1. Theory

SMU: A source-measure unit combines a precise voltage or current source with simultaneous read-back of current and voltage, and can source or sink power in all four quadrants (Keithley).
Compliance: Each source has a limit on the other quantity, protecting the device and the operator (Keithley).
Probe station: A shielded, often temperature-controlled chuck holds the wafer while probes or probe cards land on pads, connecting the SMUs to individual devices (Tektronix; FormFactor).
Limits: Offsets, leakage, settling, noise and contact resistance set what can be measured, from femtoamps to amperes (Tektronix; Keithley; Sia).

2. Working Principle

Feedback ammeter: Low currents are measured with a feedback ammeter whose noise gain depends on the source resistance (Tektronix).
Guarding: A driven guard at the same potential as the high-impedance node removes leakage through cable and fixture insulation (Tektronix; Keithley).
Remote sense: Separate sense leads measure voltage at the device so that lead and probe drops are corrected (Keithley; Sia).
Shielding and dark enclosure: The probe station is enclosed in an electrostatic shield tied to Force LO and kept dark (Tektronix).

3. Applications

Device I-V: Transistor transfer and output curves, diode characteristics and leakage (Keithley).
Compact-model extraction: Kelvin-probed data for parameter extraction (FormFactor; Sia; Parameter Extraction pages).
Power devices: Pulsed high-current I-V without self-heating (Keithley).

Source and Measure Relations

Name	Formula	Related Formulae	Variables/Constants
Measured current	$I_{m e a s} = I_{D U T} + I_{o f f se t} + I_{L}$	$I_{L} = \frac{V _{H I} - V _{G}}{R _{in s}} \to 0 when V_{G} = V_{H I} (guard)$	$I_{m e a s} : r e a d in g$ $I_{D U T} : d e v i ce c u r r e n t$ $I_{o f f se t} : in s t r u m e n t o f f se t$ $I_{L} : l e ak a g e t h r o ug h in s u l a t i o n$ $V_{H I} : F or ce H I p o t e n t ia l$ $V_{G} : g u a r d p o t e n t ia l$ $R_{in s} : in s u l a t i o n r es i s t an ce; T e k t r o ni x : I_{M E A S U R E} = I_{S O U R C E} + I_{O F F S E T} an d I_{M} = I_{D U T} + I_{L}, g u a r d d r i v e n b y a u ni t y - g ain l o w - im p e d an ce am pl i f i er so t ha t t h e F or ce H I t o g u a r d v o l t a g e i s n e a r l y 0 V, o f f se t in t h e f e m t o am p r an g e w i t h t h e p r e am pl i f i er, w a r m - u p o f a t l e a s t 60 min an d m o n t h l y o f f se t r e m e a s u r e m e n t; K e i t h l ey : g u a r d b u f f er a t n e a r l y t h e s am e p o t e n t ia l a s t h e hi g h - im p e d an ce n o d e; l e ak a g e a s V / R_{in s} (co m p u t e d, O h m^{'} s l a w)$ $(co m p u t e d : 10 V a cr oss 1 \times 1 0^{14} Ω o f in s u l a t i o n l e ak s 0.1 pA; a g u a r d h o l d in g t ha t v o l t a g e t o 1 mV c u t s i t t o 1 \times 1 0^{- 5} pA)$
Compliance and four-quadrant operation	$source V : ∣ I ∣ \leq I_{co m p}; source I : ∣ V ∣ \leq V_{co m p}$	$P = V I > 0 (source), P = V I < 0 (sink)$	$I_{co m p}, V_{co m p} : co m pl ian ce l imi t s$ $P : p o w er d e l i v er e d b y t h e S M U; K e i t h l ey : S M U s co mbin e a so u r ce w i t h r e a d - ba c k m e a s u r e m e n t, c an so u r ce or s ink in f o u r q u a d r an t s, an d in c l u d e a co m pl ian ce l imi t f or d e v i ce an d o p er a t or s a f e t y; s i g n co n v e n t i o n f or so u r c in g an d s ink in g (m y r e a d in g)$ $(co m p u t e d : an S M U so u r c in g 2 V in t o a 1 kΩ r es i s t or w i t h 1 mA co m pl ian ce hi t s t h e l imi t an d d e l i v er s 1 mA a t 1 V)$
Remote (four-wire) sense	$V_{D U T} = V_{se t} - I R_{l e a d} (two-wire)$	$V_{D U T} = V_{se t} (sense leads at the DUT, negligible sense current)$	$V_{D U T} : v o l t a g e a t t h e d e v i ce$ $V_{se t} : p r o g r amm e d v o l t a g e$ $R_{l e a d} : l e a d an d co n t a c t r es i s t an ce; K e i t h l ey : 1 A t h r o ug h 0.5 Ω o f l e a d r es i s t an ce l i f t s t h e so u r ce 0.5 V ab o v e g r o u n d an d r e m o t e se n se cor r ec t s t h e o u tp u t b y - 0.5 V; t h e d r o p f or m u l a i s im pl i e d b y t h e e x am pl e$ $(co m p u t e d : 1 A x 0.5 Ω = 0.5 V)$

Low-Current Limits

Name	Formula	Related Formulae	Variables/Constants
Settling time	$τ = R_{S} C_{s h u n t}$	$I (t) = I_{f ina l} (1 - e^{- t / τ}), t_{1%} = τ ln 100 = 4.6 τ$	$τ : t im e co n s t an t$ $R_{S} : so u r ce r es i s t an ce o f t h e D U T$ $C_{s h u n t} : c ab l e an d f i x t u r e c a p a c i t an ce; T e k t r o ni x : 10 pF an d 1 T Ω g i v e 10 s, f i v e t im e co n s t an t s (50 s) t o se ttl e w i t hin 1 p er ce n t, 63 p er ce n t a f t er o n e t im e co n s t an t, t r ia x w i t h g u a r d se ttl es ab o u t t e n t im es f a s t er t han co a x an d l e ak s a f e w p i co am p s l ess a t 100 G Ω an d 10 V$ $(co m p u t e d : 4.6 τ = 46 s f or 1 p er ce n t; t h e so u r c e^{'} s 5 τ l e a v es 0.67 p er ce n t)$
Noise gain and thermal noise	$V_{n, o u t} = V_{n, in} (1 + \frac{R _{F}}{R _{S}})$	$i_{n} = \frac{4 k _{B} T B}{R}$	$V_{n, o u t}, V_{n, in} : o u tp u t an d in p u t n o i se v o l t a g es o f t h e f ee d ba c k amm e t er$ $R_{F} : f ee d ba c k r es i s t or$ $R_{S} : so u r ce r es i s t an ce$ $i_{n} : J o hn so n n o i se c u r r e n t o f r es i s t an ce R$ $k_{B} : B o l t z mann co n s t an t$ $T : t e m p er a t u r e$ $B : ban d w i d t h; T e k t r o ni x : t h e n o i se - g ain e q u a t i o n an d minim u m so u r ce r es i s t an ce p er r an g e (1 t o 100 G Ω f or t h e 1 t o 100 pA r an g es, 1 t o 100 MΩ f or 1 t o 100 nA, 1 t o 100 kΩ f or 1 t o 100 μ A, 1 t o 100 Ω f or 1 t o 100 mA), so u r ce c a p a c i t an ce r ai s in g t h e n o i se g ain; K e i t h l ey : n o i se f l oor a s l o w a s 0.4 fA p e ak t o p e ak; J o hn so n n o i se c u r r e n t f r o m B a l o g h e t a l .^{'} s S_{V} = 4 k_{B} T R d i v i d e d b y R^{2} (co m p u t e d)$ $(co m p u t e d : a t 300 K in 1 Hz, i_{n} = 0.13 fA f or 1 T Ω an d 4.1 fA f or 1 G Ω)$
Spurious currents	$I_{t r ib o} \sim tens of nA, I_{e p o x y} \sim a few nA$	$electrostatic pickup important for I \leq 1 nA or R \geq 1 G Ω$	$I_{t r ib o} : t r ib oe l ec t r i c c u r r e n t f r o m c ab l e f l e x in g$ $I_{e p o x y} : c u r r e n t f r o m u n c l e an e d e p o x y b o a r d s; T e k t r o ni x : t h ese ma g ni t u d es, g r a p hi t e - im p r e g na t e d t r ia x in s u l a t i o n, h u mi d i t y b e l o w 50 p er ce n t, s hi e l d s t i e d t o F or ce L O, s in g l e - p o in t g r o u n d in g, l i g h t b l oc k in g, p a r a s i t i c c u r r e n t s t ak in g min u t es t o h o u r s t o d ec a y a f t er r eco nn ec t i o n$ $(co m p u t e d : a 10 nA t r ib oe l ec t r i c b u r s t i s 1 \times 1 0^{5} t im es a 0.1 pA l e ak a g e s i g na l)$

Probe Station Effects

Name	Formula	Related Formulae	Variables/Constants
Probe and contact resistance	$V_{D S, in t} = V_{D S} - I_{D} (R_{p, S} + R_{p, D})$	$R_{D S, m e a s} = R_{D S} + R_{p, S} + R_{p, D} (without Kelvin sense)$	$V_{D S, in t} : in t r in s i c d r ain - so u r ce v o l t a g e$ $R_{p, S}, R_{p, D} : p r o b e an d co n t a c t r es i s t an ces a t so u r ce an d d r ain; S ia (I C M T S 2017) : 0.4 Ω p er p r o b e a t 25^{\circ} C an d 2.5 Ω a t 150^{\circ} C, co n t a c t 0.8 t o 1 Ω f or t h e f i r s t 75 t o u c h d o w n s an d 20 Ω a t t h e 100 t h, ab o u t 5 Ω a t 150^{\circ} C w i t h an o p e n c i r c u i t a t t h e 43 r d t o u c h d o w n a s co pp er o x i d i z e d, a s i x - p a d t r u e - K e l v in s t r u c t u r e g i v in g 10 t o 25 p er ce n t hi g h er I_{D} o n a 60 nm N M O S; F or m F a c t or : t r u e - K e l v in f or ce - se n se M E M S p r o b es, co pp er o x i d a t i o n an d s ma l l p a d s l imi t in g s t ab l e co n t a c t; e q u a t i o n (co m p u t e d f r o m t h e ser i es p r o b e an d co n t a c t r es i s t an ces)$ $(co m p u t e d : tw o 0.8 Ω co n t a c t s a dd 1.6 Ω, 8.5 p er ce n t o f an 18.8 Ω d e v i ce; a t 64 mA t h ey d r o p 102 mV)$
Self-heating and pulsed I-V	$Δ T = P R_{t h} = I_{D} V_{D S} R_{t h}$	$t_{p u l se} ≪ τ_{t h} \Rightarrow Δ T \approx 0$	$Δ T : d e v i ce t e m p er a t u r e r i se$ $P : d i ss i p a t e d p o w er$ $R_{t h} : t h er ma l r es i s t an ce$ $t_{p u l se} : p u l se w i d t h$ $τ_{t h} : t h er ma l t im e co n s t an t; K e i t h l ey : S M U s w i t h l o w o u tp u t c a p a c i t an ce an d hi g h s l e w r a t e g i v e p u l ses w i t h 60 ns e d g es an d 500 ns w i d t h s, u p t o 1 kW f or p o w er d e v i ces; h e a t in g r e l a t i o n (co m p u t e d f r o m t h e d e f ini t i o n o f R_{t h}), p u l se co n d i t i o n (m y r e a d in g)$ $(a ss u m e d : 77 mW a t 64 mA an d 1.2 V w i t h R_{t h} = 2000 K/W; co m p u t e d : Δ T = 154 K in D C, n e g l i g ib l e in a p u l se m u c h s h or t er t han τ_{t h})$

Important Questions

Ques: What does an SMU do that a power supply and meter do not?

It sources and measures in one fast, tightly controlled loop and can absorb power as well as deliver it. Keithley describes SMUs as fast-response, read-back voltage and current sources that operate in four quadrants, so they can force positive or negative voltage or current and act as a load. Each source has a compliance limit on the other quantity: sourcing 2 $V$ into 1 $kΩ$ with a 1 $mA$ limit, the SMU stops at 1 $mA$ and 1 $V$ (computed). Built-in sweeps reach about 2000 readings per second, and the range runs from microvolts and femtoamps to more than 1000 $V$ or 10 $A$ . Pulsed SMUs give 60 $ns$ edges and 500 $ns$ widths, which a general-purpose supply with large output capacitance cannot. Reference: Keithley, source-measure unit application article 6058 (fetch-tool summary).

Ques: Why are Kelvin connections needed on a probe station?

Because probe and contact resistances are no longer small compared with modern devices. Keithley’s example shows 1 $A$ through 0.5 $Ω$ of lead resistance lifting a MOSFET source 0.5 $V$ above ground, which remote sense corrects. On wafers, Sia measured 0.4 $Ω$ per probe at 25 $^{\circ} C$ and 2.5 $Ω$ at 150 $^{\circ} C$ , with contact resistance of 0.8 to 1 $Ω$ for the first 75 touchdowns rising to 20 $Ω$ by the 100th. Two 0.8 $Ω$ contacts add 8.5 per cent to an 18.8 $Ω$ device (computed), and a six-pad true-Kelvin structure gave 10 to 25 per cent more drain current on a 60 $nm$ NMOS than the conventional four-pad layout. FormFactor’s true-Kelvin probes address the same problem. Reference: Keithley, source-measure unit application article 6058 (fetch-tool summary); C. B. Sia, ‘True Kelvin CMOS Test Structure’, ICMTS 2017 slides, FormFactor (fetch-tool summary); FormFactor blog, ‘DC probes for accurate and consistent device modelling measurements’, 23 May 2024 (fetch-tool summary).

Ques: How does guarding remove leakage current?

By removing the voltage across the leakage path. Leakage through cable and fixture insulation adds to the device current, $I_{M} = I_{D U T} + I_{L}$ , and matters when the device impedance approaches the insulation’s (Tektronix). A guard conductor surrounds the high-impedance lead and is driven by a unity-gain buffer to the same potential, so the voltage across the insulation, and hence the leakage, is nearly zero. With 10 $V$ across $1 \times 1 0^{14}$ $Ω$ , leakage is 0.1 $pA$ (computed); holding the guard within 1 $mV$ cuts it ten thousandfold (computed). Guarding also stops the cable capacitance from charging, which is why triax with guard settled about ten times faster than coax in Tektronix’s test. For safety, the metal shield must still be earthed. Reference: Tektronix/Keithley, ‘Optimizing Low Current Measurements with the 4200A-SCS’ application note (fetch-tool summary); Keithley, source-measure unit application article 6058 (fetch-tool summary).

Ques: Why are low-current measurements so slow?

Because the device’s source resistance charges the cable and fixture capacitance through a long time constant. Tektronix gives $τ = R_{S} C_{s h u n t}$ : 10 $pF$ with 1 $T Ω$ is 10 $s$ , reaching 63 per cent of the final value after one time constant, and it recommends five time constants, 50 $s$ , to settle within 1 per cent. The exact figure is $4.6 τ$ , 46 $s$ ; five time constants leave 0.67 per cent (computed). The delay is added in the sweep-delay or interval settings, and the settling is checked by stepping the bias and plotting current against time. Guarded triax reduces the effective capacitance and speeds settling about tenfold. Averaging more samples lowers noise but slows the measurement further. Reference: Tektronix/Keithley, ‘Optimizing Low Current Measurements with the 4200A-SCS’ application note (fetch-tool summary).

Ques: What sets the noise floor of an SMU measurement?

The thermal noise of the device and the ammeter’s noise gain. A resistance R has Johnson noise current $4 k_{B} T B / R$ : 0.13 $fA$ for 1 $T Ω$ and 4.1 $fA$ for 1 $G Ω$ at 300 $K$ in a 1 $Hz$ bandwidth (Balogh et al. give $S_{V} = 4 k_{B} T R$ ; the current form and values are computed). The feedback ammeter amplifies its input noise voltage by $1 + R_{F} / R_{S}$ , so a low source resistance raises the output noise; Tektronix therefore gives minimum source resistances for each range, 1 to 100 $G Ω$ on the picoamp ranges and 1 to 100 $Ω$ on the milliamp ranges. Capacitive sources also raise the noise gain, which a series resistor or diode reduces. Keithley quotes noise floors as low as 0.4 $fA$ peak to peak. Reference: Z. Balogh et al., ‘1/f noise spectroscopy and noise tailoring of nanoelectronic devices’, arXiv:2106.02683: thermal noise S_V = 4k_{B}TR (fetch-tool summary); Tektronix/Keithley, ‘Optimizing Low Current Measurements with the 4200A-SCS’ application note (fetch-tool summary); Keithley, source-measure unit application article 6058 (fetch-tool summary).

Ques: Which spurious currents spoil picoamp measurements?

Several, from the cables, the fixture and the environment. Tektronix lists triboelectric currents from flexing cables, which can reach tens of nanoamps and are reduced by graphite-impregnated triax insulation, short and secured cables and preamplifiers near the device; currents of a few nanoamps between conductors on poorly cleaned epoxy boards; piezoelectric currents from stressed insulators; and electrostatic pickup, important below 1 $nA$ or above 1 $G Ω$ . Humidity should stay below 50 per cent, the shield should connect to Force LO, the system should be grounded at one point, and light must be blocked because diodes and transistors are photosensitive. After reconnection, parasitic currents can take minutes to hours to decay. A 10 $nA$ burst is $1 \times 1 0^{5}$ times a 0.1 $pA$ signal (computed). Reference: Tektronix/Keithley, ‘Optimizing Low Current Measurements with the 4200A-SCS’ application note (fetch-tool summary).

Ques: How do temperature and self-heating affect probe-station measurements?

Hot chucks degrade contacts, and the device can heat itself. Sia found probe resistance rising from 0.4 $Ω$ at 25 $^{\circ} C$ to 2.5 $Ω$ at 150 $^{\circ} C$ ; at 150 $^{\circ} C$ contact resistance was about 5 $Ω$ , and the contact opened at the 43rd touchdown as the exposed copper under the aluminium cap oxidized. Sia therefore recommends testing hot first, then at room temperature, then cold. Self-heating raises the device temperature by $P R_{t h}$ : 77 $mW$ with an assumed 2000 $K/W$ gives about 154 $K$ (computed), distorting DC curves. Pulsed SMUs, with 500 $ns$ pulses, measure before the device heats when the pulse is much shorter than its thermal time constant (Keithley; the condition on pulse width is my reading). Reference: C. B. Sia, ‘True Kelvin CMOS Test Structure’, ICMTS 2017 slides, FormFactor (fetch-tool summary); Keithley, source-measure unit application article 6058 (fetch-tool summary).

References

Keithley Instruments, “Source-measure units” application article no. 6058 (date not stated). Available: https://docs.ampnuts.ru/eevblog.docs/Keithley/Appnotes/6058_source_measure.pdf
C. B. Sia, “True Kelvin CMOS Test Structure,” presented at the IEEE International Conference on Microelectronic Test Structures (ICMTS), 2017, FormFactor. Available: https://www.formfactor.com/wp-content/uploads/ICMTS2017-True-Kelvin-CMOS-Test-Structure.pdf
FormFactor, “DC probes for accurate and consistent device modelling measurements,” FormFactor blog, May 23, 2024. Available: https://www.formfactor.com/blog/2024/dc-probes-for-accurate-and-consistent-device-modelling-measurements/
Tektronix/Keithley, “Optimizing Low Current Measurements with the 4200A-SCS Parameter Analyzer,” application note. Available: https://www.tek.com.cn/-/media/china-marketing-documents/24-01/4200a-scs_optimizing_low-current_measurements.pdf
Z. Balogh, G. Mezei, L. Posa, B. Santa, A. Magyarkuti and A. Halbritter, “1/f noise spectroscopy and noise tailoring of nanoelectronic devices,” arXiv:2106.02683. Available: https://arxiv.org/abs/2106.02683

Quartz 5

Explorer

SMU and Probe Station