~O~UGRAP~S FOR EVALUATING PARAMETERS OF SCHOTTKY BARRIER I.R. DETECTORS S. C. GUPTA, B. L. SHARMAand V. V. AGASHE Solid State Physics laboratory,
Lucknow Road. Delhi, India
~bs~aet-tomographs have been developed in this paper for direct evaluation of various parameters at 77K of Schottky barrier infrared detectors. Similar nomographs can also be constructed for other temperatures.
Although homojun~tio~ diodes using narrow-ba~dgap semiconductors have been fabricated and extensiveiy investigated for detection of infrared radiation in the past, the use of heterojunction diodes’“,“” and Schottky barrier diodes (3s4)for this purpose is relatively new. The theoretical detectivity limits for heterojunction diodes have been evaluated by Sharma et af.(s) white Gupta et ~$1. (6) have recently calculated the theoretical detectivities of PbSnTe, PbSnSe and HgCdTe Schottky barrier diodes. The latter have also compared the Schottky barrier detectivities with corresponding homojunction photodiode detectivities and have shown that even though the homojunction detectivities are higher, the theoretical detectivities of PbSnTe and PbSnSe Schottky diodes can be greater than 10’” cm HzsW-‘. Recently experimental detectivities greater than 5 x 1O”‘cm Hz*W-” l(e V)
Fig. 1. Nomograph for determining R,,A or A* at 77K for any Schottky barrier diode having & in the range 0. I-O.2 eV.
S. C. G~!PTA.
6. I_. S~~AKMA
arid V. V. AGASHL.
in the ~avclength range 8-12 pm for PbSnSe Schottky barrier diodes have also been reported by Hohnke er LZ!.(” Considering the technological importance of Schottky barrier photodiodes in the future, nomographs for evaluating their parameters have been developed in this paper. In the case of Schottky barrier photodiodes the expression for detectivity D): at any temperature Tcan be expressed as
(1) where q is the quantum efficiency, i is the wavelength of incident photon, A is the area of the junction and R0 is the zero bias resistance. In the above expression, Roil can be obtained by differentiating the current-voItage relation of the Schottky barrier diode (i.e. (df/dli) at I’= 0) and can be written as
where A* is the effective Richardson constant and (ba is the metal-semiconductor barrier height. Using relation (2) a nomograph (see Fig. 1) is drawn which relates the various Schottky barrier diode parameters, namely f&A, A* and &, at 77K for all metal-semiconductor contacts having & in the range 0.1-0.2 eV. It is clear from this nomograph that any of the above mentioned three parameters can be determined by the intercept of the line
Fis. 2. Nomograph
for a wavelength
E, and a given value of R,A
joining the experimentally or theoretically known values of two of them. For example, if one asumes A* and (?jBfor a PbSnSe Schottky barrier diode to be 3.24A crnp2 I(-’ and 0.1 eV respectively then the value of RoA equals I.2 0 cm’ can be easily determined from the nomograph (see Fig. 1). Knowing ROA from the nomograph given in Fig. 1 the detectivity DT at 77K for given wavelength 3. can be determined from the nomograph drawn in Fig. 2 by assuming tj = 1. The method of determining Df for a given wavelength J. is illustrated by considering a typical example. If, for example, R,A equals 1.2 fi cm2 is assumed for PbSnSe Schottky barrier i.r. detector then DX for the cutoff wavelength of 12.4 /irn can be determined directly by reading the value of 0: corresponding to the point of intersection of the line ‘48 for i. = 12.4 iirn drawn paralIe1 to the continuous lines (shown in Fig. 2) and the line para~~e~to the ordinate at &A equals I.2 Q cm2. In order to cover the complete range of values of &A, two scales for RJ and 0: are provided in the same graph. Apart from the above mentioned parameters, the effective Richardson coefficient A* for a given metal-semiconductor Schottky contact can also be determined from Fig. 1 by experimentally knowing &A (= kT/qlo where I0 is the reverse saturation current) and 4B. In conclusion, it can be mentioned that similar nomographs for various temperatures may prove quite useful to workers in this field for easy evaluation of various parameters of Schottky barrier i.r. detectors. Ackrro~(~~~rtni~~~r--The authors ~ncour~lgement and permission
are thankful to Dr S. C. Jain. Director. to publish this work.
Solid State Physics
REFERENCES 1. Dlt VAUX L. H.. H. KIIMLZA.M. J. SHWTS. F. J. RENDA, J. R. BALON, P. S. CHIA & A. H. LOCKWOOD, I+md PELT. 15, 271 (I 975). 2. ROLLS W. li$w