C-DLTS C-DLTS Principle of operation and limits of applicationPrinciple of operation and limits of application

E. Fretwurst

Institute for Experimental Physics, University of Hamburg

Principle of operation and basics

The C-DLTFFT-System at HamburgDifferent hardware toolsPrinciple of operationMethods of defect parameter evaluation, limits and systematic errorsHigh Resolution option, basics, an example and practical limits

Summary

1 E. Fretwurst, University of Hamburg Workshop on Defects, Hamburg, August 23-2006

Principle of OperationPrinciple of Operation

[1] Constant reverse bias (VR) traps empty traps filled

Traps in the space charge region of a p+-n diode

Left: Electron trap Right: Hole trap

2 E. Fretwurst, University of Hamburg Workshop on Defects, Hamburg, August 23-2006

Bias pulse Vp < 0 Vp > 0

Capacitance transients C(t) = C(t) – CR

for t > tp negative positive

[2] Carrier injection (Vp) electron capture hole capture

[3] Thermal emission of trapped carriers (VR) electron emission hole emission

Transient analysisTransient analysis

Capacitance transient:

C(t) = C(t) – CR = C0·exp(-(t+t0)/e)

Emisson time constant: 1/e = en + ep

for en » ep 1/e = en

en,ep emission rates for electrons, holesFrom measured transients as function of T:

e(T) values are extracted From Arrhenius plot activation energy Ea,n,p and capture cross section n,p can be extracted using:

assuming n,p independent on T

3 E. Fretwurst, University of Hamburg Workshop on Defects, Hamburg, August 23-2006

Tk

ENe

B

pnaVCpnthpnpn

,,,,,,, exp

Tk

EN

B

pnapnVCpnthe

,,,,,, lnln

Different DLTS techniques:

Analog signal processing: double boxcar integrator lock-in amplifier analog correlator

Digital signal processing: various correlator functions Fast Fourier Transformation FFT Laplace Transformation Refolding of “period scans”

Determination of Defect ConcentrationDetermination of Defect Concentration

Band bending diagrams for deep acceptor:[2] during filling pulse[3] during transient phase

Transition region:

Defect concentration Nt:Amplitude of the C-transient C0 Nt

For << WR simplifies to:

4 E. Fretwurst, University of Hamburg Workshop on Defects, Hamburg, August 23-2006

D

tF

Nq

EE20

0 )(2

1

10

22

102

pCRC

ARC

pCRC

RC

C

DNtN

RC

C

DNtN 02

Requirements, Limitations Requirements, Limitations

C-DLTS requirement:Exponential behavior of capacitance transient if

C CR or Nt Ns

Trap concentration shallow doping concentration This implies a limitation for the maximal particle fluence range which canbe investigated

E.g. for Ns = 1012 cm-3, Nt/Ns = 0.1 and a defect with an introduction rate of

g = 1 cm-1 the maximal fluence would be max ≈ 1011 cm-2

Lower limit for detectable trap concentrations:Depends on the sensitivity of the C-bridge and S/N ratio

E.g. for C0,min ≈ 5 fF, CR ≈ 50 pF (Nt/Ns)min ≈ 2(C0,min/CR) ≈ 2·10-4

Limitations in the detection of trap levels: Very shallow trap levels could not be measured due to freeze-out of free charge carriers

(wR d = diode thickness; CR = Cd = constant) Detection of very deep trap levels might be difficult since the change of the occupation might be very small Minority carrier trap levels could only be detected by forward biasing if cp >> cn , otherwise optical injection of minority carriers

5 E. Fretwurst, University of Hamburg Workshop on Defects, Hamburg, August 23-2006

PULSECONTROL

VOLTAGEAMP

ANTI-ALIAS.FILTER

TRANSIENTRECORDER

PROCESSOR

Bias: +/- 20 VHV: +/- 100 Vtp min: 1 µs

FAST PULSEBias:+/- 16 Vtp min: 10 ns

Rin = 1 M gain: 1-128

Bessel 8. order1 Hz to 100 kHz

32 K d.p.64xoversampl.12 bit resolution

18 correl. functionsFFT processingC compensation

PC

BOONTON 72B

Capacitance Meter

LakeShore 340Temperature

Controller

Optical Injection

DUT

T-sensorDT-470 SD

CRYOSTAT

DLTDLTFFFT-System in HamburgFT-System in Hamburgfrom PhysTech GmbHfrom PhysTech GmbH

6 E. Fretwurst, University of Hamburg Workshop on Defects, Hamburg, August 23-2006

Digital signal processingDigital signal processingusing 18 correlator functionsusing 18 correlator functions

7 E. Fretwurst, University of Hamburg Workshop on Defects, Hamburg, August 23-2006

0 TWTime-1

1 DR (Tw/4)

DR

a2N

a1M

a1H

a1(Tw/16)

a1(Tw/4)

a1(Tw/2)

a1

0 TWTime-1

1 b2N

b1M

b1H

b1

b1(Tw/16)

b1(Tw/2)

b1(Tw/32)

b1(TW/4)

b1(Tw/8)

DLTS spectra and maximum analysisDLTS spectra and maximum analysis

DLTS spectra obtained with different correlators (left). Arrhenius plot (right) contains data obtained with all 18 correlators. ( transition V(-/0), 60Co irrad. 10 Mrad; VR=-10 V, Vp=0 V, Tw=200 ms, t0=6 ms)

8 E. Fretwurst, University of Hamburg Workshop on Defects, Hamburg, August 23-2006

180 200 220 240temperature [K]

0

0.1

0.2

0.3

DL

TS

- si

gnal

[pF

]

b1b1

b1 (TW/4)b1 (TW/4)b1 Mb1 M

b1Hb1H

DRDR

b1 (TW/2)b1 (TW/2)

b1 (TW/8)b1 (TW/8)

b1 (TW/16)b1 (TW/16)

b1 (TW/32)b1 (TW/32)

4.4 4.6 4.8 51000/T [K-1]

55

56

57

58

ln( e

vth

,n N

C)

DLTFFT spectra and direct analysisDLTFFT spectra and direct analysis

DLTS spectra obtained with sine and cosine correlators a1, b1, a2 and b2. Same measurement as shown before. Arrhenius plot contains data obtained from the direct evaluation method.

9 E. Fretwurst, University of Hamburg Workshop on Defects, Hamburg, August 23-2006

180 200 220 240temperature [K]

0

0.1

0.2

0.3

DL

TS

- si

gnal

[pF

]

b1b1

a1a1

a2a2

b2b2

4.6 4.8 51000/T [K-1]

56

57

58

ln( e

vth

,n N

C)

e (a1,b1)e (a1,b1)e (a2,b2)e (a2,b2)

Direct evaluation:

The emission time constant can be evaluated from the correlator signals an(T), bn(T) at all temperatures where the signals are above a given threshold

E.g.

n

nnne a

b

nba

1

,

Variable time window methodVariable time window method

Time window Tw is changed with temperature TThe ratio e/Tw is kept constant (≈ 0.2) optimal signal e values extracted from an and bn for first T-steps Program produces Arrhenius plot allows calculation of optimal Tw for

the next temperatureRestriction: transients have to be exponential (estimated by the program)Advantage: large T-range for the Arrhenius plot accurate defect parametersDraw back: no DLTS spectrum is produced

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4 4.5 5 5.5 61000/T K-1]

52

54

56

58

60

62

64

ln( e

vth

,n N

C)

Example: Arrhenius plot for same defect as shown before. T-range: 170 – 245 K

Comparison of the three methodsComparison of the three methods

Defect parameters obtained for the 3 different methods for V(-/0):

11 E. Fretwurst, University of Hamburg Workshop on Defects, Hamburg, August 23-2006

Type of evaluation Ea [eV] n [cm2]

Maxima with 3 Tw 0.427 2.610-15

Direct with 3 Tw 0.420 1.710-15

Variable time window 0.424 2.210-15

Tw = 40, 200, 2000 ms

Recalculation of time constants for different temperatures:

Temperature 180 K 200 K 230 K

e - maxima evaluation 3.05 s 157 ms 4.70 ms

e - direct evaluation 2.97 s 160 ms 5.05 ms

e - variable Tw 2.97 s 156 ms 4.77 ms

High resolution methodHigh resolution method

Simulated DLTS spectrum for two levels with similar properties: E1 = 0.410 eV, = 1·10-15 cm2 N1 = 4·1010 cm-3; E2 = 0.400 eV, = 2·10-15 cm2 N2 = 6·1010 cm-3

12 E. Fretwurst, University of Hamburg Workshop on Defects, Hamburg, August 23-2006

0.001 0.01 0.1 1 10 100 1000/TW

0

0.2

0.4

0.6

0.8

1

norm

. b1

[pF]

0

0.2

0.4

0.6

0.8

1

Normalized b1 coefficient versus /Tw with constant t0/Tw = 0.25 (t0: delay time after fill pulse, Tw: time window for recorded transient)

Principle of operation:

Period scan at constant temperature: Transients measured as function of Tw near the DLTS peak max.

Calculated correlator coeff. an(Tw), bn(Tw) are normalized and transformed a’n(), b’n()

Refolding of a’n(), b’n() distribution function f() (Gaussian-like) of the involved trap levels

Refolded spectra Refolded spectra

Refolding of the normalized coefficient a’1() with order N1= 40 (left) or N2 = 60 (right)[N is related to the width of the distribution function of the values (Gauss-like)]Squares: transformed data points of measured transients during Tw scanSolid lines: refolded function f() for two levels for different order N Vertical lines: indicate the peak maxima

13 E. Fretwurst, University of Hamburg Workshop on Defects, Hamburg, August 23-2006

Results from simulations at different temperatures:For both trap levels the parameters Ea, n and Nt are well reproducedEa/Ea 0.5 %, n/n 10 %, Nt/Nt 1 %

Limitations: Time constants of transitions should differ by a factor of > 2 and the ratio of the concentrations should be 0.1

SummarySummary

C-DLTS is a very powerful tool for:Evaluation of defect parameters (majority and minority carrier traps):- Activation energy Ea and capture cross sections n,p

- Accuracy of Ea and n,p depends on S/N of transients, accuracy of T

measurement, extent of temperature range and evaluation method - Direct measurement of via variation of filling pulse duration, with fast pulse option ≈ 10-12 cm2 detectable (e.g. for TD)- Separation of closely spaced trap levels possible by Laplace- or High Resolution- DLTS (limited by minimal difference and ratio of trap concentrations)

Evaluation of trap concentrations Nt:

- Nt/Ns C/CR sets lower and upper limit for detectable Nt,

- (Nt/Ns)min 10-4, (Nt/Ns)max 0.1 (C « CR), for higher values up to 0.4 CC-DLTS

- Accurate Nt evaluation needs correction

- Nt depth profiles could be measured by variation of fill pulse and reverse bias

14 E. Fretwurst, University of Hamburg Workshop on Defects, Hamburg, August 23-2006