Determination of the Schottky barrier height in diodes based on Au TiB 2 n-sic 6H from the current-voltage and capacitance-voltage characteristics

Transcription

1 Semiconuctor Phyic, Quantum Electronic & Optoelectronic, 014. V. 17, 4. P PACS y, c, De Determination of the Schottky barrier height in ioe bae on Au TiB n-sic 6H from the current-voltage an capacitance-voltage characteritic Ya.Ya. Kuryk 1, V.V. Shynkarenko 1, V.S. Slipokurov 1, R.I. Bigun, R.Ya. Kuryk 1 V. Lahkaryov Intitute of Semiconuctor Phyic, AS of Ukraine, 41, propect auky, 0308 Kyiv, Ukraine; kuryk@ip.kiev.ua Ivan Franko ational Univerity of Lviv 1, Univerytetka tr Lviv, Ukraine Abtract. We preent the reult of invetigation of the barrier height an ieality factor in Schottky barrier ioe bae on Au TiB n-sic 6H relying on meauring the current-voltage an capacitance-voltage characteritic. Improving the accuracy of the metho that take into account the effect of the erie reitance in calculating the ieality factor an barrier height ha been hown with the Cheung metho an irect approximation one. It ha been acertaine that an inconitency between real currentvoltage characteritic an it moel the temperature epenence of the barrier height, the ieality factor epenence on the voltage introuce the baic error into the calculate parameter in the ioe uner tuy. Keywor: Schottky barrier, wie-gap emiconuctor, ieality factor, current-voltage an capacitance-voltage characteritic. Manucript receive ; revie verion receive ; accepte for publication ; publihe online Introuction Schottky barrier height (ShBH) an ieality factor are the mot important parameter of the Schottky contact. A number of metho for their etermination, incluing etermination from the current-voltage characteritic, i well known [1-0]. Attempt to generalize an ytematize the exiting metho were mae in a number of paper [1-4], but etimation of accuracy, carrie out in the mot of work, oe not take into account the peculiaritie of contact to wie-gap emiconuctor. Coniering the accuracy of etermining ShBH, a applie to the contact bae on wie-gap emiconuctor, it i neceary to take into account three factor: the accuracy of meaurement of initial value (current, voltage, capacitance), accuracy of the approximation metho an accuracy of correlation between the propoe mechanim of charge tranport an that implemente in reality. In thi work, a batch of Schottky barrier ioe (ShBD) bae on Au TiB n-sic 6H were invetigate uing ifferent metho, a comparion of thee reult wa mae, an the reaon of their ifference were icue.. Sample uner tuy Schottky barrier ioe bae on Au TiB n-sic 6H were create on bulk emiconuctor with the concentration of ilocation 10 cm [19]. The concentration of non-compenate impuritie in emiconuctor, which wa obtaine from the capacitance-voltage (C V) characteritic, amounte cm. The layer TiB x with the thickne ~50 nm an thoe of Au with the thickne 100 nm were ucceively epoite uing the magnetron puttering onto the urface of n-6h-sic (0001), ubjecte to photon 014, V. Lahkaryov Intitute of Semiconuctor Phyic, ational Acaemy of Science of Ukraine 398

2 Semiconuctor Phyic, Quantum Electronic & Optoelectronic, 014. V. 17, 4. P cleaning. Back ohmic contact were forme uing the magnetron puttering i(100 nm), TiB x (100 nm) an Au(100 nm) with followe RTA at T a = 1000 C for Calculation of barrier parameter from current-voltage characteritic The metho ecribe by Rhoerick [5] i the mot imple in implementation among the metho coniere. In accor with thi metho, the current through the Schottky ioe i ecribe by the relation: V nkt 1 exp V kt I I0 exp. (1) Plotting the current-voltage characteritic in the coorinate ln I / 1 exp V kt V an approximating the line part with traight line y = a + bx, the coefficient b = ln (I 0 ) an a = / nkt, were obtaine, an knowing thee coefficient it i eay to fin b an n. With automating the metho, it i convenient to etermine the ieality factor, when plotting the epenence: V ln I kt n( V ). () If in the curve n(v) there preent i the portion weakly epenent of the voltage, then from thi range of voltage the value of ieality factor an ShBH were etermine uing the Rhoerick metho. It i worth noting that for wie-gap emiconuctor, often even in a highlighte portion in the curve, it i impoible to aert that the ieality factor oe not change with voltage. Thi epenence will make an error into accuracy of etermining the ieality factor an, therefore, the barrier height, which i ubtantially greater than the error introuce by the meaurement inaccuracy. Typical local maximum n for low voltage an increae of the ieality factor with the voltage at high voltage were oberve by everal author [3, 7, 1, ]. The avantage of the Rhoerick metho i the ability to ecribe forwar an backwar branche of the current-voltage characteritic with one epenence, a well a the account of meaurement at V < 3kT/. The iavantage of the metho inclue the lack of account for the influence of the erie reitance. In practice, for mall value of ShBH or large erie reitance, it i impoible to eparate the portion unaffecte by the erie reitance, there i no portion of the I V curve that i ecribe by E. (1). One way to olve thi problem wa propoe by ore. He ha evelope a metho to etermine the barrier height at the voltage V > 3kT/ an with account of the large erie reitance. The ore metho [7] wa evelope for the ieality factor cloe to unity for the cae when the effect of erie reitance on the current-voltage characteritic introuce a ignificant error in etermination of the barrier height by uing the impler metho. For correct ecription of the current-voltage characteritic at V > 3kT/, the formula (1) mut be moifie to the form I A T S exp ( V IR b) kt, where R i the erie reitance. It i eay to ee that, plotting the function * ln I T ln A S, F( V ) V kt we obtain F( V ) IR b V : the lope of the function 1/, with the prevalence of the voltage rop on the erie reitance the lope will be 1/. If there i a portion with a lope of 1/, the barrier height i etermine a the cut-off portion of linear approximation of thi portion on the orinate axi. If the effect of erie reitance i large in the whole voltage range, there ue i the earch of minimum of function F, which i achieve at ome value V min an I min, then the value of the erie reitance an barrier height can be obtaine a R = kt/i min an b F( Vmin ) Vmin kt, repectively. Along with it avantage, the metho ha ome rawback: in many cae, the ieality factor i not eual to unity, which introuce error into reult of calculation. The latter are performe from a ingle point of the current-voltage characteritic, which may alo negatively affect the accuracy of calculation. Below we will conier a number of tuie, in which attempt were mae to neutralize thee iavantage. The Lien metho [8] i bae on the contruction of everal ore-like function of the form, where γ i an arbitrary parameter, γ > n. From thee curve, the current value I min can be obtaine, when G(I min ) i minimal. For V > 3kT/, taking the erie reitance into account, the formula (1) can be rewritten a follow: I I exp ( V IR kt. (3) ) We can ee that from etermining G an formula (3), the epenence of I min (γ) i linear an i ecribe by the expreion I min ( ) ( n) kt R. The erie reitance i etermine uing the lope of the epenence, the ieality factor from the cut-off portion. The barrier height can be foun extrapolating the G min (γ) epenence to the value γ = n. Propoe in the paper by Cibil an Buitrago [9] i a imilar moification of the ore metho, however, intea of the γ parameter, ome parametric voltage performing the ame function wa introuce. Propoe in the metho by Cheung et al. [10] i tranformation of the formula (3): nkt nkt * V ln I explni R lna T S nb, whence epenence V ln I V ln I nkt IR I. That i, plotting the an approximating it with the traight line, we obtain the coefficient a = nkt/ an b = R. To etermine the barrier height, we hall plot the 014, V. Lahkaryov Intitute of Semiconuctor Phyic, ational Acaemy of Science of Ukraine 399

3 Semiconuctor Phyic, Quantum Electronic & Optoelectronic, 014. V. 17, 4. P * epenence H ( I) V nkt ln I T ln A S. A een from E. (3), H ( I) IR nb, i.e., approximating the epenence with the traight line, we obtain the coefficient R an n. The avantage of the Cheung b metho lie in etermination of the erie reitance along with the barrier height an ieality factor, which not only give an aitional information about the contact, but it i alo convenient from the viewpoint of automating the calculation proce. The iavantage inclue the applicability of the metho only at the voltage V > 3kT/. Werner [11] examine three ifferent metho for etermining the parameter of Schottky ioe from the current-voltage characteritic. One of them coincie with the Cheung metho. However, a it wa hown, the other from the metho coniere by Werner, which we will name the Werner metho, gave the mot accurate value b, n an R. The Werner metho ue the ifferential conuctance of the real ioe L = I/V at a forwar bia. For V IR 3kT, with taking into account the euation (3), it can be written: L 1 LR, (4) I nkt whence it follow that plotting the epenence L I f (L) an approximating it with a traight line, one can calculate R from the lope coefficient, an one can get the value of the ieality factor from the cut-off portion. Carrie out in the work by Aubry an Meyer [3] wa a comparative analyi of the metho by Lien an Werner, an it wa hown that the metho have mathematically imilar proceure, accoringly, their accuracy an limitation are cloe. Another way to olve the ientifie problem i to ue the metho of irect approximation (DA) to the entire length of the current-voltage characteritic with the implifie expreion (3) [1] or more complete one that take into account the hunt reitance [13-16]. The iavantage of the metho i the relative complexity of the calculation, however, we have evelope a program [17], allowing eaily-to-make calculation with the majority of the above metho, incluing the batch calculation parameter, which i important for tatitical meaurement. In all the cae ecribe above, the prouct of the effective Richaron contant by the effective area i aume to be known. However, thi prouct can be etermine experimentally in a cae when the temperature meaurement of the current-voltage characteritic were performe. For thi purpoe, it i neceary to ue the metho of activation energy (AE) [9] or the Sato metho [18]. However, ShBH obtaine uing thee two metho i etermine on the aumption that it epenence on temperature i miing. In the preence of a linear temperature epenence of ShBH, the reulting value i often enote by b0, to inicate that thi value obtaine by extrapolating to zero temperature. But thi i true only for the linear temperature epenence of ShBH, in the cae when it i nonlinear we hall obtain ifferent b0 value for ifferent temperature range. In thi cae, it houl be ure to pecify the range of temperature, in which the meaurement were performe, a well a to take into account the error in etermining the value A S ln eual to k, where i the temperature coefficient of ShBH. The metho of activation energy [5] etermine ln (I 0 ) with one of the above metho (by Rhoerick, Cheung an DA) for each temperature eparately. Plotting the epenence I T kt ln 0 an approximating it with the traight line, we obtain the coefficient a lna S an b b 0. The Sato metho [18] lie in the fact that for etermining the barrier height, taken i no ln (I 0 ) but the pecific point on the I V characteritic, which i obtaine from minimum V kt lni 1min F of the function F1 T at certain current I min. In thi cae, the following euality mut be fulfille F n F1min nlni min T ln SA 1 n kt, b 0 an * whence the barrier height b0 ln A * S are etermine a coefficient of the linear approximation a n ln SA 1 an b nb0 for the known ieality factor. Along with the metho of the current-voltage characteritic for etermining the barrier height, the metho of the capacitance-voltage characteritic i often ue. Accoring to [, 5], the epenence of capacitance on the applie voltage in the revere-biae Schottky barrier i ecribe by the euation: 1 C (5) b V kt /, (6) where C = (C E С 0 ) S i the reuce capacitance; С 0 capacitance of a cae, contact; C E experimentally etermine capacitance; concentration of uncompenate onor; permittivity of emiconuctor. If the concentration i contant over the whole area of eplete layer, when plotting the epenence 1/C on V, we get a traight line. Approximating thi line, we hall obtain the coefficient: a b kt an b. 014, V. Lahkaryov Intitute of Semiconuctor Phyic, ational Acaemy of Science of Ukraine 400

4 Semiconuctor Phyic, Quantum Electronic & Optoelectronic, 014. V. 17, 4. P From thee, it i imply to calculate the concentration of uncompenate carrier an ShBH: an a b b kt The metho can be implemente only uner conition of uniform oping emiconuctor, owing to which one can alo etermine the parameter C 0, achieving the linearity of epenence 1/C on V (minimum of error in linear approximation). b, V b0 ioe 1 ioe ioe 3 ioe 4 4. Reult an icuion The parameter of the Schottky barrier calculate by variou metho at the temperature 340 an 480 K are lite in Table 1 an, repectively. For the calculation by uing the AE metho, applie here are the reult of the aturation current etermine by the Rhoerick metho. The reulting value of ShBH i trongly uneretimate (ee Table 1). The reaon for thi i the temperature epenence of b. It i een that the value of the barrier height obtaine from AE an Sato metho i cloe to the value obtaine uing linear extrapolation to zero of the temperature epenence of ShBH, calculate by the Roerick metho (figure). Table 1. The parameter of the Schottky barrier calculate uing ifferent metho. The calculation i performe for the temperature cloe to 340 K. Metho of calculation n b, V lna S Rhoerick 1.51± ± * R, Ohm Cheung 1.50± ± * 934±30 DА 1.493± ± * 951±40 АE Sато C V 0.98 ote. The aterik * enote the value taken for calculation. Table. The parameter of the Schottky barrier calculate uing ifferent metho. The calculation i performe for the temperature cloe to 480 K. Metho of calculation n b, V R, Ohm Rhoerick 1.6± ±0.005 Cheung 1.5± ± ±5 DА 1.45± ± ± T, K Temperature epenence of the barrier height calculate uing the Rhoerick metho. The reaon for increaing the error of calculation of the barrier height in all three metho i the reuction of the length of the logarithmic plot of current-voltage characteritic an increaing in the complexity of etermining it bounarie. In the cae of the Cheung metho, the error i maximum, ince in thi cae the account of the portion of current-voltage characteritic V ~ kt/ play a ignificant role in the total meaurement accuracy. 5. Concluion Coniering the erie reitance an portion of currentvoltage characteritic at V ~ kt/ can contribute a ubtantial correction to the value of the etermine erie reitance, an therefore, the metho of Lien, Werner a well a irect approximation are preferable to etermine the height of the potential barrier at the mall extent of the exponential portion of the current-voltage characteritic, a for example, it i oberve for the current-voltage characteritic of the invetigate ioe at T 480 K. The value of the barrier height, obtaine by the metho of activation energy an Sato, are only vali in the abence of the temperature epenence of ShBH. It ha acertaine that an inconitency between the real current-voltage characteritic an it moel the temperature epenence of the barrier height, ieality factor epenence on the voltage introuce the baic error into the calculate parameter in the ioe uner tuy. In relation with the foregoing, it can be conclue that for the wie-gap emiconuctor, at thi tage of their tuy, the greatet accuracy i inherent to metho allowing to etect an ientify a icrepancy between the moel an meaure ata, namely, metho by Lien, Werner an Cheung. The neceity to tuy the temperature epenence of the ieality factor for correct etermination of the mechanim reponible for the charge tranfer an Schottky barrier height ha been hown. 014, V. Lahkaryov Intitute of Semiconuctor Phyic, ational Acaemy of Science of Ukraine 401

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