The Parametric Measurement Handbook. Third Edition March 2012

Transcription

1 The Parametric Measuremet Hadbook Third Editio March 2012

2 Chater 7: Diode ad Trasistor Measuremet Choose a job you love, ad you will ever have to work a day i your life Cofucius Itroductio It is ot the itet of this hadbook to teach a course o semicoductor device hysics as there are already a abudace of ecellet tetbooks available o this subject. However, it is difficult to discuss makig arametric diode ad trasistor measuremets without first sedig a little time uderstadig their oeratio. Therefore, we will give a brief review of juctios, diodes, ad MOS ad biolar trasistor oeratio with a emhasis o how we characterize them i arametric test as oosed to detailed theoretical derivatios. PN juctios ad diodes Review of PN diode oeratio I trisic semicoductor materials (such as silico) do ot have a abudace of either electros or electro holes. However, silico ca be doed with other materials such that it becomes either -tye (ossessig ecess electros) or -tye (ossessig ecess electro holes). Whe cosidered idividually these materials are ot articularly iterestig. However, cosider the case show below whe these two materials are brought ito close cotact. Q - + E Figure 7.1. The cross sectio of a juctio assumig a abrut chage from -doed to -doed material. The grah shows the fied charge remaiig after the mobile carrier diffusio has stabilized. Assumig the etremely idealized case of a abrut juctio (i.e. oe that istataeously trasitios from to material) as show i Figure 7.1, we ca see that somethig very iterestig haes. The force of diffusio causes holes from the -tye material to flow ito the -tye material (leavig behid fied egative charge), ad similarly the force of diffusio causes electros from the -tye material to flow ito the -tye material (leavig behid fied ositive charge). This diffusio rocess will cotiue util the electric field created by the fied charge i what is ormally called the sace-charge regio becomes strog eough to eactly balace the diffusio tedecies of the mobile carriers. 126

3 The oe-dimesioal (-ais) equatios defiig curret flow i semicoductor are show below. d J = qμε + qd (Equatio 7.1) d J = q μ Ε qd d d Where J is the curret desity of electros () ad holes () q is the electro charge is the electric field i the -dimesio is the mobility of electros () ad holes () D is the diffusio costat for electros () ad holes () is the electro desity is the hole desity (Equatio 7.2) These equatios basically state what was alluded to i the revious discussio of a abrut juctio. Namely, curret flow i a semicoductor cosists of two arts: a drift curret roortioal to the alied electric field ad a diffusio curret roortioal to the satial first derivative of the mobile carrier desity. I additio to the above curret flow equatios we also have the Eistei relatioshi which relates the ratios of the mobility ad diffusios costats as show below. D D kt = = (Equatio 7.3) μ μ q Where q is the magitude of the electro charge ( Coulomb) k is Boltzma s costat ( J/K) T is the absolute temerature [deg K] The geeral form of Poisso s equatio relates the secod derivative of the electric otetial to the total sace charge desity ( ). ce we kow that i a semicoductor this has to be related to the desities of mobile ad fied charge, we ca write this as follows. 2 d j = 2 d q e ( + N d N a ) (Equatio 7.4) Where Nd is the door desity cocetratio Na is the accetor desity cocetratio is the ermittivity of silico I the case of the abrut juctio show i Figure 7.1 we make what is kow as the deletio aroimatio, which assumes that the semicoductor is divided ito distict regios which are either comletely eutral or comletely deleted of mobile carriers. Therefore, i the deletio regio we ca write the above equatio as follows. 2 d j q = ( N ) 2 d Na d e (Equatio 7.5) 127

4 Usig the deletio aroimatio we ca itegrate the above equatio to get the electric field i both the ad regios as show below. qna Ε ( ) = ( + ) 0 e (Equatio 7.6) qn d Ε( ) = ( ) 0 e (Equatio 7.7) Where is the width of the sace charge i the regio (see Figure 7.1) is the width of the sace charge i the regio (see Figure 7.1) Grahically, these equatios have the aearace show below. E E (0) Figure 7.2. The electric field i a abrut juctio uder the deletio aroimatio assumtio. We kow that the electric field has to be cotiuous at = 0. qnd qn a Ε ( 0) = = ε ε (Equatio 7.8) This gives us the result show below. N d = N a (Equatio 7.9) Equatio 7.9 shows a imortat characteristic of juctios: the width of the deletio regio varies iversely with the magitude of the doat cocetratio. I other words, higher doat cocetratios result i arrower sace charge regios. 128

5 Whe o voltage is alied to the juctio a barrier eists to curret flow ad the diode acts as a oe circuit. The derivatio of the curret flow equatios are ivolved ad beyod the scoe of this tet. However, it should be somewhat ituitive that as we aly a ositive voltage (i.e. electric field) to the -regio we are actig to reduce the built-i electric field of the juctio. At some oit the electric field is reduced eough to allow curret to flow through the juctio. Sace charge regio Ohmic cotact Ohmic cotact I + - Va Figure 7.3. The behavior of a juctio uder ositive alied bias. Therefore, without ay detailed derivatios we will ask the reader to take it o faith that the curret flow through a diode ehibits eoetial deedece uo alied voltage (Va) ad is give by the equatio show below. qva kt I = Io e 1 (Equatio 7.10) This is sometimes called the ideal diode equatio. It redicts a saturatio curret of I o for egative values of Va ad a eoetially risig curret for ositive values of Va. To emhasize that a diode oly coducts curret i oe directio, it has the circuit symbol show below. I D Aode Cathode + - V A Figure 7.4. The circuit symbol for a diode. 129

6 The -doed regio is deoted as the aode, ad the -doed regio is deoted as the cathode. Note: I actuality diodes ca coduct curret i both directios. However, tyically much larger voltages eed to be alied to the cathode (relative to the aode) i order for curret flow to occur i the reverse directio. I this coditio the diode is said to breakdow, which is a logical term for this heomeo sice it is a aberratio from ormal diode behavior. The hysics of semicoductor juctio breakdow will ot be discussed i this hadbook, but later some ractical measuremet eamles will be elored. The Ohmic cotacts show at the eds of the diode i Figure 7.3 simly mea that the semicoductor material is heavily doed eough such that the metal to semicoductor cotact does ot reset ay sort of barrier to the flow of curret. If the semicoductor material is lightly doed the metal to semicoductor cotact ca actually behave as aother form of diode kow as a Schottky barrier diode. Curret flow i a Schottky barrier diode has a deedece o alied voltage as show below. qv kt I = I' e 1 (Equatio 7.11) o a I Equatio 7.11 is a costat usually ragig from betwee 1.02 ad The rime symbol is reset o I o to emhasize that this costat is differet i value from that for the case of a juctio. Schottky diodes tyically have a effective tur-o voltage that is several hudred millivolts less tha that of a juctio diode, which makes them essetial i the desig of biolar logic circuits sice they ca kee the base to collector juctio from forward biasig ad therefore kee the trasistor out of saturatio. Oe imortat oit to ote about juctios is that they behave as voltagedeedet arallel late caacitors, sice as we aly eteral voltages we modify the charges i ad aroud the sace-charge regio. Therefore, juctio caacitace is oe imortat arameter that must be characterized for all semicoductor devices, sice this imacts the seed at which the devices will switch whe used i a itegrated circuit. However, sice caacitace measuremet is much more challegig to erform correctly tha simle curret ad voltage (IV) measuremets, we will defer a detailed discussio of semicoductor caacitace measuremet to Chater

7 Basic diode characterizatio Diodes are relatively simle devices to characterize. From Equatio 7.10 we ca see that a lot of the log of the diode curret (Id) should be liear with resect to alied voltage. A lot of diode curret ad the log of the diode curret for a tyical diode are show below. Figure 7.5. A diode swee i the forward directio lottig both Id ad Log(Id). Of course, aother imortat arameter is the reverse breakdow characteristics of the diode. A lot of this is show below. Figure 7.6. The reverse breakdow characteristics of a diode. Usig various rocessig techiques it is ossible to cotrol the reverse breakdow characteristics of certai classes of diodes very recisely. Diodes with these sorts of recisely cotrolled breakdow characteristics are kow as zeer diode. This has some obvious beeficial uses i circuit desig, sice it ermits the zeer diodes to be used as voltage clams withi the circuit. 131

8 To Get Comlete Hadbook If you wat to have more iformatio, visit the followig URL. You ca get the comlete "Parametric Measuremet Hadbook". This total guide cotais may valuable iformatio to measure your semicoductor devices accurately, also icludes may hits to solve may measuremet challeges. Now, Eglish, Jaaese, Traditioal Chiese, ad mlified Chiese versios are available. Cotets of Hadbook Chater 1: Parametric Test Basics What is arametric test? Why is arametric test erformed? Where is arametric test doe? Parametric istrumet history Chater 2: Parametric Measuremet Basics Measuremet termiology Shieldig ad guardig Kelvi (4-wire) measuremets Noise i electrical measuremets Chater 3: Source/Moitor Uit (SMU) Fudametals SMU overview Uderstadig the groud uit Measuremet ragig Elimiatig measuremet oise ad sigal trasiets Low curret measuremet Sot ad swee measuremets Combiig SMUs i series ad arallel Safety issues Chater 4: O-Wafer Parametric Measuremet Wafer rober measuremet cocers Switchig matrices Positioer based switchig solutios

9 Positioer based switchig solutios Chater 5: Time Deedet ad High-Seed Measuremets Parallel measuremet with SMUs Time samlig with SMUs Maitaiig a costat swee ste High seed test structure desig Fast IV ad fast ulsed IV measuremets Chater 6: Makig Accurate Resistace Measuremets Resistace measuremet basics Resistivity Va der Pauw test structures Accoutig for Joule self-heatig effects Elimiatig the effects of electro-motive force (EMF) Chater 7: Diode ad Trasistor Measuremet PN juctios ad diodes MOS trasistor measuremet Biolar trasistor measuremet Chater 8: Caacitace Measuremet Fudametals MOSFET caacitace measuremet Quasi-static caacitace measuremet Low frequecy (< 5 MHz) caacitace measuremet High frequecy (> 5 MHz) caacitace measuremet Makig caacitace measuremets through a switchig matri High DC bias caacitace measuremets Aedi A: Agilet Techologies Parametric Measuremet Solutios Aedi B: Agilet O-Wafer Caacitace Measuremet Solutios Aedi C: Alicatio Note Referece