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z2^VHZ$hpJ}cmFpF^DB?>T7)Drynu`y(IjF0`<)C{EJYN_;GM5TRT*HYmj4;51{z9b z%?~~bhN_6|?>=8J{3bn+m_XK%Afz4^Fc|h4GXG+Wy!YU5*vE8;3q!z4qh*qr&sUn{ z7rZ95{L%yGmL4)vuPXNTfAbn;?VW1mo+E(P3HD&qBlpR<)|kQV#;QJYJKntxb0#8W zTpqA>WcsHYaN@@wpSaho4qf|Ppa!Hk9(>QqG`st6i-5(w0nCAtyDca%p`L?rpL^t} z{WmVQU9Gc8rxwdK7`&5^kn!6>H2e8{VsEy8LycGN(-@cb>GM~!10$xnlv{o7TJUaK z1_B@k0*R>bLy*^s7o6+yfC3`8{c?kMBS&=kQcXwP|HWss-}+#)s8(71sH!pd(KT=c z6yCg7&gYW@*QuWvf zW3c&ucA~85_VRGfG6EnV&z;x4nC(`YuB3Adj3C zGu#&8t2P}opp-#|rN#K#D)#>Q0YGymlx*_+KQ93MFRKh#b*?7fxd@zj%Bw&CWoR|d z!(V96P*1>dKheo~aK1EX^8dFT`TqwzKU3uY^Lv=V#>L0SCrR%s?lUWwl#qasLWDMH z8nZvdIiJJ@R1#ijSXhq0$>~OKg{{?LRs_HQ3}>3J*xXdPjG>|7XtlN0XsNTca*mS7 zD@ZP{=a4y{Yb7wP(M=8Yp8cOMUN%<}3U0q=U>VTODPQwlON%adDElLsx~)PL;lziTn3 zPuAB4>Eu#L1JTTKx=;O|Zh;J{vBN=8!Txf(IHqf#a0D-YKW=Dfuj!D<+PzpRsSH7$ zPx-^78L6!tWi&sZ(O8=k!xEKgQr2zZ6={_?ga=?(7>XJzR^JHg+ zqzdfz_+(z_f3^&KpaZ@*()J Positiv forspenning er definert som å koble positiv terminal til p-siden og - til n-siden. +> Negativ forspenning er det motsatte. + +Forspenningen vil ha alt spenningsfallet over deplesjonsområdet $W$. +Med andre ord vil E-feltet endre størrelse med forspenningen. +Desto større negativ forspenning, desto større E-felt (opp til et visst punkt). +For positive forspenninger vil vi minke E-feltet med økt positiv forspenning. + +![Forspent p-n-overgang](figures/biasPN.png) + +### Kvalitativ analyse + +![Steady State p-n-overgang](figures/steadyStatePN.png) + +![Steady State p-n-overgang](figures/pnSteady.png) + +Vi kan nå evaluere hullstrømmen. + +$$ I_p(x_n) = -qAD_p \frac{d \delta p(x_n)}{d x_n} = qA\frac{D_p}{L_p} \delta p(x_n) $$ + +Der strømmen inn i deplesjonsområdet er gitt ved + +$$ +\begin{align*} + I_p(x_n = 0) &= qA\frac{D_p}{L_p}\Delta p_n \\ + &= qA\frac{D_p}{L_p} p_n \left[\exp{\frac{qV}{k_B T}} - 1\right] +\end{align*} +$$ + +For elektroner, er det et minustegn foran, som skifter retningen, men ellers helt lik. + +$$ +\begin{align*} + I_n(x_p = 0) &= -qA\frac{D_n}{L_n}\Delta n_p \\ + &= -qA\frac{D_n}{L_n} n_p \left[\exp{\frac{qV}{k_B T}} - 1\right] +\end{align*} +$$ + +Videre bruker vi enda en forenkling: + +**S6** All strømmen som sendes inn i deplesjonsområdet vil ende opp på andre siden. + +$$ +\begin{align*} + I_p(x_p = 0)&= I_p(x_n = 0) \\ + I_n(x_p = 0)&= I_n(x_n = 0) +\end{align*} +$$ + +Dette gir oss en total strøm: + +$$ I = I_p (x_n = 0) + \left(-I_n(x_p = 0)\right) $$ + +Setter alt sammen og får "diodelikningen": + +$$ I = qA\left[ \frac{D_p}{L_p}p_{n0} + \frac{D_n}{L_n}n_{p0} \right] \cdot \left[\exp{\frac{qV}{k_B T}} - 1\right] $$ + +Dersom vi setter $I_0\equiv\left[ \frac{D_p}{L_p}p_{n0} + \frac{D_n}{L_n}n_{p0} \right]$, kan vi skrive: + +$$ I = I_0 \left[\exp{\frac{qV}{k_B T}} - 1\right]  $$ + +#### Alternativ måte å løse denne på + +Den baserer seg på at det finnes ladninger på hver side av deplesjonsområdet. +Det er da mulig å integrere over ladningene og se på gradienten ved $x_p = x_n = 0$. + +![Alternativ måte å løse likningen på](figures/alternateDiodeEq.png) + +### Sammenbruddsdioder + +Dersom man reversforspenner (negativ forspenning) så vil situasjonen der dioden får et sammenbrudd skje. +Sammenbruddet er kun elektronisk og ikke skadelig for dioden, med mindre man setter på veldig mye negativ forspenning. + +![Sammenbrudd](figures/breakdown.png) + + +#### *Zener*sammenbrudd + +Et Zenersammenbrudd baserer seg på kvantetunnelering mellom energibåndene i dioden. +Elektronene kan da "hoppe" fra valensbåndet til ledningsbåndet. + +![Zener](figures/zener.png) + +#### Avalanche Breakdown (Skredsammenbrudd?) + +Baserer seg på at ved et stort E-felt i sperreretning vil elektroner få stor hastighet. +Når elektronene treffer et atom el. vil den kunne "sparke løs" et annet elektron-hull-par. +Dette medfører at det nå er to elektroner i ene retningen og to hull i andre retningen. + +![Avalanche Breakdown](figures/avalanche.png) + + +### Transienter i en p-n-overgang + +#### Stegtransient + +Vi vil se på tilfellet der vi skrur av strømmen abrupt ved $t=0$. + +Kommer tilbake til dette... + + +### Forskjellige typer p-n-overganger + +Også sees på senere + +## Felt Effekt Transistorer (FET) + +### Historie + +* **1915** - Første radiorør +* **1926** - Patent på en CuS FET +* **1934** - Design av en FET +* **1947** - Den første transistoren ble laget +* **1954** - Første transistor i Si +* **1959** - Første IC +* **1960** - Første MOSFET +* **1971** - Intel kom med første komersielle mikroprosessor, Intel 4004 + +### Forskjellige typer FET + +#### JFET + +JFET (Junction Field Effect Transistor), fungerer ved å styre/modulere bredden på deplesjonsområdet på en revers forspent p-n-overgang, ved hjelp av en påsatt spenning $V_G$. +Dette medfører at vi kan kontrollere strømmen mellom kilde (source) og brønn (drain) kontaktene. + +![JFET](figures/JFET.png) + +#### MESFET + +Fungerer på samme måte som en JFET, men styrer bredden på deplesjonsområdet i en Schottky diode. +Dette er derfor en Metall-Silisium overgang (M-S overgang). + +![MESFET](figures/MESFET.png) + +#### MOSFET + +Dette er den mest brukte transistoren i dag. +Her er gate-kontakten elektrisk separert fra resten av transistoren med et isolerende lag. +Transistoren fungerer da ved å sette opp mellom gate og substratet i transistoren for å lage en elektrisk ledene kanal mellom kilde og brønnkontaktene. +Det er derfor den har navnet MOSFET, Metal-Oksid-Silikon Felt Effekt Transistor (Metal-Oxide-Silicon Field Effect Transistor). + +![MOSFET](figures/MOSFET.png) + + +### Fordeler med FET over BJT + +* Høy inngangsimpedanse. + * I JFET er det pga. en revers forspend p-n-overgang. + * I MESFET er det pga. en revers forspent m-s-overgang. + * I MOSFET er det pga. en isolator mellom gate og resten av transistoren. +* Veldig god som en bryter for å styre mellom en ledende tilstand og en ikke ledende tilstand. +* Negativ temperaturkoeffisient ved store strømmer, som gjør den veldig stabil. +* Har ingen lagring av minoritetsladningsbærere, som fører til ingen uønsket kapasitanse. +* Har høyere endringshastighet (switching speed) enn en vanlig BJT. + + +### Virkemåte til en transistor + +En transistor har i prinsippet to funksjoner: + +1. Forsterkning av små AC-signaler. +2. Som en bryter, for å styre en strøm. + +![Virkemåte Transistor](figures/virkemåteTransistor.png) + +#### I-V-kurve + +Strømmen til en transistor kan beskrives med spenningen over transistoren. + +$$ i_D = f(v_D)$$ + +Der lastlinjen er definert som + +$$ i_D = \frac{E}{R} - \frac{v_D}{R} $$ + +For en komponent med to terminaler vil vi kun ha disse likningene, men for en komponent med tre poler kan vi også styre hvordan $f(v_D)$ fungerer ved hjelp av $v_G$. + +### JFET + + + +
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