7thINTERNATIONAL SIBERIAN WORKSHOP AND TUTORIAL EDM'2006, SESSION VII, JULY 1-5, ERLAGOL

The Method of Semiconductor StructureImpedance Measurement

Nikolay G. ZayeevTomsk State University ofControl ofSystem ofRadioelectronic,Tomsk, Russia

Abstract - A semiconductor structure impedancemeawrement circuit calculation using the differencingcircuit is presented. Alsw the developed method ofmeawrement of phase difference by three-amplitudemethod is presented. These presented methods excel bytheir simplicity and performance.

Index terms - differentiating operational amplifier,semiconductor structure impedance measurement,three-phase method.

I. INTRODUCTIONTHE QUALITY OF MEASUREMENT semi-

conductor structures' physical parameters couldbe increased by measuring not admittance only but atest signal phase shift on measurement system out-put. By knowledge of both signal's components onecan determine active and reactive components of ametal-isolator-semiconductor (MIIS) structure andconsequently its main parameters.

In the presence time in majority of works on de-veloping of MIS-structure properties measurementdevices the phase measurement is implementing byindustrial phasometers ((D2-34 as an example) that'snot always suitable because of their size, low per-formance (more than 10 sec) and unsatisfactory ac-curacy. A digitization of a sinusoidal signal shapeusing software is also possible.

However for digitization of the sinusoidal signalwith frequency of IMHz, it is that frequency whichrequired for hi-frequency C-V behavior measuring,hi-performance ADCs with high grade quantityshould be used. These engineering solutions whichcombine some conflicting objectives on precisionand capacity of digitization are interrelated with highfinancial and technical expenses.

III. THE METHODIC CALCULATIONTo exanimate the differentiating circuit we have

to make a mathematical conversion in the circuit.Express the complex conductance Rx, Cx as serialelements Rx0, CX, (Fig. 1.)

R2RX

U1U2

CX0

U2

R4R

b.Fig I. Conversion of R., C. in Ro, C.,

The Zx impedance (parallel plugging of Rx, Cx onfig. l.a.) can be presented as:

RX9CR+R I

jwcx

RX j oraRX1+±w2 . 2 1+±2 T.2

II MEASUREMENT METHOD

The proposed method of measurement of activeand passive properties of semiconductor devices isbased on method of measurement of MIS-structureadmittance using a differentiating circuit supple-mented by sinusoidal signal phasometer which func-tions on the "three-module" method [1].

This found result shows a possibility of conver-sion of parallel elements Rx, Cx in to serial Rx0, CX0:

R .( 1)R(I)

(2)

Al I+w2 .r2

z = I orA-XRXt9CA I + 02 . T

ISSN 1815-3712 ISBN 5-7782-0646-1 © Novosibirsk State Technical University

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71 INTERNATIONAL SIBERIAN WORKSHOP AND TUTORIAL EDM'2006, SESSION VII, JULY 1-5, ERLAGOL

IV. THE EQUIVALENT CIRCUITCALCULATION

With taking into account that point I (fig. l,b) isa virtual ground one can write the following:

i Ca. dU, Ul

In accordance with these conditions:x Ra= A -arcig-,2 Z

tt = tg = tg(Z 2 A) x

R

where U- is a voltage on CQ. capacitor.

U,=U1 UR=UI JR j Z

whereU2 isavoltageonR,+R,, resistor

U2 =i-2R2 =CO [ j ZJR2dtjR 2 dU

OJ(R jZ) dtReplace in (3.):

I w(R JZ) _,.a jR2 R2

where ;p arctg Rz

From (8.) U2Z x+

(10)z R2 UlU211,

We have an expression forR by substituting ofexpression (10.) in (9.):

(3)

* e' .

(4)

Hence the differentiating circuit output voltagedepends on voltage on circuit input in common case:

U2 = a. dU= R2 e i dU_ (5)dt co. R2Z2 dt

The test signal must have no harmonics and notchange the structure state for developing of semi-conductor devices. The signal with sinusoidal shapemeets all these requirements, i.e.

Ul = UO ejM (6)The signal derivative on circuit input results:

dtIU UO eir i = (7)

Uoej. oew 2= UO .0 e2eDue to expression (7.), expression (5.) becomes:

U2= R2 U0 {j(v+2 9) (8)

PR2 ±Z2

V. DEFINITION OF THE EQUIVALENT CIR-CUIT CONDUCTIVITY PARAMETERS

According to measurement principle on the cir-cuit (fig. 1) one can define the following parameters:* Ul -atestsignal module on the measurement

circuit input;* U, - a signal module on differentiating circuit

output,7

2 a - a test signal phase shift on the

VI. THE IMPEDANCE COMPONENTSDEFINITION

Present R. and Cx as functions of Rx, and CX0,Z I I

Rao a,C0o RO0 txoDivide (2.) on (I.):

z

OraOa,

Or,, T e.

(12)

From expression (1.):RX - (I+ oN2 . ra) -Rao,

Put it under the expression (12.):RX 1±+ , 2V Rao

From expression (2.):OCA .-R 2 =[I +a 2],

a,lcxoPut it under the expression (12.):

C [= Io . (14)X~ 2 -CAO R A

Taking into account that R,0 equals to (R-Rd, andsubstituting R in expression (11.), we have:

o *RC x _R U2 1+ ,(15.)Using o(15.): U

Using (15.):

2 2a, V,A

where bh (x R2. U

using (16.):

[ + 212measurement circuit output.

Rl U2 1'x'2j

b2R. U1 2

(9)

P= xUR Zx- R2 XUl

U2 1r+X2(I 1)

(13)

,2 2'b

(16)

(17)

(18)

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ZAYCEV: THE METHOD OF SEMICONDUCTOR STRUCTURE IMPEDANCE MEASUREMENT

Set expressions (18.) and (11.) under (13.) withtaking into consideration that RxO equals to (R-R1):

Rb+R, U1lrR, x-U R2]. (19)

After simplifying (19.):

b+R2-|UJ2X + R2.-'b. U2 1''+x2

(20)

In the same manner after substitution of expres-sions (18.), (10.), (19.) in (14):

CR2 Ul U2* C+X2 (21)w(b+RR2. U1 2

For expressions (20.) and (21.) the b parameter isdefined from (17.).

Behaviors of MIS-structure capacity are drawnon fig.2. Dependences of an active conductance onthe differentiating circuit output voltage and itsphase are drawn on fig.3. All obtained results arematching with simplified calculations without takinginto account its active component and are linearfunction. Some collapses are observed on the dia-gram of the active conductivity (fig.3). The RI resis-tor actively influences on their appearance. Thecurve becomes linear without it.

Cx, F

1.10- y

4.

1.10-9_ ,

12- / U2,V0 .o01 0.1

Fig.2. The capacity dependence on output signal with taking intoaccount its phase shift. (1.- R2= 160 Ohm, 2.- R2= 1.6 KcOhm,3.- R2= 16KOhm, 4.- R2= 160 KcOhm, y 32 )

gx, S

U2,\

Fig.3. The conductivity dependence on output signal with taking intoaccount its phase shift.(1.- R2= 160 Ohm, 2.- R2= 1.6 KOhm,3.- R2= 16 KOhm, 4.- R2= 160 KOhm, y = 32 )

VII. A PHASE CALCULATION USING THREE-AMPLITUDE METHOD

The principle of phase shift measurement isbased on test signal amplitude, MIS-structure meas-urement circuit output signal amplitude and thesesignals sum amplitude measuring (fig.4).

U, mv

3. - -

2

1.1../

--

13(,, rad

Fig.4. The correlation of sum signal with time shifted signals

Let's evaluate Ul, U2, U3 in terms of trigonome-try:* U1 U01 sin(co t) - the test signal on the circuitinput;* U2 U02 sin(co t + y) - the signal on capacitymeasuring circuit output;*U3 = U, + U2 - Sum of signals U1 and U2.

When it is considered that U3 voltage has a phaseshift relatively U1 and U2, therefore:

U3 = U03 'sin(o t +g) (22)Since U3 is the sum of U1 and U2, then:

U3 =U01 * sin(o t) + U02 sin(o t + 6) (23)After comparing (22.) to (23.) we have:.

sin( . t + v) = U03 *sin(o)t +8) - U01 * sin(o t) (24)s02

For determining of y we are using the followingboundary condition:

If t , then it follows from (24):2

U03 * cos(,6) - UoiU02

If c t = 0, then it follows from (24):

sin(y)= U03 sin(lG)U02

(25)

(26)

With having two variables b and g in both ex-pressions (25.) and (26.) one can evaluate cos(,8)through sin(y):

The following we obtain from (26) using sumsquares formula:

(27)cos(,6) = I1- . sin2(y) .

Obtain after substituting (27) in (25):

_-l ,,t _ i, _r _ _-

317

15-

1H

-L.43,f, -06.5 .1 1.5

10-

7th INTERNATIONAL SIBERIAN WORKSHOP AND TUTORIAL EDM'2006, SESSION VII, JULY 1-5, ERLAGOL318

U2U0 ' 1 -0'2 .sin2 (yV) - U02 cos(yV) = UOI (2803

After simplifying of the expression (28.) we ob-tain dependence of phase shift on Ul, U2, U3 volt-ages modules:

u2 u2 u2Cos(;y) U 03 U02 U012 U1 U2

The diagram of formula (29.)fig.6.

oc, rad

measurement circuit (based on DAI, watch fig.l.a)¢) and the phase shift measurement circuit (based on

DA2, watch fig.6).

(29)

is presented on

IU3

2 6. \ Fig.7. The circuit of measurement of C-V, G-V behaviors of semi-conductor devices.

Fig.5. The diagram of phase dependence on U1, U2, Uout(1. -U =450mV,U2= 900mV,2. -U =450mV,U2 =450nm-U =450mV,U2 =50mV)

The combination of two sinusoidal signals isfered to made on an op amp which is plugged aadder (fig.6)

This circuit output voltage is equal to:U bZX k*U -kU6SblX =-I 1 22 2'

where kl, k2- are coefficients of signals' gaining.Without taking into account that a signal on t

circuit output is inverted its module isn't changing

In that way by simultaneously measuring of volt-age amplitudes on the input and output of the differ-entiator and also the adder output voltage one coulddefine a MIS-structure admittance module and thetest signal phase shift induced by it. These givenparameters are sufficient for proper definition of a

U3, mV MIS-structure equivalent capacity and equivalent400 resistance which characterizes a semiconductor near-W, 3. surface layer quality and boundary of semiconduc-

tor-isolator characteristic.

of- REFERENCESis a [1] Kovalev V.N. Phase shift measurement H Devices and

technique of experiment Xo2, 1958. (in Russian).

30)

this

R1=R2=R3

Ul

UoutR5

MIS U2

Nikolay G. Zaycev. He graduated fromTomsk State University of Control ofSystem of Radioelectronic in 2002 withprofessional skill as an engineer of micro-electronic and semiconductor devices. Theinterest area lays in MIS-structure propertyresearching.

Fig.6. The circuit of two signals adding

As all the three signals U1, U2, Uo0t are knownwe can define the U2 voltage phase relatively the U1.It has been checked on experiment that when MIS-structure (capacitor) capacity is changing then U2and UBb,x amplitudes are also changing that is theevidence of phase shifting.

VIII. THE FINAL CIRCUIT OF MIS-STRUCTURES IMPEDANCE MEASUREMENT

The complete C-V, G-V measurement circuit isshowed on fig.7 and includes the full conductivity