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The diffusion coefficient of zinc in indium antimonide
LETTERS
TO
order of magnitude of that of photosensitive CdS or CdSe crystals. The temperature-dependence of the photocurrent for several light levels is shown in Fig. 3, together with the temperature-dependence of the dark current. Instead of thermal quenching of photoconductivity occurring rapidly over a narrow range of temperatures, as in CdS or CdSe,@) the photocurrent decreases almost exponentially with temperature over a wide temperature range. Using the analysis of temperature quenching presented in a previous publication,(s) it can be shown that the onset of quenching corresponds to an activation energy of about 0.1 eV, whereas the termination of quenching corresponds to an energy of about O-8 eV. This behavior is similar to that reported for ZnSe crystals with Group V acceptors,@) and for certain CdS and CdSe crystals with high acceptor concentrations.(s) An effectively continuous distribution of sensitizing levels is indicated in these materials.
THE
EDITORS
335
stant concentration of zinc. The n-type specimens were cut from tellurium-doped single-crystal material, and had carrier concentrations ranging from 3 x 101s to 2x lOr* cm-s, as determined by Hall-constant measurements at 77’K; by using heavily doped material, the effect of rapidly difIusing acceptors of lower solubility was minimized (HULME, to be published). The specimens were etched and mechanically ground, one surface being subsequently polished to a mirror finish with Linde fine abrasive type A-5175 ; they were then reetched in dilute “Analar” HCl, washed in doubly distilled water, and finally sealed off with several mg of etched “spectrographically” pure zinc, N 10-s mm Hg pressure, in N 1 l-cm under lengths of quartz tubing, 5 mm in internal diameter, which had previously been cleaned with “Analar” acids and washed with doubly distilled water. The diffusion process was performed in a furnace, the temperature of which was controlled to f2”C by a platinum resistance thermometer. RCA Laboratories RICHARD H. BUBE The specimen was arranged to be close to the Princeton, N. J. WILLIAM H. MCCARROLL thermometer and also to a calibrated Chromeli Alumel thermocouple, used in conjunction with a REFERENCES potentiometer to measure its temperature; the zinc was arranged to be in a region of the furnace about 1. HAHNH. and KLiNCER W., Z. anorg. Chem. 260,97 15°C colder than the specimen. Annealing times (1949). 2. STIJBBS M. F., S~HUFLBJ. A., THOMPSOKA. J. and ranged from 1 to 240 hr; when the allotted time DUNCE J. M., J. Amer. Chem. Sot. 74, 1441 had elapsed, the specimen was removed from the (1952). furnace and allowed to cool in its tube to room tem3. BUBE R. H., J. Phys. Chem. Solids 1, 234 (1957). 4. BUBE R. H. and LIND E. L., Phys. Rev. 110, 1040 perature. A technique closely similar to that of (1958). BOND and SMITS(2) was used to obtain the depths 5. BuB~:R. H., J. Chem. Phys. 30, 266 (1959). of the p-n junctions. Bevels (- 2”) were polished across the previously polished surfaces of the specimens; the p-n junctions were then located by thermoelectric probing at 77’K,* and their posiThe diftusion coeiikient of zinc in indium tions were marked with the sharp tungsten point a&m&de used for probing. The depths were then measured interferometrically, or, in the case of depths (Received 24 Fetiry 1959) greater than N 25~, by using the calibrated finefocus adjustment of a microscope fitted with a THE diffusion coefficient D has been measured for 4-mm metallurgical objective (depth of focus zinc in InSb by thep-n junction method developed by FULLER(~). This involved diffusing zinc (an N 1~); the measured depths ranged from.5 to 81~. In calculating the diffusion coefficients it was acceptor) from the vapour phase into two differently doped n-type samples of InSb under identical assumed that the concentration C of diffused zinc was of the form conditions; by measuring the depths of the p-n C = Cs erfce, junctions, two points on the complementary error function distribution of the diffusant are obtained, l At this temperature the correction aaaociate’d with and D may be calculated. It is assumed that. the the concentration of intrinsic carriers is negligibly small; boundary condition at the surface is one of conit is not small at 290°K (seeVVErss(*)).
LETTERS
336
TO
where x being the distance below the surface and t the time. The assumption that the surface concentration of zinc, CO, is constant ought to be valid, the vapour pressure of zinc being between 1 and 10-z mm Hg (in the temperature range involved); even if this assumption is not strictly valid, the effect on the diffusant distribution is not large (see SMITS(4)), and the values of D derived should not be greatly in error. An approximate calculation shows that the other assumption involved-that there is no loss of tellurium from the specimen surface-will be valid provided that the tellurium is not absorbed into the quartz at the temperatures used. For values of 5 > 2, the approximate method of FULLER(~)was used to calculate the values of D. lo
-7
l--l-
I
103/T, OK-’ FIG. 1. The dif%sion coefficient of zinc in indium antimonide determined by the p-n junction depth method. D = 1-6x 108 ~p~-(53,~~6,~~~~~~
THE
EDITORS
For 5 < 2, a graphical method suggested by Dr. P. N. BUTCHERof this laboratory was used; this involved the sliding of a log-log plot of erfc &/erfc (2 against 5;/5S over a log-log plot of erfc 6 against 6, 51 and 5s being the values of 6 appropriate to the two junction depths. For one pair of specimens a result was not obtained because the junction depths were too small to measure, for another pair because the zinc alloyed into the specimen surfaces, and in the case of a third pair the junction depth was anomalously greater in the more heavily doped specimen. The results obtained are shown in Fig. 1; the expected linear relationship between log D and l/T appears to be satisfied. The scatter of the experimental points is accounted for by the errors in determining carrier concentrations and junction depths. The calculated surface concentrations ranged from 4x 1017 to 8~ 101s per ems, but, because of the unreliability of determinations of CO by this method, no correlation with source or specimen temperature was obtained. The equation of the line in the figure, obtained by a weighted leastsquares method, is D = 1 a6x 10s exp[( --53,000& &6,OOO),‘RT] cms/sec with R in cal/deg. mol. The activation energy for zinc diffusion, 53f6 k&/mole (or 2.3hO.3 eV), thus appears to be close to those for self-diffusion, -42&6 and 45&g kcal/mole for indium and antimony, respectively, as determined by EISEN and BIRCHENALLt5), although much lower values, 6.5 and 17.5 kcal/mole, respectively, were obtained by BOLTAKS and KULIKOV.@)+Our results suggest that the measurements of EISEN and BIRCHENALL(~)are the more reliable-the activation energies for selfand impurity-diffusion are generally close to one another if the impurity is substitutional; it is usually assumed that zinc in InSb is located substitutionally on indium sites.
* In both cares the self-diffusion coeflicients were measured by means of radioactive isotopes. Perhaps the explanation for the enormous discrepancies between the two results is due to one group carrying out the diffusion annealing under conditions in which there was a continuous loss of antimony by evaporation from the apecimens. In our experiments the quartz tubes used to contain the specimens were short enough to prevent their temperature anywhere dropping low enough for antimony to condense ; a rough calculation shows that u&as antimony were absorbed into the quartz at this temperature, losses would be negligible.
LETTERS
TO
THE
Acknowledgements-The authors would like to thank
REFERENCES
their colleagues for useful discussions, also Miss J. M. WRIGHT and Dr. J. B. MULLIN, who were involved in the preparation of the tellurium-doped single-crystal specimens of InSb. We also acknowledge the permission of the Controller of Her Britannic Majesty’s Stationery OfBce to publish this letter.
Royal Radar Establishment, Great Malvern, Worcs.
337
EDITORS
1. FULLERC. S., Phys. Rev. 86, 136 (1952). 2. BONDW. L. and SMITS F. M., BeU Syst. Tech. J. 35, 1209 (1956). 3. WEISSH., Z. Nutqfonch. lla, 131 (1956). 4. sM1l-S F. M., Proc. Inst. Radio Engn. a,1049 (1958). 5. ENEN F. E. and BIRCHENALLC. E., Acta Met. 5,265 (1957). 6. BOLTAKS B. I. and KULIKOVG. S., Zh. Tekh. Fiz. 27, 82 (1957).
K. F. HULME JANET E. KEMP
I500
1000
000
600
s 400 t :: Cu. E ” E 3 I e
200
‘00150
I50 TEMPERATURE
200
250
300 3;O
( OK )
FIG. 1. The Hall mobility of p-type InP crystals as a function of temperature. The dashed curve is the lattice mobility calculated from the 214 curve, assuming m+ = 0.2 ms.
Electrical
properties of p-type InPt
(Received 20 Februmy 1959) BECAUSEof the recent availability of InP with impurity concentrations of 101s cm-s and less,(l) it
t Supported in part by the U.S. Air Force.
has become possible to produce crystals of relatively pure P-type InP and to investigate their properties. Fig. 1 is a plot of the temperaturedependence of the measured Hall mobilities of two samples prepared by doping with cadmium. It is important to note that the mobility of the purer
TO
order of magnitude of that of photosensitive CdS or CdSe crystals. The temperature-dependence of the photocurrent for several light levels is shown in Fig. 3, together with the temperature-dependence of the dark current. Instead of thermal quenching of photoconductivity occurring rapidly over a narrow range of temperatures, as in CdS or CdSe,@) the photocurrent decreases almost exponentially with temperature over a wide temperature range. Using the analysis of temperature quenching presented in a previous publication,(s) it can be shown that the onset of quenching corresponds to an activation energy of about 0.1 eV, whereas the termination of quenching corresponds to an energy of about O-8 eV. This behavior is similar to that reported for ZnSe crystals with Group V acceptors,@) and for certain CdS and CdSe crystals with high acceptor concentrations.(s) An effectively continuous distribution of sensitizing levels is indicated in these materials.
THE
EDITORS
335
stant concentration of zinc. The n-type specimens were cut from tellurium-doped single-crystal material, and had carrier concentrations ranging from 3 x 101s to 2x lOr* cm-s, as determined by Hall-constant measurements at 77’K; by using heavily doped material, the effect of rapidly difIusing acceptors of lower solubility was minimized (HULME, to be published). The specimens were etched and mechanically ground, one surface being subsequently polished to a mirror finish with Linde fine abrasive type A-5175 ; they were then reetched in dilute “Analar” HCl, washed in doubly distilled water, and finally sealed off with several mg of etched “spectrographically” pure zinc, N 10-s mm Hg pressure, in N 1 l-cm under lengths of quartz tubing, 5 mm in internal diameter, which had previously been cleaned with “Analar” acids and washed with doubly distilled water. The diffusion process was performed in a furnace, the temperature of which was controlled to f2”C by a platinum resistance thermometer. RCA Laboratories RICHARD H. BUBE The specimen was arranged to be close to the Princeton, N. J. WILLIAM H. MCCARROLL thermometer and also to a calibrated Chromeli Alumel thermocouple, used in conjunction with a REFERENCES potentiometer to measure its temperature; the zinc was arranged to be in a region of the furnace about 1. HAHNH. and KLiNCER W., Z. anorg. Chem. 260,97 15°C colder than the specimen. Annealing times (1949). 2. STIJBBS M. F., S~HUFLBJ. A., THOMPSOKA. J. and ranged from 1 to 240 hr; when the allotted time DUNCE J. M., J. Amer. Chem. Sot. 74, 1441 had elapsed, the specimen was removed from the (1952). furnace and allowed to cool in its tube to room tem3. BUBE R. H., J. Phys. Chem. Solids 1, 234 (1957). 4. BUBE R. H. and LIND E. L., Phys. Rev. 110, 1040 perature. A technique closely similar to that of (1958). BOND and SMITS(2) was used to obtain the depths 5. BuB~:R. H., J. Chem. Phys. 30, 266 (1959). of the p-n junctions. Bevels (- 2”) were polished across the previously polished surfaces of the specimens; the p-n junctions were then located by thermoelectric probing at 77’K,* and their posiThe diftusion coeiikient of zinc in indium tions were marked with the sharp tungsten point a&m&de used for probing. The depths were then measured interferometrically, or, in the case of depths (Received 24 Fetiry 1959) greater than N 25~, by using the calibrated finefocus adjustment of a microscope fitted with a THE diffusion coefficient D has been measured for 4-mm metallurgical objective (depth of focus zinc in InSb by thep-n junction method developed by FULLER(~). This involved diffusing zinc (an N 1~); the measured depths ranged from.5 to 81~. In calculating the diffusion coefficients it was acceptor) from the vapour phase into two differently doped n-type samples of InSb under identical assumed that the concentration C of diffused zinc was of the form conditions; by measuring the depths of the p-n C = Cs erfce, junctions, two points on the complementary error function distribution of the diffusant are obtained, l At this temperature the correction aaaociate’d with and D may be calculated. It is assumed that. the the concentration of intrinsic carriers is negligibly small; boundary condition at the surface is one of conit is not small at 290°K (seeVVErss(*)).
LETTERS
336
TO
where x being the distance below the surface and t the time. The assumption that the surface concentration of zinc, CO, is constant ought to be valid, the vapour pressure of zinc being between 1 and 10-z mm Hg (in the temperature range involved); even if this assumption is not strictly valid, the effect on the diffusant distribution is not large (see SMITS(4)), and the values of D derived should not be greatly in error. An approximate calculation shows that the other assumption involved-that there is no loss of tellurium from the specimen surface-will be valid provided that the tellurium is not absorbed into the quartz at the temperatures used. For values of 5 > 2, the approximate method of FULLER(~)was used to calculate the values of D. lo
-7
l--l-
I
103/T, OK-’ FIG. 1. The dif%sion coefficient of zinc in indium antimonide determined by the p-n junction depth method. D = 1-6x 108 ~p~-(53,~~6,~~~~~~
THE
EDITORS
For 5 < 2, a graphical method suggested by Dr. P. N. BUTCHERof this laboratory was used; this involved the sliding of a log-log plot of erfc &/erfc (2 against 5;/5S over a log-log plot of erfc 6 against 6, 51 and 5s being the values of 6 appropriate to the two junction depths. For one pair of specimens a result was not obtained because the junction depths were too small to measure, for another pair because the zinc alloyed into the specimen surfaces, and in the case of a third pair the junction depth was anomalously greater in the more heavily doped specimen. The results obtained are shown in Fig. 1; the expected linear relationship between log D and l/T appears to be satisfied. The scatter of the experimental points is accounted for by the errors in determining carrier concentrations and junction depths. The calculated surface concentrations ranged from 4x 1017 to 8~ 101s per ems, but, because of the unreliability of determinations of CO by this method, no correlation with source or specimen temperature was obtained. The equation of the line in the figure, obtained by a weighted leastsquares method, is D = 1 a6x 10s exp[( --53,000& &6,OOO),‘RT] cms/sec with R in cal/deg. mol. The activation energy for zinc diffusion, 53f6 k&/mole (or 2.3hO.3 eV), thus appears to be close to those for self-diffusion, -42&6 and 45&g kcal/mole for indium and antimony, respectively, as determined by EISEN and BIRCHENALLt5), although much lower values, 6.5 and 17.5 kcal/mole, respectively, were obtained by BOLTAKS and KULIKOV.@)+Our results suggest that the measurements of EISEN and BIRCHENALL(~)are the more reliable-the activation energies for selfand impurity-diffusion are generally close to one another if the impurity is substitutional; it is usually assumed that zinc in InSb is located substitutionally on indium sites.
* In both cares the self-diffusion coeflicients were measured by means of radioactive isotopes. Perhaps the explanation for the enormous discrepancies between the two results is due to one group carrying out the diffusion annealing under conditions in which there was a continuous loss of antimony by evaporation from the apecimens. In our experiments the quartz tubes used to contain the specimens were short enough to prevent their temperature anywhere dropping low enough for antimony to condense ; a rough calculation shows that u&as antimony were absorbed into the quartz at this temperature, losses would be negligible.
LETTERS
TO
THE
Acknowledgements-The authors would like to thank
REFERENCES
their colleagues for useful discussions, also Miss J. M. WRIGHT and Dr. J. B. MULLIN, who were involved in the preparation of the tellurium-doped single-crystal specimens of InSb. We also acknowledge the permission of the Controller of Her Britannic Majesty’s Stationery OfBce to publish this letter.
Royal Radar Establishment, Great Malvern, Worcs.
337
EDITORS
1. FULLERC. S., Phys. Rev. 86, 136 (1952). 2. BONDW. L. and SMITS F. M., BeU Syst. Tech. J. 35, 1209 (1956). 3. WEISSH., Z. Nutqfonch. lla, 131 (1956). 4. sM1l-S F. M., Proc. Inst. Radio Engn. a,1049 (1958). 5. ENEN F. E. and BIRCHENALLC. E., Acta Met. 5,265 (1957). 6. BOLTAKS B. I. and KULIKOVG. S., Zh. Tekh. Fiz. 27, 82 (1957).
K. F. HULME JANET E. KEMP
I500
1000
000
600
s 400 t :: Cu. E ” E 3 I e
200
‘00150
I50 TEMPERATURE
200
250
300 3;O
( OK )
FIG. 1. The Hall mobility of p-type InP crystals as a function of temperature. The dashed curve is the lattice mobility calculated from the 214 curve, assuming m+ = 0.2 ms.
Electrical
properties of p-type InPt
(Received 20 Februmy 1959) BECAUSEof the recent availability of InP with impurity concentrations of 101s cm-s and less,(l) it
t Supported in part by the U.S. Air Force.
has become possible to produce crystals of relatively pure P-type InP and to investigate their properties. Fig. 1 is a plot of the temperaturedependence of the measured Hall mobilities of two samples prepared by doping with cadmium. It is important to note that the mobility of the purer