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Calculated laser damage thresholds of Ge:Hg photoconductive detectors
/nfrard Phjsm. Vol 18. pp. 3lM25 gr Perganon Press Ltd 1978 Printed in Greet Britam
CALCULATED LASER DAMAGE THRESHOLDS Ge:Hg PHOTOCONDUCTIVE DETECTORS
OF
M. KRUER, L. ESTEROWITZ,F. BARTOLIand R. ALLEN Naval Research Laboratory, Washington DC 20375, U.S.A. (Receiued 10 February 1978)
Abstract-Thermal damage in laser irradiated mercury-doped germanium detectors is investigated. Threshold levels of 10.6 pm laser radiation corresponding to onset of irreversible damage in Ge:Hg crystals are measured. The dependence of the damage thresholds on irradiaton time agrees favorably with thermal model predictions. Thresholds for both onset of irreversible damage and complete loss of photoresponse for Ge:Hg detectors are then calculated as a function of irradiation time, using parameters obtained from experimental results on laser damage in Ge:Hg crystals.
1. INTRODUCTION The increasing use of lasers in electro-optical systems has generated interest in the susceptibility of infrared detectors to laser damage. Extrinsic germanium detectors,(‘) because of their spectral responsivity and response times, are often used to measure radiation from CO2 lasers. In this paper we investigate damage thresholds for mercurydoped germanium (Ge:Hg) photoconductive detectors exposed to 10.6~ laser radiation. In order to determine the unknown parameters which are required for, the calculation of damage thresholds, laser damage in Ge:Hg crystals is investigated experimentally and theoretically. Two thermal models for laser damage in Ge:Hg crystals and detectors are discussed in Section 2. Measured thresholds for onset of damage in ambient temperature crystals are reported in Section 3 as a function of irradiation time for 10.6 m laser radiation. These experimental data are fitted by thermal models yielding parameter values characterizing the irradiated materials. In Section 4 Ge:Hg photoconductors are assumed to have the same mode of thermal damage as the crystalline samples, and thresholds for onset of laser damage for typical Ge:Hg detectors are calculated. These thresholds are compared to those of other detectors for 10.6pm radiation. Qnset of laser damage in photoconductive detectors corresponds to only a small permanent reduction in photoresponse. Total loss of photoresponse in photoconductors is expected only’ if no active detector material remains to provide an electrical path between the ,lea& Thresholds for complete loss of photoresponsc in Ge:Hg photoconductors are calculated in Section 5 and are much larger than the corresponding thresholds of most photovoltaic and intrinsic photoconductive detectors. For the reader’s convenience, Ge:Hg detectors are compared in Section 4 with other common electro-optical components,whiah have high damage thresholds, such as metal mirrors. 2. THERMAL
ANALYSIS
Irreversible thermal damage in Ge:Hg materials involves vaporization and melting. Thresholds for thermal damage in detectors and detector materials depend on the temperature increase AT required for damage, the irradiation time, beam diameter, optical and thermal properties of materials used in the detector construction, and the quality of thermal coupling to the heat sink. Since these parameters can vary from one sample to another, thermal modelling of laser damage is required to extrapolate experimental results to arbitrary sample configurations and irradiation conditions. Ge:Hg material is quite susceptible to laser damage since a large. part OFthe inoident radiation is absorbed within a small volume. For irradiation times su@cietily short that thermal conduction is insignificant, the irradiated sample is heated down to some 315
M. KRUER et al.
316
PO= Constant
I03 10-e
I 10-7
I 10-6
I
I
10-3 7,
10-d
I 10-3
I 10-2
I IO“
set
Fig. 1. Calculated power density threshold P,, for onset of melting in laser irradiated Ge:Hg material as a function of laser pulse duration T. This figure illustrates that P,, varies as 7-l at short times and is independent of T at long times.
depth 6. In general 6 depends on the optical absorption coefficient a and the ambipolar diffusion distance.‘2) However, for the 10.6 pm damage thresholds studied here, the effects of ambipolar diffision could be neglected, and 6 is simply equal to the absorption depth. For long irradiation times, thermal conduction becomes important. This causes the damage threshold to depend strongly ‘on irradiation time. In this paper two thermal models are employed for laser damage in Ge:Hg. The tirst model considers a semi-infinite solid irradiated by a Gaussian laser beam of arbitrary diameter. This thermal model employs a closed-form solution to the thermal diffusion equation and is described in Appendix A. The second model employs a numerical calculation baaed on a finite-element technique and is discussed in Appendix B. The numerical model treats arbitrary beam profiles and composite sample configurations, and can be used when the more convenient closed-form model does not apply. Both models give expressions for the energy density E,, required to damage the sample as a function of irradiation time t. The power density threshold PO is obtained from the relation PO = E&. The thresholds predicted by the two models have the same qualitative dependence on r. For the range of parameters considered in this work, both models were found to yield the same results for T < lo-* sec. Therefore, the more convenient closed-form model was used for ‘c < 10m4 set, while the numerical model was employed for r > lo-‘sec. In the short time limit where the effects of thermal conduction are negligible, the absorbed energy remains within the depth S. E. is independent of r in this limit and depends linearly on 6 and A1: P,, varies as r - ‘. This condition exists for time t 4 d2/k, where k is the thermal diffusivity of Ge:Hg In the long time limit, heat is conducted away from the absorbing region at the same rate as it is deposited by the laser and the sample surface reaches a steady-state temperature distribution. In this limit PO approaches a constant and E. approaches a linear variation with T. These two time regimes are illustrated for Ge:Hg in Fig.‘l, which shows the power density of 10.6 pm radiation required to heat the sample surface to the melting temperature. These results were calculated using the material parameters listed in Table 1. Laser beam and sample dimensions are described in Section 3. 3. DAMAGE IN Ge:Hg MATERIAL Mercury-doped germanium crystals were soldered onto large ambient temperature copper blocks, as illustrated in Fig. 2. The samples were also retained by mechanical clamps to prevent sample movement if solder melted during the tests. The samples were approximately 3 mm long and the irradiated surfaces (0.6 x 0.6 mm) were chemically etched. The physical properties of these samples are expected to be the same
317
Calculated laser damage thresholds of Ge:Hg Table I. Effective material properties for Ge:Hg detectors Germanium
Property Density, P Wd Specific heat, c (J/g. K) Thermal conductivity, K (W/cm. K) Melting temperature, 7, (K) Heat of fusion, H, (J/g) Vaporization temperature, K (K) Heat of vaporization, H,. (J/g) Reflectivity, R’ 6 (cm) Skin depth tn 10pm (cm)
5.33’*’ tI:y;; 1210 ‘.I’ 467 ‘.I’ 3107 ‘ll’ 3921 ‘“’ 0.37”’ 6.25 x 10-4”’ -
Copper ;;z: 3.8 1356 207 2839 4730 -
(” I” ‘@’ ‘I’ “’
1.3 x 1Gk)
(“)NEULIERGER, M.. Handbook of Elecrronic Materials, Vol. 5. Plenum Press. Washington (1971). (b)Ref. 5, pp. 2-28. lc)Ref. 5, pp. 4-106. Id’Determined empirically from melting threshold data. w Ref. 5, pp. 4-154. If)Ref. 5, pp. 4-229. Is)Ref. 5. pp. 4-223. orRef. 5, pp. 4-231. “’ MO=, A. J., Handbook of Electronic Materials, Vol. 1. Plenum Press, Washington (1971). ‘“Determined empirically from damage threshold data as discussed in the text. “‘Ref. 5. pp. 6-134.
as for crystals used in operating Ge:Hg photoconductors. The samples were irradiated with 10.6 pm laser pulses whose durations, r, varied from 0.15 psec to several seconds. The laser e -’ beam radius R was 0.3 mm. The experimental apparatus and procedure is discussed elsewherej3’ Uncertainty in the experimental damage thresholds is estimated at 35%. The nature of damage first observed in these experiments on Ge:Hg’ depends on the irradiation time. For long irradiation times (7 > 1OO~sec) the first sigh of damage was due to melting. Small craters could be seen microscopically, indicating that the irradiated material had melted and resolidified. If the laser power density is increased, so that the sample reaches the vaporization temperature, plasma formation is observed. The vaporization threshold is found to be several times larger than the melting threshold. For short irradiation times (7 < 100 psec), a visual determination of the melting threshold is more difficult. For this range of times we report only the vaporization threshold which is characterized by plasma formation and visible surface damage. Threshold values of PO for melting in Ge:Hg are plotted in Fig. 3 using triangles. Using published values of material parameters given in Table 1 and the numerical model (Appendix B), P,, was calculated as a function of irradiation time. The calculated
Fig 2. Illustration of the Ge:Hg material and heat sink.
318
M. KRUERet al. IO9
106
IO'
“E
P
106
_
a”
I05 IO4 I03 10-u
lo-’
10-J
lo-’
10-4
r,
IO-J
10-z
lo-’
I
S6C
Fig. 3. PO for onset of damage in Ge:Hg material as a function of T. Triangles: experimental thresholds for melting. Squares: thresholds for vaporization.
results are shown by Curve A in Fig. 3. At long times, the melting thresholds are determined primarily by the rate at which heat can flow into the copper heat sink. The thermal conductance per unit area of the solder interface was assumed to be approximately 200 W/cm2. K. (4) In the calculation the thermal conductivity of germanium was assumed to have a constant value. Although it changes as a function of temperature, an ‘effective value’ was found by using it as an adjustable parameter in the fit. A value of 0.2 W/cm *K was obtained in this way. This corresponds to the thermal conductivity of germanium at an intermediate temperature (‘v 800 K)(s) between room temperature and the melting point. As shown in Fig. 3,’ the calculated Curve A agrees well with the experimental melting thresholds. Experimental vaporization thresholds are shown in Fig. 3 using squares. At short times PO varies’linearly with 6 2 a-l. The value of a is not well known for the high temperatures,encountered in the damage experiment. At 10 K, a has a value of about 4,cm-‘.(6) As germanium is heated above room temperature, free carrier absorption increases exponentially, giving rise to the familiar thermal runaway process!‘) Since 6 was assumed to be constant in the thermal analyses, an ‘effective value’ for the parameter was determined empirically. Using published values of Ge:Hg material parameters (see Table I), the vaporization thresholds were calculated employing the closed-form model of Appendix A for T < 10m4 sec. For r > 10e4 set the numerical model was used. At .threshold the surface temperature was set equal to the vaporization temperature. It was estimated that the depth of material melted is approximately 6, and the depth vaporized approximately S/4. The calculated vaporization thresholds, shown as Curve B in Fig. 3, are in good with experimental data. The ‘empirically determined value of agreement 6 = 6.2 x 10e4cm corresponds to an absorption coefficient of 16OOcm-‘, which is much. larger than the room temperature absorption coefficient. This is attributed to the thermal runaway process. The minimum observable damage in Ge:Hg corresponds to vaporization at short times and melting at long times. To obtain a single curve indicating minimum observable damage, a dashed curve has been interpolated between’ Curves A and B in Fig. 3. 4. ONSET The
OF
DAMAGE
IN DETECTORS
onset of material damage in Ge:Hg photoconductive detectors will involve the same mechanisms discussed in the preceeding section on Ge :Hg materials. At this threshold only slight degradation of the detector photoresponse is expected since the fraction of the total detector material damaged is very small. .The detector thresholds are expected to be slightly larger than the thresholds of ambient temperature materials given in
Calculated laser damage thresholds of Ge:Hg
r,
319
see
Fig. 4. Comparison of thresholds for onst of damage in detectors used for radiation in the 8-14 pm spectral window.
Fig 3 since detectors usually operate near 10 K. Detectors considered here have a structure similar to that shown in Fig. 2. A 0.6 x 0.6 x 3 mm Ge:Hg crystal is soldered onto a 10K copper heat sink which serves as one of the leads. The other lead is placed on the opposite face of the crystal. The detector is fairly thick (- 3 mm) because its optical absorption coefficient is relatively low (5 4 cm-‘). Thresholds for onset of material damage in Ge:Hg photoconductors were calculated using the same approach as for Ge:Hg materials (Section 3). The thresholds calculated for detectors irradiated by a ~Gaussian laser beam (R = 0.3 mm) are presented in Fig. 4. These thresholds have a time dependence similar to those given in Fig. 3 for ambient temperature materials. It is interesting to compare the thresholds for onset of damage in Ge:Hg photoconductors to those of other detectors commonly used in the g-14 pm spectral range. Thresholds for onset of damage in HgCdTe photoconductors and photodiodes’s’ and TGS pyroelectric detectors(3) are also shown in Fig 4. The thresholds of the photovoltaic and phot~onductive HgCdTe detectors are the same at short times, but at long times the photovoltaic detector becomes less susceptible to thermal damage because of more efficient radial heat conduction. The TGS detector has the lowest threshold because of its inferior strength and thermal properties. The Ge:Hg detector has the highest threshold at all irradiation times because of its superior thermal and mechanical properties and because of the efficient heat sinking possible for this detector. 5. COMPLETE LOSS OF PHOTORESPONSE IN Ge:Hg DETECTORS Complete failure of photoconductive Ge:Hg detectors is expected only if all the Ge:Hg material is removed through vaporization or melting. This mode of damage is suggested by experiments(g) showing that lead salt photoconductors lose all photoresponse only if the active detector material is vaporixed and no longer provides an electrically conducting path between the leads. We now calculate the thresholds for this extreme type of laser induced damage in Ge:Hg detectors. For very short irradiation times detector failure is caused predominantly by vaporization. On the other hand, at long times Ge:Hg material is removed by &9ting. There is an intermediate time regime where both melting and vaporization are involved in the damage process. It is beyond the scope of this work to precisely calculate thresholds the damage process. It is beyond the scope of this work to calculate precisely thresholds for complete detector failwe when both mechanisms are involved. The approach used here is to calculate thresholds for vaporization at short times and for melting at long
320
M. KRUER et al.
104 -
I03 to-6
I 10-S
I 10-4
I 10-3 r*
Fig. 5. Calculated
I 10-2
I 10-I
I I
IO
see
PO vs T for complete loss of photoresponse in a Ge:Hg photoconductar. Curve A: vaporization. Curve B: melting.
values of
times, and then interpolate between these regions to describe the damage thresholds at intermediate times. The crossover from vaporization to melting was centered at 0.3 msec to coincide with results of laser drilling studies which addressed the problem.““*“) The errors involved in interpolating vs a more exact calculation is estimated to be less than a factor of 2 at intermediate irradiation times. The vaporization thresholds at short ‘times can be calculated from simple analytical expressions since thermal conduction has no appreciable effect on the damage thresholds for these times. The power density Pb required to vaporize a detector of thickness b is given by the approximate expression: p6 = (Ekr + %,)lr
(1)
where Ekr is given by Eqn 2A of Appendix A with 6 replaced by b. The energy density, Evap,is associated with the latent heats of vaporization and melting as given by Eqn 3A. This vaporization threshold calculated using Eqn 1 is shown in Fig. 5 by Curve A. Although Curve A is shown for irradiation times as long as 2 x 10m3 set, vaporization can be considered the dominant mechanism for complete detector failure only for r < 10e4 set (solid portion of Curve A). Between 10-4sec and 2 x 10e3 set (dashed portion) Curve A overestimates the actual detector thresholds. For long irradiation times, where the material is removed in a molten rather than vapor form, thermal.conduction becomes important and Eqn 1 is not appropriate. At these long times the power density required to melt the entire detector element was calculated using the numerical technique discussed in Appendix B, and is shown in Fig 5 (Curve B). For the sake of illustration Curve B is shown for irradiation times as low as 10m4sec. However, only for r > 10m3 set (solid portion) does Curve B represent detector thresholds. The dashed portion of the curve (10-4-10-3 set) underestimates the actual detector thresholds. The thresholds for intermediate times are estimated by interpolating between the solid portions of Curves A and B. The composite curve in Fig. 5 gives the threshold for total loss of photoresponse in Ge:Hg detector as a function of irradiation time. The thresholds have the same general dependence on irradiation time as ,the thresholds for onset of damage. The magnitude of PO is very high for all ~r~iat~n times ranging from greater than 10” W/cm’ at one psec to greater than 10“ W/cm’ in the long time limit. The power densities at short times are sufficiently great that several of the assumptions of the above thermal analysis may no longer be valid. For example, effects such as vapor shielding, nonlinear optical processes, etc. may be important and should have been
Calculated laser damage thresholdsof Ge:Hg
321
IO4
7%
SW
Fig. 6. Calculated POfor complete loss of photoresponsein Ge:Hg photoconductors for various values of R (i.e. e-’ beam radius).
considered. However, because the competing.nature of these processes can Eead to cancellation, these effects were not considered in our analysis. The thresholds for complete loss of photoresponse in Ge:Hg detectors are much larger than those of most infrared detectors. The thresholds at short times are much larger than those of intrinsic photoconductors because the Ge:Hg is about a thousand times thicker than the active material of a typical intrinsic photoconductor. At long times the thresholds for Ge:Hg are higher than for other detectors because of the highly efficient heat sinking possible for this detector and its superior thermal and mechanical properties. Detector damage thresholds at long irradiation times will depend strongly on detector size and laser beam diameter. Figure 6 shows the calculated thresholds, for complete loss of photoresponse in Ge:Hg detectors for different beam radii, R, and detector sizes. In each case it was assumed that the detector width was equal to the ee2 diameter (2R) of the laser beam, so that 90% of the incident Gaussian beam falls on the active detector area. The damage thresholds are independent of beam diameter at short times when thermal conduction has a negligible effect on the damage thresholds. In the long time limit, the damage thresholds depend strongly on beam diameter. As the detector size (and beam diameter) decrease, transverse heat conduction become increasingly important and the damage thresholds increase significantly. These results are useful for determining thresholds for an arbitrary detector size. It is worth noting that although the power density threshold is higher for smaller beams, the total laser power required is actually lower. For example, at T = 3 set a reduction of the beam radius by a factor of 10 raises the Rower density threshold P, by approximately a factor of 10. However, the beam area is reduced by a factor of 100, and the total laser power required (power = PO x beam area) is decreased by a factor of 10. This is reasonable since smaller detectors should require less total power to melt. 6. COMPARISON DETECTORS
OF DAMAGE THRESHOLDS OF Ge:Hg TO THOSE FOR METAL MIRRORS
The damage thresholds calculated for Ge:Hg detectors not only are high compared to other infrared detectors but, for some irradiation times, are higher than thresholds for metal laser mirrors. A comparison of laser damage in Ge:Hg detectors and metal mirrors is now considered in detail. Recently published damage thresholds of metal mirrorso2-15) are listed in Table 2 and are plotted as a function of t in Fig 7 @iangIe@. PO is found to vary as r-* INF18/4--S
M. KRIJERet a[.
322
Table 2. Damage thresholds of copper mirrors at 10.6pm e-* radius (cm)
T
(set) 2
x
10-9’12’
>2 x lo9 lo9 2 x lo* 2 x lo5
10-8”3’ 6 x 10-7’L4’ 1 (ISI
0.028 0.042
>4 10 120 2 x IO5
over several decades of irradiation time. This behavior has been observed previously by Saito et aLo6’ who applied a one-dimensional thermal model to describe the r-* dependence of P,,. Their one-dimensional model, which assumes a uniformly irradiated semi-infinite solid with an infinite absorption coefficient, is actually a special case of the closed-form model discussed in Section 2 and presented in detail in Appendix A. Saito’s model, however, is valid only at short irradiation times where radial heat conduction is negligible. In this section we calculate thresholds using Eqn 1A with R = 0.042 cm and the material parameters of copper given in Table 1. The optical absorptance A’ = 1 - R’ (where R’ is the reflectance) is treated as an adjustable parameter in fitting Eqn 1A to the short time data. The results are shown as Curve A in Fig. 7. The value of optical absorptance (A’ = 0.034) obtained from the fit at short times is within a factor of 2 of the intrinsic optical absorptance for copper.“‘) This implies that these mirrors are operating close to their intrinsic limit at short times. At long irradiation times (1 set) the experimental threshold is about an order of magnitude below the calculated Curve A. This implies that A’ is not constant for all irradiation times and that some additional thermal coupling phenomena must be operative at long times. Studies on other metalsoar also show increased thermal coupling at long irradiation times. The thresholds for onset of damage in Ge:Hg detectors are included in Fig 7 (Curve B) for comparison with the mirror thresholds. As shown in the figure, the thresholds for mirrors at very short times (r < lo-* set) are lower than those for the onset of detector damage. One might expect the opposite to be true, since the absorptance of mirror surfaces is appreciably lower than for Ge:Hg detectors. However, the region which absorbs the laser energy in copper is very thin compared to that of Ge:Hg. The skin depth in copper is only 1.3 x lo-’ pm, whereas 6 = 6.2 pm for Ge:Hg. For longer irradiation times, when thermal conduction becomes important, the absorption depth no longer has a dominant effect on the damage thresholds. As shown in Fig. 7, the mirrors have higher thresholds for onset of damage than do Ge:Hg detectors for 7 > 10-s sec. This results from the lower optical absorptance and better thermal conduction of the copper mirrors. From the above considerations, it can be seen that
I I I I I I 10-s IO-B 10-T to-6 10-J ,10-a IO-3
104
r.
1
I
10-Z 10-l
I
I
666
Fig. 7. Comparison of the calculated thresholds corresponding to (A) onset of damage in metal mirrors, (B) onset of damage in Ge:Hg photoconductors, and (C) complete loss of photoresponse in Ge:Hg detectors.
Calculated laser damage thresholds of Ge:Hg
323
the calculated thresholds for onset of damage in Ge:Hg detectors are consistent with experimental and theoretical thresholds for damage in metal mirrors. Calculated thresholds for complete detector failure are also shown in Fig. 7 (Curve C). These thresholds are found to be considerably higher than the mirror thresholds for short irradiation times. This is attributed to the large volume of material vaporized for Ge:Hg detectors compared to the extremely thin layer damaged for the mirror. Instead of comparing the thresholds for complete detector failure to those for onset of damage in mirrors, it is more appropriate to compare them to those for burnthrough in metal samples. Although there exist little experimental data for cutting laser resistant materials, such as copper or beryllium copper which are used for mirrors, the thresholds for cutting other metals(19) are similar td the corresponding thresholds calculated here for complete failure of a Ge:Hg detector. SUMMARY
Thermal damage in Ge:Hg materials due to 10.6 pm laser radiation was investigated. Damage thresholds were measured as a function of irradiation time and their time dependence was shown to agree with thermal model predictions. Thermal damage thresholds of Ge:Hg photoconductive detectors were then calculated using parameters obtained from the experimental results on Ge:Hg materials. The thresholds for both onset of damage and complete loss of photoresponse in Ge:Hg detectors are larger than the corresponding thresholds in intrinsic photoconductors and photodiodes because of the larger bulk volume and better thermal characteristics of the Ge,:Hg detector. These thresholds are consistent with thresholds for damage in metal mirrors. REFERENCES 1. For a review of the characteristics of extrinsic germanium detectors see LEVINSIEIN, H., Appl. Opt. 4,
639 (1965). 2. The effects of 6 on damage thresholds will be discussed more fully in a future publication. F., M. KRUER,L. ESTEROWITZ& R. ALLEN,J. Appl. Phys. 44, 3713 (1973). 3. BAR’IT)LI. Y. S.. R. W. POWELL, 4. The thermal diffusivity of polycrystalline indium is obtained from TOIJLOUKIAN, C. Y. Ho & P. G. KLEMENS, Thermophysicol Properties of Matter, Vol. 10, Fig. 28R. Plenum Press, New York (1970). 5. GRAY,D. E. (editor) American Institute of Physics Handbook, pp. 4-154. McGraw-Hill, New York (1972). R. A., G. R. KRONIN,W. G. HUTCHINSON & R. A. CHAPMAN,Texas Instruments Technical 6. REYNOLDS, Report AFAL-TR-66-336 (1966). Unpublished. 7. YOUNGP. A.. Appl. Opt. 10, 638 (1971). F., L. ES~ROWITZ,M. KRUER& R. ALLEN,J. Appl. Phys. 46.4519 (1975). 8. BARTOLI 9. KRUERM., L. ES’FEROWITZ, F. BARTOLI L R. ALLEN,J. Appl. Phys. 47, 2867 (1976). 10. WAGNER,R. E. J. Appl. Phys. 45, 4631 (1974). 11. CHUN,M. K. & K. Rosa, J. Appl. Phys. 41, 614 (1970). 12. STARK, E. E., JR & W. H. REICHELT, Loser Induced Damage in Optical Materials: 1974 (edited by Gm A. J. & A. H. GUENTHER). NBS Special Publication 414 (Dee 1974). The laser pulse duration is characterized in REICHELT, W. H. & E. E. STARKJR, Laser Induced Damage in Optical Materials (edited by GLAS$ A. J. & A. H. GUENTHER). NBS Special Publication 387 (Dec. 1973). 13. SINGER,S. Laser Focus 12, 32 (1976). 14. S~IL~AU,M. J. & V. WANG, Appl. Opt. 13, 1286 (1974). 15. SAITO,T. T., G. B. CHARLTON JL J. S. LooMls, Laser Induced Damage in Optical Materials (edited by Guss. A. J. & A. H. GUENTHER). NBS Special Publication 414 (Dee 1974). 16. SAITO,T. T., D. MILAM,P. BAKER& G. MURPHY,Laser Induced Damage in Optical Materials: 1975 (edited by GLAS$ A. J. & A. H. GUENTHER). NBS Special Publication 435 (July 1975). 17. WEITING,T. J. & J. T. !~CHRIEMPF, Report of NRL Progress, June 1972 (unpublished). 18. READY,J. F., E@cts of High Power Laser Radiation, chap. 3. Academic Press, New York (1971). 19. LOCKE,E. V., E. D. HOAG& R. A. HELLA,I.E.E.E. J. Quant.Electr. QE-8, 132 (1972). 20. TORVIK.P. J., A Numerical Procedure for Two-Dimensional Heating and Melring Calculations with Applications to Laser EApcrs, Tech. Rpt. AFIT TR 72-2. March 1972.
APPENDIX
A
Laser irradiated materials experience thermal damage if the material is heated beyond a qeshold temperature. The threshold temperature change is denoted by AT,,,. If heat does not difise to the edges of the material, the thresholds can be approximated using a thermal model in which tbc samplb is treated as a semi-infinite solid irradiated by a Gaussian beam of the form: p(r) = PO exp(-2$/R’). We have shown
324
M. KRUERet al.
previously that the energy density E,, required to heat the crystal as a function of irradiation be approximated by the expression’s):
time T can
where k is the thermal diffusivity and S the depth of material heated in the absence of thermal conduction. The r-independent value Edr is simply the energy required to heat the crystal surface by ATh in the absence of phase changes and thermal conduction. Its value is given by: EIT = AT,, p&/(1 - R’)
(24
where p is the density, c the specific heat, and R’ the reflectance. The r-independent term E,, is the energy density associated with the latent heat for phase changes and can be approximated by the relation(*):
(34 where b is the thickness of the material damaged and H is the latent heat per unit volume. APPENDIX
B
The numerical model is baaed on a finite element technique developed by Torvik.“” In this numerical model, the sample is divided into elements each having the form of a solid rectangle. The thermal and optical properties of the elements are contained in arrays which may be updated after each time increment. This approach allows one to treat sample inhomogeneities, composite layered structures, time dependent irradiation conditions and changes in material properties as a function of temperature on optical flux. The rate Qr,,,,.k, at which heat flows in the Z direction from element (i,j,k) into element (i,j,k + 1) is given approximately by the product of the thermal conductance and the temperature difference (T,,,, - ‘I;,l,t+i) between the centers of the two elements. If both elements have the same thermal conductivity, the thermal conductance is given simply by the product of the thermal conductivity K and the area of the interface A z,,,,.L, divided by the distance between the centers of the elements. Generally, the thermal conductivities of adjacent elements (K,,,,t and K,,,,r+ i) are not the same and the thermal conductance between the centers of two adjacent elements is:
Therefore &c,,J,k, is given by
QZ (1.1. k)
=
(T,.J,k
-
Ti.J.k+
lhi.J.k,
z
+
*I-‘. 1.J.k + 1
Similar expressions describe heat flow in the X and Y directions. Heat can also enter the element by absorption from external sources (e.g. optical radiation) or from internal reactions. An additional teim, Pi,,,k (watts), represents the rate at which heat is added externally or internally to the (ij,k) element. The net rate of energy flow into the (ij,k) element is determined by adding the heat flux entering the element and subtracting the flux leaving, using the equation:. AQ 4J.k
=
po,J.k
+
Qxu-1.j.k)
-
QXti.J.k)
+
Qr(i,i-1.k)
-
&u.j,.t, + &e.I.k-i)
If the i, j, k cell has a temperature less than a phase transformation Al;,,,, during the time increment, At is
- Qzo.,.~,.
temperature, the temperature
increase
A&k At
AT.1.i= -
c i.J.k M
i,J.k
where C,. jVk and MiSJ,k are the specific heat and mass, respectively, is performed repeatedly using a small time increment At until the time of interest. At each time step the temperature change AT.,,, T;.j.t The temperature after an irradiation. time T -_ = nAt (i.e. n time Tr.J.k -- T,er + i *=
of the (i,j,k) element. This heat balance sum of the time increments equals the is added to the previous temperature intervals) is
AT,,,,&?) L
where A4.J.k (q) is the temperature change calculated for the q’th time interval. The temperature of each element increases until it reaches the phase transformation temperature. Starting with the first increment (q = m), in which the temperature is above the melting temperature T,, Tf.J,k is held fixed at T, and the energy addition is used to supply the latent heat. The latent heat which must be added in order to e&t a change of phase of the (i,j,k) element is JL,,,,~ Mr,J,k where I, is the latent heat per unit mass. This quantity is computed for each element of the detector and stored as an array H,,, k. For each time increment during which the temperature of the element is equal to the melting tempera-
Calculated laser damage thresholds of Ge:Hg
325
ture, the stored value Hi,i.t is reduced by the added energy AQ,,,,k At. At p time increments after the (i,j,k) element has reached T,, the stored value is
WhenHi.1.k equals zero. the element has completed the phase change. For calculating thresholds where melting is the damage mechanism, the melted element is assumed to be instantaneously incident flux is transferred to the element immediately below the melted element.
removed and the
CALCULATED LASER DAMAGE THRESHOLDS Ge:Hg PHOTOCONDUCTIVE DETECTORS
OF
M. KRUER, L. ESTEROWITZ,F. BARTOLIand R. ALLEN Naval Research Laboratory, Washington DC 20375, U.S.A. (Receiued 10 February 1978)
Abstract-Thermal damage in laser irradiated mercury-doped germanium detectors is investigated. Threshold levels of 10.6 pm laser radiation corresponding to onset of irreversible damage in Ge:Hg crystals are measured. The dependence of the damage thresholds on irradiaton time agrees favorably with thermal model predictions. Thresholds for both onset of irreversible damage and complete loss of photoresponse for Ge:Hg detectors are then calculated as a function of irradiation time, using parameters obtained from experimental results on laser damage in Ge:Hg crystals.
1. INTRODUCTION The increasing use of lasers in electro-optical systems has generated interest in the susceptibility of infrared detectors to laser damage. Extrinsic germanium detectors,(‘) because of their spectral responsivity and response times, are often used to measure radiation from CO2 lasers. In this paper we investigate damage thresholds for mercurydoped germanium (Ge:Hg) photoconductive detectors exposed to 10.6~ laser radiation. In order to determine the unknown parameters which are required for, the calculation of damage thresholds, laser damage in Ge:Hg crystals is investigated experimentally and theoretically. Two thermal models for laser damage in Ge:Hg crystals and detectors are discussed in Section 2. Measured thresholds for onset of damage in ambient temperature crystals are reported in Section 3 as a function of irradiation time for 10.6 m laser radiation. These experimental data are fitted by thermal models yielding parameter values characterizing the irradiated materials. In Section 4 Ge:Hg photoconductors are assumed to have the same mode of thermal damage as the crystalline samples, and thresholds for onset of laser damage for typical Ge:Hg detectors are calculated. These thresholds are compared to those of other detectors for 10.6pm radiation. Qnset of laser damage in photoconductive detectors corresponds to only a small permanent reduction in photoresponse. Total loss of photoresponse in photoconductors is expected only’ if no active detector material remains to provide an electrical path between the ,lea& Thresholds for complete loss of photoresponsc in Ge:Hg photoconductors are calculated in Section 5 and are much larger than the corresponding thresholds of most photovoltaic and intrinsic photoconductive detectors. For the reader’s convenience, Ge:Hg detectors are compared in Section 4 with other common electro-optical components,whiah have high damage thresholds, such as metal mirrors. 2. THERMAL
ANALYSIS
Irreversible thermal damage in Ge:Hg materials involves vaporization and melting. Thresholds for thermal damage in detectors and detector materials depend on the temperature increase AT required for damage, the irradiation time, beam diameter, optical and thermal properties of materials used in the detector construction, and the quality of thermal coupling to the heat sink. Since these parameters can vary from one sample to another, thermal modelling of laser damage is required to extrapolate experimental results to arbitrary sample configurations and irradiation conditions. Ge:Hg material is quite susceptible to laser damage since a large. part OFthe inoident radiation is absorbed within a small volume. For irradiation times su@cietily short that thermal conduction is insignificant, the irradiated sample is heated down to some 315
M. KRUER et al.
316
PO= Constant
I03 10-e
I 10-7
I 10-6
I
I
10-3 7,
10-d
I 10-3
I 10-2
I IO“
set
Fig. 1. Calculated power density threshold P,, for onset of melting in laser irradiated Ge:Hg material as a function of laser pulse duration T. This figure illustrates that P,, varies as 7-l at short times and is independent of T at long times.
depth 6. In general 6 depends on the optical absorption coefficient a and the ambipolar diffusion distance.‘2) However, for the 10.6 pm damage thresholds studied here, the effects of ambipolar diffision could be neglected, and 6 is simply equal to the absorption depth. For long irradiation times, thermal conduction becomes important. This causes the damage threshold to depend strongly ‘on irradiation time. In this paper two thermal models are employed for laser damage in Ge:Hg. The tirst model considers a semi-infinite solid irradiated by a Gaussian laser beam of arbitrary diameter. This thermal model employs a closed-form solution to the thermal diffusion equation and is described in Appendix A. The second model employs a numerical calculation baaed on a finite-element technique and is discussed in Appendix B. The numerical model treats arbitrary beam profiles and composite sample configurations, and can be used when the more convenient closed-form model does not apply. Both models give expressions for the energy density E,, required to damage the sample as a function of irradiation time t. The power density threshold PO is obtained from the relation PO = E&. The thresholds predicted by the two models have the same qualitative dependence on r. For the range of parameters considered in this work, both models were found to yield the same results for T < lo-* sec. Therefore, the more convenient closed-form model was used for ‘c < 10m4 set, while the numerical model was employed for r > lo-‘sec. In the short time limit where the effects of thermal conduction are negligible, the absorbed energy remains within the depth S. E. is independent of r in this limit and depends linearly on 6 and A1: P,, varies as r - ‘. This condition exists for time t 4 d2/k, where k is the thermal diffusivity of Ge:Hg In the long time limit, heat is conducted away from the absorbing region at the same rate as it is deposited by the laser and the sample surface reaches a steady-state temperature distribution. In this limit PO approaches a constant and E. approaches a linear variation with T. These two time regimes are illustrated for Ge:Hg in Fig.‘l, which shows the power density of 10.6 pm radiation required to heat the sample surface to the melting temperature. These results were calculated using the material parameters listed in Table 1. Laser beam and sample dimensions are described in Section 3. 3. DAMAGE IN Ge:Hg MATERIAL Mercury-doped germanium crystals were soldered onto large ambient temperature copper blocks, as illustrated in Fig. 2. The samples were also retained by mechanical clamps to prevent sample movement if solder melted during the tests. The samples were approximately 3 mm long and the irradiated surfaces (0.6 x 0.6 mm) were chemically etched. The physical properties of these samples are expected to be the same
317
Calculated laser damage thresholds of Ge:Hg Table I. Effective material properties for Ge:Hg detectors Germanium
Property Density, P Wd Specific heat, c (J/g. K) Thermal conductivity, K (W/cm. K) Melting temperature, 7, (K) Heat of fusion, H, (J/g) Vaporization temperature, K (K) Heat of vaporization, H,. (J/g) Reflectivity, R’ 6 (cm) Skin depth tn 10pm (cm)
5.33’*’ tI:y;; 1210 ‘.I’ 467 ‘.I’ 3107 ‘ll’ 3921 ‘“’ 0.37”’ 6.25 x 10-4”’ -
Copper ;;z: 3.8 1356 207 2839 4730 -
(” I” ‘@’ ‘I’ “’
1.3 x 1Gk)
(“)NEULIERGER, M.. Handbook of Elecrronic Materials, Vol. 5. Plenum Press. Washington (1971). (b)Ref. 5, pp. 2-28. lc)Ref. 5, pp. 4-106. Id’Determined empirically from melting threshold data. w Ref. 5, pp. 4-154. If)Ref. 5, pp. 4-229. Is)Ref. 5. pp. 4-223. orRef. 5, pp. 4-231. “’ MO=, A. J., Handbook of Electronic Materials, Vol. 1. Plenum Press, Washington (1971). ‘“Determined empirically from damage threshold data as discussed in the text. “‘Ref. 5. pp. 6-134.
as for crystals used in operating Ge:Hg photoconductors. The samples were irradiated with 10.6 pm laser pulses whose durations, r, varied from 0.15 psec to several seconds. The laser e -’ beam radius R was 0.3 mm. The experimental apparatus and procedure is discussed elsewherej3’ Uncertainty in the experimental damage thresholds is estimated at 35%. The nature of damage first observed in these experiments on Ge:Hg’ depends on the irradiation time. For long irradiation times (7 > 1OO~sec) the first sigh of damage was due to melting. Small craters could be seen microscopically, indicating that the irradiated material had melted and resolidified. If the laser power density is increased, so that the sample reaches the vaporization temperature, plasma formation is observed. The vaporization threshold is found to be several times larger than the melting threshold. For short irradiation times (7 < 100 psec), a visual determination of the melting threshold is more difficult. For this range of times we report only the vaporization threshold which is characterized by plasma formation and visible surface damage. Threshold values of PO for melting in Ge:Hg are plotted in Fig. 3 using triangles. Using published values of material parameters given in Table 1 and the numerical model (Appendix B), P,, was calculated as a function of irradiation time. The calculated
Fig 2. Illustration of the Ge:Hg material and heat sink.
318
M. KRUERet al. IO9
106
IO'
“E
P
106
_
a”
I05 IO4 I03 10-u
lo-’
10-J
lo-’
10-4
r,
IO-J
10-z
lo-’
I
S6C
Fig. 3. PO for onset of damage in Ge:Hg material as a function of T. Triangles: experimental thresholds for melting. Squares: thresholds for vaporization.
results are shown by Curve A in Fig. 3. At long times, the melting thresholds are determined primarily by the rate at which heat can flow into the copper heat sink. The thermal conductance per unit area of the solder interface was assumed to be approximately 200 W/cm2. K. (4) In the calculation the thermal conductivity of germanium was assumed to have a constant value. Although it changes as a function of temperature, an ‘effective value’ was found by using it as an adjustable parameter in the fit. A value of 0.2 W/cm *K was obtained in this way. This corresponds to the thermal conductivity of germanium at an intermediate temperature (‘v 800 K)(s) between room temperature and the melting point. As shown in Fig. 3,’ the calculated Curve A agrees well with the experimental melting thresholds. Experimental vaporization thresholds are shown in Fig. 3 using squares. At short times PO varies’linearly with 6 2 a-l. The value of a is not well known for the high temperatures,encountered in the damage experiment. At 10 K, a has a value of about 4,cm-‘.(6) As germanium is heated above room temperature, free carrier absorption increases exponentially, giving rise to the familiar thermal runaway process!‘) Since 6 was assumed to be constant in the thermal analyses, an ‘effective value’ for the parameter was determined empirically. Using published values of Ge:Hg material parameters (see Table I), the vaporization thresholds were calculated employing the closed-form model of Appendix A for T < 10m4 sec. For r > 10e4 set the numerical model was used. At .threshold the surface temperature was set equal to the vaporization temperature. It was estimated that the depth of material melted is approximately 6, and the depth vaporized approximately S/4. The calculated vaporization thresholds, shown as Curve B in Fig. 3, are in good with experimental data. The ‘empirically determined value of agreement 6 = 6.2 x 10e4cm corresponds to an absorption coefficient of 16OOcm-‘, which is much. larger than the room temperature absorption coefficient. This is attributed to the thermal runaway process. The minimum observable damage in Ge:Hg corresponds to vaporization at short times and melting at long times. To obtain a single curve indicating minimum observable damage, a dashed curve has been interpolated between’ Curves A and B in Fig. 3. 4. ONSET The
OF
DAMAGE
IN DETECTORS
onset of material damage in Ge:Hg photoconductive detectors will involve the same mechanisms discussed in the preceeding section on Ge :Hg materials. At this threshold only slight degradation of the detector photoresponse is expected since the fraction of the total detector material damaged is very small. .The detector thresholds are expected to be slightly larger than the thresholds of ambient temperature materials given in
Calculated laser damage thresholds of Ge:Hg
r,
319
see
Fig. 4. Comparison of thresholds for onst of damage in detectors used for radiation in the 8-14 pm spectral window.
Fig 3 since detectors usually operate near 10 K. Detectors considered here have a structure similar to that shown in Fig. 2. A 0.6 x 0.6 x 3 mm Ge:Hg crystal is soldered onto a 10K copper heat sink which serves as one of the leads. The other lead is placed on the opposite face of the crystal. The detector is fairly thick (- 3 mm) because its optical absorption coefficient is relatively low (5 4 cm-‘). Thresholds for onset of material damage in Ge:Hg photoconductors were calculated using the same approach as for Ge:Hg materials (Section 3). The thresholds calculated for detectors irradiated by a ~Gaussian laser beam (R = 0.3 mm) are presented in Fig. 4. These thresholds have a time dependence similar to those given in Fig. 3 for ambient temperature materials. It is interesting to compare the thresholds for onset of damage in Ge:Hg photoconductors to those of other detectors commonly used in the g-14 pm spectral range. Thresholds for onset of damage in HgCdTe photoconductors and photodiodes’s’ and TGS pyroelectric detectors(3) are also shown in Fig 4. The thresholds of the photovoltaic and phot~onductive HgCdTe detectors are the same at short times, but at long times the photovoltaic detector becomes less susceptible to thermal damage because of more efficient radial heat conduction. The TGS detector has the lowest threshold because of its inferior strength and thermal properties. The Ge:Hg detector has the highest threshold at all irradiation times because of its superior thermal and mechanical properties and because of the efficient heat sinking possible for this detector. 5. COMPLETE LOSS OF PHOTORESPONSE IN Ge:Hg DETECTORS Complete failure of photoconductive Ge:Hg detectors is expected only if all the Ge:Hg material is removed through vaporization or melting. This mode of damage is suggested by experiments(g) showing that lead salt photoconductors lose all photoresponse only if the active detector material is vaporixed and no longer provides an electrically conducting path between the leads. We now calculate the thresholds for this extreme type of laser induced damage in Ge:Hg detectors. For very short irradiation times detector failure is caused predominantly by vaporization. On the other hand, at long times Ge:Hg material is removed by &9ting. There is an intermediate time regime where both melting and vaporization are involved in the damage process. It is beyond the scope of this work to precisely calculate thresholds the damage process. It is beyond the scope of this work to calculate precisely thresholds for complete detector failwe when both mechanisms are involved. The approach used here is to calculate thresholds for vaporization at short times and for melting at long
320
M. KRUER et al.
104 -
I03 to-6
I 10-S
I 10-4
I 10-3 r*
Fig. 5. Calculated
I 10-2
I 10-I
I I
IO
see
PO vs T for complete loss of photoresponse in a Ge:Hg photoconductar. Curve A: vaporization. Curve B: melting.
values of
times, and then interpolate between these regions to describe the damage thresholds at intermediate times. The crossover from vaporization to melting was centered at 0.3 msec to coincide with results of laser drilling studies which addressed the problem.““*“) The errors involved in interpolating vs a more exact calculation is estimated to be less than a factor of 2 at intermediate irradiation times. The vaporization thresholds at short ‘times can be calculated from simple analytical expressions since thermal conduction has no appreciable effect on the damage thresholds for these times. The power density Pb required to vaporize a detector of thickness b is given by the approximate expression: p6 = (Ekr + %,)lr
(1)
where Ekr is given by Eqn 2A of Appendix A with 6 replaced by b. The energy density, Evap,is associated with the latent heats of vaporization and melting as given by Eqn 3A. This vaporization threshold calculated using Eqn 1 is shown in Fig. 5 by Curve A. Although Curve A is shown for irradiation times as long as 2 x 10m3 set, vaporization can be considered the dominant mechanism for complete detector failure only for r < 10e4 set (solid portion of Curve A). Between 10-4sec and 2 x 10e3 set (dashed portion) Curve A overestimates the actual detector thresholds. For long irradiation times, where the material is removed in a molten rather than vapor form, thermal.conduction becomes important and Eqn 1 is not appropriate. At these long times the power density required to melt the entire detector element was calculated using the numerical technique discussed in Appendix B, and is shown in Fig 5 (Curve B). For the sake of illustration Curve B is shown for irradiation times as low as 10m4sec. However, only for r > 10m3 set (solid portion) does Curve B represent detector thresholds. The dashed portion of the curve (10-4-10-3 set) underestimates the actual detector thresholds. The thresholds for intermediate times are estimated by interpolating between the solid portions of Curves A and B. The composite curve in Fig. 5 gives the threshold for total loss of photoresponse in Ge:Hg detector as a function of irradiation time. The thresholds have the same general dependence on irradiation time as ,the thresholds for onset of damage. The magnitude of PO is very high for all ~r~iat~n times ranging from greater than 10” W/cm’ at one psec to greater than 10“ W/cm’ in the long time limit. The power densities at short times are sufficiently great that several of the assumptions of the above thermal analysis may no longer be valid. For example, effects such as vapor shielding, nonlinear optical processes, etc. may be important and should have been
Calculated laser damage thresholdsof Ge:Hg
321
IO4
7%
SW
Fig. 6. Calculated POfor complete loss of photoresponsein Ge:Hg photoconductors for various values of R (i.e. e-’ beam radius).
considered. However, because the competing.nature of these processes can Eead to cancellation, these effects were not considered in our analysis. The thresholds for complete loss of photoresponse in Ge:Hg detectors are much larger than those of most infrared detectors. The thresholds at short times are much larger than those of intrinsic photoconductors because the Ge:Hg is about a thousand times thicker than the active material of a typical intrinsic photoconductor. At long times the thresholds for Ge:Hg are higher than for other detectors because of the highly efficient heat sinking possible for this detector and its superior thermal and mechanical properties. Detector damage thresholds at long irradiation times will depend strongly on detector size and laser beam diameter. Figure 6 shows the calculated thresholds, for complete loss of photoresponse in Ge:Hg detectors for different beam radii, R, and detector sizes. In each case it was assumed that the detector width was equal to the ee2 diameter (2R) of the laser beam, so that 90% of the incident Gaussian beam falls on the active detector area. The damage thresholds are independent of beam diameter at short times when thermal conduction has a negligible effect on the damage thresholds. In the long time limit, the damage thresholds depend strongly on beam diameter. As the detector size (and beam diameter) decrease, transverse heat conduction become increasingly important and the damage thresholds increase significantly. These results are useful for determining thresholds for an arbitrary detector size. It is worth noting that although the power density threshold is higher for smaller beams, the total laser power required is actually lower. For example, at T = 3 set a reduction of the beam radius by a factor of 10 raises the Rower density threshold P, by approximately a factor of 10. However, the beam area is reduced by a factor of 100, and the total laser power required (power = PO x beam area) is decreased by a factor of 10. This is reasonable since smaller detectors should require less total power to melt. 6. COMPARISON DETECTORS
OF DAMAGE THRESHOLDS OF Ge:Hg TO THOSE FOR METAL MIRRORS
The damage thresholds calculated for Ge:Hg detectors not only are high compared to other infrared detectors but, for some irradiation times, are higher than thresholds for metal laser mirrors. A comparison of laser damage in Ge:Hg detectors and metal mirrors is now considered in detail. Recently published damage thresholds of metal mirrorso2-15) are listed in Table 2 and are plotted as a function of t in Fig 7 @iangIe@. PO is found to vary as r-* INF18/4--S
M. KRIJERet a[.
322
Table 2. Damage thresholds of copper mirrors at 10.6pm e-* radius (cm)
T
(set) 2
x
10-9’12’
>2 x lo9 lo9 2 x lo* 2 x lo5
10-8”3’ 6 x 10-7’L4’ 1 (ISI
0.028 0.042
>4 10 120 2 x IO5
over several decades of irradiation time. This behavior has been observed previously by Saito et aLo6’ who applied a one-dimensional thermal model to describe the r-* dependence of P,,. Their one-dimensional model, which assumes a uniformly irradiated semi-infinite solid with an infinite absorption coefficient, is actually a special case of the closed-form model discussed in Section 2 and presented in detail in Appendix A. Saito’s model, however, is valid only at short irradiation times where radial heat conduction is negligible. In this section we calculate thresholds using Eqn 1A with R = 0.042 cm and the material parameters of copper given in Table 1. The optical absorptance A’ = 1 - R’ (where R’ is the reflectance) is treated as an adjustable parameter in fitting Eqn 1A to the short time data. The results are shown as Curve A in Fig. 7. The value of optical absorptance (A’ = 0.034) obtained from the fit at short times is within a factor of 2 of the intrinsic optical absorptance for copper.“‘) This implies that these mirrors are operating close to their intrinsic limit at short times. At long irradiation times (1 set) the experimental threshold is about an order of magnitude below the calculated Curve A. This implies that A’ is not constant for all irradiation times and that some additional thermal coupling phenomena must be operative at long times. Studies on other metalsoar also show increased thermal coupling at long irradiation times. The thresholds for onset of damage in Ge:Hg detectors are included in Fig 7 (Curve B) for comparison with the mirror thresholds. As shown in the figure, the thresholds for mirrors at very short times (r < lo-* set) are lower than those for the onset of detector damage. One might expect the opposite to be true, since the absorptance of mirror surfaces is appreciably lower than for Ge:Hg detectors. However, the region which absorbs the laser energy in copper is very thin compared to that of Ge:Hg. The skin depth in copper is only 1.3 x lo-’ pm, whereas 6 = 6.2 pm for Ge:Hg. For longer irradiation times, when thermal conduction becomes important, the absorption depth no longer has a dominant effect on the damage thresholds. As shown in Fig. 7, the mirrors have higher thresholds for onset of damage than do Ge:Hg detectors for 7 > 10-s sec. This results from the lower optical absorptance and better thermal conduction of the copper mirrors. From the above considerations, it can be seen that
I I I I I I 10-s IO-B 10-T to-6 10-J ,10-a IO-3
104
r.
1
I
10-Z 10-l
I
I
666
Fig. 7. Comparison of the calculated thresholds corresponding to (A) onset of damage in metal mirrors, (B) onset of damage in Ge:Hg photoconductors, and (C) complete loss of photoresponse in Ge:Hg detectors.
Calculated laser damage thresholds of Ge:Hg
323
the calculated thresholds for onset of damage in Ge:Hg detectors are consistent with experimental and theoretical thresholds for damage in metal mirrors. Calculated thresholds for complete detector failure are also shown in Fig. 7 (Curve C). These thresholds are found to be considerably higher than the mirror thresholds for short irradiation times. This is attributed to the large volume of material vaporized for Ge:Hg detectors compared to the extremely thin layer damaged for the mirror. Instead of comparing the thresholds for complete detector failure to those for onset of damage in mirrors, it is more appropriate to compare them to those for burnthrough in metal samples. Although there exist little experimental data for cutting laser resistant materials, such as copper or beryllium copper which are used for mirrors, the thresholds for cutting other metals(19) are similar td the corresponding thresholds calculated here for complete failure of a Ge:Hg detector. SUMMARY
Thermal damage in Ge:Hg materials due to 10.6 pm laser radiation was investigated. Damage thresholds were measured as a function of irradiation time and their time dependence was shown to agree with thermal model predictions. Thermal damage thresholds of Ge:Hg photoconductive detectors were then calculated using parameters obtained from the experimental results on Ge:Hg materials. The thresholds for both onset of damage and complete loss of photoresponse in Ge:Hg detectors are larger than the corresponding thresholds in intrinsic photoconductors and photodiodes because of the larger bulk volume and better thermal characteristics of the Ge,:Hg detector. These thresholds are consistent with thresholds for damage in metal mirrors. REFERENCES 1. For a review of the characteristics of extrinsic germanium detectors see LEVINSIEIN, H., Appl. Opt. 4,
639 (1965). 2. The effects of 6 on damage thresholds will be discussed more fully in a future publication. F., M. KRUER,L. ESTEROWITZ& R. ALLEN,J. Appl. Phys. 44, 3713 (1973). 3. BAR’IT)LI. Y. S.. R. W. POWELL, 4. The thermal diffusivity of polycrystalline indium is obtained from TOIJLOUKIAN, C. Y. Ho & P. G. KLEMENS, Thermophysicol Properties of Matter, Vol. 10, Fig. 28R. Plenum Press, New York (1970). 5. GRAY,D. E. (editor) American Institute of Physics Handbook, pp. 4-154. McGraw-Hill, New York (1972). R. A., G. R. KRONIN,W. G. HUTCHINSON & R. A. CHAPMAN,Texas Instruments Technical 6. REYNOLDS, Report AFAL-TR-66-336 (1966). Unpublished. 7. YOUNGP. A.. Appl. Opt. 10, 638 (1971). F., L. ES~ROWITZ,M. KRUER& R. ALLEN,J. Appl. Phys. 46.4519 (1975). 8. BARTOLI 9. KRUERM., L. ES’FEROWITZ, F. BARTOLI L R. ALLEN,J. Appl. Phys. 47, 2867 (1976). 10. WAGNER,R. E. J. Appl. Phys. 45, 4631 (1974). 11. CHUN,M. K. & K. Rosa, J. Appl. Phys. 41, 614 (1970). 12. STARK, E. E., JR & W. H. REICHELT, Loser Induced Damage in Optical Materials: 1974 (edited by Gm A. J. & A. H. GUENTHER). NBS Special Publication 414 (Dee 1974). The laser pulse duration is characterized in REICHELT, W. H. & E. E. STARKJR, Laser Induced Damage in Optical Materials (edited by GLAS$ A. J. & A. H. GUENTHER). NBS Special Publication 387 (Dec. 1973). 13. SINGER,S. Laser Focus 12, 32 (1976). 14. S~IL~AU,M. J. & V. WANG, Appl. Opt. 13, 1286 (1974). 15. SAITO,T. T., G. B. CHARLTON JL J. S. LooMls, Laser Induced Damage in Optical Materials (edited by Guss. A. J. & A. H. GUENTHER). NBS Special Publication 414 (Dee 1974). 16. SAITO,T. T., D. MILAM,P. BAKER& G. MURPHY,Laser Induced Damage in Optical Materials: 1975 (edited by GLAS$ A. J. & A. H. GUENTHER). NBS Special Publication 435 (July 1975). 17. WEITING,T. J. & J. T. !~CHRIEMPF, Report of NRL Progress, June 1972 (unpublished). 18. READY,J. F., E@cts of High Power Laser Radiation, chap. 3. Academic Press, New York (1971). 19. LOCKE,E. V., E. D. HOAG& R. A. HELLA,I.E.E.E. J. Quant.Electr. QE-8, 132 (1972). 20. TORVIK.P. J., A Numerical Procedure for Two-Dimensional Heating and Melring Calculations with Applications to Laser EApcrs, Tech. Rpt. AFIT TR 72-2. March 1972.
APPENDIX
A
Laser irradiated materials experience thermal damage if the material is heated beyond a qeshold temperature. The threshold temperature change is denoted by AT,,,. If heat does not difise to the edges of the material, the thresholds can be approximated using a thermal model in which tbc samplb is treated as a semi-infinite solid irradiated by a Gaussian beam of the form: p(r) = PO exp(-2$/R’). We have shown
324
M. KRUERet al.
previously that the energy density E,, required to heat the crystal as a function of irradiation be approximated by the expression’s):
time T can
where k is the thermal diffusivity and S the depth of material heated in the absence of thermal conduction. The r-independent value Edr is simply the energy required to heat the crystal surface by ATh in the absence of phase changes and thermal conduction. Its value is given by: EIT = AT,, p&/(1 - R’)
(24
where p is the density, c the specific heat, and R’ the reflectance. The r-independent term E,, is the energy density associated with the latent heat for phase changes and can be approximated by the relation(*):
(34 where b is the thickness of the material damaged and H is the latent heat per unit volume. APPENDIX
B
The numerical model is baaed on a finite element technique developed by Torvik.“” In this numerical model, the sample is divided into elements each having the form of a solid rectangle. The thermal and optical properties of the elements are contained in arrays which may be updated after each time increment. This approach allows one to treat sample inhomogeneities, composite layered structures, time dependent irradiation conditions and changes in material properties as a function of temperature on optical flux. The rate Qr,,,,.k, at which heat flows in the Z direction from element (i,j,k) into element (i,j,k + 1) is given approximately by the product of the thermal conductance and the temperature difference (T,,,, - ‘I;,l,t+i) between the centers of the two elements. If both elements have the same thermal conductivity, the thermal conductance is given simply by the product of the thermal conductivity K and the area of the interface A z,,,,.L, divided by the distance between the centers of the elements. Generally, the thermal conductivities of adjacent elements (K,,,,t and K,,,,r+ i) are not the same and the thermal conductance between the centers of two adjacent elements is:
Therefore &c,,J,k, is given by
QZ (1.1. k)
=
(T,.J,k
-
Ti.J.k+
lhi.J.k,
z
+
*I-‘. 1.J.k + 1
Similar expressions describe heat flow in the X and Y directions. Heat can also enter the element by absorption from external sources (e.g. optical radiation) or from internal reactions. An additional teim, Pi,,,k (watts), represents the rate at which heat is added externally or internally to the (ij,k) element. The net rate of energy flow into the (ij,k) element is determined by adding the heat flux entering the element and subtracting the flux leaving, using the equation:. AQ 4J.k
=
po,J.k
+
Qxu-1.j.k)
-
QXti.J.k)
+
Qr(i,i-1.k)
-
&u.j,.t, + &e.I.k-i)
If the i, j, k cell has a temperature less than a phase transformation Al;,,,, during the time increment, At is
- Qzo.,.~,.
temperature, the temperature
increase
A&k At
AT.1.i= -
c i.J.k M
i,J.k
where C,. jVk and MiSJ,k are the specific heat and mass, respectively, is performed repeatedly using a small time increment At until the time of interest. At each time step the temperature change AT.,,, T;.j.t The temperature after an irradiation. time T -_ = nAt (i.e. n time Tr.J.k -- T,er + i *=
of the (i,j,k) element. This heat balance sum of the time increments equals the is added to the previous temperature intervals) is
AT,,,,&?) L
where A4.J.k (q) is the temperature change calculated for the q’th time interval. The temperature of each element increases until it reaches the phase transformation temperature. Starting with the first increment (q = m), in which the temperature is above the melting temperature T,, Tf.J,k is held fixed at T, and the energy addition is used to supply the latent heat. The latent heat which must be added in order to e&t a change of phase of the (i,j,k) element is JL,,,,~ Mr,J,k where I, is the latent heat per unit mass. This quantity is computed for each element of the detector and stored as an array H,,, k. For each time increment during which the temperature of the element is equal to the melting tempera-
Calculated laser damage thresholds of Ge:Hg
325
ture, the stored value Hi,i.t is reduced by the added energy AQ,,,,k At. At p time increments after the (i,j,k) element has reached T,, the stored value is
WhenHi.1.k equals zero. the element has completed the phase change. For calculating thresholds where melting is the damage mechanism, the melted element is assumed to be instantaneously incident flux is transferred to the element immediately below the melted element.
removed and the