Semiconductor Device and Material...
Transcript of Semiconductor Device and Material...
ECE 4813 Dr. Alan Doolittle
ECE 4813
Semiconductor Device and Material Characterization
Dr. Alan Doolittle School of Electrical and Computer Engineering
Georgia Institute of Technology
As with all of these lecture slides, I am indebted to Dr. Dieter Schroder from Arizona State University for his generous contributions and freely given resources. Most of (>80%) the figures/slides in this lecture came from Dieter. Some of these figures are copyrighted and can be found within the class text, Semiconductor Device and Materials Characterization. Every serious microelectronics student should have a copy of this book!
ECE 4813 Dr. Alan Doolittle
Doping Profiling Secondary Ion Mass Spectrometry
Spreading Resistance Capacitance – Voltage
Threshold Voltage
ECE 4813 Dr. Alan Doolittle
Secondary Ion Mass Spectrometry SIMS is the most common doping profiling technique Incident ions knock out atoms and ions from the substrate The mass of these ions is analyzed
BSi
Cs, O MassAnalyzer
0 200 400 600 Time (s)
0 0.2 0.4 0.6 0.8 1 Depth (µm)
1020
1019
1018
1017
1016
1015
1014
Den
sity
(cm
-3)
Ion
Cou
nts
106
105
104
103
102
101
100
ECE 4813 Dr. Alan Doolittle
Secondary Ion Mass Spectrometry The use of Cs or O results in a modification of the surface
work function (low work function for Cs and high for O) producing either + or – ions.
BSi
Cs, O MassAnalyzer
Charging of the sample can effect both the sputter yield (changes the acceleration energy) and the focus into the mass analyzer Can be offset by an electron flood gun
for –ions and a +H source (rarely used) for +ions
ECE 4813 Dr. Alan Doolittle
Secondary Ion Mass Spectrometry Mass Spectra can be obtained Depth Profiling can be obtained Time of Flight Versions Dominate technology now
ECE 4813 Dr. Alan Doolittle
Secondary Ion Mass Spectrometry
10 15 20 25 30 35 40102
103
104
105
Co
unt R
ate
(per
sec
)
Mass (amu)
S1-O S2-O S3-O
Mass Spectra can be obtained
Mg impurities
Oxygen
Oxygen
Cl impurities
ZnO
ECE 4813 Dr. Alan Doolittle
Secondary Ion Mass Spectrometry
ECE 4813 Dr. Alan Doolittle
Secondary Ion Mass Spectrometry While rarely used in simple SIMS analysis, energy spectrums
for sputtered ions can tell you a great deal about the sample including in-situ resistivity analysis
Care must be taken since SIMS often measures charge to mass ratio. Time of Flight SIMS analyzers correct this problem.
0 20 40 60 80 100
B
A
Conc
entra
tion
(cm
-3)
Sputter Time (min)
Ga Ga-12V Ga+12V Mg
ECE 4813 Dr. Alan Doolittle
Spreading Resistance The wafer is bevelled extending the layer thickness Compare R to calibrated standards; Rsp dominates
~ 20 µm
Original Surface Beveled Surface
∆z = ∆x sin(θ)
spspcp RRRRIVR 2222/ ≈++==
I I V
Current Spreading
I
Rsp
Rp Rc
∆x
htpp://www.ssm-inc.com
ECE 4813 Dr. Alan Doolittle
Spreading Resistance The spreading resistance of ideal metal-
semiconductor contacts can be calculated For flat-bottom probe of diameter d
For hemispherical probe of radius r
For a “real” probe
k must be experimentally determined
dRsp 2
ρ=
rRsp π
ρ2
=
rkRsp π
ρ2
= For ρ = 1 Ω-cm, r = 1 µm, Rsp = 1000-2000 Ω
d
r
ECE 4813 Dr. Alan Doolittle
Spreading Resistance Spreading resistance is measured and
converted to resistivity and NA or ND profiles
10141015101610171018101910201021
102
103
104
105
0 0.02 0.04 0.06 0.08 0.1
ND (c
m-3
) Rsp (Ω
)
Depth (µm)
ECE 4813 Dr. Alan Doolittle
Capacitance-Voltage Capacitance-voltage measurements used for
Doping profiling Flatband voltage, oxide charge etc. in MOS devices Capacitance is a measured charge responding to a time varying voltage
Actual capacitance meters use ac current amps with phase-sensitive detectors to measure “in phase” and “out of phase” components.
G
R L v o
v i C
R L
v i
p
n LiL
iL
Lo
RsmallforvRCjG
vCjGR
Rv
)()/(1
ωω
+≈++
=
In phase: Out of phase:
GvGRv iLo ~≈
CvCRv iLo ~ω≈
ECE 4813 Dr. Alan Doolittle
Capacitance-Voltage Need a device with a space-charge region
Schottky diode, pn junction, MOS-C, MOSFET The dc bias, V, determines W The ac bias, vi, measures the capacitance
−==dVdQ
dVdQC sm
V
v i
W dW
N A
+ + + + -
- - -
Q s Q m
Q
V
dQ/dV
Q/V
VVQVVW
WqNQ
bis
bi
As
−∴
−
=
~~
ECE 4813 Dr. Alan Doolittle
Capacitance - Voltage
))(0
dVdNneglectingdVdWWqANdxN
dVdqAC AA
W
A (== ∫
( ) CAKW
dVCdAqKdVdCAqKCWN os
ososA
εεε
= =−= ;1
2)( 222
3
( )∫ ∫−≈−+−= −+W W
AADs dxNqAdxNNnpqAQ0 0
N A
+ + + + -
- - -
Q s Q m
W dW
V
dVdC
CAK
dVdW
CAKW
WAKC ososos
2 ; ; εεε−===
Depletion region approximation for a p-type substrate
Y-axis X-axis
ECE 4813 Dr. Alan Doolittle
Capacitance - Voltage What to use?
Or
For both
0
2 10-11
4 10-11
6 10-11
8 10-11
1 10-10
0 2 4 6 8 10
Cap
acita
nce
(F)
Voltage (V)
C
V
Slope = dC/dV
0
1 1021
2 1021
0 2 4 6 8 10
1/C
2 (F-
2 )
Voltage (V)
Slope = d(1/C2)/dV
dVdCAqKCWN
osA 2
3
)(ε
−=
( ) dVCdAqKWN
osA 22 1
2)(ε
=
CAKW osε=
The 1/C2 – V curve has less curvature!
ECE 4813 Dr. Alan Doolittle
Capacitance - Voltage C - V curves are always nonlinear 1/C2 - V curves clearly show carrier or doping
density non-uniformities
0
200
400
600
0
2 1020
4 1020
6 1020
-1 1 3 5 7 9
Cap
acita
nce
(pF)
1/C2 (F
-2)
Voltage (V)
C
1/C2
Linear (Uniform Doping)
Nonlinear (Nonuniform Doping)
0
2 1015
4 1015
6 1015
8 1015
1 1016
0 0.5 1 1.5 2Dop
ing
Den
sity
(cm
-3)
Depth (µm)
p p+
ECE 4813 Dr. Alan Doolittle
Capacitance - Voltage C - V curves can determine channel depths in
compound semiconductors
ECE 4813 Dr. Alan Doolittle
MOS Capacitance - Voltage Oxides (insulators) in series with the junctions
create an additional fixed capacitor.
Coxide = εA/tox
CAKW
WAKC osos εε
== ;
Depletion Layer
Substrate
Oxide
VVW bi −~
( ) ( ) ( ) ( )
( ) ( )AbiDA
DAoSnp
AbiDAA
DoSpAbi
DAD
AoSn
VVNN
NNq
KxxW
VVNNN
Nq
KxandVV
NNNN
qK
x
−+
=+=
−+
=−+
=
ε
εε
2
22
ECE 4813 Dr. Alan Doolittle
MOS Capacitance
ECE 4813 Dr. Alan Doolittle
MOS Capacitance
0
0.2
0.4
0.6
0.8
1
-5 -3 -1 1 3 5
C/C
ox
Chf
Gate Voltage (V)
Clf
Cdd
CFB/Cox •
p-Substrate0
0.2
0.4
0.6
0.8
1
-5 -3 -1 1 3 5
C/C
oxChf
Gate Voltage (V)
Clf
Cdd
CFB/Cox•
n-Substrate
Sox
Sox
CCCCC+
=
Oxides (insulators) in series with the junctions create an additional fixed capacitor.
Capacitance approaches the Cox in accumulation. More MOS in chapter 8…
Accumulation Accumulation
+=
OXOS CC
AKW 11ε
ECE 4813 Dr. Alan Doolittle
Max-Min MOS Capacitance
0
0.2
0.4
0.6
0.8
1
-5 -3 -1 1 3 5
C/C
ox
Chf
Gate Voltage (V)
Clf
Cdd
CFB/Cox •
p-Substrate
Sox
Sox
CCCCC+
=
Measure the maximum accumulation Capacitance (high frequency measurement) and the minimum capacitance in strong inversion
Accumulation
A
invSurfaceOSinversion qN
KW ,
@
2 φε=
C2φf
2
2
22
2
22
2
1
4
1
4
−
≈
−
=
ox
inversion
inversion
OS
F
ox
f
f
OS
FA
CC
CAqK
CC
CAqK
Nεφ
εφ
φ
φ
Clf = Low frequency capacitance where the measurement frequency is small enough such that the carriers can respond to the stimulus. Sweep rate of bias is also slow.
Chf = High frequency capacitance where the carriers cannot respond to the stimulus. Sweep rate of bias is also slow.
Cdd = When the bias sweep rate is faster than generation rate such that inversion cannot take place. Typically also measured with a high frequency stimulus.
ECE 4813 Dr. Alan Doolittle
Built-In Voltage Determination from Capacitance-Voltage
The intercept of the C-V curve can determine the VBI
In practice, care should be exercised as in practice the ohmic- contacts (particularly the “back contact”) can lead to errors in the determination of VBI
0
1 1021
2 1021
0 2 4 6 8 10
1/C
2 (F-
2 )Voltage (V)
Slope = d(1/C2)/dV
Accounting for the majority carrier tail in the depletion region (introduces a kT/q factor – this effect is ignored in the depletion region approximation) The voltage intercept is,
For a p-n junction,
For a Schottky diode,
qkTVV BIi +−=
= 2ln
i
DABI n
NNq
kTV
qkT
NN
qkTV
D
CBi +
+−= lnφ
ECE 4813 Dr. Alan Doolittle
Contactless C - V Contact C-V measurements
pn junctions Evaporated metal Schottky diodes Mercury Schottky diodes MOS capacitors
Can also be implemented contactless Compressed air escapes through porous
disc; air cushion forms between electrode and semiconductor surface
dVCdAqKdVdCAqKCN
ososA /)/1(
2/ 222
3
εε=−=
−=
airos CCAKW 11ε;
Sair
Sair
CCCCC+
=
d ≈ 1 µm
Bellows Ceramic Air Filter
Pressurized Air
d
http://www.semitest.com
W
ECE 4813 Dr. Alan Doolittle
Contactless C -V Contact diameter ~
1 mm Need calibrated
standard wafer Can be used on
product wafers Gives doping
profiles Used mainly by
wafer manufacturers
150 mm wafer
Ω-cm
ECE 4813 Dr. Alan Doolittle
Contactless C -V
Hg probe Liquid metal
contacts Some “contact”
occurs so some concern for contamination (in production) exists.
Insulating substrates can be used (not shown) Two series
capacitors, one being substantially larger than the other
Photo from MDC Corporation
Photo from SSM Corporation
ECE 4813 Dr. Alan Doolittle
Electrochemical C -V
Simultaneously performs CV analysis while electrochemically etching the semiconductor
Holes needed for etching P-type is easy N-type needs light to
generate holes
Works best with direct bandgap semiconductors but is used with Si
ECE 4813 Dr. Alan Doolittle
What Is Measured ?
The previous equations indicate the doping profile is measured
The entities that respond to the ac voltage are the majority carriers, not the dopant atoms
Detailed modeling has shown that the majority carrier profile is measured
Debye Length≡ a measure of the distance over which a charge imbalance is neutralized by majority carriers (under steady state conditions). The Debye length sets the spatial limit (resolution) of an electrically measured profile.
)(2 npqkTKL os
D +=
ε
NAp
NA
p
0 x
NAp
NA
p
0 xW
NAp
NA
p
0 x
NAp
NA
p
0 xW
ECE 4813 Dr. Alan Doolittle
Debye, Thomas-Fermi or Other Limit? You will hear physicists often using the “Thomas-Fermi” length as a
resolution limit instead of the Debye length – why? Both are a measure of the distance over which a charge imbalance is neutralized
by majority carriers (under steady state conditions). The Debye length sets the spatial limit (resolution) of an electrically measured profile. Debye Length valid for non-generate semiconductors at any temperature
Thomas-Fermi Screening Length is valid for degenerate semiconductors and metals and is strictly valid only at low temperatures (but is more generally applied at all temperatures)
Quantum Confined Length: When an electron (hole) is confined by a potential well to form a 2D sheet with planar doping density N2D, its spatial extent is described by a “wavefunction” that has limited width. In this special and common case, the resolution limit is described by:
)(2 npqkTKL os
D +=
ε
( ) *2
261
3 mqK
npL os
TFεππ
+
=
[ ]31
2*2
2
94
572
=
D
osQCS Nmq
KL ε
ECE 4813 Dr. Alan Doolittle
What Is Measured ? C-V and VT profiling methods determine the carrier density,
not necessarily the doping density For uniformly doped material: p = NA, n = ND
For non-uniformly doped material: p ≠ NA, n ≠ ND
Important Limitation: When the contact area becomes comparable to the depletion width, a simple parallel plate capacitor model cannot be used. A 3D solution is needed.
W.C. Johnson and P.T. Panousis, “The Influence of Debye Length on the C-V Measurement Doping Profiles,” IEEE Trans. Electron Dev. ED-18, 965-973, Oct. 1973.
NAp
NA
p
0 x
ECE 4813 Dr. Alan Doolittle
Series Resistance
Device As Seen By C Meter
Cp, Cs, Gp and Rs are all capacitance meter measured values. Series connection is preferred if series resistance is important! Never trust a Capacitance measurement with a quality factor (Q=ωC/G) < 5.
+=
++=
2
22 1;)()1( actual
actualactuals
actualsactuals
actualp C
GCCCrGr
CCωω
0
50
100
150
200
10-7 10-6 10-5 10-4 10-3
Cs,
Cp
(pF)
G (S)
Cs
Cp
rs = 100 -10,000 Ω
rs = 10,000 Ω1,000 Ω
100 Ω
f = 100 kHz
G
rs
C
(a)
Gp Cp
(b)
Rs
Cs
(c)
actual actual
Capacitance Meter Error
ECE 4813 Dr. Alan Doolittle
“Deep” Concerns When an acceptor or defect energy is deep in the bandgap a concern
as to whether the carriers can adequately respond to the ac stimulus is warranted.
If for a p-type material with (for example) a deep acceptor at EA eV above the valance band,
So for 0.16 eV deep acceptor (In in Si or Mg in GaN), τemission~ 0.5 uS (~5 x [1/ω] for a 1MHz signal). τemission increases by a factor of ~10 when EA=0.22 eV.
In such cases, the capacitance does not accurately reflect p or NA
tmeasuremenVthermalp
kTE
emission Nve
A
ωστ 1
>=
3195215 10sec/1010 −− ≈≈≈ cmNcmvcm Vthermalpσ
EA
EV
EC
ECE 4813 Dr. Alan Doolittle
Series Resistance If more than 2 parameters are needed, then more than one frequency will be
required.
There are limits to the 2-frequency technique and cautions should be exercised to insure measurements are valid. The reader is encouraged to examine Agilent application note 4294-3 : “Evaluation of MOS Capacitor Oxide C-V Characteristics Using the Agilent 4294A”, section 7.
MAIN POINT: LEAKAGE CURRENT CAN LOWER APPARENT CAPACITANCE AND IS BIAS DEPENDENT – HUGE ERRORS! Thin dielectrics Semiconductors with inverted surfaces
21
22
1212
22
ωωωω
−−
= SSactual
CCC
ECE 4813 Dr. Alan Doolittle
MOSFET Threshold Voltage Based on I-V not C-V so the technique scales better. The threshold voltage, VT, dependence on substrate bias
can be used to determine the doping profile under the gate
( )
( )A
SBFos
os
oxA
ox
Aos
SBF
T
qNVKW
qKmCWN
mC
NqKVd
dV
+=
=
==+
φε
ε
εφ
222
22
22
( )
MOSFETnforVC
VNqKVV
SB
ox
SBFAosFFBT
−>
+++=
0
222 φεφ
p
n n
SVG
VD=0.1V
VB
ECE 4813 Dr. Alan Doolittle
MOSFET Threshold Voltage Measure VT as a function of back bias VB Assume a value for 2φF , say 0.6 V; plot VT vs. (2φF +VB)1/2 Find NA from the slope, Use this NA to then find a new 2φF and replot VT vs. (2φF +VB)1/2 One or two iterations are sufficient Find density NA and depth W and plot the profile
D. Feldbaumer and D.K. Schroder, “MOSFET Doping Profiling,” IEEE Trans. Electron Dev. 38, 135-140, Jan. 1991.
0
2 1016
4 1016
6 1016
8 1016
1 1017
0 0.1 0.2 0.3 0.4 0.5
Dop
ing
Den
sity
(cm
-3)
Depth (µm)
SRP
C-V
SUPREM
VT
ECE 4813 Dr. Alan Doolittle
Profiling Limits There are two limits
Close to surface Junction breakdown
10-3
10-2
10-1
100
101
102
1014 1015 1016 1017 1018 1019 1020
Dis
tanc
e (µ
m)
NA (cm-3)
WBD
3LD
Si, T=300K DA
bios LqN
VKW 652−≈=
ε
Schottky:
W
N A
MOS-C:
NA
3LD
KTatSifor
cmNNq
kTKLAA
osD
300
4102
=
==ε
ECE 4813 Dr. Alan Doolittle
Review Questions What is secondary ion mass spectrometry? Name a disadvantage of spreading resistance
profiling. How is the capacitance measured? Why is 1/C2 - V preferred over C – V? What is important in contactless C – V? What is measured in most profiling techniques,
i.e., doping density or majority carrier density? What is the Debye length? What does series resistance do? How does the threshold voltage technique work? What determines the profiling limits?