V-measuremet basics
M-capacitor V measuremet measuremet of differetial by small ac modulatio of the bias voltage (dc d d G G M j G M ω M j ω Y M G M G M M
ualitative poit of view
ad diagram i geeral (here -type!!! AM aff s s LF
deal: o work fuctio differece o oxide charges o iterface charges o curret through isulator o tuelig bad diagram p-type!!! with o bias Φ m ->Φ m Φ s Φ -> s just for simplificatio of bad diagrams
accumulatio ( g <, p-type mall L Debey M max
depletio ( g >, p-type eries of ad D ( M M
versio ( g >>, p-type defiitio: arrier cocetratio of surface (iverted carrier cocetratio of substrate F Threshold voltage: Thr '' F '' F F g > Thr strog iversio
(typical <1Hz, uasi static Miority carriers ca follow the -sigal versio layer (small dimesio v M max (typical 1kHz, 1MHz Miority carriers ca ot follow the -sigal further expasio of space charge regio is screeed by iversio layer Pulsed V ( mi M v Pulsed icreasig of bias voltage from accumulatio to iversio. Formatio of iversio layer is ihibited. < M M mi mi mi slide slide 3
/-V for p ad -type semicoductor (-chael, p-chael!!! slide 9 Pulsed V
harge distributio
Real world differece i work fuctio betwee semicoductor ad metal, φ M fixed oxide charges f usaturated i- or O-valeces, result i positive i-o-omplexes moveable ioic charges i the isulator m impurities, should be avoided iterface states it daglig bods, tesio i the iterface ceters of recombiatio ca avoid i extreme a built-up of the iversio layer mostly: > f m it ad bedig without ay bias: F φ M K '' greff ''
F φ M K '' greff '' Thr F '' '' F
uatitative poit of view (of ideal M
idex Germa eglish L AM Voltage balace aff s s F strege Eergieschreibweise M g aff χ, E F Φ Φ M af, f χ ( x E F ( x di M ( also K or M x xd F g harge balace g ti g ideal M
Poisso euatio i the isulator x ρ ( x c x c * 1 ideal c 1 d dx d d ρ '' it dx dx '' '' c 1 ideal " dρ dx ''
Poisso euatio i the semicoductor ρ x ( D A N N p ρ exp( W W N F exp( W W N p V F V ( ( d ( ( x W x W ( ( x W x W V V exp( W W N F A D ulk N p N exp( W W N p V F V exp( exp( p p i p p
(exp( (exp( 1 1 x i Poisso euatio i the semicoductor charge i the semicoductor (exp( ( exp( * '' 1 1 i M g
Differetial capacity G M d d G G d d M j G M ω ideal G M M g g d 1 M d 1 d d 1 g d d g g d d d d g M M
-V (-type ack view slide 9 d d '' M p exp( ( ( exp( 1 1 ω g M D-Voltage with miorities!!!
3.5x1-4 i b 1 15 cm -3 io d i 1m " M [F/m ] 3.x1-4.5x1-4.x1-4 1.5x1-4 1.x1-4 5.x1-5 -5-4 -3 - -1 1 3 4 5 gideal [V]
Approximatios -V (-type Accumulatio M Acc 1 ( g M exp >> M g 1 Flat bad F '' L Debye M F F F F f ( M Depl '' 1 ( g Depletio exp 1 M < versio v '' ( l i 1 M v cost v v v v ( W F W l( i i
-V (-type 1 1 1 1 i i exp( ( exp( exp( ( exp( '' M g ack view slide 9 ω d d D-Voltage with miorities!!! M ( ( with miorities!!!
3.5x1-4 i b 1 15 cm -3 io d i 1m " M [F/m ] 3.x1-4.5x1-4.x1-4 1.5x1-4 1.x1-4 5.x1-5 -5-4 -3 - -1 1 3 4 5 gideal [V]
p > Approximatios -V (-type Accumulatio, Flat bad, Depletio,, M Acc M F M depl omehow similar to versio '' i v exp( M v 1 ( g M M g
3.5x1-4 i b 1 15 cm -3 io d i 1m " M [F/m] 3.x1-4.5x1-4.x1-4 1.5x1-4 accumulatio depletio iversio iversio 1.x1-4 5.x1-5 -4 - gideal [V]
i: b 1 15 cm -3 (-type p b 1 15 cm -3 (p-type io : d i 1m 3.5x1-4 " M [F/m ] 3.x1-4.5x1-4.x1-4 1.5x1-4 -type semicoductor p-type semicoductor 1.x1-4 5.x1-5 -5-4 -3 - -1 1 3 4 5 gideal [V]
3.5x1-4 i io d i 1m " M [F/m ] 3.x1-4.5x1-4.x1-4 1.5x1-4 b 1 17 cm -3 b 1 16 cm -3 1.x1-4 b 1 15 cm -3 5.x1-5 -1-8 -6-4 - 4 gideal [V]
3.5x1-4 i b 1 15 cm -3 io 3.x1-4 d i 1m d i 1m " M [F/m ].5x1-4.x1-4 1.5x1-4 d i m d i m 1.x1-4 d i 3m d i 3m 5.x1-5 -1-8 -6-4 - 4 gideal [V]
From V-measuremets Determiatio of type of semicoductor i the substrate (p or d or estimatio of threshold voltage slide 9 dopig profile desity of iterface states fixed oxide charge life time of miorities