. In such situations the corrected emissivity may be calculated using the further simplified formula (4): (4) e1= em I + e2 In the extreme condition where no infra-red radiation is measured as being emitted by the point on the surface of the first material (i.e. when em = 0) it follows from formula (1) that the corrected emissiv ity of the first material will also be zero.

Furthermore, in the alternative extreme condition wherein the first material is mounted on a material with an emissivity of zero (e2 0) then, it follows from formulae (I) that the measured emissivity of the first material will simply be equal to the corrected emissivity of the first material.

The accuracy of the emissivity calculated using either of the approximated formulae (3) or (4) is dependent upon how accurately the approximations mirror the reality of the material being examined. Therefore, it is preferable that the formulae are used to estimate the surface emissivity of thin sections of materials that are substantially transparent to infrared radiation and thus absorb very little energy during the JR imaging measurement. Therefore, the approximated formulae are most suitable for estimating the surface emissivity of very thin samples of the first material. Preferably the sample will have a thickness of less than 1mm, even more preferably the sample will have a thickness of less than 0.5mm.

Formula (3) and more preferably formula (4) are particularly suitable for estimating the surface emissivity of thin semiconductor devices. As will be appreciated by the person skilled in the art, the formulae are particularly suitable for estimating the surface emissivity of thin silicon (Si), Gallium Arsenide (GaAs) and Gallium Nitride (GaN) devices. Due to the very high infrared transparency of GaN, formula (4) is most suitable for estimating the surface emissivity of thin GaN based semiconductor devices.

Once the surface emissivity of a point on the surface of a device has been measured using the method of the present invention the surface temperature of that point may be calculated in a conventional manner using the known relationship according to formula (5): (5) lTm) where: T3 is the surface temperature of the point on the surface; and Tm is the measured temperature of the device.

A profile of the emissivity or of the temperature of a surface of a device may be built up by analysing a series of points across the surface of the device.

The method of the present invention requires the first material to be mounted on a surface of a second material of known emissivity. The first material may be either permanently mounted on the second material or temporarily placed in contact with a surface of the second material. The first material may form part of a device wherein it is already mounted on a surface of the second material. Alternatively, the first material may be mounted on the surface of the second material as part of the method of the present invention in order to measure the surface emissivity of the first material. For example, semiconductor devices may be simply placed on a black surface. In order to ensure the accuracy of the method of the present invention it is preferable that a back surface of the first material is in direct contact with the surface of the second material and there is no gap (for example no air gap) between the two materials at the point being examined. Therefore it is preferable that both the back surface of the first material and the surface of the second material are substantially planar and are in direct contact over the whole area being examined using the method of the present invention.

It is to be noted that formulae (1), (2), (3) and (4) do not take into account refraction within the first material. However, refraction within the first material may be neglected if its height is sufficiently small when compared with the distance between the surface of the first material and the objective lens of the microscope. For example, if a first material of height 200jtm is used and the distance between the surface of the first material and the objective lens is 20mm, which is a difference of two orders of magnitude, refraction from within the material may be ignored.

Drawings Figure 1 is a schematic cross-section through a semiconductor structure mounted on a back surface of known emissivity; Figure 2 is a graph showing the variations in surface temperature across a cross-section of the semiconductor structure of Figure 1 when in use as measured using standard techniques and as measured using the method of the present invention; and Figure 3 is a graph showing the variations in surface emissivity across a cross-section of the semiconductor device according to Figure 1 as measured using standard techniques and as measured using the method of the present invention.

A cross-section of a semiconductor structure 1 is shown in Figure 1. The semiconductor structure I is typical of a conventional semiconductor device. It is formed of a thin planar section 2 of a single semiconductor material that is substantially transparent to infrared radiation, for example Si, GaAs or GaN. The planar section 2 is approximately 2O0im in height. Two surface portions 3 of the semiconductor device I are coated with a thin layer of metal 3. There is a gap 4 formed between the metal layers 3 that exposes a top surface 5 of the semiconductor material. A rear surface 6 of the semiconductor material is mounted on a back surface 7 of known surface emissivity e2.

An electric current was passed through the semiconductor structure 1 and the surface emissivity and temperature of the structure were measured at a plurality of points across the first surface 5 of the structure using a conventional!R imaging method according to the prior art. The first surface 5 was not coated with a high emissivity material as this would have lead to heat spreading across the surface 5 from the metal layers 3 and may have affected the electrical performance of the structure 1. The results were plotted to give a temperature and surface emissivity profile across a top surface of the structure 1 including the first surface 5 of the semiconductor material and the metal layers 3. These profiles are shown as dotted lines in Figure 2 and Figure 3 respectively.

The temperature and surface emissivity profile were then measured again using the method of the present invention and formula (3), set out above. The assumption was made that the back surface 7 approximated to a black body and e2 was equal to 0.9.

The resulting temperature and surface emissivity profiles are shown as solid lines in Figure 2 and Figure 3 respectively.

As can be seen in Figure 2, when the surface temperature of the semiconductor structure I is measured using a conventional IR method the temperature of the first surface 5 appears to be cooler than that of the metal layers 3. This is contrary to expectations as the majority of the ohmic heating due to the electric current passing through the structure 1 would be expected to occur in the semiconductor. In contrast, the temperature profile resulting from the method of the present invention appears to be more accurate as it clearly shows that the temperature of the first surface 5 is higher than the temperature of the metal layers 3.

Claims

Claims 1. A method of measuring the surface emissivity of a first material that is at least partially transparent to infrared radiation, comprising the steps of: measuring, using infrared imaging, the infrared radiation emitted from the first material when that first material is mounted on a surface of a second material of known surface emissivity; calculating the surface emissivity of the first material using the measured infrared radiation emission, a spreading factor and the surface emissivity of the second material.
2. A method according to claim I wherein, the first material is substantially transparent to infrared radiation.
3. A method according to claim 1 or claim 2, wherein the surface emissivity of a point on the surface of the first material is calculated using the formulae: (1) e,= em l+e2F12 (2) F = JJD exp[-a(x2 +y2 + D2)°51d [x2 +y2+D2}2 wherein: e1 is the corrected emissivity of the first material; em is the measured emissivity of the first material as calculated by conventional means; a is the attenuation factor of the first material (m'); D is the thickness of the thickness of the sample of the first material (m); e2 is the emissivity of the second material; F12' is a spreading factor of the first material; x is a linear distance from the source of the radiation to the point on the surface being analysed in a first direction perpendicular to the thickness of the material (in); and y is a linear distance from the source of the radiation to the point on the surface being analysed in a second direction perpendicular to the thickness of the material and the first direction. (m)
4. A method according to claim I or claim 2, wherein the surface emissivity of a point on the surface of the first material is calculated using the approximated formula: (3) e1=-em I + e2 exp(-aD) wherein: is the corrected emissivity of the first material; em is the measured emissivity of the first material as calculated by conventional means; a is the attenuation factor of the first material (md); D is the thickness of the thickness of the sample of the first material (m); and e2 is the emissivity of the second material.
5. A method according to claim 1 or claim 2, wherein the first material is very thin and/or an infra-red attenuation factor (a) of the first material is very small and the surface emissivity of a point on the surface of the first material is calculated using the approximated formula: (4) e1= em I+e2 wherein: El is the corrected emissivity of the first material; em is the measured emissivity of the first material as calculated by conventional means; and e2 is the emissivity of the second material.
6. A method according to any preceding claim wherein, the thickness of the first material is less than or equal to 1mm.
7. A method according to claim 6 wherein, the thickness of the first material is less than or equal to 500g.tm.
8. A method according to any preceding claim, wherein the first material is a semiconductor.
9. A method according to claim 5, wherein the first material is silicon, gallium arsenide or gallium nitride.
10. A method according to any preceding claim, wherein during the infrared imaging measuring step, the first material is temporarily mounted on the surface of the second material.
ii. A method according to any of claims I to 9, wherein the first material is substantially permanently mounted on the surface of the second material.
12. A method of determining a surface emissivity profile across a first material by measuring the surface emissivity of the first material at a plurality points on the surface of the first material using a method according to any preceding claim and thereby forming a profile.
13. A method of measuring the surface temperature of a first material that is substantially transparent to infrared radiation comprising the steps of: measuring the surface emissivity of the first material using a method according to any preceding claim; and -13 -calculating the temperature of the first material using the equation: I 4, ("J (e',, i) , where: e1 is the surface emissivity of the first material; em is the measured emissivity of the first material calculated in a conventional maimer based upon the measured infrared radiation emission from the first material; 7' is the surface temperature of the point on the surface; and Tm is the measured emissivity of the first material calculated in a conventional manner based upon the measured infrared radiation emission from the first material;
14. A method of determining a temperature profile across a first material that is substantially transparent to infrared radiation by measuring the temperature of the first material at a plurality of points on the surface of the first material using the method of claim 13 and thereby forming a profile.