1. Theory

Definition: A thin-film metal resistor is a strip of a resistive alloy film, tantalum nitride (TaN), nickel-chromium (NiCr) or silicon-chromium (SiCr), a few to a few tens of nanometres thick, deposited on oxide in the back end of the process and contacted by the interconnect metal (TI; National).
Sheet resistance: The value is set by the film resistivity and thickness, $R_{s} = ρ_{f} / t$ , about 25 to 125 $Ω/ □$ for TaN, 50 to 250 $Ω/ □$ for NiCr and 30 to 2000 $Ω/ □$ for SiCr (Vishay; TI).
Low temperature coefficient: The alloys are disordered, so their resistivity is high and depends only weakly on temperature; NiCr and annealed SiCr reach about 0 plus or minus 25 $ppm/K$ and below, TaN about -100 to -125 $ppm/K$ (Vishay; National; Skyworks).
Tunable TCR: Annealing moves the TCR of SiCr from negative through zero to positive, and the nitrogen content sets the TCR of TaN, so the process can target a near-zero or a deliberately positive coefficient (TI; Skyworks).
Isolation and linearity: The film sits on oxide and conducts like a metal, so it has no junction, almost no voltage coefficient and low parasitic capacitance (background knowledge; compare the Diffused and Implanted Resistors and Polysilicon Resistors pages).
Stability: Stabilized films drift by less than about 0.5 per cent in 1000 $h$ at 125 $^{\circ} C$ , and the drift doubles for every 10 $K$ above that (Vishay).

2. Working Principle

Conduction: Electrons scatter strongly at the disorder of the alloy, at grain boundaries and at the film surfaces, so the resistivity is high and the contribution of phonon scattering, which gives normal metals their positive TCR, is small (background knowledge).
Sign of the TCR: Above a resistivity of roughly 150 $μ Ω cm$ such alloys tend to have a negative TCR, and annealing that orders the film or grows grains lowers the resistivity contribution of disorder and pushes the TCR positive (Mooij correlation, background knowledge; TI).
Nitrogen in TaN: More nitrogen gives a nitride phase with a negative TCR and good uniformity; too little nitrogen leaves a metallic phase with a positive TCR and poor uniformity (Skyworks).
Protection: TaN forms a thin Ta2O5 layer where moisture reaches it, while NiCr corrodes unless passivated (Stackpole).
Trimming: Thin films are trimmed by laser cutting to tolerances down to 0.01 per cent in discrete NiCr resistors (Stackpole; background knowledge for the method).

3. Applications

Precision analog on chip: Data converters, references, instrumentation amplifiers and gain networks that need low TCR, low voltage coefficient and stable ratios, where thin films outperform poly (TI; National; Vishay).
RF and III-V MMICs: TaN resistors with tight uniformity in GaAs and GaN front-end circuits (Skyworks).
Temperature compensation: Resistors with a deliberately positive TCR next to zero-TCR ones on one die, to offset the coefficients of other circuit elements (TI).
Current status: Integrated thin films need extra deposition and masking steps, so they are used in analog and mixed-signal processes and in III-V MMICs, while mainstream CMOS uses polysilicon resistors (TI; Polysilicon Resistors page).

Sheet Resistance and Temperature Coefficient

Name	Formula	Related Formulae	Variables/Constants
Sheet resistance of a thin metal film	$R_{s} = \frac{ρ _{f}}{t}, R = R_{s} \frac{L}{W}$	$ρ_{f} \approx ρ_{b} (1 + \frac{3 λ}{8 t}) (t ≳ λ, diffuse surface scattering)$	$R_{s} : s h ee t r es i s t an ce$ $ρ_{f} : f i l m r es i s t i v i t y$ $t : f i l m t hi c k n ess$ $R : r es i s t an ce$ $L an d W : l e n g t h an d w i d t h$ $ρ_{b} : b u l k r es i s t i v i t y$ $λ : e l ec t r o n m e an f r ee p a t h (F u c h s - S o n d h e im er a pp r o x ima t i o n, ba c k g r o u n d k n o w l e d g e); T I : S i C r r es i s t or s o f t y p i c a l l y 30 t o 2000 Ω/ □, ab o u t 1000 Ω/ □ f or t h e z er o - T C R u pp er r es i s t or, w i t h ann e a l b e ha v i o u r g i v e n f or 30, 50 an d 120 \overset{˚}{A} l a y er s; N a t i o na l : S i C r f i l m s o f 1000 Ω/ □ f r o m a 72 p er ce n t S i an d 28 p er ce n t C r t a r g e t; S k y w or k s : T a N t a r g e t e d a t 50 Ω/ □ w i t h b e l o w 1.5 p er ce n t s i g ma u ni f or mi t y; V i s ha y : T a N 25 t o 125 Ω/ □ (10 t o 150) an d N i C r 50 t o 250 Ω/ □ (10 t o 350) o n cer ami cs$ $(co m p u t e d : 100 kΩ t ak es 100 s q u a r es o f 1000 Ω/ □ S i C r b u t 2000 o f 50 Ω/ □ T a N; a f i l m ha l f t h e m e an f r ee p a t h t hi c k ha s ab o u t 1.75 t im es t h e b u l k r es i s t i v i t y in t h e a pp r o x ima t i o n (e x am pl e λ = 40 nm, t = 20 nm, a ss u m e d))$
Temperature coefficient of resistance	$T C R = \frac{R ( T _{1} ) - R ( T _{0} )}{R ( T _{0} ) ( T _{1} - T _{0} )}$	$ρ ≳ 150 μ Ω cm \Rightarrow T C R ≲ 0 (Mooij correlation)$	$T C R : t e m p er a t u r e coe f f i c i e n t b e tw ee n T_{0} an d T_{1}$ $R : r es i s t an ce; S k y w or k s d e f in es i t w i t h R_{1} in t h e d e n o mina t or (n o n s t an d a r d, t h e d i f f er e n ce i s seco n d or d er); t h e M oo ij cor r e l a t i o n o f d i sor d er e d a l l oy s i s ba c k g r o u n d k n o w l e d g e; V i s ha y : T a N ab o u t - 125 \pm 25 ppm/K (- 25 t o - 150) an d N i C r ab o u t 0 \pm 25 ppm/K (- 25 t o + 25), w i t h \pm 25 ppm/K l o t t o l er an ce; S t a c k p o l e : N i C r c hi p s d o w n t o 2 ppm/K an d T a N t y p i c a l l y 15 ppm/K; S k y w or k s : T a N t a r g e t - 100 t o - 125 ppm/K, m e a s u r e d b e tw ee n 25 an d 75^{\circ} C, - 162.9 ppm/K a t 10 sccm N 2 an d + 255 ppm/K (m e t a l l i c p ha se) a t 4 sccm$ $(co m p u t e d : o v er 100 K, - 1.25 p er ce n t f or - 125 ppm/K T a N an d \pm 0.25 p er ce n t f or \pm 25 ppm/K N i C r, a g ain s t - 10 p er ce n t f or hi g h - o hmi c p o l y o n t h e P o l y s i l i co n R es i s t or s p a g e)$
Tuning the TCR of SiCr by annealing	$T C R (t_{a}, T_{a}) : < 0 as deposited \to 0 \to > 0 with anneal$	$\frac{R _{s, a}}{R _{s, 0}} - 1 (sheet-resistance rise on anneal)$	$T C R (t_{a}, T_{a}) : t e m p er a t u r e coe f f i c i e n t a f t er an ann e a l o f t im e t_{a} a t t e m p er a t u r e T_{a}$ $R_{s, 0} an d R_{s, a} : s h ee t r es i s t an ce b e f or e an d a f t er; T I : a s - d e p os i t e d S i C r ha s a n e g a t i v e T C R t ha t cr osses z er o an d b eco m es p os i t i v e w i t h co n t in u e d ann e a l in g, t y p i c a l l y ab o v e 475^{\circ} C f or ab o u t 30 min u t es b y R T A or t u b e, t hinn er l a y er s a r e m or e se n s i t i v e, an d a l o w er r es i s t or c an b e ann e a l e d t o a p os i t i v e T C R f i r s t w hi l e an u pp er o n e i s d e p os i t e d a t n e a r z er o an d n o t ann e a l e d; N a t i o na l : R T A in N 2 a t 550 t o 650^{\circ} C f or ab o u t 60 s, 980 t o 1450 Ω/ □ an d T C R r an g es f r o m 43 t o - 250 ppm/K b e tw ee n - 60 an d 130^{\circ} C, 650^{\circ} C g i v in g 28 t o - 31 ppm/K f r o m - 30 t o 90^{\circ} C an d - 1.0 ppm/K (σ = 5.7) f r o m 25 t o 60^{\circ} C, an d p r i or a r t o f 475^{\circ} C f or 30 min u t es r ai s in g R_{s} b y ab o u t 280 p er ce n t$ $(co m p u t e d : t h e 650^{\circ} C R T A r ai se d t h e s h ee t r es i s t an ce f r o m 980 t o 1410 Ω/ □, 44 p er ce n t)$

Process Control, Drift and Humidity

Name	Formula	Related Formulae	Variables/Constants
Process control of TaN by nitrogen content	$% σ = \frac{100}{x ˉ} \frac{\sum _{i} ( x _{i} - x ˉ ) ^{2}}{n - 1}$	$N_{2} flow ↓ \Rightarrow metallic Ta(N), T C R > 0$	$% σ : r e l a t i v e s t an d a r d d e v ia t i o n o f t h e s h ee t r es i s t an ce o v er n ma p p o in t s x_{i} w i t h m e an \overset{x}{ˉ}; S k y w or k s : 49 - p o in t ma p s, b e l o w 1.3 p er ce n t s i g ma a t 8 an d 10 sccm N 2 (50.9 an d 49.4 Ω/ □), ab o u t 3.0 a t 6 sccm an d 13.1 a t 4 sccm, pl a t e n t e m p er a t u r es o f 40 t o 60^{\circ} C c han g in g R_{s} b y o n l y 0.6 Ω/ □, d esc u m, a s h a t 200 t o 240^{\circ} C, a 300^{\circ} C ann e a l an d p o l y imi d e c u r es a t 300 t o 350^{\circ} C k ee p in g R_{s} w i t hin ab o u t 1 Ω/ □ an d T C R b e tw ee n - 104 an d - 113 ppm/K; T I : T a N T C R an d s h ee t r es i s t an ce a r e se t b y t h e ni t r o g e n co n t e n t$ $(co m p u t e d : 1.3 p er ce n t s i g ma o f 50 Ω/ □ i s 0.65 Ω/ □; a s hi f t b e l o w 1 Ω/ □ i s b e l o w 2 p er ce n t)$
Drift and its temperature acceleration	$\frac{Δ R}{R} (t, T) = \frac{Δ R}{R} (t, T_{r e f}) exp [\frac{E _{a}}{k _{B}} (\frac{1}{T _{r e f}} - \frac{1}{T})]$	$factor 2 per 10 K \Rightarrow E_{a} = \frac{k _{B} l n 2}{1/ T _{1} - 1/ T _{2}}$	$Δ R / R (t, T) : r e l a t i v e d r i f t a f t er t im e t a t ab so l u t e t e m p er a t u r e T$ $T_{r e f} : r e f er e n ce t e m p er a t u r e$ $E_{a} : a c t i v a t i o n e n er g y$ $k_{B} : B o l t z mann co n s t an t (8.617 \times 1 0^{- 5} eV / K)$ $T_{1} an d T_{2} : t e m p er a t u r es 10 K a p a r t (A r r h e ni u s sc a l in g o f a d r i f t r a t e, a ss u m e d; m o d e l s o n t h e T e m p er a t u r e A cce l er a t i o n p a g e); V i s ha y : s t abi l i z e d an d t r imm e d T a N an d N i C r c han g e s i g ni f i c an tl y l ess t han 0.5 p er ce n t o v er 1000 h a t 125^{\circ} C, an d s t abi l i t y d e g r a d es b y a f a c t or o f 2 f or e v er y 10^{\circ} C ab o v e 125^{\circ} C in ai r; S t a c k p o l e : N i C r ab o u t tw i ce a s s t ab l e a s T a N, u p t o t e n t im es a t t h e t i g h t es t t o l er an ces, in t es t s o t h er t han h u mi d i t y$ $(co m p u t e d : a f a c t or o f 2 p er 10 K n e a r 125^{\circ} C i s 0.97 eV; w i t h i t, 0.5 p er ce n t a t 125^{\circ} C b eco m es 0.021 p er ce n t p er 1000 h a t 85^{\circ} C)$
Biased humidity drift of NiCr and TaN	$(\frac{Δ R}{R})_{85/85} after 1000 h, 10% rated power$	$Ta \to Ta_{2} O_{5} (self-passivating)$	$Δ R / R : r es i s t an ce c han g e in a bia se d h u mi d i t y t es t a t 85^{\circ} C an d 85 p er ce n t R H; S t a c k p o l e : p a ss i v a t e d N i C r d r i f t s \pm 0.1 t o \pm 0.3 p er ce n t d e p e n d in g o n c hi p s i z e, n o n - p a ss i v a t e d N i C r t y p i c a l l y f ai l s w i t hin 1000 h (500 h f or s ma l l c hi p s) b y cor r os i o n or d i sso l u t i o n t ha t r ai ses t h e r es i s t an ce t o an o p e n, an d T a N d r i f t s t y p i c a l l y l ess t han \pm 0.05 p er ce n t, man y l ess t han 0.01 p er ce n t, b ec a u se i t f or m s t an t a l u m p e n t o x i d e w h er e m o i s t u r e r e a c h es i t, w hi l e N i C r r e a c h es 0.01 p er ce n t t o l er an ce a g ain s t 0.1 p er ce n t f or T a N; C ai e t a l . : N i C r c hi p r es i s t or s a f t er 3000 h a t 85/85 s h o w e d d r i f t an d o p e n s f r o m cr a c k in g an d s u l f i d e cor r os i o n o f t h e A g t er mina l e l ec t r o d e; m o i s t u r e m ec hani s m s o n t h e E n v i r o nm e n t a l an d C h e mi c a l p a g e$ $(co m p u t e d : n o n e; f or in t e g r a t e d r es i s t or s u n d er t h e c hi p p a ss i v a t i o n t h e h u mi d i t y r i s k i s t ha t o f t h e p a ss i v a t i o n, n o t o f t h e o p e n f i l m (m y r e a d in g))$

Important Questions

Ques: Is the TCR of tantalum nitride about -125 or about 15 ppm per kelvin?

The sources describe different products. Vishay lists TaN at about -125 plus or minus 25 $ppm/K$ , within -25 to -150, and Skyworks targets -100 to -125 $ppm/K$ for MMIC resistors and measured -105 to -113 $ppm/K$ after optimization, so a negative value of about 100 to 125 $ppm/K$ is what an as-processed nitride film has. Stackpole states that TaN chip resistors typically reach 15 $ppm/K$ , which refers to finished, compensated discrete parts whose film and termination are tuned for a low coefficient (my reading). For an integrated TaN resistor the negative value is therefore the more likely one. Skyworks also shows how fragile it is: a lower nitrogen flow gave a metallic phase with +255 $ppm/K$ , so the TCR is a process variable. Reference: Vishay Electro-Films, ‘Applications and Design of Thin Film Resistors’, Document 61083 (2004) (fetch-tool summary); S. Y. Chang, S. Tiku and L. Luu-Henderson, Skyworks Solutions, ‘Optimizing Process Conditions for High Uniformity and Stability of Tantalum Nitride Films’, CS MANTECH 2022, 91-94 (fetch-tool summary); K. Schroeder (Stackpole Electronics), ‘Precision Thin Film Resistors - Nichrome vs Tantalum Nitride - a Comparison’, Power Systems Design (June 2023) (fetch-tool summary).

Ques: How does annealing bring the TCR of a SiCr resistor to zero?

As-deposited SiCr has a negative TCR, and annealing moves it through zero to positive values, according to TI, which anneals typically above 475 $^{\circ} C$ for about 30 minutes and notes that thinner films are more sensitive. National used rapid thermal anneals in nitrogen at 550 to 650 $^{\circ} C$ for about 60 $s$ on 1000 $Ω/ □$ films. At 650 $^{\circ} C$ the average TCR was 28 to -31 $ppm/K$ from -30 to 90 $^{\circ} C$ and -1.0 $ppm/K$ with a standard deviation of 5.7 from 25 to 60 $^{\circ} C$ , while the sheet resistance rose from 980 to 1410 $Ω/ □$ , 44 per cent (computed). The prior-art furnace anneal at 475 $^{\circ} C$ raised it by about 280 per cent. Both value and coefficient must therefore be targeted together. Reference: E. W. Beach, Texas Instruments, ‘Integration of thin film resistors having different TCRs into single die’, US Patent 7,704,871 B2 (2010) (fetch-tool summary); P. Maghsoudnia, National Semiconductor, ‘SiCr thin film resistors having improved temperature coefficients of resistance and sheet resistance’, US Patent 6,171,922 B1 (2001) (fetch-tool summary).

Ques: Why is NiCr more precise but TaN more robust in humidity?

Stackpole compares the two in discrete chip resistors. NiCr reaches tolerances down to 0.01 per cent and TCRs down to 2 $ppm/K$ , against typically 0.1 per cent and 15 $ppm/K$ for TaN, and it is about twice as stable in tests other than humidity. In biased humidity at 85 $^{\circ} C$ and 85 per cent RH, however, non-passivated NiCr typically fails within 1000 $h$ , or 500 $h$ for small chips, as corrosion raises its resistance to an open, and passivated NiCr still drifts by 0.1 to 0.3 per cent, while TaN drifts less than 0.05 per cent because it forms a protective tantalum pentoxide. Cai et al. found that NiCr chips can also fail at their silver terminations by sulfide corrosion and cracking after 3000 $h$ at 85/85. Reference: K. Schroeder (Stackpole Electronics), ‘Precision Thin Film Resistors - Nichrome vs Tantalum Nitride - a Comparison’, Power Systems Design (June 2023) (fetch-tool summary); Y. Cai, L. Liu, W. Dai et al., ‘Failure Analysis of Ni-Cr Film Resistor in High Temperature and High Humidity Environment’, Journal of Integration Technology 11(5), 88-98 (2022) (abstract only).

Ques: How stable are thin-film resistors over life?

Vishay states that stabilized and trimmed TaN and NiCr films change by significantly less than 0.5 per cent over 1000 $h$ at 125 $^{\circ} C$ , and that the stability degrades by a factor of 2 for every 10 $^{\circ} C$ above 125 $^{\circ} C$ in air. That factor corresponds to an activation energy of about 0.97 $eV$ near 125 $^{\circ} C$ (computed), and with it the same drift becomes about 0.021 per cent per 1000 $h$ at 85 $^{\circ} C$ (computed, assuming the drift rate follows Arrhenius). Skyworks shows the process side: back-end steps such as ash, a 300 $^{\circ} C$ anneal and polyimide cures up to 350 $^{\circ} C$ shifted TaN by less than 1 $Ω/ □$ of 50. For the highest stability, Stackpole finds NiCr about twice as stable as TaN outside humidity. Reference: Vishay Electro-Films, ‘Applications and Design of Thin Film Resistors’, Document 61083 (2004) (fetch-tool summary); S. Y. Chang, S. Tiku and L. Luu-Henderson, Skyworks Solutions, ‘Optimizing Process Conditions for High Uniformity and Stability of Tantalum Nitride Films’, CS MANTECH 2022, 91-94 (fetch-tool summary); K. Schroeder (Stackpole Electronics), ‘Precision Thin Film Resistors - Nichrome vs Tantalum Nitride - a Comparison’, Power Systems Design (June 2023) (fetch-tool summary); Temperature Acceleration Models (Arrhenius and Eyring) page of this vault.

Ques: How can two thin-film resistors with different TCRs be made on one die?

TI describes a stack of two SiCr layers. The lower resistor is deposited first and annealed, typically above 475 $^{\circ} C$ , until its TCR becomes the desired, usually positive, value; the upper resistor is then deposited with near-zero TCR and is not annealed, so that the second film keeps its as-deposited properties and the first is not changed again. The sheet resistances can be chosen between about 30 and 2000 $Ω/ □$ , with about 1000 $Ω/ □$ for the precision upper layer. The positive-TCR resistor can then compensate the negative coefficients of other parts of the circuit, while the zero-TCR one sets precise ratios. TaN can replace either layer, with its coefficient set by the nitrogen content. Reference: E. W. Beach, Texas Instruments, ‘Integration of thin film resistors having different TCRs into single die’, US Patent 7,704,871 B2 (2010) (fetch-tool summary); S. Y. Chang, S. Tiku and L. Luu-Henderson, Skyworks Solutions, ‘Optimizing Process Conditions for High Uniformity and Stability of Tantalum Nitride Films’, CS MANTECH 2022, 91-94 (fetch-tool summary).

Ques: Why does a thin-film resistor have almost no voltage coefficient?

Because it is a metal film on oxide with no junction and no grain-boundary barriers that the voltage could lower (background knowledge). A diffused resistor changes with the voltage to its isolation because the junction depletion narrows its conducting layer, by about 100 to 20 000 $ppm/V$ depending on doping, and a polysilicon resistor is nonlinear because its grain boundaries act as barriers, at about 10 to 200 $ppm/V$ , as described on the two other resistor pages. A disordered alloy film carries the current through a high density of free electrons, so the field at practical voltages does not change its carrier density or mobility. The remaining nonlinearity comes mostly from self-heating through the TCR, which is small because the TCR is low, which is why thin films are preferred for linear precision networks. Reference: Diffused and Implanted Resistors page of this vault; Polysilicon Resistors page of this vault; Vishay Electro-Films, ‘Applications and Design of Thin Film Resistors’, Document 61083 (2004) (fetch-tool summary).

Quartz 5

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Thin-Film Metal Resistors (TaN, NiCr and SiCr)