1. Theory

Definition: A polysilicon resistor is a strip of doped gate polysilicon on field oxide, with the silicide blocked over its body and kept only at the contact heads (IHP; GF180MCU).
Isolation by oxide: Because the strip sits on oxide, it has no junction to the substrate, so it has much less parasitic capacitance, no junction leakage and no depletion modulation of its body, unlike a diffused resistor (Allen; Diffused and Implanted Resistors page).
Range of values: Salicided poly gives about 5 to 7 $Ω/ □$ , unsalicided n+ and p+ poly about 250 to 420 $Ω/ □$ , and lightly doped or compensated high-ohmic poly about 1000 to 3000 $Ω/ □$ (Niknejad and Boser; GF180MCU; IHP).
Grain boundaries: The film consists of grains separated by boundaries with traps that capture carriers and form potential barriers; the barriers dominate the resistivity at light doping and become negligible at heavy doping (Santonen et al.; TI US 4,579,600).
Temperature coefficient: The barriers give a negative TCR, while the grains themselves give a positive one, so the sign depends on doping and grain structure: heavily doped poly is positive and high-ohmic poly strongly negative, about -1000 to -1650 $ppm/K$ (TI; GF180MCU; Allen).
Linearity: The voltage coefficient is small, about 10 to 200 $ppm/V$ , and long resistors are the most linear because each grain boundary sees only a small voltage (Kraft; GF180MCU).
Trimmability: The resistance can be lowered permanently by current pulses that heat the film and restructure the grain boundaries, which allows ppm-level adjustment (Microbridge; Dallas).

2. Working Principle

Conduction: Carriers drift through the grains and cross the boundaries by thermionic emission over the barrier $V_{B}$ , so the film resistivity contains a factor $exp (q V_{B} / k_{B} T)$ (Santonen et al.).
Barrier height: For grains that are fully depleted the barrier grows with doping, and once the traps are filled it falls as $Q_{t}^{2} / N$ , so heavy doping removes it (Santonen et al.; background knowledge for the limits).
Temperature: Heating helps carriers over the barrier, which lowers the resistance, while lattice scattering in the grains raises it; the balance sets the TCR, and grain growth or hydrogen passivation of the traps moves it toward zero or positive values (TI; TCAD abstract).
Voltage: The applied voltage divides over many grain boundaries, so the barrier lowering at each is small and the resistor is linear; a short resistor or a high voltage puts more voltage on each boundary and makes it nonlinear (Kraft).
Trimming: Current pulses heat the strip to several hundred degrees Celsius, which redistributes dopants and restructures the boundaries; the resistance falls to as little as 0.3 of its initial value and can be partly recovered (Microbridge; Dallas).
Self-heating: The oxide below the strip insulates it thermally, so dissipation heats the resistor and changes its value through the TCR (TCAD abstract; Microbridge).

3. Applications

Precision analog resistors: Ratios in data converters, references and amplifier gain networks, where the oxide isolation gives low capacitance, low voltage coefficient and good matching (Allen; Kraft).
High-value resistors in small area: High-ohmic poly for bias networks and RC filters (GF180MCU; IHP).
Trimmed references: Electrically trimmed poly resistors set ppm-level offsets and gains after packaging (Microbridge; Dallas).
Fuses: Salicided poly links blown by current pulses for one-time programming and redundancy (Allen; covered in detail on the planned fuse and antifuse page).
Temperature sensing on chip: High-TCR poly heaters and sensors on micro-membranes, where the resistor is part of a thermal MEMS device (Microbridge).

Sheet Resistance and Grain-Boundary Conduction

Name	Formula	Related Formulae	Variables/Constants
Sheet resistance and layout of a poly resistor	$R = R_{s} \frac{L}{W _{e f f}} + \frac{2 R _{h e a d}}{W}$	$R_{s} = \frac{ρ _{p o l y}}{t _{p o l y}}$	$R : r es i s t an ce$ $R_{s} : s h ee t r es i s t an ce o f t h e (u n s a l i c i d e d) p o l y b o d y$ $L : b o d y l e n g t h$ $W_{e f f} : e l ec t r i c a l w i d t h$ $R_{h e a d} : h e a d r es i s t an ce p er w i d t h in c l u d in g t h e s i l i c i d e d co n t a c t r e g i o n$ $ρ_{p o l y} : f i l m r es i s t i v i t y$ $t_{p o l y} : f i l m t hi c k n ess (f or m i s ba c k g r o u n d k n o w l e d g e; h e a d s a s o n t h e D i f f u se d an d I m pl an t e d R es i s t or s p a g e); I H P S G 13 G 2 : s a l i c i d e d n + p o l y (r s i l) 7, u n s a l i c i d e d p + p o l y (r pp d) 260 an d p a r t ia l l y co m p e n s a t e d hi g h - o hmi c p o l y (r hi g h) 1360 Ω/ □, w i t h a t l e a s t 2 μ m w i d t h r eco mm e n d e d f or p r ec i s i o n; GF 180 M C U : u n s a l i c i d e d n + an d p + p o l y 310 (250 t o 370) an d 350 (280 t o 420) Ω/ □, s a l i c i d e d 6.8 an d 7.3 Ω/ □, an d o pt i o na l hi g h - p o l y r es i s t or s o f 1000, 2000 or 3000 Ω/ □ w i t h an e x t r a ma s k, w hi c h c ann o t coe x i s t in o n e p r ocess; S K Y 130 : p o l y 48.2 Ω/ □; A l l e n : 30 t o 100 Ω/ □ u n s hi e l d e d an d 100 t o 500 Ω/ □ s hi e l d e d, \pm 30 p er ce n t ab so l u t e an d 2 p er ce n t r e l a t i v e a t 5 μ m; N ik n e j a d an d B oser : ab o u t 5 Ω/ □ s i l i c i d e d, so 100 kΩ n ee d s a l in e 1 μ m w i d e an d 20000 μ m l o n g$ $(co m p u t e d : 100 kΩ t ak es 74 s q u a r es o f r hi g h, 385 o f r pp d an d 14300 o f r s i l)$
Grain-boundary trapping model of the resistivity	$ρ = \frac{2 π m ^{*} k _{B} T}{2 W q ^{2} f n} exp (\frac{q V _{B}}{k _{B} T})$	$V_{B} = \frac{q N L _{g}^{2}}{8 ε _{s}} (L_{g} N < Q_{t}), V_{B} = \frac{q Q _{t}^{2}}{8 ε _{s} N} (L_{g} N > Q_{t})$	$ρ : r es i s t i v i t y, m^{*} : e f f ec t i v e ma ss$ $k_{B} : B o l t z mann co n s t an t (8.617 \times 1 0^{- 5} eV / K)$ $T : ab so l u t e t e m p er a t u r e$ $W : d e pl e t i o n w i d t h (L_{g} /2 in S an t o n e n e t a l .)$ $q : e l e m e n t a r y c ha r g e$ $f : f i tt in g f a c t or$ $n : c a r r i er d e n s i t y in t h e g r ain$ $V_{B} : g r ain - b o u n d a r y ba r r i er h e i g h t$ $N : d o p in g$ $L_{g} : g r ain s i z e$ $ε_{s} : p er mi tt i v i t y o f S i$ $Q_{t} : t r a p d e n s i t y p er a r e a o f b o u n d a r y; S an t o n e n e t a l . : t h e S e t o m o d e l w i t h t h e cor r ec t i o n s o f Lu e t a l ., t h er mi o ni c e mi ss i o n w i t h o u t t u nn e l l in g, f d e p e n d s o n t h e ba r r i er h e i g h t an d h e n ce o n t h e d o p in g, a 3 μ m b or o n - d o p e d f i l m m e a s u r e d ab o u t 11000 Ω cm (2200 t o 15000) an d ab o u t 3500 Ω cm a f t er 1 h a t 370^{\circ} C in o x y g e n, an d hi g h er d o p in g in cr e a ses t h e in f l u e n ce o f t h e ba r r i er s; t h e tw o ba r r i er f or m s a r e S e t o^{'} s p a r t ia l - an d f u l l - d e pl e t i o n l imi t s (ba c k g r o u n d k n o w l e d g e)$ $(co m p u t e d w i t h Q_{t} = 3 \times 1 0^{12} c m^{- 2} an d L_{g} = 50 nm (a ss u m e d) : a t N = 1 \times 1 0^{18} c m^{- 3}, L_{g} N = 5 \times 1 0^{12} > Q_{t} an d V_{B} = 0.17 V; a t 1 \times 1 0^{19} an d 1 \times 1 0^{20} c m^{- 3}, 0.017 an d 0.0017 V)$

Temperature and Voltage Dependence

Name	Formula	Related Formulae	Variables/Constants
Temperature coefficient and its sign	$T C_{1} = \frac{1}{ρ} \frac{d ρ}{d T} \approx \frac{1}{2 T} - \frac{q V _{B}}{k _{B} T ^{2}}$	$R (T) = R_{0} [1 + T C_{1} (T - T_{0}) + T C_{2} (T - T_{0})^{2}]$	$T C_{1} an d T C_{2} : f i r s t - an d seco n d - or d er t e m p er a t u r e coe f f i c i e n t s$ $ρ : r es i s t i v i t y$ $T : ab so l u t e t e m p er a t u r e$ $V_{B} : ba r r i er h e i g h t$ $k_{B} : B o l t z mann co n s t an t (8.617 \times 1 0^{- 5} eV / K)$ $q : e l e m e n t a r y c ha r g e$ $R_{0} : r es i s t an ce a t T_{0} (t h e a pp r o x ima t i o n f o l l o w s f r o m t h e t r a pp in g m o d e l ab o v e w i t h n an d f co n s t an t, m y d er i v a t i o n); T I (U S 4, 579, 600) : p o l y ha s a n e g a t i v e T C R f r o m a l a r g e g r ain - b o u n d a r y t er m, l a ser ann e a l in g t o 3 t o 5 μ m g r ain s an d h y d r o g e n p a ss i v a t i o n o f t h e t r a p s r e d u ce i t, an d 10 p er ce n t h y d r o g e n g a v e ab o u t z er o T C R; K r a f t : 100 t o 500 ppm/K (200 ppm/K f or 300 μ m a t 2 V); A l l e n : 500 t o 1000 ppm/K; GF 180 M C U : T C R_{1} = - 1000 ppm/K (- 1200 t o - 800) f or t h e 1000 Ω/ □ hi g h - p o l y an d - 1650 ppm/K (- 1300 t o - 1900) f or 2000 Ω/ □; D a l l a s : ab o u t 1000 ppm/K a t 6 \times 1 0^{19} c m^{- 3} an d 285 Ω/ □; T C A D ab s t r a c t : a t f i x e d d o p in g, g r ain g r o w t h c an g i v e a p os i t i v e or a n e g a t i v e T C R$ $(co m p u t e d w i t h t h e a ss u m e d t r a p s : ab o u t - 20800 ppm/K a t 1 \times 1 0^{18}, - 580 ppm/K a t 1 \times 1 0^{19} an d + 1440 ppm/K a t 1 \times 1 0^{20} c m^{- 3}, so t h e T C R cr osses z er o b e tw ee n ab o u t 1 \times 1 0^{19} an d 1 \times 1 0^{20} c m^{- 3} f or t hi s t r a p d e n s i t y; t h e GF 180 M C U hi g h - p o l y r es i s t or s c han g e b y - 10 an d - 16.5 p er ce n t o v er 100 K)$
Zero-TC series combination	$T C_{t o t} = \frac{R _{a} T C _{a} + R _{b} T C _{b}}{R _{a} + R _{b}} = 0$	$\frac{R _{a}}{R _{a} + R _{b}} = \frac{- T C _{b}}{T C _{a} - T C _{b}}$	$T C_{t o t} : f i r s t - or d er coe f f i c i e n t o f tw o r es i s t or s R_{a} an d R_{b} in ser i es$ $T C_{a} an d T C_{b} : t h e i r coe f f i c i e n t s o f o pp os i t e s i g n; N ik n e j a d an d B oser : N + an d P + p o l y r es i s t or s in ser i es c an b e s i z e d so t ha t t h e t o t a l T C i s z er o; D a l l a s : e a r l i er z er o - T C m e t h o d s n ee d e d tw o d o p in g s o f o pp os i t e T C 1, w hi l e l a t e r es i s t or im pl an t s an d t r immin g a d j u s t T C 1 w i t hin o n e d o p in g$ $(co m p u t e d : w i t h + 200 ppm/K (a ss u m e d, u n s a l i c i d e d p + p o l y) an d - 1000 ppm/K (GF 180 M C U hi g h - p o l y), t h e p os i t i v e r es i s t or m u s t b e 83 p er ce n t o f t h e t o t a l)$
Voltage coefficient and the voltage per grain boundary	$R (V) = R_{0} (1 + V C_{1} V + V C_{2} V^{2})$	$V_{g b} \approx V \frac{L _{g}}{L} ≪ \frac{k _{B} T}{q} (linear regime)$	$R (V) : r es i s t an ce a t t h e v o l t a g e V a cr oss i t$ $V C_{1} an d V C_{2} : v o l t a g e coe f f i c i e n t s$ $V_{g b} : v o l t a g e a cr oss o n e g r ain b o u n d a r y$ $L_{g} : g r ain s i z e$ $L : r es i s t or l e n g t h$ $k_{B} : B o l t z mann co n s t an t (8.617 \times 1 0^{- 5} eV / K)$ $T : ab so l u t e t e m p er a t u r e$ $q : e l e m e n t a r y c ha r g e (t h e l in e a r i t y cr i t er i o n i s ba c k g r o u n d k n o w l e d g e); K r a f t : t h e c u r r e n t i s n o n l in e a r b ec a u se o f t h e g r ain b o u n d a r i es, l o n g r es i s t or s a r e m or e l in e a r, V C o f 10 t o 100 ppm/V an d 30 ppm/V f or 25 x 2500 μ m; A l l e n : ab o u t 100 ppm/V; GF 180 M C U : V C R_{1} = - 200 ppm/V f or 1000 Ω/ □ an d - 150 ppm/V (- 100 t o - 200) f or 2000 Ω/ □; t h e p o l y i s i so l a t e d b y o x i d e, so t h er e i s n o d e pl e t i o n m o d u l a t i o n o f t h e b o d y a s in d i f f u se d r es i s t or s (D i f f u se d an d I m pl an t e d R es i s t or s p a g e)$ $(co m p u t e d : w i t h 50 nm g r ain s an d 2 V, V_{g b} = 0.33 mV f or 300 μ m an d 0.04 mV f or 2500 μ m, f a r b e l o w k_{B} T / q = 25.9 mV, b u t 100 mV f or a 1 μ m r es i s t or; 30 ppm/V o v er 5 V i s 0.015 p er ce n t)$

Trimming and Self-Heating

Name	Formula	Related Formulae	Variables/Constants
Electrical (thermal) trimming of poly resistors	$R_{t r im} \approx (0.3 to 0.5) R_{ini} (down-trim limit)$	$Δ R / R per pulse : \sim 1 0^{- 4} to a few 1 0^{- 6}$	$R_{t r im} : r es i s t an ce a f t er t r immin g$ $R_{ini} : a s - ma d e r es i s t an ce; M i cr o b r i d g e : e l ec t r o - t h er ma l t r immin g l o w er s p o l y t o ab o u t 0.3 t o 0.5 o f t h e a s - ma d e v a l u e an d c an b e p a r tl y r e v er se d, t e m p er a t u r es c an e x cee d 600 t o 700^{\circ} C o n m e mb r an es w i t h 30 t o 50 K/mW t h er ma l i so l a t i o n, r eco v er y o f 8 t o 20 p er ce n t in 4 t o 20 s se q u e n ces, f in e p u l ses o f a f e w h u n d r e d d o w n t o a f e w pp m, f ina l a cc u r a c i es o f ab o u t 10 t o 50 pp m an d 5.5 pp m mi s ma t c h in a b r i d g e, w i t h g r ain an d d o p an t r es t r u c t u r in g a s t h e m ec hani s m; c i t e d p r i or a r t : 0.02 p er ce n t d ecr e a se f or 0.5 μ s p u l ses a t 24 t o 28 V, an d ab o u t 20 p er ce n t r eco v er y a f t er 40 000 s a t co n s t an t c u r r e n t; D a l l a s : 500 μ s p u l ses a t a 10.5 m/s p er i o d, t r immin g s t a r t in g a t ab o u t 5 mA an d 1.5 V (p r i or a r t ab o u t 20 mA a t 16 V), l a t e - im pl an t r es i s t or s t r immin g t o ab o u t 30 p er ce n t o f t h e ini t ia l v a l u e a g ain s t 60 p er ce n t f or e a r l y - im pl an t o n es, t r immin g l o w er in g R_{s} an d r ai s in g T C 1 l in e a r l y; A l l e n : p o l y i s a l so u se d f or f u ses an d l a ser t r immin g$ $(co m p u t e d : n o n e)$
Self-heating of a poly resistor	$Δ T = R_{t h} P = R_{t h} \frac{V ^{2}}{R}$	$\frac{Δ R}{R} = T C_{1} Δ T$	$Δ T : t e m p er a t u r e r i se o f t h e b o d y$ $R_{t h} : t h er ma l r es i s t an ce t o t h e s u b s t r a t e t h r o ug h t h e f i e l d o x i d e$ $P : d i ss i p a t e d p o w er$ $V : v o l t a g e a cr oss t h e r es i s t or$ $R : r es i s t an ce$ $T C_{1} : t e m p er a t u r e coe f f i c i e n t (ba c k g r o u n d k n o w l e d g e; t h er ma l m o d e l s o n t h e T h er ma l S t r ess p a g e); T C A D ab s t r a c t : ser p e n t in e p o l y r es i s t or s s u f f er m u t u a l se l f - h e a t in g b e tw ee n f in g er s, w hi c h a f f ec t s b o t h t h e r es i s t an ce a g ain s t v o l t a g e an d r e l iabi l i t y; M i cr o b r i d g e : a m e mb r an e g i v es 30 t o 50 K/mW, so se l f - h e a t in g m u s t b e l imi t e d b y a m e a s u r e m e n t c u r r e n t b e l o w 100 μ A (b e l o w 1.5^{\circ} C r i se)$ $(co m p u t e d : o n a 40 K/mW m e mb r an e, 1 mW h e a t s t h e r es i s t or b y 40 K, w hi c h c han g es a - 1000 ppm/K r es i s t or b y 4 p er ce n t; t h e s am e se l f - h e a t in g a pp e a r s a s an a pp a r e n t v o l t a g e coe f f i c i e n t (m y r e a d in g))$

Important Questions

Ques: Why can the temperature coefficient of a poly resistor be positive or negative?

Because two effects compete. The trapped charge at grain boundaries forms barriers that carriers cross by thermionic emission, which becomes easier when hot and gives a negative TCR, while scattering inside the grains gives a positive one (Santonen et al.; TI US 4,579,600). With an assumed trap density of $3 \times 1 0^{12}$ $c m^{- 2}$ and 50 $nm$ grains, the simple trapping model gives about -20 800 $ppm/K$ at $1 \times 1 0^{18}$ $c m^{- 3}$ , -580 $ppm/K$ at $1 \times 1 0^{19}$ and +1440 $ppm/K$ at $1 \times 1 0^{20}$ $c m^{- 3}$ (computed), so the sign changes between them. This is why GF180MCU high-poly resistors of 1000 and 2000 $Ω/ □$ have -1000 and -1650 $ppm/K$ , while Allen lists +500 to +1000 $ppm/K$ for doped poly. The TCAD abstract adds that grain growth alone can switch the sign at fixed doping. Reference: M. Santonen, A. Lahti, Z. Jahanshah Rad et al., ‘A Detailed Examination of Polysilicon Resistivity Incorporating the Grain Size Distribution’, IEEE Transactions on Electron Devices 72(3) (2025) (University of Turku copy, fetch-tool summary); R. Shah and S. L. Hughey, Texas Instruments, ‘Method of making zero temperature coefficient of resistance resistors’, US Patent 4,579,600 (1986) (fetch-tool summary); GlobalFoundries GF180MCU PDK documentation, electrical specifications 5.1 ‘Sheet Resistance’ and 6.1A to 6.1C ‘High Poly Resistor’ (fetch-tool summary); P. E. Allen, ‘ECE 6440 Frequency Synthesizers, Lecture 040: Integrated Circuit Technology - II’, Georgia Institute of Technology (2003) (fetch-tool summary); IEEE paper on mutual self-heating in serpentine poly-Si resistors with a grain-boundary TCAD model (Infona record; abstract only, authors and year not in the text read).

Ques: Is the TCR of doped poly 100 to 500 or 500 to 1000 ppm per kelvin?

Kraft gives 100 to 500 $ppm/K$ , with 200 $ppm/K$ for a 300 $μ m$ resistor, while Allen gives 500 to 1000 $ppm/K$ . Both describe doped gate polysilicon but with different doping and grain structure, and the Dallas patent shows how much the value depends on the process: at $6 \times 1 0^{19}$ $c m^{- 3}$ and 285 $Ω/ □$ its resistors had about 1000 $ppm/K$ , and trimming raises TC1 further. Since the coefficient falls toward zero as the barrier term grows, a lower doping or smaller grains move a film from Allen’s range toward Kraft’s (my reading). Neither range should be used for design: the PDK value for the specific layer is the more likely one, and IHP and GF180MCU give separate layers with different sheet resistances for this reason. Reference: M. Kraft, ‘ELEN0037 Microelectronic IC Design, Lecture 2: Technological Aspects’, University of Liege (year not stated) (fetch-tool summary); P. E. Allen, ‘ECE 6440 Frequency Synthesizers, Lecture 040: Integrated Circuit Technology - II’, Georgia Institute of Technology (2003) (fetch-tool summary); Dallas Semiconductor, ‘Method of making polysilicon resistor having adjustable temperature coefficients’, US Patent 6,306,718 B1 (2001) (fetch-tool summary).

Ques: How can two poly resistors be combined into a resistor with zero temperature coefficient?

By connecting resistors with opposite coefficients in series and sizing them so that their temperature changes cancel. Niknejad and Boser show this with N+ and P+ poly resistors. The total first-order coefficient is the resistance-weighted average, so the positive resistor must make up $- T C_{b} / (T C_{a} - T C_{b})$ of the total. With an assumed +200 $ppm/K$ for unsalicided p+ poly and the GF180MCU high-poly value of -1000 $ppm/K$ , the positive part must be 83 per cent (computed). The cancellation holds only to first order and only while both layers track the process, so the second-order terms and the spread of the two coefficients remain. The TI patent instead reached about zero TCR in a single film by hydrogen passivation of the grain-boundary traps. Reference: A. M. Niknejad and B. Boser, ‘EECS 240 Lecture 2: CMOS Technology and Passive Devices’, UC Berkeley (2006) (fetch-tool summary); GlobalFoundries GF180MCU PDK documentation, electrical specifications 5.1 ‘Sheet Resistance’ and 6.1A to 6.1C ‘High Poly Resistor’ (fetch-tool summary); R. Shah and S. L. Hughey, Texas Instruments, ‘Method of making zero temperature coefficient of resistance resistors’, US Patent 4,579,600 (1986) (fetch-tool summary).

Ques: Why is a long poly resistor more linear than a short one?

Because the voltage divides over all the grain boundaries along its length. Kraft states that the current is nonlinear because of the grain boundaries and that long resistors are more linear, with a voltage coefficient of 10 to 100 $ppm/V$ and 30 $ppm/V$ for a 25 by 2500 $μ m$ resistor. With 50 $nm$ grains and 2 $V$ , each boundary sees 0.33 $mV$ in a 300 $μ m$ resistor and 0.04 $mV$ in a 2500 $μ m$ one, far below the thermal voltage of 25.9 $mV$ , but 100 $mV$ in a 1 $μ m$ resistor, where the barriers are visibly lowered (computed, assumed grain size). GF180MCU specifies -200 $ppm/V$ for its 1000 $Ω/ □$ high-poly layer, so lightly doped poly with higher barriers is less linear than heavily doped poly. Reference: M. Kraft, ‘ELEN0037 Microelectronic IC Design, Lecture 2: Technological Aspects’, University of Liege (year not stated) (fetch-tool summary); GlobalFoundries GF180MCU PDK documentation, electrical specifications 5.1 ‘Sheet Resistance’ and 6.1A to 6.1C ‘High Poly Resistor’ (fetch-tool summary).

Ques: How does electrical trimming change a poly resistor, and how precise is it?

Current pulses heat the strip strongly, and the grains and boundaries restructure and the dopants redistribute, which lowers the resistance permanently. The Microbridge patent reports trimming down to about 0.3 to 0.5 of the as-made value, partial recovery of 8 to 20 per cent with lower pulses, temperatures above 600 to 700 $^{\circ} C$ on thermally isolated membranes, and steps from a few hundred ppm down to a few ppm, reaching about 10 to 50 ppm and 5.5 ppm in a bridge. The Dallas patent trims with 500 $μ s$ pulses starting at about 5 $mA$ and 1.5 $V$ , against about 20 $mA$ and 16 $V$ in earlier work, and its late-implant resistors trim to 30 per cent of their value. Trimming raises TC1, so value and coefficient change together. Reference: Grudin, Landsberger, Frolov and Grudina, Microbridge Technologies, ‘Bidirectional thermal trimming of electrical resistance’, US Patent 7,667,156 B2 (2010) (fetch-tool summary); Dallas Semiconductor, ‘Method of making polysilicon resistor having adjustable temperature coefficients’, US Patent 6,306,718 B1 (2001) (fetch-tool summary).

Ques: Why does a poly resistor heat itself more than a diffused one?

Because it sits on oxide, which conducts heat about a hundred times worse than silicon (background knowledge), so its dissipation raises its temperature instead of flowing into the substrate. The TCAD abstract notes that serpentine poly resistors suffer mutual self-heating between neighbouring fingers, which changes the measured resistance against voltage and raises reliability concerns. On a membrane with the 30 to 50 $K/mW$ of the Microbridge patent, 1 $mW$ heats the resistor by about 40 $K$ and changes a -1000 $ppm/K$ resistor by 4 per cent (computed), which is why that patent limits the measurement current to below 100 $μ A$ . Ordinary poly resistors on field oxide are much less isolated, but the same effect appears as an apparent voltage coefficient at high voltage (my reading). Reference: IEEE paper on mutual self-heating in serpentine poly-Si resistors with a grain-boundary TCAD model (Infona record; abstract only, authors and year not in the text read); Grudin, Landsberger, Frolov and Grudina, Microbridge Technologies, ‘Bidirectional thermal trimming of electrical resistance’, US Patent 7,667,156 B2 (2010) (fetch-tool summary); Thermal Stress page of this vault.

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Polysilicon Resistors