Nanda, K K

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indian J. Phys. 73A (2). 245-248 (1999)U P  A- an mteraauonal jouroalDetermination of the band gap of semiconductors from the electrical measurement on respective diodesK K N anda*Institute of Physics, Sachivalaya Marg, Bhubaneswai-751 QDS, Onssa, IndiaReceived 13 November 1997, accepted 22 June 199SAbstract : Here, we report the determination of band gap from the forward voltage (t^>- temperature ( f )  measurement at different cutrent and capacitance (C) -  voltage (V) measurements on semiconducting diode. From the analysis, it is concluded that latter measurement provides the coirect information of the band gap unambiguousley.Keywords : Semiconductor diode, electrical properties, barrier height, band gap PACS Nos. : 85.30.Kk, 73.40.LqThere are variety o f techniques that have been used for the determination o f the band gap (Eg) for a  sem iconductor. One o f  them is the transm ittance m easurem ents which also envisages the nature o f the optical transition (direct or indirect) [1]. But, the sam ple has to he in thin film  form. It is also possible to determine the band gap o f silicon and germanium by m easuring the resistivity o f the pure sem iconductor as a  function o f tem perature 12]. There are also reports on the determ ination o f the band gap from the I -V  characteristics o f respective diodes m easured at different temperatures [3,4] and from the forward voltage (Vf) -  tem perature (7) m easurem ents by extrapolating the curve to 0  K [5-7]. Here, we use different current values to determ ine the band gap from the Vf-T  m easurem ents on their respective diodes. The determination o f Eg from c^a c ita n c e  (O -v o lta g e  (V) measurements has also been reported [6]. The m ethod is based upon the temperature dependence o f Fermi level o f  the sotniconductor the details for which has been discussed in R e f [6].T he m easurem ents were carried out from 10 to 300 K using an autom ated setup built a round a  L eybold closed-cycle refrigerator. The experim ental details are given elsewhere [8]. The epoxy encapsulation o f the diodes was ground flat on one side and fixed to the sam ple site w ith GE7031 varnish. C igarette p ^ e r  fixed with GE7031 varnishe-nuul addreM ; iuiida®iopb.stpbh.soft.iiet©  1999 lACS246 KKNandaprovided the required electrical isolation. The electrical leads (insulated copper wires) are thermally anchored to the cold parts in order to reduce the stray thermal emf. The usual four probe electrical connections are made to the sample. A stable constant current was provided to the diode from Keithley model 224/2243 program m able current source. The forward voltage w as m easured using a Keithley m odel 182 digital voltm eter. The diodes are operated at a constant current ranging from 10 nA to 200 ttA  while the voltage variation with temperature is monitored. This amount o f current corresponds to a  value below the knee in the Vf - I  characteristic o f the diode in the entire temperature range studied. The tem perature o f  the samj>le site is controlled using a  calibrated  type D  silicon diode therm om eter in conjunction with a  Leybold model LTC60 tem perature controller. The tem perature is determ ined using the same silicon diode thermometer. This has a standard measurement accuracy o f ± 1 % or better.The C-V  measurements were carried out at different frequencies in the temperature range 77 to 351 K using a hom e-built setup. The details o f the experim ental setup is published elsewhere [6]. For low temperature C-V  measurement the whole system is dipped in liquid nitrogen (LN j) in order to cool down the sample. For temperatures higher than the room temperature (298 K), the hole system is dipped in boiling water and m aintained the distance between water level and the sample. The thermal contact between the sample and the thermocouple junction is made using GE7031 varnish. The temperature is monitored by using a chrom el-constanton thermocouple whose one junction  is a t ice tem perature and other is placed near the sample. The therm ocouple output is m easured using a Hewlett Packard 34401A multimeter. The voltage was provided to the sample from the HP4284A precision LCR m eter and the capacitance was m easured using the sam e m eter. The oscillator level is set to 10 mV for all measurements.Fignrc 1. The Vf - T  diaraoteristic of an 1N4007 Si diode for 10 nA, 100 nA, 500 nA, 1 ^A, 10 ^A, 100 m^ A and 200 m^ A of current in the temperature range 30-300 K. All the curves are least-square fitted and extrapolated to 0 K (ihown hy solid lines).Flfpre 2. The Vy -  f  characteristic of a cryogenic silicon diode for 10 nA (lowest curve), 100 nA, 1 pA, 10 pA, 100 pA, 1 mA and 10 mA (topmost curve) of current in the temperature range 100-300 K. All the curves are least-square fitted and extrapolated to 0 K (shown by solid lines).Determination of the band gap of semiconductors etc 247Shown in Figure 1 is the - T  p lo t o f  an 1N4007 Si diode in the tem perature range 30 to 300 K. The lower limit to the linear V f-T  region is usually that temperature at which carrier 'freeze ou t’ occurs. In this region, the resistance o f the diode becomes very large and the voltage increases rapidly with sm all decrease in temperature. Extrapt>lating to 0 K it is seen from Figure 1 that all the curves merge alm ost at a point irrespective of the current value. As discussed in Ret. [6] and |7], this gives the value of which is found tobe -1 .17  eV in good agreement with earlier reported results [9^\W e have also extrapolated the data o f a different Si di^de (cryogenic silicon diode supplied by the American C!ryo Inc. [lOJ) as shown in Figure t .  On exu-apolation to 0 K, it is noted from  the figure that the curves do not merge a particular point and hence, am biguity arises in the determ ination o f E^. In this context, it is worth pointing out that the curves do not m eet at a point because of the scries resistance effect 17J. For current values 1 pA , 10 p A  and 100 pA , the effect o f series resistance is negligible and hence, the curves converge at a point in the voltage axis to give 1.19 eV as the value o f f .,.Figure 3 shows the room temperature measurement (300 K) curves of 1N4007 Si diode at different frequencies : 1 kHz, 1(X) kHz and 1 M Hz. Frequency-dependent capacitance is observed where aJl the slopes converge to a common point. This implies that is independent o f frequency.Figure 3. CapacTiance voltage (298 K) characteristics of an 1N4007 Si diode at different freqiiencie.<;T he C-^-V  curves o f  an 1N4007 diode at different tem perature are shown in F igure 4. The frequency in all cases is 1 kHz. The barrier height V<, is obtained by e x t r ^ l a t i n g  to zero. The tem perature dependence of Vf, are shown in Figure 5. As di.scused in Ref. [6], the band gap a t 0  K can also be determ ined from the Vj, -T  plot by extrapolating it to 0  K. Extrapolating to 0  K, the band gap is found to be 1.189 eV which is very close to the earlier reported results. Sim ilar inve,stigations carried ou t on different 1N4007 diodes and cryogenic diodes confirm  the result quantitatively.73A(2)-16248 K K NandaAs the extrapolation of V ^ -rcu rv e  to 0  K yields different value for different current in the case of ayo g en ic  diodes, ambiguity arises for the idenification of Eg. But, there is no such ftmbiguity in the determination o f Eg from C -ym easurem ents,Figure 4. CapacUancc-voltage (1 kHz) characteristics of an 1N4007 vSi diode at different temperaturesFigure 5, The temperature dependence of obtained from Figure 4 tor an IN4007 Si diode. Extrapolating to 0 K, Eg is found to be 1.189 eV.in  sum m ary, the determ ination o f the band gap at 0 K from  the electrical measurement o f several semiconducting diodes is reported. Eg of silicon, estimated from the Vj -T  measurements on I N4(X)7 silicon diode is found to be ~1.17 eV. But, ambiguity arises in the case o f cryogenic diodes a.s the curves for different current do not m erge at a particular point at 0 K. On the other hand, the band gap determined from C~V m easurement is very close to the earlier reported value and hence, can be used unam biguously for the determination o f  Eg.References111 P Martik and G Gonzalez Diaz Am. J .  Phys. 60 83 (1992)12) P Liebenauer L ab o ra to ry  M an u a l f o r  C o llege  P hysics (C'olumbus : Collegiate) p 107 (1978)13) P I rollings Am. J .  Phys 48 197 (1982)[41 B D Sukliecia Am. J  Phys, SI 12  (1983)[5J L KLirkup and F Placido Am. /  Phys. 54 918 (1986)[61 K K Nanda and S N Sarangi Rev Set. Instrum . 68 3289 (1997)(7) K K Nanda CurrSet. 74 234 (1998)[8J S B Ota and K K Nanda Rev. S c i  Instrum . 65 3289 (1994)[9] C  Kittel In troduction to S o lid  State  P h y sic s (New York : John Wiley) (1976)110] C ty o  In d ustrie s o f  A m erica  Inc. (Atkinson, lI.vS.A.)

Determination of the Band Gap of Semiconductors from the Electrical Measurement on Respective Diodes

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Determination of the Band Gap of Semiconductors from the Electrical Measurement on Respective Diodes

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